Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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Author: Salusbury, Thomas
Title: Mathematical collections and translations (Tome I)
Date: 1667

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Document ID: MPIWG:FH6G65NP
Permanent URL: http://echo.mpiwg-berlin.mpg.de/MPIWG:FH6G65NP

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Copyright: Max Planck Institute for the History of Science (unless stated otherwise)
License: CC-BY-SA (unless stated otherwise)
1
MATHEMATICAL
Collections and Tranſlations:
In two
TOMES.
1
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1
MATHEMATICAL
COLLECTIONS
AND
TRANSLATIONS:
THE FIRST
TOME.
IN TWO PARTS.
THE FIRST PART;
Containing,
I. GALILEUS GALILEUS His SYSTEM of the
WORLD.
II. GALILEUS His EPISTLE to the GRAND
DUTCHESSE MOTHER, concerning the Au­
thority of Holy SCRIPTURE in Philoſophical
Controverſies.
III. JOHANNES KEPLERUS His Reconcilings of SCRI­
PTURE Texts, &c.
IV. DIDACUS à STUNICA His Reconcilings of SCRI­
PTURE Texts, &c.
V. P. A. FOSCARINUS His Epiſtle to Father FANTONUS,
reconciling the Authority of SCRIPTURE, and Judg­
ments of Divines alledged againſt this SYSTEM.
By THOMAS SALUSBURY, Eſque
LONDON,
Printed by WILLIAM LEYBOURN, MDCLXI.
1
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1
To the Noble and moſt perfectly Accompliſhed
S^{t.} JOHN DENHAM
Knight of the Noble Order of the
BATH,
And Surveyor General of his Ma^{ties} Works, &c.
SIR,
I humbly begge your Pardon for
bringing this Book under your Pro­
tection. Were it a Work of my
own, or I any thing but the Tranſla­
tour, I should maſter my Thoughts to a meaner
Dedication; But being a Collection of ſome of
the greateſt Maſters in the World, and never
made English till now, I conceived I might
ſooner procure their Welcome to a perſon ſo
eminent for Noble Candor, as well as for all
thoſe Intellectual Excellencies wherewith
Your Rich Soulis known to be furnished. I
reſolv'd to be as kind to this Book as I could,
1and ſeriouſly conſidering which way to effect
it, I at laſt concluded to prefix Your Name,
whom His Majeſty and all his Subjects, (who
have a higher Senſe and Judgement of Excel­
lent Parts) know beſt able to defend my Im­
perfections. And yet I confeſs there's one
thing makes againſt me, which is your eminent
Integrity and great Affection to Truth, where­
by my Lapſesin a Work of this Nature might
juſtly deſpair of Shelter, but that the Excel­
lency of Your Native Candor ſtrives for Pre­
dominancy over all Your great Abilities. For
'tis all-moſt impoſſible to think what Your
Matchleſs Wit is not able to Conquer, would
Your known Modeſty but give leave: there­
fore Galileus, Kepler, and thoſe other worthies
in Learning are now brought before You in
English Habit, having chang'd their Latine,
Italian and French, whereby they were almoſt
Strangers to our Nation, unleſs to ſuch as You,
who ſo perfectly maſter the Originals. I know
you have ſo much and great imployment for
His Majeſty, and his good Subjects that I shall
not robb you of another Minutes loſs; beſides
the liberty of ſubſcribing my Self;
SIR,
Your Honours
Moſt Humble
and
Moſt obedient Servant
THOMAS SALUSBURY.
1
READER,
Mathematical Learning (to ſpeak nothing touching the neceſsity & delight thereof) hath bin ſo ſparing­
ly imparted to our Countrymen in their native Engliſh, eſpecially the nobler and ſublimer part,
that in Compliance with the Solicitations of ſeveral of my noble and learned Friends, and the Incli­
nations of ſuch as are Mathematically diſpoſed, more eſpecially thoſe, who either want Time or
Patience to look into the vulgar and unſtudied Languages, I did adventure upon this Work of Collecting & Tranſ­
lating from amongſt the excellent Pieces that are ſo abounding in the Italian and French Tongues, ſome of thoſe
that my own obſervation and the intimation of Friends were moſt uſefull and deſired, and with all moſt wanting
in their Own.
I was, indeed, at firſt ſeriouſly Conſcious, and am now, by experience, fully convinced how diſproportionate the
weight of the Enterprize is to the weakneſs of the Vndertaker, but yet the Paſsion I ever had to be ſubſervient to
my Friends and Compatriots in their Inquiſition after theſe Sublime Studies, and a Patience which I owe to the
Flegme that is predominant in my Conſtitution, joyned with a nine-years converſence in theſe Languages, as alſo an
unhappy and long Vacation that the perſecutions of the late Tyrants gave me from more advantagious employ­
ments ſo prevailed with me, that I reſolved to improve even my very Confinement to ſerve thoſe Friends, whom, as
the Times then ſtood, I could not ſee.
The Book being for Subject and Deſign intended chiefly for Gentlemen, I have hin as careleſs of uſing a ſtudied
Pedantry in my Style; as careful in contriving a pleaſant and beautiful Impreſſion. And when I had conſidered
the hazard, and computed the charge of the undertaking, I found it to exceed the ability of a private Purſe, eſpe­
cially of mine, that had bin ſo lately emptied by the hand of violent enemies, and perfidious friends; not to
make mention here of the Sums that a Loyal Reflexion upon my Princes Affairs had at the ſame time drawn
from me; and judg'd that the most ſafe, eaſy, and reaſonable way was to invite thoſe Perſons who had appeared
deſirous of the Book, to be contributary to their own Contentment, by ſubſcribing towards the charge of this Pu­
blication.
And for the better management of the Work, I joyned to my ſelf a Printer, whoſe Genius having rendered
him Mathematical, and my overtures of profit having intereſſed his diligence, I was induced to promiſe my ſelf a
more than common Aſſiſtance from him: and at his door I with reaſon lay all miſcarriages that concerns his
Profeſſion in the Buſineſs.
In this Work I found more than ordinary Encouragement from that publick ſpirited Perſon the Reverend and
Learned Dr. Thomas Barlow, Provoſt of Queens Colledge Oxford, and Margaret Profeſſor in that Vniver­
ſity, as alſo from thoſe two able Mathematicians and my Reall Friends Major Miles Symner, and Mr. Robert
Wood of Trinity Colledge Dublin, and ſome few others whoſe Modeſty hath expreſly enjoin'd me a concealment
of their Names.
Well, at length I have got to the end of my firſt Stage; and if I have not rid Poſt, let my excuſe be that my long
ſtay for my Warrant cauſed me to ſet out late; and being ill mounted, and in a road full of rubbs, I could not with
any ſafety go faſter; but hope to get it up in the next Stage, for in that I intend to ſhift my Horſes.
The names of thoſe Authors and Treatices which I judged would moſt grace our Language, and gratify Stu­
dents, are particularly expreſt in the General Title of the two Tomes. Diſtinct Tomes they are as conſiſting of
ſeverat Pieces: Collections I call them, becauſe they have bin ſo publiſhed, diſperſt, and worn out of Print, that
they very rarely meet in one hand: and Tranſlations I own them to be, as not pretending to any thing more than
the diſpoſure and converſion of them: thoſe Tracts only excepted which compoſe the ſecond Part of the ſecond
Tome.
The firſt Book which offers it ſelf to your view in this Tome is that ſingular and unimitable Piece of Reaſon
and Demonſtration the Syſteme of Galilco. The ſubject of it is a new and Noble port of Aſtronomy, to wit the
Doctrine and Hypotheſis of the Mobility of the carth and the Stability of the Sun; the Hiſtory whereof I ſhall
hereafter give you at large in the Life of that famous Man. Only this by the by; that the Reader may not wonder
why theſe Dialogues found ſo various entertainment in Italy (for he cannot but have heard that though they have
been with all veneration valued, read & applauded by the Iudicious yet they were with much deteſtation perſecuted,
ſuppreſſed & exploded by the Superſtitious) I am to tell him that our Author having aſſigned his intimate Friends
Salviati and Sagredo the more ſucceßfull Parts of the Challenger, and Moderater, he made the famous Commen­
tator Simplicius to perſonate the Peripatetick. The Book coming out, and Pope Urban the VIII. taking his Ho­
nour to be concern'd as having in his private Capacity bin very poſitive in declaiming against the Samian Philo­
ſophy, and now (as he ſuppoſed) being ill delt with by Galilco who had ſummed up all his Arguments, and pur
them into the mouth of Simplicius; his Holineſs thereupon conceived an implacable Diſpleaſure against our Au­
thor, and thinking no other revenge ſufficient, he employed his Apoſtolical Authority, and deals with the Conſiſtory
to condemn him and proſcribe his Book as Heretical; proſtituting the Cenſure of the Church to his private revenge.
This was Galilco's fortune in Italy: but had I not reaſon to hope that the Engliſh will be more hoſpitable, on the
account of that Principle which induceth them to be civil to (I ſay not to dote on) Strangers, I ſhould fear to be
charged with imprudence for appearing an Interpreter to that great Philoſopher. And in this confidence I ſhall
forbear to make any large Exordium concerning him or his Book: & the rather in regard that ſuch kind of Gau­
deries become not the Gravity of the Subject; as alſo knowing how much (coming from me) they must fall ſhort of
the Merits of it, or him: but principally becauſe I court only perſons of Judgement & Candor, that can diſtinguiſh
between a Native Beauty, and ſpurious Verniſh. This only let me premiſe, though more to excuſe my weakneſs in
the menaging, than to inſinuate my ability in accompliſhing this ſo arduous a Task, that theſe profound Dialogues
have bin found ſo uneaſy to Tranſlate, that neither affectation of Novelty could induce the French, nor the
Tranſlating humour perſwade the Germans to undertake them. This difficulty, as I conceived, was charged either
upon the Intricacy of this manner of Writing, or upon the ſingular Elegance in the ſtile of Galilco, or elſe upon the
1miſcarriage of the unfortunate Mathias Berneggeius who firſt attempted to turn them into Latine for the benefit
of the Learned World.
I ſhall not preſume to Cenſure the Cenſure which the Church of Rome paſt upon this Doctrine and its Aſſectors.
But, on the contrary, my Author having bin indefinite in his diſcourſe, I ſhall forbear to exaſperate, and attempt
to reconcile ſuch perſons to this Hypotheſis as devout eſteem for Holy Scripture, and dutifull Reſpect to Canonical
Injunctions hath made to ſtand off from this Opinion: and therefore for their ſakes I have at the end of the Dia­
logues by way of ſupplement added an Epiſtle of Galilco to Her Most Serene Highneſs Chriſtina Lotharinga the
Grand Dutcheſſe Mother of Tuſcany; as alſo certain Abſtracts of John Kepler, Mathematician to two Empe­
rours, and Didacus à Stunica a famous Divine of Salamanca, with an Epiſtle of Paulo Antonio Foſcarini a learn­
ed Carmelite of Naples, that ſhew the Authority of Sacred Scripture in determining of Philoſophical and Natu­
ral Controverſies: hoping that the ingenious & impartial Reader will meet with full ſatisfaction in the ſame.
And leaſt what I have ſpoken of the prohibiting of theſe Pieces by the Inquiſition may deterre any ſcrupulous
perſon from reading of them, I have purpoſely inſerted the Imprimatur by which that Office licenced them. And
for a larger account of the Book or Author, I refer you to the Relation of his Life, which ſhall bring up the Reare
in the Second Tome.
What remains of this, is that Excellent Diſcourſe of D. Benedetto Caſtelli Abbate di San Benedetto Aloyſio,
concerning the Menſuration of Running waters, with other Treatiſes of that Learned Prelate, & of the Superin­
tendent Corſini. Some may alledge, and I doe confeſs that I promiſed to publiſh the Life of Galilco in this place:
But the great miſcarriages of Letters from ſome Friends in Italy and elſe where, to whom I am a Debtor for ſe­
veral Remarques, & from whom I daily expect yet greater Helps concerning the Hiſtory of that famous Perſonage:
theſe diſappointments, I ſay, joyned with the undeniable Requeſt of ſome Friends, who were impatient to ſee Caſtelli
in Engliſh, together with a conſideration of the diſproportionate Bulk that would otherwiſe have bin betwixt the
two Volumes, perſwaded me to this exchange. This deviation from my Promiſe I hope is Venial, and for the ex­
plating of it I plead Supererrogation: having in each Tome made ſo large Aditions (though to my great ex­
penſe) that they make neer a third part more than I ſtood by promiſe bound to Publiſh. That this is ſo will appearby
comparing the Contents I here prefix with the Advertiſment I formerly Printed. For not to mention thoſe Epitomes
of Kepler and à Stunica, the whole ſecond and following Books of Caſtclli, were not come to my hands at the time of
my penning that Paper; yet knowing how imperfect the Volume would be without them, they being partly a ſup­
plement to the Theoremes and Problemes which the Abbot had formerly Printed, and partly experiments that
had procured him and his Doctrine a very great Reputation, knowing this I ſay, I apprehended a neceſſity of pu­
bliſhing them with the reſt: and hope that if you think not the ſervice I have done therein worth your acknowledge­
ment, you will yet at leaſt account the encreaſe of my expence a ſufficient extenuation of the Treſpaſs that thoſe
Additions have forced me to commit upon your Patience in point of Time.
As for the ſecond Tome, I have only this to aſſure the Generous Readers; 1 that I am very confident I ſhall
be much more punctual in publiſhing that, than (for the reaſons above related.) I was able to be in ſetting forth
this: 2 that they ſhall not be abuſed in advancing of their moneys, (as hath bin uſed in the like caſe) by ſelling
the remaining Copyes at an under rate; and 2 that I have a very great care that no diſeſteem may by my means a­
riſe unto this way of publiſhing Books, for that it is of excellent uſe in uſhering Great and Coſtly Volumes into
the World.
To ſay nothing of the diſadvantages of Tranſlations in general, this of mine doubtleſs is not without it's Er­
rours, and overſights: but thoſe of the Printer diſcounted, I hope the reſt may be allowed me upon the ſcore of Hu­
man Imbecilitic. The truth is, I have aſſumed the Liberty to note the Miſtakes in the Florid Verſion of Bernegge­
rus in the Margent, not ſo much to reproach him, as to convince thoſe who told me that they accounted my pains
needleſs, having his Latine Tranſlation by them. The like they ſaid of the whole two Tomes: but they thereby cauſed
me to question their Underſtanding or Veracity. For ſome of the Books were yet never extant: As for inſtance;
the Mcchanicks of Monſieur Des Cartes, a Manuſcript which I found amongſt the many other Rarities that en­
rich the well-choſen Library of my Learned and Worthy Friend Dr. Charles Scarburgh; the Experiments of Gra­
vity, and the Life of Galileo, both my own: Others were included in Volumes of great price, or ſo diſperſed that
they were not to be purchaſed for any money; as thoſe of Kepler, à Stunica, Archimedes, Tartaglia, and the Mecha­
nicks of Galileo: And the remainder, though eaſyer to procure, were harder to be underſtood; as Tartaglia his notes
on Archimedes, Torricellio his Doctrine of Projects, Galileo his Epiſtle to the Dutcheſſe of Tuſcany, and above all
his Dialogues de Motu; (never till now done into any Language) which were ſo intermixt of Latine and Italian,
that the difficulty of the Stile, joyned with the intricatneſſe of the Subject rendered them Unpleaſant, if not wholly
Vnintelligible, to ſuch as were not abſolute Maſters of both the Tongues.
To conclude; according to the entertainment that you pleaſe to afford theſe Collections, I ſhall be encouraged to
proceed with the Publication of a large Body of Hydrography; declaring the Hiſtory, Art, Lawes, and Apendages
of that Princely Study of Navigation, wherein I have omitted nothing of note that can be found either in Dud­
ley, Fournier, Aurigarius, Nonius, Snellus, Marſennus, Bayſius, Moriſetus, Blondus, Wagoner, abroad, or learnt
amongst our Mariners at home, touching the Office of an Admiral, Commander, Pilot, Modelliſt, Shipwright,
Gunner, &c.
But order requiring that I ſhould diſcharge my firſt Obligation before I contract a ſecond; I ſhall detein you no
longer in the Portall, but put you into poſſeſſion of the Premiſes,
Novemb. 20, 1661.
T. S.
1
The CONTENTS of the FIRST
TOME.
PART THE FIRST.
Treatiſe
I. GALILEUS GALILEUS, his SYSIEME of the WORLD: in Four DIALOGUES.
II. HIS EPISTLE to her SERENE HIGHNESSE CHRISTIANA LOTHERINGA
GRAND DUTCHESSE of TUSCANY, touching the Ancient and Modern
DOCTRINE of HOLY FATHERS, and JUDICIOUS DIVINES, concerning
the AUTHORITY of SACRED SCRIPTURE in PHYLOSOPHICAL
CONTROVERSIES.
III. JOHANNES KEPLERUS, his RECONCILINGS of TEXTS of SACRED
SCRIPTURE that ſeem to oppoſe the DOCTRINE of the EARTHS MOBILI­
TY: abſtracted from his INTRODUCTION unto his LEARNED COMMEN­
TARIES upon the PLANET MARS.
IV. DIDACUS A STUNICA, a learned SPANISH DIVINE, his RECONCILINGS of
the ſaid DOCTRINE with the TEXTS of SACRED SCRIPTURE; abſtracted
from his COMMENTARIE upon JOB.
V. PAULUS ANTONIUS FOSCARINUS, a CARMELITE, his EPISTLE to
SEBASTIANUS FANTONUS, the GENERAL of his ORDER, concerning
the PYTHAGOREAN and COPERNICAN OPINION of the MOBILITY OF
THE EARTH, and STABILITY OF THE SUN; and of the NEW SYSTEME
or CONSTITUTION of the WORLD: in which he reconcileth the TEXTS
OF SACRED SCRIPTURE, and ASSERTIONS of DIVINES, commonly
alledged against this OPINION.
A Table of the most obſervable Perſons and Matters mentioned in the Firſt Part.
PART THE SECOND.
I. D. BENEDICTUS CASTELLUS, ABBOT OF S. BENEDICTUS ALOYSIUS, his
DISCOURSE of the MENSURATION OF RUNNING WATERS: The Firſt
BOOK.
II. HIS LETTER to GALILEUS, repreſenting the ſtate of the Lake of PERUGIA in
TUSCANY.
III. HIS GEOMETRICAL DEMONSTRATIONS of the MEASURE of RUNNING
WATERS.
IV. HIS DISCOURSE of the MENSURATION OF RUNNING WATERS: The Second
BOOK.
V. HIS CONSIDERATIONS concerning the LAKE OF VENICE. In two DISCOURSES.
VI. HIS RULE for computing the quantity of MUD and SAND that LAND-FLOODS bring
down to, and leave in the LAKE of VENICE.
VII. HIS LETTER to Father FRANCESCO DI S. GIVSEPPE, wherein, at the inſtance
of PRINCE LEOPALDO, he delivereth his judgment concerning the turning
FIUME MORTO (a River near PISA in TUSCANY) into the SEA, and into
the River SERCHIO.
VIII. HIS ſecond LETTER in anfwer to certain OBJECTIONS propoſed, and DIFFICUL­
TIES obſerved by SIGNORE BARTOLOTTI, in that affair of the
DIVERSION of FIUME MORTO.
IX. HIS CONSIDERATION upon the DRAINING of the PONTINE FENNS in CALA­
BRIA.
X. HIS CONSIDERATION upon the DRAINING of the TERRITORIES of BOLOG­
NA, FERRARA, and ROMAGNA.
XI. HIS LETTER to D. FERRANTE CESARINI, applying his DOCTRINE to the
MENSURATION of the LENGTH, and DISTRIBUTION of the QUANTITY
of the WATERS of RIVERS, SPRINGS, AQUEDUCTS, &c.
XII. D. CORSINUS, SUPERINTENDENT of the GENERAL DRAINS and PRESIDENT
of ROMAGNA, his RELATION of the ſtate of the WATERS in the
TERRITORIES of BOLOGNA and FERRARA.
A Table of the moſt obſervable Perſons and Matters mentioned in the Second Part.
1
The CONTENTS of the SECOND
TOME,
PART THE FIRST.
Treatiſe
I. GALILEUS GALILEUS, his MATHEMATICAL DISCOURSES and DEMON­
STRATIOMS touching two NEVV SCIENCES, pertaining to the MECHA­
NICKS, and LOCAL MOTION: with an APPENDIX of the CENTRE of
GRAVITY of ſome SOLIDS in Four DIALOGUES.
II. HIS MECHANICKS; a New PEICE.
III. RHENATUS DES CARTES, his MECHANICKS; tranſlated from his FRENCM
MANUSCRIPT; a New PEICE.
IV. ARCHIMEDES, his Tract DE INSIDENTIBUS HUMIDO; with the NOTES and
DEMONSTRASIONS of NICOLAUS TARTALEUS, in Two BOOKS.
V. GALILEUS his DISCOURSE of the things that move in or upon the WATER.
VI. NICOLAUS TARTALEUS his INVENTIONS for DIVING UNDER WATER,
RAISING OF SHIPS SUNK, &c. in Two BOOKS.
PART THE SECOND.
I. EVANGELISTA TORRICELLIUS, his DOCTRINE OF PROJECTS, and TABLES
of the RANGES of GREAT GUNNS of all ſorts; wherein he detects ſundry
ERRORS in GUNNERY: An EPITOME.
II T. S. his EXPERIMENTS of the COMPARATIVE GRAVITY OF BODIES in the
AIRE and WATER.
III. GALILEUS GALILEUS, his LIFE: in Five BOOKS,
BOOK I. Containing Five Chapters.
Chap. 1. His Country.
2. His Parents and Extraction.
3. His time of Birth.
4. His firſt Education.
5. His Maſters.
II. Containing Three Chapters.
Chap. 1. His judgment in ſeveral Learnings.
2. His Opinions and Doctrine.
3. His Auditors and Scholars.
III. Containing Four Chapters.
Chap. 1. His behaviour in Civil Affairs.
2. His manner of Living.
3. His morall Virtues.
4. His misfortunes and troubles.
IV. Containing Four Chapters.
Chap. 1. His perſon deſcribed.
2. His Will and Death.
3. His Inventions.
4. His Writings.
5. His Dialogues of the Syſteme in particular, containing Nine Sections.
Section 1. Of Aſtronomy in General; its Definition, Praiſe, Original.
2. Of Aſtronomers: a Chronological Catalogue of the
moſt famous of them.
3. Of the Doctrine of the Earths Mobility, &c. its Antiquity,
and Progreſſe from Pythagoras to the time of Copernicus.
4. Of the Followers of Copernicus, unto the time of Galileus.
5. Of the ſeverall Syſtemes amongſt Aſtronomers.
6. Of the Allegations againſt the Copern. Syſteme, in 77
Arguments taken out of Ricciolo, with Anſwers to them.
7. Of the Allegations for the Copern. Syſteme in so Arguments.
8. Of the Scriptures Authorities produced againſt and for the
Earths mobility.
9. The Concluſion of the whole Chapter.
V. Containing Four Chapters.
Chap. 1. His Patrons, Friends, and Emulators.
2. Authors judgments of him.
3. Authors that have writ for, or againſt him.
4. A Concluſion in certain Reflections upon his whole Life.
A Table of the whole Second TOME.
1
THE
SYSTEME
OF THE
WORLD:
IN FOUR
DIALOGUES.
Wherein the Two
GRAND SYSTEMES
Of PTOLOMY and COPERNICUS
are largely diſcourſed of:
And the REASONS, both Phyloſophical and Phyſical,
as well on the one ſide as the other, impartially
and indefinitely propounded:
By GALILEUS GALILEUS LINCEUS,
A Gentleman of FLORENCE: Extraordinary Profeſſor of
the Mathematicks in the UNIVERSITY of PISA; and
Chief Mathematician to the GRAND DUKE of TVSCANY.
Ingliſhed from the Original Italián Copy, by THOMAS SALUSBURY.
ALCINOUS,
Δεῑ δ̓ ἐλευγέριον εἰ̄ναι τῃ̄ γνωμῃ̄ ρ̀ν μέλλοντα φιλοσοφεῑν.
SENECA,
Inter nullos magis quam inter PHILOSOPHOS eſſe debet aqua LIBERTAS.
LONDON,
Printed by WILLIAM LEYBOURNE. MDCLXI.
1
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1
To the moſt Serene Grand DUKE
OF
TUSCANY.
Though the difference between Men and other
living Creatures be very great, yet happly he that
ſhould ſay that he could ſhew little leſs between
Man and Man would not ſpeak more than he
might prove. What proportion doth one bear to
athouſand? and yet it is a common Proverb, One Man is
worth athouſand, when as a thouſand are not worth one. This difference
hath dependence upon the different abilities of their
ctuals; which I reduce to the being, or not being a
pher; in regard that Philoſophy as being the proper food of
ſuch as live by it, diſtinguiſheth a Man from the common
ſence of the Vulgar in a more or leſs honourable degree
ing to the variety of that diet. In this ſence he that hath the
higheſt looks, is of higheſt quality; and the turning over of
the great Volume of Nature, which is the proper Object of
Philoſophy is the way to make one look high: in which Book,
although whatſoever we read, as being the Work of
mighty God, is therefore moſt proportionate; yet
ſtanding that is more abſolute and noble wherein we more
plainly deſerne his art and skill. The Conſtitution of the Vnivers,
among all Phyſical points that fall within Humane
henſion, may, in my opinion, be preferred to the Precedency:
for if that in regard of univerſal extent it excell all others, it
ought as the Rule and Standard of the reſt to goe before
them in Nobility. Now if ever any perſons might challenge
to be ſignally diſtinguiſhed for Intellectuals from other men;
1Ptolomey and Copernicus were they that have had the honour to
ſee fartheſt into, and diſcourſe moſt profoundly of the Worlds
Syſteme. About the Works of which famous Men theſe
lous being chiefly converſant, I conceived it my duty to
dicate them only to Your Highneſs. For laying all the weight
upon theſe two, whom I hold to be the Ableſt Wits that
have left us their Works upon theſe Subjects; to avoid a
ciſmein Manners, I was obliged to addreſs them to Him, who
with me, is the Greateſt of all Men, from whom they can
ceive either Glory or Patrociny. And if theſe two perſons
have ſo farre illuminated my Underſtanding as that this my
Book may in a great part be confeſſed to belong to them, well
may it alſo be acknowledged to belong to Your Highneſs, unto
whoſe Bounteous Magnificence I owe the time and leaſure I
had to write it, as alſo unto Your Powerful Aſſiſtance, (never
weary of honouring me) the means that at length I have had
to publiſh it. May Your Highneſs therefore be pleaſed to accept
of it according to Your accuſtomed Goodneſs; and if any
thing ſhall be found therein, that may be ſubſervient towards
the information or ſatisfaction of thoſe that are Lovers of
Truth; let them acknowledge it to be due to Your Self, who are
ſo expert in doing good, that Your Happy Dominion cannot
ſhew the man that is concerned in any of thoſe general
mities that diſturb the World; ſo that Praying for Your
rity, and continuance in this Your Pious and Laudable
ſtome, I humbly kiſs Your Hands;
Your Moſt Serene Highneſſes
Moſt Humble and moſt devoted
Servant and Subject
GALILEO GALILEI.
1
THE AUTHOR'S
INTRODUCTION.
Judicious Reader,
There was publiſhed ſome years ſince in Rome a ſalutiferous Edict, that, for
the obviating of the dangerous Scandals of the preſent Age, impoſed a
ſonable Silence upon the Pythagorean Opinion of the Mobility of the Earth.
There want not ſuch as unadviſedly affirm, that that Decree was not the
ction of a ſober Scrutiny, but of an ill informed Paſsion; & one may hear ſome
ter that Conſultors altogether ignorant of Aſtronomical Obſervations ought not
to clipp the Wings of Speculative Wits with raſh Prohibitions. My zeale
not keep ſilence when I hear theſe inconſiderate complaints. I thought fit, as being thoroughly
quainted with that prudent Determination, to appear openly upon the Theatre of the World as a
neſs of the naked Truth. I was at that time in Rome; and had not only the audiences, but applauds of
the moſt Eminent Prelates of that Court; nor was that Decree Publiſhed without Previous Notice given
me thereof. Therefore it is my reſolution in the preſent caſe to give Foraign Nations to ſee that this
point is as well under stood in Italy, and particularly in Rome, as Tranſalpine Diligence can imagine
it to be: and collecting together all the proper Speculations that concern the Copernican Syſteme,
to let them know, that the notice of all preceded the Cenſure of the Roman Court; and that there
proceed from this Climate not only Doctrines for the health of the Soul, but alſo ingenious Diſcoveries
for the recreating of the Mind.
To this end I have perſonated the Copernican in this Diſcourſe; proceeding upon an Hypotheſis
purely Mathematical; ſtriving by all artificial wayes to repreſent it Superiour, not to that of the
mobility of the Earth abſolutely, but according as it is mentioned by ſome, that retein no more, but the
name of Peripateticks, and are content, without going farther, to adore Shadows, not philoſophizing
with requiſit caution, but with the ſole remembrance of four Principles, but badly under ſtood.
We ſhall treat of three principall heads. Firſt I will endeavour to ſhew that all Experiments that can
be made upon the Earth are inſufficient means to conclude it's Mobility, but are indifferently applicable
to the Earth moveable or immoveable: and I hope that on this occaſion we ſhall diſcover many
vable paſſages unknown to the Ancients. Secondly we will examine the Cœleſtiall Phœnomena
that make for the Copernican Hypotheſis, as if it were to prove abſolutely victorious; adding by the
way certain new Obſervations, which yet ſerve only for the Aſtronomical Facility, not for Natural
Neceßity. In the third place I will propoſe an ingenuous Fancy. I remember that I have ſaid many
years ſince, that the unknown Probleme of the Tide might receive ſome light, admitting the Earths
Motion. This Poſition of mine paſsing from one to another had found charitable Fathers that
adopted it for the Iſſue of their own wit. Now, becauſe no ſtranger may ever appear that defending
ſelf with our armes ſhall charge us with want of caution in ſo principal an Accident, I have thought
good to lay down thoſe probabilities that would render it credible, admitting that the Earth did
move. I hope, that by theſe Conſider ations the World will come to know, that if other Nations have
Navigated more than we, we have not ſtudied leſs than they; & that our returning to aſſert the Earths
Stability, and to take the contrary only for a Mathematical Capriccio, proceeds not from inadvertency
of what others have thought thereof, but (had we no other inducements) from thoſe Reaſons that
ty, Religion, the Knowledge of the Divine Omnipotency, and a conſciouſneſs of the incapacity of mans
Vnderſtanding dictate unto us.
1
With all I conceived it very proper to expreſs theſe conceits by way of Dialogue, which, as not being
bound up to the riggid obſervance of Mathematical Laws, gives place alſo to Digreſsions that are
ſometimes no leſs curious than the principal Argument.
I chanced to be ſeveral years ſince, at ſeveral times, in the Stupendious Citty of Venice, where I
converſed with Signore Giovan Franceſco Sagredo of a Noble Extraction, and piercing wit. There
came thither from Florence at the ſame time Signore Filippo Salviati, whoſe leaſt glory was the
nence of his Blood, and Magnificence of his Eſtate: a ſublime Wit that fed not more hungerly upon
any pleaſure than on elevated Speculations. In the company of theſe two I often diſcourſed of theſe
matters before a certain Peripatetick Philoſopher who ſeemed to have no geater obſtacle in
ing of the Truth, than the Fame he had acquired by Ariſtotelical Interpretations.
Now, ſeeing that inexorable Death hath deprived Venice and Florence of thoſe two great Lights in
the very Meridian of their years, I did reſolve, as far as my poor ability would permit, to perpetuate
their lives to their honour in theſe leaves, bringing them in as Interlocutors in the preſent Controverſy.
Nor ſhall the Honest Peripatetick want his place, to whom for his exceſsive affection to wards the
mentaries of Simplicius, I thought fit, without mentioning his own Name, to leave that of the Author
he ſo much reſpected. Let thoſe two great Souls, ever venerable to my heart, pleaſe to accept this
blick Monument of my never dying Love; and let the remembr ance of their Eloquence aſsiſt me in
delivering to Poſterity the Conſider ations that I have promiſed.
There caſually happened (as was uſuall) ſeveral diſcourſes at times between theſe Gentlemen, the
which had rather inflamed than ſatisfied in their wits the thirſt they had to be learning; whereupon
they took a diſcreet reſolution to meet together for certain dayes, in which all other buſineſs ſet aſide,
they might betake themſelves more methodically to contemplate the Wonders of God in Heaven, and in
the Earth: the place appointed for their meeting being in the Palace of the Noble Sagredo, after the
due, but very ſhort complements; Signore Salviati began in this manner.
1
GALILÆUS
Galilæus Lyncæus,
HIS
SYSTEME
OF THE
WORLD.
The Firſt Dialogue.
INTERLOCVTORS.
SALVIATUS, SAGREDUS, and SIMPLICIUS.
SALVIATUS.
It was our yeſterdayes reſolution, and
greement, that we ſhould to day diſcourſe
the moſt diſtinctly, and particularly we
could poſſible, of the natural reaſons, and
their efficacy that have been hitherto
ledged on the one or other part, by the
maintainers of the Poſitions, Aristotelian,
and Ptolomaique; and by the followers

of the Copernican Syſteme: And becauſe
Copernicus placing the Earth among the moveable Bodies of
ven, comes to conſtitute a Globe for the ſame like to a Planet; it
would be good that we began our diſputation with the
tion of what, and how great the energy of the Peripateticks
guments is, when they demonſtrate, that this Hypotheſis is
1ſible: Since that it is neceſſary to introduce in Nature, ſubſtances

different betwixt themſelves, that is, the Cœleſtial, and
ry; that impaſſible and immortal, this alterable and corruptible.
Which argument Ariſtotle handleth in his book De Cœlo,
ating it firſt, by ſome diſcourſes dependent on certain general
ſumptions, and afterwards confirming it with experiments and
ticular demonſtrations: following the ſame method, I will
pound, and freely ſpeak my judgement, ſubmitting my ſelf to
your cenſure, and particularly to Simplicius, a Stout Champion
and contender for the Ariſtotelian
Copernicus
teth the earth œ
Globe like to a
net.
Cœleſtial
ces that are
rable, and
tary that be
rable, are neceſſary
in the opinion of
Ariſtotle.
Ariſtotle maketh
the World perfect,
becauſe it hath the
threefold
on.
And the firſt Step of the Peripatetick arguments is that, where
riſtotle proveth the integrity and perfection of the World, telling
us, that it is not a ſimple line, nor a bare ſuperficies, but a body
adorned with Longitude, Latitude, and Profundity; and becauſe
there are no more dimenſions but theſe three; The World having
them, hath all, and having all, is to be concluded perfect. And
again, that by ſimple length, that magnitude is conſtituted, which
is called a Line, to which adding breadth, there is framed the
perficies, and yet further adding the altitude or profoundity, there
reſults the Body, and after theſe three dimenſions there is no
paſſing farther, ſo that in theſe three the integrity, and to ſo ſpeak,
totality is terminated, which I might but with juſtice have
red Ariſtotle to have proved to me by neceſſary conſequences, the
rather in regard he was able to do it very plainly, and ſpeedily.
SIMPL. What ſay you to the excellent demonſtrations in the

2. 3. and 4. Texts, after the definition of Continual? have you it
not firſt there proved, that there is no more but three dimenſions,
for that thoſe three are all things, and that they are every where?
And is not this confirmed by the Doctrine and Authority of the

Pythagorians, who ſay that all things are determined by three,
ginning, middle, and end, which is the number of All? And where
leave you that reaſon, namely, that as it were by the law of
ture, this number is uſed in the ſacrifices of the Gods? And why
being ſo dictated by nature, do we atribute to thoſe things that
are three, and not to leſſe, the title of all? why of two is it ſaid
both, and not all, unleſs they be three? And all this Doctrine you
have in the ſecond Text. Afterwards in the third, Ad pleniorem

ſcientiam, we read that All, the Whole, and Perfect, are formally
one and the ſame; and that therefore onely the Body, amongſt
magnitudes is perfect: becauſe it is determined by three, which is
All, and being diviſible three manner of waies, it is every way
viſible; but of the others, ſome are dividible in one manner, and
ſome in two, becauſe according to the number aſſixed, they have
their diviſion and continuity, and thus one magnitude is

ate one way, another two, a third, namely the Body, every way.
1Moreover in the fourth Text; doth he not after ſome other
ctrines, prove it by another demonſtration? Scilicet, That no
ſition is made but according to ſome defect (and ſo there is a
ſition or paſſing from the line to the ſuperficies, becauſe the line is
defective in breadth) and that it is impoſſible for the perfect to
want any thing, it being every way ſo; therefore there is no
ſition from the Solid or Body to any other magnitude. Now
think you not that by all theſe places he hath ſufficiently proved,
how that there's no going beyond the three dimenſions, Length,
Breadth, and Thickneſs, and that therefore the body or ſolid,
which hath them all, is perfect?
Ariſtotles
ſtrations to prove
the dimenſions to be
three and no more.
The number three
celebrated among ſt
the Pythagorians
Omne, Totum &
Perfectum.
Or Solid.
SALV. To tell you true, I think not my ſelf bound by all theſe
reaſons to grant any more but onely this, That that which hath
beginning, middle, and end, may, and ought to be called perfect: But
that then, becauſe beginning, middle, and end, are Three, the
ber Three is a perfect number, and hath a faculty of conferring
Perfection on thoſe things that have the ſame, I find no inducement
to grant; neither do I underſtand, nor believe that, for example,
of feet, the number three is more perfect then four or two, nor do
I conceive the number four to be any imperfection to the
ments: and that they would be more perfect if they were three.
Better therefore it had been to have left theſe ſubtleties to the
Rhetoricians, and to have proved his intent, by neceſſary
tion; for ſo it behoves to do in demonſtrative ſciences.
SIMPL. You ſeem to ſcorn theſe reaſons, and yet it is all the
Doctrine of the Pythagorians, who attribute ſo much to numbers;
and you that be a Mathematician, and believe many opinions in
the Pythagorick Philoſophy, ſeem now to contemn their
ſteries.
SALV. That the Pythagorians had the ſcience of numbers in
high eſteem, and that Plato himſelf admired humane
ing, and thought that it pertook of Divinity, for that it

ſtood the nature of numbers, I know very well, nor ſhould I be
far from being of the ſame opinion: But that the Myſteries for
which Pythagoras and his ſect, had the Science of numbers in ſuch
veneration, are the follies that abound in the mouths and writings

of the vulgar, I no waies credit: but rather becauſe I know that they,
to the end admirable things might not be expoſed to the
tempt, and ſcorne of the vulgar, cenſured as ſacrilegious, the

liſhing of the abſtruce properties of Numbers, and
ſurable and irrational quantities, by them inveſtigated; and
vulged, that he who diſcovered them, was tormented in the other
World: I believe that ſome one of them to deter the common
ſort, and free himſelf from their inquiſitiveneſs, told them that the
myſteries of numbers were thoſe trifles, which afterwards did ſo
1ſpread amongſt the vulgar; and this with a diſcretion and ſubtlety
reſembling that of the prudent young man, that to be freed
from the importunity of his inquiſitive Mother or Wife, I know
not whether, who preſſed him to impart the ſecrets of the Senate,
contrived that ſtory, which afterwards brought her and many
ther women to be derided and laught at by the ſame Senate.
Plato held that
humane
ſtanding partook
of divinity, becauſe
it understood
bers.
The Myſtery of
Pythagorick
bers fabulous.
De Papyrio
textato, Gellius
2. 3.
SIMPL. I will not be of the number of thoſe who are over
ous about the Pythagorick myſteries; but adhering to the point
in hand; I reply, that the reaſons produced by Ariſtotle to prove
the dimenſions to be no more than three, ſeem to me
dent, and I believe, That had there been any more evident
ſtrations thereof, Ariſtotle would not have omitted them.
SAGR. Put in at leaſt, if he had known, or remembred any more.
But you Salviatus would do me a great pleaſure to alledge unto
me ſome arguments that may be evident, and clear enough for me
to comprehend.
SALV. I will; and they ſhall be ſuch as are not onely to be
prehended by you, but even by Simplicius himſelf: nor onely
to be comprehended, but are alſo already known, although
ly unobſerved; and for the more eaſie underſtanding thereof,
we will take this Pen and Ink, which I ſee already prepared for

ſuch occaſions, and deſcribe a few figures. And firſt we will note
[Fig. 1. at the end of this Dialog.] theſe two points AB, and draw
from the one to the other the curved lines, ACB, and ADB, and the
right line A B, I demand of you which of them, in your mind, is
that which determines the diſtance between the terms AB, & why?
A Geometrical
monſtration of the
triple dimenſion.
SAGR. I ſhould ſay the right line, and not the crooked, as well
becauſe the right is ſhorter, as becauſe it is one, ſole, and
minate, whereas the others are infinit, unequal, and longer; and my
determination is grounded upon that, That it is one, and certain.
SALV. We have then the right line to determine the length
tween the two terms; let us add another right line and parallel to
AB, which let be CD, [Fig. 2.] ſo that there is put between them a
ſuperficies, of which I deſire you to aſſign me the breadth, therefore
departing from the point A, tell me how, and which way you will
go, to end in the line C D, and ſo to point me out the breadth
prehended between thoſe lines; let me know whether you will
terminate it according to the quantity of the curved line A E, or
the right line A F, or any other.
SIMPL. According to the right A F, and not according to the
crooked, that being already excluded from ſuch an uſe.
SAGR. But I would take neither of them, ſeeing the right line
A F runs obliquely; But would draw a line, perpendicular to C
D, for this ſhould ſeem to me the ſhorteſt, and the propereſt of
infinite that are greater, and unequal to one another, which may be
1produced from the term A to any other part of the oppoſite line
C D.
SALV. Your choice, and the reaſon you bring for it in my
ment is moſt excellent; ſo that by this time we have proved that
the firſt dimenſion is determined by a right line, the ſecond
ly the breadth with another line right alſo, and not onely right,
but withall, at right-angles to the other that determineth the
length, and thus we have the two dimenſions of length and
breadth, definite and certain. But were you to bound or
nate a height, as for example, how high this Roof is from the
ment, that we tread on, being that from any point in the Roof,
we may draw infinite lines, both curved, and right, and all of
verſe lengths to infinite points of the pavement, which of all theſe
lines would you make uſe of?
SAGR. I would faſten a line to the Seeling, and with a plummet
that ſhould hang at it, would let it freely diſtend it ſelf till it
ſhould reach well near to the pavement, and the length of ſuch a
thread being the ſtreighteſt and ſhorteſt of all the lines, that could
poſsibly be drawn from the ſame point to the pavement, I would
ſay was the true height of this Room.
SALV. Very well, And when from the point noted in the
ment by this pendent thread (taking the pavement to be levell
and not declining) you ſhould produce two other right lines, one
for the length, and the other for the breadth of the ſuperficies of
theſaid pavement, what angles ſhould they make with the ſaid
thread?
SAGR. They would doubtleſs meet at right angles, the ſaid
lines falling perpendicular, and the pavement being very plain and
levell.
SALV. Therefore if you aſſign any point, for the term from whence
to begin your meaſure; and from thence do draw a right line, as
the terminator of the firſt meaſure, namely of the length, it will
follow of neceſſity, that that which is to deſign out the largeneſs
or breadth, toucheth the firſt at right-angles, and that that which is
to denote the altitude, which is the third dimenſion, going from the
ſame point formeth alſo with the other two, not oblique but right
angles, and thus by the three perpendiculars, as by three lines, one,
certain, and as ſhort as is poſſible, you have the three dimenſions
A B length, A C breadth, and A D height; and becauſe, clear it
is, that there cannot concurre any more lines in the ſaid point, ſo
as to make therewith right-angles, and the dimenſions ought to
be determined by the ſole right lines, which make between
ſelves right-angles; therefore the dimenſions are no more but
three, and that which hath three hath all, and that which hath all,
is diviſible on all ſides, and that which is ſo, is perfect, &c.
1
SIMPL. And who ſaith that I cannot draw other lines? why
may not I protract another line underneath, unto the point A,
that may be perpendicular to the reſt?
SALV. You can doubtleſs, at one and the ſame point, make no
more than three right lines concurre, that conſtitute right angles
between themſelves.
SAGR. I ſee what Simplicius means, namely, that ſhould the
ſaid D A be prolonged downward, then by that means there might
be drawn two others, but they would be the ſame with the firſt
three, differing onely in this, that whereas now they onely touch,
then they would interſect, but not produce new
In phyfical proofs
geometrical
neſs is not
ry.
SIMPL. I will not ſay that this your argument may not be
cludent; but yet this I ſay with Ariſtotle, that in things natural
it is not alwaies neceſſary, to bring Mathematical demonſtrations.
SAGR. Grant that it were ſo where ſuch proofs cannot be had,
yet if this caſe admit of them, why do not you uſe them? But it
would be good we ſpent no more words on this particular, for I
think that Salviatus will yield, both to Ariſtotle, and you,
out farther demonſtration, that the World is a body, and perfect,
yea moſt perfect, as being the greateſt work of God.
SALV. So really it is, therefore leaving the general contempla­

tion of the whole, let us deſcend to the conſideration of its parts,
which Ariſtotle, in his firſt diviſion, makes two, and they very
rent and almoſt contrary to one another; namely the Cœleſtial,
and Elementary: that ingenerable, incorruptible, unalterable,
paſſible, &c. and this expoſed to a continual alteration,
on, &c. Which difference, as from its original principle, he
rives from the diverſity of local motions, and in this method he
proceeds.
Parts of the world
are two, according
to Ariſtotle,
ſtial and
tary contrary to
one another.
Leaving the ſenſible, if I may ſo ſpeak, and retiring into the
Ideal world, he begins Architectonically to conſider that nature
being the principle of motion, it followeth that natural bodies be

indued with local motion. Next he declares local motion to be
of three kinds, namely, circular, right, and mixt of right and
cular: and the two firſt he calleth ſimple, for that of all lines the

circular, and right are onely ſimple; and here ſomewhat
ſtraining himſelf, he defineth anew, of ſimple motions, one to be
circular, namely that which is made about the medium, and the
other namely the right, upwards, and downwards; upwards, that
which moveth from the medium; downwards, that which goeth
wards the medium. And from hence he infers, as he may by and

ceſſary conſequence, that all ſimple motions are confined to theſe
three kinds, namely, to the medium, from the medium, and about
the medium; the which correſponds ſaith he, with what hath been
ſaid before of a body, that it alſo is perfected by three things, and ſo
1is its motion. Having confirmed theſe motions, he proceeds ſaying,
that of natural bodies ſome being ſimple, and ſome compoſed of
them (and he calleth ſimple bodies thoſe, that have a principle
of motion from nature, as the Fire and Earth) it follows that
ſimple motions belong to ſimple bodies, and mixt to the
pound; yet in ſuch ſort, that the compounded incline to the part
predominant in the compoſition.
Local motion of
three kinds, right,
circular, & mixt.
Circular, and
ſtreight motions
are ſimple, as
ceeding by ſimple
lines.
Ad medium, à
dio, & circa
um.
SAGR. Pray you hold a little Salviatus, for I find ſo many
doubts to ſpring up on all ſides in this diſcourſe, that I ſhall be
conſtrained, either to communicate them if I would attentively
hearken to what you ſhall add, or to take off my attention from
the things ſpoken, if I would remember objections.
SALV. I will very willingly ſtay, for that I alſo run the ſame
hazard, and am ready at every ſtep to loſe my ſelf whilſt I ſail
tween Rocks, and boiſterous Waves, that make me, as they ſay, to
loſe my Compaſs; therefore before I make them more, propound
your
The definition of
Nature, either
perfect, or
nable, produced by
Ariſtotle.
SAGR. You and Ariſtotle together would at firſt take me a
little out of the ſenſible World, to tell me of the Architecture,
wherewith it ought to be fabricated; and very appoſitly begin to
tell me, that a natural body is by nature moveable, nature being
(as elſewhere it is defined) the principle of motion. But here I
am ſomewhat doubtfull why Ariſtotle ſaid not that of natural
dies, ſome are moveable by nature, and others immoveable, for
that in the definition, nature is ſaid to be the principle of Motion,
and Reſt; for if natural bodies have all a principle of motion,
either he might have omitted the mention of Reſt, in the
on of nature: or not have introduced ſuch a definition in this place.
Next, as to the declaration of what Ariſtotle intends by ſimple
motions, and how by Spaces he determines them, calling thoſe
ple, that are made by ſimple lines, which are onely the right, and

circular, I entertain it willingly; nor do I deſire to tenter the
inſtance of the Helix, about the Cylinder; which in that it is in
very part like to it ſelf, might ſeemingly be numbred among
ple lines. But herein I cannot concurre, that he ſhould ſo
ſtrain ſimple motions (whilſt he ſeems to go about to repeat the
ſame definition in other words) as to call one of them the motion
about the medium, the others Surſum & Deorſum, namely
wards and downward; which terms are not to be uſed, out of the
World fabricated, but imply it not onely made, but already
habited by us; for if the right motion be ſimple, by the ſimplicity
of the right line, and if the ſimple motion be natural, it is made on
every ſide, to wit, upwards, downwards, backwards, forwards, to
the right, to the left, and if any other way can be imagined,
vided it be ſtraight, it ſhall agree to any ſimple natural body; or
1if not ſo, then the ſuppoſion of Ariſtotle is defective. It appears

moreover that Ariſtotle hinteth but one circular motion alone to
be in the World, and conſequently but one onely Center, to
which alone the motions of upwards and downwards, refer. All
which are apparent proofs, that Ariſtotles aim is, to make white
black, and to accommodate Architectur to the building, and not
to modle the building according to the precepts of Arthitecture:
for if I ſhould ſay that Nature in Univerſal may have a
ſand Circular Motions, and by conſequence a thouſand
ters, there would be alſo a thouſand motions upwards, and
downwards. Again he makes as hath been ſaid, a ſimple motion,
and a mixt motion, calling ſimple, the circular and right; and
mixt, the compound of them two: of natural bodies he calls ſome
ſimple (namely thoſe that have a natural principle to ſimple
tion) and others compound: and ſimple motions he attributes
to ſimple bodies, and the compounded to the compound; but by
compound motion he doth no longer underſtand the mixt of right
and circular, which may be in the World; but introduceth a mixt
motion as impoſſible, as it is impoſſible to mixe oppoſite motions
made in the ſame right line, ſo as to produce from them a motion
partly upwards, partly downwards; and, to moderate ſuch an
ſurdity, and impoſſibility, he aſſerts that ſuch mixt bodies move

according to the ſimple part predominant: which neceſſitates
others to ſay, that even the motion made by the ſame right line is
ſometimes ſimple, and ſometimes alſo compound: ſo that the
plicity of the motion, is no longer dependent onely on the
plicity of the line.
The Helix about
the Cylinder may
be ſaid to be a
ple line.
Ariſtotle
modates the rules of
Architecture to
the frame of the
World, and not the
frame to the rules.
Right motion,
times ſimple, ard
ſometimes mixt
cording to Ariſt.
SIMPL. How? Is it not difference ſufficient, that the ſimple and
abſolute are more ſwift than that which proceeds from
nion? and how much faſter doth a piece of pure Earth deſcend,
than a piece of Wood?
SAGR. Well, Simplicius; But put caſe the ſimplicity for this
cauſe was changed, beſides that there would be a hundred
ſand mixt motions, you would not be able to determine the
ple; nay farther, if the greater or leſſe velocity be able to alter
the ſimplicity of the motion, no ſimple body ſhould move with a
ſimple motion; ſince that in all natural right motions, the
ty is ever encreaſing, and by conſequence ſtill changing the
city, which as it is ſimplicity, ought of conſequence to be
table, and that which more importeth, you charge Ariſtotle with
another thing, that in the definition of motions compounded, he
hath not made mention of tardity nor velocity, which you now
inſert for a neceſſary and eſſential point. Again you can draw
no advantage from this rule, for that there will be amongſt the
mixt bodies ſome, (and that not a few) that will move ſwiftly,
1and others more ſlowly than the ſimple; as for example, Lead, and
Wood, in compariſon of earth; and therefore amongſt theſe
tions, which call you the ſimple, and which the mixt?
SIMPL. I would call that ſimple motion, which is made by a
ſimple body, and mixt, that of a compound body.
SAGR. Very well, and yet Simplicius a little before you ſaid,
that the ſimple, and compound motions, diſcovered which were
mixt, and which were ſimple bodies; now you will have me by
ſimple and mixt bodies, come to know which is the ſimple, and
which is the compound motion: an excellent way to keep us
rant, both of motions and bodies. Moreover you have alſo a little
above declared, how that a greater velocity did not ſuffice, but
you ſeek a third condition for the definement of ſimple motion, for
which Ariſtotle contented himſelf with one alone, namely, of the
ſimplicity of the Space, or Medium: But now according to you,
the ſimple motion, ſhall be that which is made upon a ſimple line,
with a certain determinate velocity, by a body ſimply moveable.
Now be it as you pleaſe, and let us return to Ariſtotle, who
neth the mixt motion to be that compounded of the right, and
cular, but produceth not any body, which naturally moveth with
ſuch a motion.
SALV. I come again to Ariſtotle, who having very well, and
Methodically begun his diſcourſe, but having a greater aim to
reſt at, and hit a marke, predefigned in his minde, then that to
which his method lead him, digreſſing from the purpoſe, he comes
to aſſert, as a thing known and manifeſt, that as to the motions
directly upwards or downwards, they naturally agree to Fire, and
Earth; and that therefore it is neceſſary, that beſides theſe bodies,
which are neer unto us, there muſt be in nature another, to which
the circular motion may agree: which ſhall be ſo much the more
excellent by how much the circular motion is more perfect, then the
ſtreight, but how much more perfect that is than this, he
mines from the greatneſs of the circular lines perfection above the

right line; calling that perfect, and this imperfect; imperfect,
cauſe if infinite it wanteth a termination, and end: and if it be
nite, there is yet ſomething beyond which it may be prolonged.
This is the baſis, ground work, and maſter-ſtone of all the Fabrick
of the Aristotelian World, upon which they ſuperſtruct all their
other properties, of neither heavy nor light, of ingenerable
ruptible, exemption from all motions, ſome onely the local, &c.
And all theſe paſſions he affirmeth to be proper to a ſimple body
that is moved circularly; and the contrary qualities of gravity,
levity, corruptibility, &c. he aſſigns to bodies naturally moveable
in a ſtreight line, for that if we have already diſcovered defects in
the foundation, we may rationally queſtion what ſoever may
1ther built thereon. I deny not, that this which Ariſtotle hitherto
hath introduced, with a general diſcourſe dependent upon
ſal primary principles, hathbeen ſince in proceſs of time, re-inforced
with particular reaſons, and experiments; all which it would be
neceſſary diſtinctly to conſider and weigh; but becauſe what hath
been ſaid hitherto preſents to ſuch as conſider the ſame many and
no ſmall difficulties, (and yet it would be neceſſary, that the
mary principles and fundamentals, were certain, firm, and
ed, that ſo they might with more confidence be built upon) it
would not be amiſs, before we farther multiply doubts, to ſee if
haply (as I conjecture) betaking our ſelves to other waies, we may
not light upon a more direct and ſecure method; and with better
conſidered principles of Architecture lay our primary
tals. Therefore ſuſpending for the preſent the method of
tle, (which we will re-aſſume again in its proper place, and
cularly examine;) I ſay, that in the things hitherto affirmed by

him, I agree with him, and admit that the World is a body
ing all dimenſions, and therefore moſt perfect; and I add, that as
ſuch, it is neceſſarily moſt ordinate, that is, having parts between
themſelves, with exquiſite and moſt perfect order diſpoſed; which
aſſumption I think is not to be denied, neither by you or any
other.
The circular line
perfect, according
to Ariſtotle, and
but the right
perfect, and why.
The world is
poſed by the
thor to be perfectly
ordinate.
SIMPL. Who can deny it? the firſt particular (of the worlds
dimenſions) is taken from Ariſtotle himſelf, and its
on of ordinate ſeems onely to be aſſumed from the order which it
moſt exactly
Streight motion
impoſſible in the
world exactly
dinate.
SALV. This principle then eſtabliſhed, one may immediately
conclude, that if the entire parts of the World ſhould be by their
nature moveable, it is impoſſible that their motions ſhould be
right, or other than circular; and the reaſon is ſufficiently eaſie,
and manifeſt; for that whatſoever moveth with a right motion,
changeth place; and continuing to move, doth by degrees more
and more remove from the term from whence it departed, and
from all the places thorow which it ſucceſſively paſſed; and if
ſuch motion naturally ſuited with it, then it was not at the
ginning in its proper place; and ſo the parts of the World were
not diſpoſed with perfect order. But we ſuppoſe them to be
fectly ordinate, therefore as ſuch, it is impoſſible that they ſhould
by nature change place, and conſequently move in a right moti­

on. Again, the right motion being by nature infinite, for that
the right line is infinite and indeterminate, it is impoſſible that

any moveable can have a natural principle of moving in a right
line; namely toward the place whither it is impoſſible to arrive,

there being no præ-ſinite term; and nature, as Ariſtotle himſelf
ſaith well, never attempts to do that which can never be done,
1nor eſſaies to move whither it is impoſſible to arrive. And if any
one ſhould yet object, that albeit the right line, and
ly the motion by it is producible in infinitum, that is to ſay, is
terminate; yet nevertheleſs Nature, as one may ſay, arbitrarily
hath aſſigned them ſome terms, and given natural inſtincts to
its natural bodies to move unto the ſame; I will reply, that this

might perhaps be fabled to have come to paſs in the firſt Chaos,
where indiſtinct matters confuſedly and inordinately wandered;
to regulate which, Nature very appoſitely made uſe of right

tions, by which, like as the well-conſtituted, moving, diſdorder
themſelves, ſo were they which were before depravedly diſpoſed
by this motion ranged in order: but after their exquiſite
tion and collocation, it is impoſſible that there ſhould remain
tural inclinations in them of longer moving in a right motion,
from which now would enſue their removal from their proper and
natural place, that is to ſay, their diſordination; we may
fore ſay that the right motion ſerves to conduct the matter to erect
the work; but once erected, that it is to reſt immoveable, or if

moveable, to move it ſelf onely circularly. Unleſs we will ſay
with Plato, that theſe mundane bodies, after they had been made
and finiſhed, were for a certain time moved by their Maker, in a
right motion, but that after their attainment to certain and
terminate places, they were revolved one by one in Spheres,
ſing from the right to the circular motion, wherein they have
been ever ſince kept and maintained. A ſublime conceipt, and

worthy indeed of Plato: upon which, I remember to have heard
our common friend the ^{*}Lyncean Academick diſcourſe in this
ner, if I have not forgot it. Every body for any reaſon
ted in a ſtate of reſt, but which is by nature moveable, being ſet

at liberty doth move; provided withal, that it have an
tion to ſome particular place; for ſhould it ſtand indifferently
fected to all, it would remain in its reſt, not having greater
ducement to move one way than another. From the having of
this inclination neceſſarily proceeds, that it in its moving ſhall

tinually increaſe its acceleration, and beginning with a moſt ſlow
motion, it ſhall not acquire any degree of velocity, before it
ſhall have paſſed thorow all the degrees of leſs velocity, or
ter tardity: for paſſing from the ſtate of quiet (which is the

finite degree of tardity of motion) there is no reaſon by which
it ſhould enter into ſuch a determinate degree of velocity, before
it ſhall have entred into a leſs, and into yet a leſs, before it entred
into that: but rather it ſtands with reaſon, to paſs firſt by thoſe
degrees neareſt to that from which it departed, and from thoſe to
the more remote; but the degree from whence the moveable

began to move, is that of extreme tardity, namely of reſt.
1
Now this acceleration of motion is never made, but when the
moveable in moving acquireth it; nor is its acquiſt other than an
approaching to the place deſired, to wit, whither its natural
clination attracts it, and thither it tendeth by the ſhorteſt way;
namely, by a right line. We may upon good grounds therefore
ſay, That Nature, to confer upon a moveable firſt conſtituted in
reſt a determinate velocity, uſeth to make it move according to

a certain time and ſpace with a right motion. This preſuppoſed,
let us imagine God to have created the Orb v. g. of Jupiter, on
which he had determined to confer ſuch a certain velocity, which
it ought afterwards to retain perpetually uniform; we may with
Plato ſay, that he gave it at the beginning a right and accelerate
motion, and that it afterwards being arrived to that intended

gree of velocity, he converted its right, into a circular motion,
the velocity of which came afterwards naturally to be uniform.
Right motion by
nature infinite.
Motion by a right
line naturally
poſſible.
Nature attempts
not things
ble to be effected.
Right motion might
perhaps be in the
firſt Chaos.
Right motion is
commodious to
range in order,
things ous of
der.
Mundane bodies
moved in the
ginning in a right
line, and
wards circularly?
according to Plato.
* Thus doth he
vertly and
ly ſtile himſelfe
throughout this
work.
A moveable
ing in a ſtate of
reſt, ſhall not move
unleſs it have an
inclination to ſome
particular place.
The moveable
celerates its
on, going towards
the place whither
it hath an
tion.
The moveable
ſing from reſt,
eth thorow all the
degrees of tardity.
Reſt the inſinioe
degree of tardity.
The moveable doth
not accelerate, ſave
only as it
eth nearer to its
term.
Nature, to
duce in the
able a certain
gree of velocity,
made it move in a
right line.
Vniform velocity
convenient to the
circular motion.
SAGR. I hearken to this Diſcourſe with great delight; and I
believe the content I take therein will be greater, when you have
ſatisfied me in a doubt: that is, (which I do not very well
prehend) how it of neceſſity enſues, that a moveable departing

from its reſt, and entring into a motion to which it had a natural
inclination, it paſſeth thorow all the precedent degrees oſ tardity,
comprehended between any aſſigned degree of velocity, and the
ſtate of reſt, which degrees are infinite? ſo that Nature was not
able to confer them upon the body of Jupiter, his circular
on being inſtantly created with ſuch and ſuch
Betwixt reſt, and
any aſſigned degree
of velocity, infinite
degrees of leſs
locity interpoſe.
Nature doth not
immediately
fer a determinate
degree of velocity,
howbeit ſhe could.
SALV. I neither did, nor dare ſay, that it was impoſſible for
God or Nature to confer that velocity which you ſpeak of,
diately; but this I ſay, that de facto ſhe did not doit; ſo that the
doing it would be a work extra-natural, and by confequence
raculous.
SAGR. Then you believe, that a ſtone leaving its reſt, and
tring into its natural motion towards the centre of the Earth,
ſeth thorow all the degrees of tardity inferiour to any degree of
velocity?
SALV. I do believe it, nay am certain of it; and ſo certain,
that I am able to make you alſo very well ſatisfied with the truth
thereof.
SAGR. Though by all this daies diſcourſe I ſhould gain no
more but ſuch a knowledge, I ſhould think my time very well
beſtowed.
SALV. By what I collect from our diſcourſe, a great part of
your ſcruple lieth in that it ſhould in a time, and that very ſhort,
paſs thorow thoſe infinite degrees of tardity precedent to any
locity, acquired by the moveable in that time: and therefore
fore we go any farther, I will ſeek to remove this difficulty, which
1ſhall be an eaſie task; for I reply, that the moveable paſſeth by
the aforeſaid degrees, but the paſſage is made without ſtaying in

any of them; ſo that the paſſage requiring but one ſole inſtant
of time, and every ſmall time containing infinite inſtants, we ſhall
not want enough of them to aſſign its own to each of the infinite
degrees of tardity; although the time were never ſo ſhort.
The moveable
parting from reſv
paſſeth thorow all
degrees of velocity
without ſtaying in
any.
SAGR. Hitherto I apprehend you; nevertheleſs it is very much
that that Ball ſhot from a Cannon (for ſuch I conceive the
dent moveable) which yet we ſee to fall with ſuch a precipice,
that in leſs than ten pulſes it will paſs two hundred yards of
titude; ſhould in its motion be found conjoyned with ſo ſmall a
degree of velocity, that, ſhould it have continued to have moved
at that rate without farther acceleration, it would not have paſt
the ſame in a day.
SALV. You may ſay, nor yet in a year, nor in ten, no nor in a
thouſand; as I will endeavour to ſhew you, and alſo happily
out your contradiction, to ſome ſufficiently ſimple queſtions that
I will propound to you. Therefore tell me if you make any
ſtion of granting that, that that ball in deſcending goeth
ſing its impetus and velocity.
SAGR. I am moſt certain it doth.
SALV. And if I ſhould ſay that the impetus acquired in any
place of its motion, is ſo much, that it would ſuffice to re-carry
it to that place from which it came, would you grant it?
SAGR. I ſhould conſent to it without contradiction, provided
waies, that it might imploy without impediment its whole impetus
in that ſole work of re-conducting it ſelf, or another equal toit, to

that ſelf-ſame height as it would do, in caſe the Earth were bored
thorow the centre, and the Bullet fell a thouſand yards from the
ſaid centre, for I verily believe it would paſs beyond the centre,
aſcending as much as it had deſcended; and this I ſee plainly in
the experiment of a plummet hanging at a line, which removed
from the perpendicular, which is its ſtate of reſt, and afterwards
let go, falleth towards the ſaid perpendicular, and goes as far
yond it; or onely ſo much leſs, as the oppoſition of the air, and
line, or other accidents have hindred it. The like I ſee in the
ter, which deſcending thorow a pipe, re-mounts as much as it had
deſcended.
The ponderous
ver deſcending
quireth impetus
ſufficient to
carry it to the like
height.
SALV. You argue very well. And for that I know you will not
ſcruple to grant that the acquiſt of the impetus is by means of the
receding from the term whence the moveable departed, and its
proach to the centre, whither its motion tendeth; will you ſtick
to yeeld, that two equal moveables, though deſcending by divers
lines, without any impediment, acquire equal impetus, provided
that the approaches to the centre be equal?
1
SAGR. I do not very well underſtand the queſtion.
SALV. I will expreſs it better by drawing a Figure: therefore
I will ſuppoſe the line A B [in Fig. 3.] parallel to the Horizon,
and upon the point B, I will erect a perpendicular B C; and after
that I adde this ſlaunt line C A. Underſtanding now the line C
A to be an inclining plain exquiſitely poliſhed, and hard, upon
which deſcendeth a ball perfectly round and of very hard matter,
and ſuch another I ſuppoſe freely to deſcend by the perpendicular
C B: will you now confeſs that the impetus of that which
ſcends by the plain C A, being arrived to the point A, may be
equal to the impetus acquired by the other in the point B, after
the deſcent by the perpendicular C
The impetuoſity of
moveables equally
approaching to the
centre, are equal.
SAGR. I reſolutely believe ſo: for in effect they have both the
ſame proximity to the centre, and by that, which I have already
granted, their impetuoſities would be equally ſufficient to re-carry
them to the ſame height.
SALV. Tell me now what you believe the ſame ball would do
put upon the Horizontal plane A B?
Vpon an
tall plane the
able lieth ſtill.
SAGR. It would lie ſtill, the ſaid plane having no declination.
SALV. But on the inclining plane C A it would deſcend, but
with a gentler motion than by the perpendicular C B?
SAGR. I may confidently anſwer in the affirmative, it
ing to me neceſſary that the motion by the perpendicular C B
ſhould be more ſwift, than by the inclining plane C A; yet
vertheleſs, iſ this be, how can the Cadent by the inclination
rived to the point A, have as much impetus, that is, the ſame
gree of velocity, that the Cadent by the perpendicular ſhall have
in the point B? theſe two Propoſitions ſeem contradictory.
The veloeity by the
inclining plane
qual to the
ty by the
oular, and the
tion by the
dicular ſwifter
than by the
nation.
SALV. Then you would think it much more falſe, ſhould I
ſay, that the velocity of the Cadents by the perpendicular, and
inclination, are abſolutely equal: and yet this is a Propoſition
moſt true, as is alſo this that the Cadent moveth more ſwiftly by
the perpendicular, than by the inclination.
SAGR. Theſe Propoſitions to my ears ſound very harſh: and
I believe to yours Simplicius?
SIMPL. I have the ſame ſenſe of them.
SALV. I conceit you jeſt with me, pretending not to
hend what you know better than my ſelf: therefore tell me
plicius, when you imagine a moveable more ſwift than
ther, what conceit do you fancy in your mind?
SIMPL. I fancie one to paſs in the ſame time a greater ſpace
than the other, or to move equal ſpaces, but in leſſer time.
SALV. Very well: and for moveables equally ſwift, what's
your conceit of them?
SIMPL. I fancie that they paſs equal ſpaces in equal times.
1
SALV. And have you no other conceit thereof than this?
SIMPL. This I think to be the proper definition of equal
tions.
Velocities are ſaid
to be equal, when
the ſpaces paſſed
are proportionate to
their time.
SAGR. We will add moreover this other: and call that equal
velocity, when the ſpaces paſſed have the ſame proportion, as the
times wherein they are paſt, and it is a more univerſal definition.
SALV. It is ſo: for it comprehendeth the equal ſpaces paſt in
equal times, and alſo the unequal paſt in times unequal, but
portionate to thoſe ſpaces. Take now the ſame Figure, and
ing the conceipt that you had of the more haſtie motion, tell me
why you think the velocity of the Cadent by C B, is greater
than the velocity of the Deſcendent by C A?
SIMPL. I think ſo; becauſe in the ſame time that the Cadent
ſhall paſs all C B, the Deſcendent ſhall paſs in C A, a part leſs
than C B.
SALV. True; and thus it is proved, that the moveable moves
more ſwiftly by the perpendicular, than by the inclination. Now
conſider, if in this ſame Figure one may any way evince the
ther conceipt, and finde that the moveables were equally ſwift
by both the lines C A and C B.
SIMPL. I ſee no ſuch thing; nay rather it ſeems to contradict
what was ſaid before.
SALV. And what ſay you, Sagredus? I would not teach you
what you knew before, and that of which but juſt now you
duced me the definition.
SAGR. The definition I gave you, was, that moveables may
be called equally ſwift, when the ſpaces paſſed are proportional
to the times in which they paſſed; therefore to apply the
tion to the preſent caſe, it will be requiſite, that the time of
ſcent by C A, to the time of falling by C B, ſhould have the
ſame proportion that the line C A hath to the line C B; but I
underſtand not how that can be, for that the motion by C B is
ſwifter than by C A.
SALV. And yet you muſt of neceſſity know it. Tell me a little,
do not theſe motions go continually accelerating?
SAGR. They do; but more in the perpendicular than in the
inclination.
SALV. But this acceleration in the perpendicular, is it yet
withſtanding ſuch in compariſon of that of the inclined, that
two equal parts being taken in any place of the ſaid
lar and inclining lines, the motion in the parts of the
lar is alwaies more ſwift, than in the part of the inclination?
SAGR. I ſay not ſo: but I could take a ſpace in the
on, in which the velocity ſhall be far greater than in the like ſpace
taken in the perpendicular; and this ſhall be, if the ſpace in the
1perpendicular ſhould be taken near to the end C, and in the
clination, far from it.
SALV. You ſee then, that the Propoſition which ſaith, that
the motion by the perpendicular is more ſwift than by the
nation, holds not true univerſally, but onely of the motions,
which begin from the extremity, namely from the point of reſt:
without which reſtriction, the Propoſition would be ſo deficient,
that its very direct contrary might be true; namely, that the
tion in the inclining plane is ſwifter than in the perpendicular:
for it is certain, that in the ſaid inclination, we may take a ſpace
paſt by the moveable in leſs time, than the like ſpace paſt in the
perpendicular. Now becauſe the motion in the inclination is in
ſome places more, in ſome leſs, than in the perpendicular;
fore in ſome places of the inclination, the time of motion of the
moveable, ſhall have a greater proportion to the time of the motion
of the moveable, by ſome places of the perpendicular, than the
ſpace paſſed, to the ſpace paſſed: and in other places, the
portion of the time to the time, ſhall be leſs than that of the
ſpace to the ſpace. As for example: two moveables departing
from their quieſcence, namely, from the point C, one by the
pendicular C B, [in Fig. 4.] and the other by the inclination C A,
in the time that, in the perpendicular, the moveable ſhall have
paſt all C B, the other ſhall have paſt C T leſſer. And therefore
the time by C T, to the time by C B (which is equal) ſhall have
a greater proportion than the line C T to C B, being that the
ſame to the leſs, hath a greater proportion than to the greater.
And on the contrary, if in C A, prolonged as much as is
ſite, one ſhould take a part equal to C B, but paſt in a ſhorter
time; the time in the inclination ſhall have a leſs proportion to
the time in the perpendicular, than the ſpace to the ſpace. If
therefore in the inclination and perpendicular, we may ſuppoſe
ſuch ſpaces and velocities, that the proportion between the ſaid
ſpaces be greater and leſs than the proportion of the times; we
may eaſily grant, that there are alſo ſpaces, by which the times
of the motions retain the ſame proportion as the ſpaces.
SAGR. I am already freed from my greateſt doubt, and
ceive that to be not onely poſſible, but neceſſary, which I but
now thought a contradiction: but nevertheleſs I underſtand not
as yet, that this whereof we now are ſpeaking, is one of theſe
poſſible or neceſſary caſes; ſo as that it ſhould be true, that the
time of deſcent by C A, to the time of the fall by C B, hath the
ſame proportion that the line C A hath to C B; whence it may
without contradiction be affirmed, that the velocity by the
nation C A, and by the perpendicular C B, are equal.
SALV. Content your ſelf for this time, that I have removed
1your incredulity; but for the knowledge of this, expect it at
ſome other time, namely, when you ſhall ſee the matters
ning local motion demonſtrated by our Academick; at which
time you ſhall find it proved, that in the time that the one
ble falls all the ſpace C B, the other deſcendeth by C A as far
as the point T, in which falls the perpendicular drawn from the
point B: and to find where the ſame Cadent by the
cular would be when the other arriveth at the point A, draw from
A the perpendicular unto C A, continuing it, and C B unto the
interfection, and that ſhall be the point ſought. Whereby you
ſee how it is true, that the motion by C B is ſwifter than by the
inclination C A (ſuppoſing the term C for the beginning of the
motions compared) becauſe the line C B is greater than C T,
and the other from C unto the interſection of the perpendicular
drawn from A, unto the line C A, is greater than C A, and
therefore the motion by it is ſwifter than by C A But when we
compare the motion made by all C A, not with all the motion
made in the ſame time by the perpendicular continued, but with
that made in part of the time, by the ſole part C B, it hinders
not, that the motion by C A, continuing to deſcend beyond, may
arrive to A in ſuch a time as is in proportion to the other time,
as the line C A is to the line C B. Now returning to our firſt
purpoſe; which was to ſhew, that the grave moveable leaving
its quieſcence, paſſeth defcending by all the degrees of tardity,
precedent to any whatſoever degree of velocity that it aequireth,
re-aſſuming the ſame Figure which we uſed before, let us
ber that we did agree, that the Deſcendent by the inclination C
A, and the Cadent by the perpendicular C B, were found to have
acquired equal degrees of velocity in the terms B and A: now to
proceed, I ſuppoſe you will not ſcruple to grant, that upon
ther plane leſs ſteep than A C; as for example, A D [in Fig. 5.]
the motion of the deſcendent would be yet more ſlow than in the
plane A C. So that it is not any whit dubitable, but that there
may be planes ſo little elevated above the Horizon A B, that the
moveable, namely the ſame ball, in any the longeſt time may
reach the point A, which being to move by the plane A B, an
nite time would not ſuffice: and the motion is made always more
ſlowly, by how much the declination is leſs. It muſt be therefore
confeſt, that there may be a point taken upon the term B, ſo near
to the ſaid B, that drawing from thence to the point A a plane,
the ball would not paſs it in a whole year. It is requiſite next
for you to know, that the impetus, namely the degree of
city the ball is found to have acquired when it arriveth at the
point A, is ſuch, that ſhould it continue to move with this ſelf-ſame
degree uniformly, that is to ſay, without accelerating or retarding;
1in as much more time as it was in coming by the inclining plane, it
would paſs double the ſpace of the plane inclined: namely (for
example) if the ball had paſt the plane D A in an hour,
tinuing to move uniformly with that degree of velocity which it
is found to have in its arriving at the term A, it ſhall paſs in an
hour a ſpace double the length D A; and becauſe (as we have
ſaid) the degrees of velocity acquired in the points B and A, by
the moveables that depart from any point taken in the
lar C B, and that deſcend, the one by the inclined plane, the
ther by the ſaid perpendicular, are always equal: therefore the
cadent by the perpendicular may depart from a term ſo near to B,
that the degree of velocity acquired in B, would not ſuffice (ſtill
maintaining the ſame) to conduct the moveable by a ſpace
ble the length of the plane inclined in a year, nor in ten, no nor
in a hundred. We may therefore conclude, that if it be true,
that according to the ordinary courſe of nature a moveable, all
external and accidental impediments removed, moves upon an
clining plane with greater and greater tardity, according as the
inclination ſhall be leſs; ſo that in the end the tardity comes to be
infinite, which is, when the inclination concludeth in, and joyneth
to the horizontal plane; and if it be true likewiſe, that the
gree of velocity acquired in ſome point of the inclined plane, is
equal to that degree of velocity which is found to be in the
able that deſcends by the perpendicular, in the point cut by a
parallel to the Horizon, which paſſeth by that point of the
ning plane; it muſt of neceſſity be granted, that the cadent
parting from reſt, paſſeth thorow all the infinite degrees of
dity, and that conſequently, to acquire a determinate degree of
velocity, it is neceſſary that it move firſt by right lines,
ing by a ſhort or long ſpace, according as the velocity to be
red, ought to be either leſs or greater, and according as the plane
on which it deſcendeth is more or leſs inclined; ſo that a plane
may be given with ſo ſmall inclination, that to acquire in it the
aſſigned degree of velocity, it muſt firſt move in a very great ſpace,
and take a very long time; whereupon in the horizontal plane, any
how little ſoever velocity, would never be naturally acquired,
ſince that the moveable in this caſe will never move: but the

motion by the horizontal line, which is neither declined or
ned, is a circular motion about the centre: therefore the
lar motion is never acquired naturally, without the right motion
precede it; but being once acquired, it will continue perpetually
with uniform velocity. I could with other diſcourſes evince and
demonſtrate the ſame truth, but I will not by ſo great a
fion interrupt our principal argument: but rather will return to
it upon ſome other occaſion; eſpecially ſince we now aſſumed the
1ſame, not to ſerve for a neceſſary demonſtration, but to adorn a
Platonick Conceit; to which I will add another particular
vation of our Academick, which hath in it ſomething of
ble. Let us ſuppoſe amongſt the decrees of the divine Architect,
a purpoſe of creating in the World theſe Globes, which we
hold continually moving round, and of aſſigning the centre of
their converſions; and that in it he had placed the Sun immoveable,
and had afterwards made all the ſaid Globes in the ſame place,
and with the intended inclinations of moving towards the Centre,
till they had acquired thoſe degrees of velocity, which at firſt
med good to the ſame Divine Minde; the which being acquired,
we laſtly ſuppoſe that they were turned round, each in his Sphere
retaining the ſaid acquired velocity: it is now demanded, in
what altitude and diſtance from the Sun the place was where the
ſaid Orbs were primarily created; and whether it be poſſible that
they might all be created in the ſame place? To make this
ſtigation, we muſt take from the moſt skilfull Aſtronomers the
magnitude of the Spheres in which the Planets revolve, and
wiſe the time of their revolutions: from which two cognitions is
gathered how much (for example) Jupiter is ſwifter than
turne; and being found (as indeed it is) that Jupiter moves more
ſwiftly, it is requiſite, that departing from the ſame altitude,
piter be deſcended more than Saturne, as we really know it is, its
Orbe being inferiour to that of Saturne. But by proceeding
wards, from the proportions of the two velocities of Jupiter and
Saturne, and from the diſtance between their Orbs, and from the
proportion of acceleration of natural motion, one may finde in
what altitude and diſtance from the centre of their revolutions,

was the place from whence they firſt departed. This found out,
and agreed upon, it is to be ſought, whether Mars deſcending
from thence to his Orb, the magnitude of the Orb, and the
locity of the motion, agree with that which is found by
tion; and let the like be done of the Eartb, of Venus, and of
Mercury; the greatneſs of which Spheres, and the velocity of
their motions, agree ſo nearly to what computation gives, that it
is very admirable.
The circular
tion is never
quired naturally,
without right
tion precede it.
Circular motion
perpetually
form.
The magnitude of
the Orbs, and the
velocity of the
tion of the Planets,
anſwer
ably, as if
ed from the ſame
place.
SAGR. I have hearkened to this conceit with extreme delight;
and, but that I believe the making of theſe calculations truly
would be a long and painfull task, and perhaps too hard for me
to comprehend, I would make a trial of them.
SALV. The operation indeed is long and difficult; nor could
I be certain to finde it ſo readily; therefore we ſhall refer it to
other time, and for the preſent we will return to our firſt
ſal, going on there where we made digreſſion; which, if I well
remember, was about the proving the motion by a right line of no
1uſe, in the ordinate parts of the World; and we did proceed to
ſay, that it was not ſo in circular motions, of which that which is
made by the moveable in it ſelf, ſtill retains it in the ſame place,

and that which carrieth the moveable by the circumference of a
circle about its fixed centre, neither puts it ſelf, nor thoſe about it
in diſorder; for that ſuch a motion primarily is finite and terminate
(though not yet finiſhed and determined) but there is no point

in the circumference, that is not the firſt and laſt term in the
culation; and continuing it in the circumference aſſigned it, it
leaveth all the reſt, within and without that, free for the uſe of
others, without ever impeding or diſordering them. This being
a motion that makes the moveable continually leave, and

tinually arrive at the end; it alone therefore can primarily be
niform; for that acceleration of motion is made in the moveable,
when it goeth towards the term, to which it hath inclination;
and the retardation happens by the repugnance that it hath to
leave and part from the ſame term; and becauſe in circular
tion, the moveable continually leaves the natural term, and
tinually moveth towards the ſame, therefore, in it, the
nance and inclination are always of equal force: from which
quality reſults a velocity, neither retarded nor accelerated, i. e. an
uniformity in motion. From this conformity, and from the being

terminate, may follow the perpetual continuation by ſucceſſively
reiterating the circulations; which in an undeterminated line,
and in a motion continually retarded or accelerated, cannot

turally be. I ſay, naturally; becauſe the right motion which is
retarded, is the violent, which cannot be perpetual; and the
celerate arriveth neceſſarily at the term, if one there be; and if
there be none, it cannot be moved to it, becauſe nature moves
not whether it is impoſſible to attain. I conclude therefore, that
the circular motion can onely naturally conſiſt with natural
dies, parts of the univerſe, and conſtituted in an excellent
ſure; and that the right, at the moſt that can be ſaid for it, is

aſſigned by nature to its bodies, and their parts, at ſuch time as
they ſhall be out of their proper places, conſtituted in a depraved
diſpoſition, and for that cauſe needing to be redured by the
eſt way to their natural ſtate. Hence, me thinks, it may
nally be concluded, that for maintenance of perfect order among ſt
the parts of the World, it is neceſſary to ſay, that moveables are
moveable onely circularly; and if there be any that move not

circularly, theſe of neceſſity are immoveable: there being
thing but reſt and circular motion apt to the conſervation of
der. And I do not a little wonder with my ſelf, that Ariſtotle,
who held that the Terreſtrial globe was placed in the centre of
the World, and there remained immoveable, ſhould not ſay, that
1of natural bodies ſome are moveable by nature, and others
veable; eſpecially having before defined Nature, to be the
ciple of Motion and Reſt.
Finite and
nate circular
tions diſorder not
the parts of the
World.
In the circular
tion, every point in
the circumference
is the begining and
end.
Circular motion
onely is uniform.
Circular motion
may be continued
perpetually.
Right motion
not naturally be
perpetual.
Right motion
ſigned to natural
bodies, to reduce
them to perfect
der, when removed
from their places.
Reſt onely, and
circular motion are
apt to conſerve
der.
SIMPL. Ariſtotle, though of a very perſpicacious wit, would
not ſtrain it further than needed: holding in all his

tations, that ſenſible experiments were to be preferred before
any reaſons founded upon ſtrength of wit, and ſaid thoſe which
ſhould deny the teſtimony of ſenſe deſerved to be puniſhed with

the loſs of that ſenſe; now who is ſo blind, that ſees not the
parts of the Earth and Water to move, as being grave,
ly downwards, namely, towards the centre of the Univerſe,
ſigned by nature her ſelf for the end and term of right motion
deorſùm; and doth not likewiſe ſee the Fire and Air to move
right upwards towards the Concave of the Lunar Orb, as to the
natural end of motion ſurſùm? And this being ſo manifeſtly ſeen,
and we being certain, that eadem est ratio totius & partium, why
may we not aſſert it for a true and manifeſt propoſition, that the
natural motion of the Earth is the right motion ad medium, and
that of the Fire, the right à medio?
Senſible
ments are to be
ferred before
mane argument
tions.
He who denies
ſenſe, deſerves to
be deprived of it.
Senſe ſheweth that
things grave move
to the medium, and
the light to the
concave.
SALV. The moſt that you can pretend from this your
courſe, were it granted to be true, is that, like as the parts of the
Earth removed from the whole, namely, from the place where
they naturally reſt, that is in ſhort reduced to a depraved and
ordered diſpoſure, return to their place ſpontaneouſly, and
fore naturally in a right motion, (it being granted, that eadem
ſit ratio totius & partium) ſo it may be inferred, that the
Terreſtrial Globe removed violently from the place aſſigned

it by nature, it would return by a right line. This, as I have
ſaid, is the moſt that can be granted you, and that onely for want
of examination; but he that ſhall with exactneſs reviſe theſe
things, will firſt deny, that the parts of the Earth, in returning to
its whole, move in a right line, and not by a circular or mixt; and
really you would have enough to do to demonſtrate the
ry, as you ſhall plainly ſee in the anſwers to the particular reaſons
and experiments alledged by Ptolomey and Ariſtotle. Secondly,
If another ſhould ſay that the parts of the Earth, go not in their
motion towards the Centre of the World, but to unite with its
Whole, and that for that reaſon they naturally incline towards the
centre of the Terreſtrial Globe, by which inclination they
ſpire to form and preſerve it, what other All, or what other Centre
would you find for the World, to which the whole Terrene

Globe, being thence removed, would ſeek to return, that ſo the
reaſon of the Whole might be like to that of its parts? It may be
added, That neither Ariſtotle, nor you can ever prove, that the
Earth de facto is in the centre of the Univerſe; but if any Centre
1
may be aſligned to the Univerſe, we ſhall rather find the Sun
placed in it, as by the ſequel you ſhall underſtand.
It is queſtionable
whether deſcending
weights move in a
right line.
The Earth
cal by the
ration of its parts
to its Centre.
The Sun more
bably in the centre
of the Vniverſe,
than the Earth.
Now, like as from the conſentaneous conſpiration of all the
parts of the Earth to form its whole, doth follow, that they with

equal inclination concurr thither from all parts; and to unite
themſelves as much as is poſſible together, they there ſphelically
adapt themſelves; why may we not believe that the Sun, Moon,
and other mundane Bodies, be alſo of a round figure, not by
ther than a concordant inſtinct, and natural concourſe of all the
parts compoſing them? Of which, if any, at any time, by any
violence were ſeparated from the whole, is it not reaſonable to
think, that they would ſpontaneouſly and by natural inſtinct
turn? and in this manner to infer, that the right motion agreeth
with all mundane bodies alike.
Natural
tion of the parts of
all the globes of
the World to go to
their centre.
SIMPL. Certainly, if you in this manner deny not onely the
Principles of Sciences, but manifeſt Experience, and the Senſes
themſelves, you can never be convinced or removed from any
pinion which you once conceit, therefore I will chooſe rather to
be ſilent (for, contra negantes principia non eſt diſputandum)
than contend with you. And inſiſting on the things alledged by
you even now (ſince you queſtion ſo much as whether grave
ables have a right motion or no) how can you ever rationally

ny, that the parts of the Earth; or, if you will, that ponderous
matters deſcend towards the Centre, with a right motion;
as, if from a very high Tower, whoſe walls are vcry upright and
perpendicular, you let them fall, they ſhall deſcend gliding and
ſliding by the Tower to the Earth, exactly in that very place
where a plummet would fall, being hanged by a line faſtned above,
juſt there, whence the ſaid weights were let fall? is not this a
more than evident argument of the motions being right, and

wards the Centre? In the ſecond place you call in doubt,
ther the parts of the Earth are moved, as Ariſtotle affirms,
wards the Centre of the World; as if he had not rationally
monſtrated it by contrary motions, whilſt he thus argueth; The
motion of heavie bodies is contrary to that of the light: but the
motion of the light is manifeſt to be directly upwards, namely,
towards the circumference of the World, therefore the motion of
the heavie is directly towards the Centre of the World: and it

happens per accidens, that it be towards the centre of the Earth,
for that this ſtriveth to be united to that. The ſeeking in the
next place, what a part of the Globe of the Sun or Moon would
do, were it ſeparated from its whole, is vanity; becauſe that

by that is ſought, which would be the conſequence of an
bility; in regard that, as Ariſtotle alſo demonſtrates, the cœleſtial
bodies are impaſſible, impenetrable, and infrangible; ſo that ſuch
1a caſe can never happen: and though it ſhould, and that the

parated part ſhould return to its whole, it would not return as
grave or light, for that the ſame Ariſtotle proveth, that the
leſtial Bodies are neither heavie nor light.
The right motion
of grave bodies
manifeſt to ſenſe.
Arguments of
riſtotle, to prove
that grave bodies
move with an
clination to arrive
at the centre of the
Vniverſe.
Heavie bodies
move towards the
centre of the Earth
per accidens.
To ſeek what
would follow upon
an impoſſibility, is
folly.
Cœleſtial bodies
neither heavie nor
light, according to
Ariſtotle.
SALV. With what reaſon I doubt, whether grave bodies move
by a right and perpendicular line, you ſhall hear, as I ſaid
fore, when I ſhall examine this particular argument. Touching
the ſecond point, I wonder that you ſhould need to diſcover the
Paralogiſm of Ariſtotle, being of it ſelf ſo manifeſt; and that
you perceive not, that Ariſtotle ſuppoſeth that which is in
on: therefore take notice.
SIMPL. Pray Salviatus ſpeak with more reſpect of Ariſtotle:
for who can you ever perſwade, that he who was the firſt, only,
and admirable explainer of the Syllogiſtick forms of demonſtration,

of Elenchs, of the manner of diſcovering Sophiſms, Paralogiſms, and
in ſhort, of all the parts of Logick, ſhould afterwards ſo notoriouſly
equivocate in impoſing that for known, which is in queſtion? It
would be better, my Maſters, firſt perfectly to underſtand him,
and then to try, if you have a minde, to oppoſe him.
Ariſtotle cannot
quivocate, being
the inventer of
gick.
SALV. Simplicius, we are here familiarly diſcourſing among
our ſelves, to inveſtigate ſome truth; I ſhall not be diſpleaſed
that you diſcover my errors; and if I do not follow the mind of
Ariſtotle, freely reprehend me, and I ſhall take it in good part.
Onely give me leave to expound my doubts, and to reply
thing to your laſt words, telling you, that Logick, as it is well
underſtood, is the Organe with which we philoſophate; but as it
may be poſſible, that an Artiſt may be excellent in making
gans, but unlearned in playing on them, thus he might be a great
Logician, but unexpert in making uſe of Logick; like as we have
many that theorically underſtand the whole Art of Poetry, and
yet are unfortunate in compoſing but meer four Verſes; others

enjoy all the precepts of Vinci^{*}, and yet know not how to paint
a Stoole. The playing on the Organs is not taught by them who
know how to make Organs, but by him that knows how to play
on them: Poetry is learnt by continual reading of Poets:
ing is learnt by continual painting and deſigning: Demonſtration
from the reading of Books full of demonſtrations, which are the
Mathematical onely, and not the Logical. Now returning to our
purpoſe, I ſay, that that which Ariſtotle ſeeth of the motion of
light bodies, is the departing of the Fire from any part of the
Superficies of the Terreſtrial Globe, and directly retreating from
it, mounting upwards; and this indeed is to move towards a
circumference greater than that of the Earth; yea, the ſame
riſtotle makes it to move to the concave of the Moon, but that
this circumference is that of the World, or concentrick to it, ſo
1that to move towards this, is a moving towards that of the World,
that he cannot affirm, unleſs he ſuppoſeth, That the Centre of the

Earth, from which we ſee theſe light aſcendent bodies to depart,
be the ſame with the Centre of the World; which is as much as
to ſay, that the terreſtrial Globe is conſtituted in the midſt of the
World: which is yet that of which we were in doubt, and which
Aristotle intended to prove. And do you ſay that this is not a

manifeſt Paralogiſm?
* A famous Italian
Painter.
Paralogiſm of
riſtotle, in proving
the Earth to be in
the Centre of the
World.
The Paralogiſme
of Ariſtotle another
way diſcovered.
SAGR. This Argument of Ariſtotle appeared to me deficient
alſo, and non-concludent for another reſpect; though it were
granted, that that Circumference, to which the Fire directly
veth, be that which includeth the World: for that in a circle,
not onely the centre, but any other point being taken, every
able which departing thence, ſhall move in a right line, and
wards any whatſoever part, ſhall without any doubt go towards
the circumference, and continuing the motion, ſhall alſo arrive
thither; ſo that we may truly ſay, that it moveth towards the
circumference: but yet it doth not follow, that that which
veth by the ſame line with a contrary motion, would go towards
the centre, unleſs when the point taken were the centre it ſelf,
or that the motion were made by that onely line, which produced
from the point aſſigned, paſſeth thorow the centre. So that to
ſay, that Fire moving in a right line, goeth towards the
rence of the World, therefore the parts of the Earth which by
the ſame lines move with a contrary motion, go towards the
tre of the World, concludeth not, unleſs then when it is
ſuppoſed, that the lines of the Fire prolonged paſs by the centre
of the World; and becauſe we know certainly of them, that they
paſs by the centre of the Terreſtrial Globe (being
lar to its ſuperficies, and not inclined) therefore to conclude, it
muſt be ſuppoſed, that the centre of the Earth is the ſame with
the centre of the World; or at leaſt, that the parts of the Fire
and Earth deſcend not, ſave onely by one ſole line which paſſeth
by the centre of the World. Which nevertheleſs is falſe, and
pugnant to experience, which ſheweth us, that the parts of
Fire, not by one line onely, but by infinite, produced from the
centre of the Earth towards all the parts of the World, aſcend
always by lines perpendicular to the Superficies of the
al Globe.
SALV. You do very ingeniouſly lead Ariſtotle to the ſame
convenience, Sagredus, ſhewing his manifeſt equivoke; but
withal you add another inconſiſtency. We ſee the Earth to be
ſpherical, and therefore are certain that it hath its centre, to which
we ſee all its parts are moved; for ſo we muſt ſay, whilſt their
motions are all perpendicular to the Superficies of the Earth; we
1mean, that as they move to the centre of the Earth, they move to
their Whole, and to their Univerſal Mother: and we are ſtill
ther ſo free, that we will ſuffer our ſelves to be perſwaded, that

their natural inſtinct is, not to go towards the centre of the Earth,
but towards that of the Univerſe; which we know not where to
find, or whether it be or no; and were it granted to be, it is but
an imaginary point, and a nothing without any quality. As to
what Simplicius ſaid laſt, that the contending whether the parts
of the Sun, Moon, or other cœleſtial Body, ſeparated from their
Whole, ſhould naturally return to it, is a vanity, for that the caſe
is impoſſible; it being clear by the Demonſtrations of Ariſtotle,
that the cœleſtial Bodies are impaſſible, impenetrable,

ble, &c. I anſwer, that none of the conditions, whereby
tle diſtinguiſheth the Cœleſtial Bodies from Elementary, hath
ther foundation than what he deduceth from the diverſity of the
natural motion of thoſe and theſe; inſomuch that it being
ed, that the circular motion is peculiar to Cœleſtial Bodies, and
affirmed, that it is agreeable to all Bodies naturally moveable, it
is behoofull upon neceſſary conſequence to ſay, either that the
attributes of generable, or ingenerable, alterable, or unalterable,
partable, or unpartable, &c. equally and commonly agree with
all worldly bodies, namely, as well to the Cœleſtial as to the
lementary; or that Ariſtotle hath badly and erroneouſly
ced thoſe from the circular motion, which he hath aſſigned to
leſtial Bodies.
Grave bodies may
more rationally be
affirmed to tend to
the Centre of the
Earth, than of the
Vniverſe.
The conditions and
attributes which
differ the cœleſtial
bodies from
mentary, depend on
the motions
ed them by Ariſt.
SIMPL. This manner of argumentation tends to the
on of all Natural Philoſophy, and to the diſorder and ſubverſion
of Heaven and Earth, and the whole Univerſe; but I believe the
Fundamentals of the Peripateticks are ſuch, that we need not
fear that new Sciences can be erected upon their ruines.
SALV. Take no thought in this place for Heaven or the Earth,
neither fear their ſubverſion, or the ruine of Philoſophy. As to
Heaven, your fears are vain for that which you your ſelf hold
unalterable and impaſſible; as for the Earth, we ſtrive to enoble
and perfect it, whilſt we make it like to the Cœleſtial Bodies,
and as it were place it in Heaven, whence your Philoſophers have
exiled it. Philoſophy it ſelf cannot but receive benefit from our

Diſputes, for if our conceptions prove true, new Diſcoveries will
be made; if falſe, the firſt Doctrine will be more confirmed.
Rather beſtow your care upon ſome Philoſophers, and help and
defend them; for as to the Science it ſelf, it cannot but improve.
And that we may return to our purpoſe, be pleaſed freely to
duce what preſents it ſelf to you in confirmation of that great
ference which Ariſtotle puts between the Cœleſtial Bodies, and
the Elementary parts of the World, in making thoſe ingenerable,
1incorruptible, unalterable, &c. and this corruptible, alterable, &c.
The diſputes and
contradictions of
Philoſophers may
conduce to the
benefit of
phy.
SIMPL. I ſee not yet any need that Ariſtotle hath of help,
ſtanding as he doth ſtoutly and ſtrongly on his feet; yea not
ing yet aſſaulted, much leſs foiled by you. And what ward will
you chooſe in this combate for this firſt blow? Aristotle writeth,

that whatever is generated, is made out of a contrary in ſome
ſubject, and likewiſe is corrupted in ſome certain ſubject from a

contrary into a contrary; ſo that (obſerve) corruption and
neration is never but onely in contraries; If therefore to a
leſtial Body no contrary can be aſſigned, for that to the circular

motion no other motion is contrary, then Nature hath done very
well to make that exempt from contraries, which was to be
generable and incorruptible, This fundamental firſt confirmed,
it immediately followeth of conſequence, that it is
ble, inalterable, impaſſible, and finally eternal, and a

tionate habitation to the immortal Deities, conformable to the
opinion even of all men that have any conceit of the Gods. He

afterwards confirmeth the ſame by ſenſe; in regard, that in all
times paſt, according to memory or tradition, we ſee nothing
moved, according to the whole outward Heaven, nor any of its

proper parts. Next, as to the circular motion, that no other is
contrary to it, Aristotle proveth many ways; but without
ting them all, it is ſufficiently demonſtrated, ſince fimple motions
are but three, to the medium, from the medium, and about the
medium, of which the two right, ſurſum and deorſum, are
feſtly contrary; and becauſe one onely hath onely one for
trary, therefore there reſts no other motion which may be
ry to the circular. You ſee the ſubtle and moſt concluding
courſe of Ariſtotle, whereby he proveth the incorruptibility of
Heaven.
Ariſtotles diſcourſe
to prove the
ruptibility of
ven.
Generation &
ruption is onely
mongſt contraries,
according to Ariſt.
To the circular
motion no other
motion is contrary.
Heaven an
tation for the
ortal Gods.
Immutability of
Heaven evident to
ſexſe.
He proveth that
the circular motion
hath no contrary.
SALV. This is nothing more, ſave the pure progreſs of
tle, by me hinted before; wherein, beſides that I affirm, that the
motion which you attribute to the Cœleſtial Bodies agreeth alſo
to the Earth, its illation proves nothing. I tell you therefore,
that that circular motion which you aſſign to Cœleſtial Bodies,
ſuiteth alſo to the Earth, from which, ſuppoſing that the reſt of
your diſcourſe were concludent, will follow one of theſe three
things, as I told you a little before, and ſhall repeat; namely,
either that the Earth it ſelf is alſo ingenerable, and incorruptible,
as the Cœleſtial bodies; or that the Cœleſtial bodies are, like as
the Elementary generable, alterable &c. or that this difference of
motion hath nothing to do with Generation and Corruption.
The diſcourſe of Ariſtotle, and yours alſo contain many
tions not to be lightly admitted, and the better to examine them,
it will be convenient to reduce them to the moſt abſtracted and
1diſtinct that can be poſſible; and excuſe me Sagredus, if haply
with ſome tediouſneſs you hear me oft repeat the ſame things,
and fancie that you ſee me reaſſume my argument in the
lick circle of Diſputations. You ſay Generation and
on are onely made where there are contraries; contraries
are onely amongſt ſimple natural bodies, moveable with contrary
motions; contrary motions are onely thoſe which are made by
a right line between contrary terms; and theſe are onely two,
that is to ſay, from the medium, and towards the medium; and
ſuch motions belong to no other natural bodies, but to the Earth,
the Fire, and the other two Elements: therefore Generation
and Corruption is onely amongſt the Elements. And becauſe
the third ſimple motion, namely, the circular about the medium,
hath no contrary, (for that the other two are contraries, and one
onely, hath but onely one contrary) therefore that natural body
with which ſuch motion agreeth, wants a contrary; and having
no contrary is ingenerable and incorruptible, &c. Becauſe where
there is no contrariety, there is no generation or corruption, &c.
But ſuch motion agreeth onely with the Cœleſtial bodies;

fore onely theſe are ingenerable, incorruptible, &c. And to
begin, I think it a more eaſie thing, and ſooner done to reſolve,
whether the Earth (a moſt vaſt Body, and for its vicinity to us,
moſt tractable) moveth with a ſpeedy motion, ſuch as its
lution about its own axis in twenty four hours would be, than it
is to underſtand and reſolve, whether Generation and Corruption
ariſeth from contrariety, or elſe whether there be ſuch things as
generation, corruption and contrariety in nature. And if you,
Simplicius, can tell me what method Nature obſerves in working,
when ſhe in a very ſhort time begets an infinite number of flies
from a little vapour of the Muſt of wine, and can ſhew me which
are there the contraries you ſpeak of, what it is that corrupteth,
and how; I ſhould think you would do more than I can; for I
profeſs I cannot comprehend theſe things. Beſides, I would
ry gladly underſtand how, and why theſe corruptive contraries are
ſo favourable to Daws, and ſo cruel to Doves; ſo indulgent to
Stags, and ſo haſty to Horſes, that they do grant to them many
more years of life, that is, of incorruptibility, than weeks to theſe.
Peaches and Olives are planted in the ſame ſoil, expoſed to the
ſame heat and cold, to the ſame wind and rains, and, in a word,
to the ſame contrarieties; and yet thoſe decay in a ſhort time,
and theſe live many hundred years. Furthermore, I never was
thorowly ſatisfied about this ſubſtantial tranſmutation (ſtill
ing within pure natural bounds) whereby a matter becometh ſo
transform'd, that it ſhould be neceſſarily ſaid to be deſtroy'd, ſo
that nothing remaineth of its firſt being, and that another body
1
quite differing there-from ſhould be thence produced; and if I
fancy to my ſelf a body under one aſpect, and by and by under
another very different, I cannot think it impoſſible but that it may
happen by a ſimple tranſpoſition of parts, without corrupting or
ingendring any thing a-new; for we ſee ſuch kinds of
phoſes dayly: ſo that to return to my purpoſe, I anſwer you,
that inaſmuch as you go about to perſwade me that the Earth can
not move circularly by way of corruptibility and generability,
you have undertook a much harder task than I, that with
ments more difficult indeed, but no leſs concluding, will prove
the contrary.
Its eaſier to prove
the Earth to move,
than that
on is made by
traries.
Bare tranſpoſition
of parts may
ſent bodies under
diverſe asp cts.
SAGR. Pardon me, Salviatus, if I interrupt your diſcourſe,
which, as it delights me much, for that I alſo am gravel'd with
the ſame doubts; ſo I fear that you can never conclude the ſame,
without altogether digreſſing from your chief deſign: therefore
if it be permitted to proceed in our firſt argument, I ſhould think
that it were convenient to remit this queſtion of generation and
corruption to another diſtinct and ſingle conference; as alſo, if
it ſhall pleaſe you and Simplicius, we may do by other particular
queſtions which may fall in the way of our diſcourſe; which I
will keep in my mind to propoſe, and exactly diſcuſs them ſome
other time. Now as for the preſent, ſince you ſay, that if
ſtotle deny circular motion to the Earth in common with other
bodies Cœleſtial, it chence will follow, that the ſame which
falleth the Earth, as to its being generable, alterable, &c. will
hold alſo of Heaven, let us enquire no further if there be ſuch
things in nature, as generation and corruption, or not; but let
us return to enquire what the Globe of the Earth doth.
SIMPL. I cannot ſuffer my ears to hear it queſtion'd, whether
generation and corruption be in rerum naturà, it being a thing
which we have continually before our eyes, and whereof Ariſtotle

hath written two whole Books. But if you go about to deny the
Principles of Sciences, and queſtion things moſt manifeſt, who
knows not, but that you may prove what you will, and maintain
any Paradox? And if you do not dayly ſee herbs, plants,
mals to generate and corrupt, what is it that you do ſee? Alſo,
do you not continually behold contrarieties contend together,
and the Earth change into Water, the Water turn to Air, the
Air into Fire, and again the Air to condenſe into Clouds, Rains,
Hails and Storms?
By denying
ciples in the
ces, any Paradox
may be
ed.
SAGR. Yes, we ſee theſe things indeed, and therefore will
grant you the diſcourſe of Ariſtotle, as to this part of generation
and corruption made by contraries; but if I ſhall conclude by
virtue of the ſame propoſitions which are granted to Ariſtotle,
that the Cœleſtial bodies themſelves are alſo generable and
1ruptible, aſwell as the Elementary, what will you ſay then?
SIMPL. I will ſay you have done that which is impoſſible to
be done.
SAGR. Go to; tell me, Simplicius, are not theſe affections
contrary to one another?
SIMPL. Which?
SAGR. Why theſe; Alterable, unalterable; paſſible, ^{*}

ſible; generable, ingenerable; corruptible, incorruptible?
* Or, Impatible.
SIMPL. They are moſt contrary.
SAGR. Well then, if this be true, and it be alſo granted,
that Cœleſtial Bodies are ingenerable and incorruptible; I prove
that of neceſſity Cœleſtial Bodies muſt be generable and
ptible.
SIMPL. This muſt needs be a Sophiſm.
SAGR. Hear my Argument, and then cenſure and reſolve it.

Cœleſtial Bodies, for that they are ingenerable and incorruptible,
have in Nature their contraries, which are thoſe Bodies that be
generable and corruptible; but where there is contrariety, there
is alſo generation and corruption; therefore Cœleſtial Bodies are
generable and corruptible.
Cœlestial Bodies
are generable and
corruptible,
cauſe they are
generable and
corruptible.
SIMPL. Did I not ſay it could be no other than a Sophiſm?
This is one of thoſe forked Arguments called Soritæ: like that

of the Cretan, who ſaid that all Cretans were lyars; but he as
being a Cretan, had told a lye, in ſaying that the Cretans were
ars; it followed therefore, that the Cretans were no lyars, and
conſequently that he, as being a Cretan, had ſpoke truth: And
yet in ſaying the Cretans were lyars, he had ſaid true, and
prehending himſelf as a Cretan, he muſt conſequently be a lyar.
And thus in theſe kinds of Sophiſms a man may dwell to eternity,
and never come to any concluſion.
The forked
giſm cal'd Ξωρίτης.
SAGR. You have hitherto cenſured it, it remaineth now that
you anſwer it, ſhewing the fallacie.
SIMPL. As to the reſolving of it, and finding out its fallacie,
do you not in the firſt place ſee a manifeſt contradiction in it?
Cœleſtial Bodies are ingenerable and incorruptible; Ergo,
ſtial Bodies are generable and corruptible. And again, the

trariety is not betwixt the Cœleſtial Bodies, but betwixt the
lements, which have the contrariety of the Motions, ſurſùm and
deorſùm, and of levity and gravity; But the Heavens which move
circularly, to which motion no other motion is contrary, want
contrariety, and therefore they are incorruptible.
Amongſt Cœleſtial
Bodies there is no
contrariety.
SAGR. Fair and ſoftly, Simplicius; this contrariety whereby
you ſay ſome ſimple Bodies become corruptible, reſides it in the
ſame Body which is corrupted, or elſe hath it relation to ſome
other? I ſay, for example, the humidity by which a piece of Earth
1is corrupted, reſides it in the ſame Earth or in ſome other bodie,
which muſt either be the Air or Water? I believe you will grant,
that like as the Motions upwards and downwards, and gravity
and levity, which you make the firſt contraries, cannot be in the
ſame Subject, ſo neither can moiſt and dry, hot and cold: you
muſt therefore conſequently acknowledg that when a bodie

rupteth, it is occaſioned by ſome quality reſiding in another
trary to its own: therefore to make the Cœleſtial Body become
corruptible, it ſufficeth that there are in Nature, bodies that have
a contrariety to that Cœleſtial body; and ſuch are the Elements,
if it be true that corruptibility be contrary to incorruptibility.
Contraries which
are the cauſes of
corruption, reſide
not in the ſame
dy that corrupteth.
SIMPL. This ſufficeth not, Sir; The Elements alter and
rupt, becauſe they are intermixed, and are joyn'd to one another,

and ſo may exerciſe their contrariety; but Cœleſtial bodies are
ſeparated from the Elements, by which they are not ſo much as
toucht, though indeed they have an influence upon the Elements.
It is requiſite, if you will prove generation and corruption in
leſtial bodies, that you ſhew, that there reſides contrarieties
tween them.
Cœleſtial Bodies
touch, but are not
touched by the
lements.
SAGR. See how I will find thoſe contrarieties between them.
The firſt fountain from whence you derive the contrariety of the
Elements, is the contrariety of their motions upwards and
wards: it therefore is neceſſary that thoſe Principles be in like

manner contraries to each other, upon which thoſe motions
pend. and becauſe that is moveable upwards by lightneſs,
and this downwards by gravitv, it is neceſſary that lightneſs and
gravity are contrary to each other: no leſs are we to believe thoſe
other Principles to be contraries, which are the cauſes that this is
heavy, and that light: but by your own confeſſion, levity and
gravity follow as conſequents of rarity and denſity; therefore

rarity and denſity ſhall be contraries: the which conditions or
affections are ſo amply found in Cœleſtial bodies, that you
ſteem the ſtars to be onely more denſe parts of their Heaven:
and if this be ſo, it followeth that the denſity of the ſtars exceeds
that of the reſt of Heaven, by almoſt infinite degrees:
which is manifeſt, in that Heaven is infinitely tranſparent, and
the ſtars extremely opacous; and for that there are there above
no other qualities, but more and leſs denſity and rarity, which
may be cauſes of the greater or leſs tranſparency. There being
then ſuch contrariety between the Cœleftial bodies, it is neceſſary
that they alſo be generable and corruptible, in the ſame manner
as the Elementary bodies are; or elſe that contrariety is not the

cauſe of corruptibility, &c.
Gravity & levity,
varity and denſity,
are contrary
lities.
The ſtars infinitely
ſurpaſs the
ſtance of the reſt of
Heaven in denſity.
Rarity & denſity
in Cœleſtial bodies,
is different from
the rarity &
ſity of the elements.
SIMPL. There is no neceſſity either of one or the other, for
that denſity and rarity in Cœleſtial bodies, are not contraries to
1each other, as in Elementary bodies; for that they depend not
on the primary qualities, cold and heat, which are contraries; but
on the more or leſs matter in proportion to quantity: now much
and little, ſpeak onely a relative oppoſition, that is, the leaſt of
oppoſitions, and which hath nothing to do with generation and
corruption.
SAGR. Therefore affirming, that denſity and rarity, which
mongſt the Elements ſhould be the cauſe of gravity and levity,
which may be the cauſes of contrary motions ſurſùm and
ſùm, on which, again, dependeth the contrarieties for generation
and corruption; it ſufficeth not that they be thoſe denſneſſes and
rareneſſes which under the ſame quantity, or (if you will) maſs
contain much or little matter, but it is neceſſary that they be
neſſes and rareneſſes cauſed by the primary qualities, hot and
cold, otherwiſe they would operate nothing at all: but if this be
ſo, Ariſtotle hath deceived us, for that he ſhould have told it us at

firſt, and ſo have left written that thoſe ſimple bodies are
rable and corruptible, that are moveable with ſimple motions
upwards and downwards, dependent on levity and gravity,
ſed by rarity and denſity, made by much or little matter, by
reaſon of heat and cold; and not to have ſtaid at the ſimple
tion ſurſùm and deorſùm: for I aſſure you that to the making
of bodies heavy or light, whereby they come to be moved with
contrary motions, any kind of denſity and rarity ſufficeth,
ther it proceed from heat and cold, or what elſe you pleaſe; for
heat and cold have nothing to do in this affair: and you ſhall
upon experiment find, that a red hot iron, which you muſt grant
to have heat, weigheth as much, and moves in the ſame manner
as when it is cold. But to overpaſs this alſo, how know you but
that Cœleſtial rarity and denſity depend on heat and cold?
Ariſtotle defective
in aſſigning the
cauſes why the
ments are
ble & corruptible.
SIMPL. I know it, becauſe thoſe qualities are not amongſt
Cœleſtial bodies, which are neither hot nor cold.
SALV. I ſee we are again going about to engulph our ſelves in
a bottomleſs ocean, where there is no getting to ſhore; for this
is a Navigation without Compaſs, Stars, Oars or Rudder: ſo that
it will follow either that we be forced to paſs from Shelf to Shelf,
or run on ground, or to ſail continually in danger of being loſt.
Therefore, if according to your advice we ſhall proceed in our
main deſign, we muſt of neceſſity for the preſent overpaſs this
general conſideration, whether direct motion be neceſſary in
ture, and agree with ſome bodies; and come to the particular
demonſtrations, obſervations and experiments; propounding in
the firſt place all thoſe that have been hitherto alledged by
ſtotle, Ptolomey, and others, to prove the ſtability of the Earth,
deavouring in the next place to anſwer them: and producing in
1the laſt place, thoſe, by which others may be perſwaded, that the
Earth is no leſs than the Moon, or any other Planet to be
bered amongſt natural bodies that move circularly.
SAGR. I ſhall the more willingly incline to this, in that I am
better ſatisfied with your Architectonical and general diſcourſe,
than with that of Ariſtotle, for yours convinceth me without the
leaſt ſcruple, and the other at every ſtep croſſeth my way with
ſome block. And I ſee no reaſon why Simplicius ſhould not be
preſently ſatisfied with the Argument you alledg, to prove that
there can be no ſuch thing in nature as a motion by a right line,
if we do but preſuppoſe that the parts of the Univerſe are
ſed in an excellent conſtitution and perfect order.
SALV. Stay a little, good Sagredus, for juſt now a way comes
into my mind, how I may give Simplicius ſatisfaction, provided
that he will not be ſo ſtrictly wedded to every expreſſion of
riſtotle, as to hold it hereſie to recede in any thing from him. Nor
is there any queſtion to be made, but that if we grant the
lent diſpoſition and perfect order of the parts of the Univerſe,
as to local ſcituation, that then there is no other but the circular
motion, and reſt; for as to the motion by a right line, I ſee not
how it can be of uſe for any thing, but to reduce to their natural
conſtitution, ſome integral bodies, that by ſome accident were
mov'd and ſeparated from their whole, as we ſaid above.
Let us now conſider the whole Terreſtrial Globe, and enquire
the beſt we can, whether it, and the other Mundane bodies are to
conſerve themſelves in their perfect and natural diſpoſition. It
is neceſſary to ſay, either that it reſts and keeps perpetually
moveable in its place; or elſe that continuing always in its place,
it revolves in its ſelf; or that it turneth about a Centre, moving

by the circumference of a circle. Of which accidents, both
ſtotle and Ptolomey, and all their followers ſay, that it hath ever
obſerved, and ſhall continually keep the firſt, that is, a perpetual

reſt in the ſame place. Now, why, I pray you, ought they not
to have ſaid, that its natural affection is to reſt immoveable,
ther than to make natural unto it the motion ^{*} downwards, with
which motion it never did or ſhall move? And as to the motion

by a right line, they muſt grant us that Nature maketh uſe of it
to reduce the ſmall parts of the Earth, Water, Air, Fire, and every
other integral Mundane body to their Whole, when any of them
by chance are ſeparated, and ſo tranſported out of their proper
place; if alſo haply, ſome circular motion might not be found
to be more convenient to make this reſtitution. In my
ment, this primary poſition anſwers much better, even according
to Ariſtotles own method, to all the other conſequences, than
to attribute the ſtraight motion to be an intrinſick and natural
1principle of the Elements. Which is manifeſt, for that if I aske
the Peripatetick, if, being of opinion that Cœleſtial bodies are
incorruptibe and eternal, he believeth that the Terreſtial Globe
is not ſo, but corruptible and mortal, ſo that there ſhall come a
time, when the Sun and Moon and other Stars, continuing their
beings and operations, the Earth ſhall not be found in the
World, but ſhall with the reſt of the Elements be deſtroyed
and annihilated, I am certain that he would anſwer me, no:

therefore generation and corruption is in the parts and not in the
whole; and in the parts very ſmall and ſuperficial, which are,
as it were, incenſible in compariſon of the whole maſſe. And
becauſe Ariſtotle deduceth generation and corruption from the
contrariety of ſtreight motions, let us remit ſuch motions to the
parts, which onely change and decay, and to the whole Globe
and Sphere of the Elements, let us aſcribe either the circular
tion, or a perpetual conſiſtance in its proper place: the only
affections apt for perpetuation, and maintaining of perfect order.
This which is ſpoken of the Earth, may be ſaid with the ſame
reaſon of Fire, and of the greateſt part of the Air; to which

Elements, the Peripateticks are forced to aſcribe for intrinſical
and natural, a motion wherewith they were never yet moved,
nor never ſhall be; and to call that motion preternatural to them,
wherewith, if they move at all, they do and ever ſhall move.
This I ſay, becauſe they aſſign to the Air aud Fire the motion
upwards, wherewith thoſe Elements were never moved, but
only ſome parts of them, and thoſe were ſo moved onely in
der to the recovery of their perfect conſtitution, when they were
out of their natural places; and on the contrary they call the
circular motion preternatural to them, though they are thereby
inceſſantly moved: forgeting, as it ſeemeth, what Ariſtotle oft
culcateth, that nothing violent can be permanent.
Ariſt. & Ptolomey
make the
strial Globe
veable.
It is better to ſay,
that the
al Globe naturally
resteth, than that
it moveth directly
downwards.
*The word is, all'
ingiù, which the
Latine verſion
dreth ſurſùm,
which is quite
trary to the
thors ſenſe.
Right Motion
with more reaſon
attributed to the
parts, than to the
whole Elements.
The Peripateticks
improperly aſſign
thoſe motious to
the Elements for
Natural, with
which they never
were moved, and
thoſe for
natural with which
they alwayes are
moved.
SIMPL. To all theſe we have very pertinent anſwers, which

I for this time omit, that we may come to the more particular
reaſons, and ſenſible experiments, which ought in concluſion to
be oppoſed, as Ariſtotle ſaitn well, to whatever humane reaſon
can preſent us with.
Senſible
ments to be
red to humane
Arguments.
SAGR. What hath been ſpoken hitherto, ſerves to clear up
unto us which of the two general diſcourſes carrieth with it moſt
of probability, I mean that of Ariſtotle, which would perſwade
us, that the ſublunary bodies are by nature generable, and
ptible, &c. and therefore moſt different from the eſſence of
leftial bodies, which are impaſſible, ingenerable, incorruptible,
&c. drawn from the diverſity of ſimple motions; or elſe this of
Salviatus, who ſuppoſing the integral parts of the World to be
diſpoſed in a perfect conſtitution, excludes by neceſſary
1quence the right or ſtraight motion of ſimple natural bodies, as
being of no uſe in nature, and eſteems the Earth it ſelf alſo to
be one of the Cœleſtial bodies adorn'd with all the prerogatives
that agree with them; which laſt diſcourſe is hitherto much
more likely, in my judgment, than that other. Therefore
ſolve, Simplicius, to produce all the particular reaſons,
ments and obſervations, as well Natural as Aſtronomical, that
may ſerve to perſwade us that the Earth differeth from the
leſtial bodies, is immoveable, and ſituated in the Centre of the
World, and what ever elſe excludes its moving like to the Planets,
as Jupiter or the Moon, &c. And Salviatus will be pleaſed to
be ſo civil as to anſwer to them one by one.
SIMPL. See here for a beginning, two moſt convincing
ments to demonſtrate the Earth to be moſt different from the
Cœleſtial bodies. Firſt, the bodies that are generable,
ptible, alterable, &c. are quite different from thoſe that are
generable, incorruptible, unalterable, &c. But the Earth is
nerable, corruptible, alterable, &c. and the Cœleſtial bodies
generable, incorruptible, unalterable, &c. Therefore the Earth
is quite different from the Cœleſtial bodies.
SAGR. By your firſt Argument you ſpread the Table with the
ſame Viands, which but juſt now with much adoe were voided.
SIMPL. Hold a little, Sir, and take the reſt along with you,
and then tell me if this be not different from what you had
fore. In the former, the Minor was proved à priori, & now you ſee
it proved à poſteriori: Judg then if it be the ſame. I prove the
Minor, therefore (the Major being moſt manifeſt) by ſenſible
perience, which ſhews us that in the Earth there are made
nual generations, corruptions, alterations, &c. which neither our
ſenſes, nor the traditions or memories of our Anceſtors, ever ſaw
an inſtance of in Heaven; therefore Heaven is unalterable, &c.

and the Earth alterable, &c. and therefore different from
ven. I take my ſecond Argument from a principal and eſſential
accident, and it is this. That body which is by its nature

ſcure and deprived of light, is divers from the luminous and
ning bodies; but the Earth is obſcure and void of light, and the
Cœleſtial bodies ſplendid, and full of light; Ergo, &c. Anſwer
to theſe Arguments firſt, that we may not heap up too many,
and then I will alledge others.
Heaven
ble, becauſe there
never was any
tation ſeen in it.
Bodies naturally
lucid, are different
from thoſe which
are by nature
ſcure.
SALV. As to the firſt, the ſtreſſe whereof you lay upon
perience, I deſire that you would a little more diſtinctly produce
me the alteration which you ſee made in the Earth, and not in
Heaven; upon which you call the Earth alterable, and the
vens not ſo.
SIMPL. I ſee in the Earth, plants and animals continually
1nerating and decaying; winds, rains, tempeſts, ſtorms ariſing; and
in a word, the aſpect of the Earth to be perpetually
ſing; none of which mutations are to be diſcern'd in the Cœleſtial
bodies; the conſtitution and figuration of which is moſt
ally conformable to that they ever were time out of mind; without
the generation of any thing that is new, or corruption of any thing
that was old.
SALV. But if you content your ſelf with theſe viſible, or to
ſay better, ſeen experiments, you muſt conſequently account
China and America Cœleſtial bodies, for doubtleſſe you never
beheld in them theſe alterations which you ſee here in Italy, and
that therefore according to your apprehenſion they are
terable.
SIMPL. Though I never did ſee theſe alterations ſenfibly in
thoſe places, the relations of them are not to be queſtioned;
beſides that, cum eadem ſit ratio totius, & partium, thoſe
Countreys being a part of the Earth, as well as ours, they
muſt of neceſſity be alterable as theſe are.
SALV. And why have you not, without being put to believe
other mens relations, examined and obſerved thoſe alterations
with your own eyes?
SIMPL. Becauſe thoſe places, beſides that they are not
poſed to our eyes, are ſo remote, that our ſight cannot reach
to comprehend therein ſuch like mutations.
SALV. See now, how you have unawares diſcovered the
cy of your Argument; for, if you ſay that the alterations that
are ſeen on the Earth neer at hand, cannot, by reaſon of the too
great diſtance, be ſeen in America, much leſſe can you ſee them
in the Moon, which is ſo many hundred times more remote:
And if you believe the alterations in Mexico upon the report of
thoſe that come from thence, what intelligence have you from
the Moon, to aſſure you that there is no ſuch alterations in it?
Therefore, from your not ſeeing any alterations in Heaven,
whereas, if there were any ſuch, you could not ſee them by
ſon of their too great diſtance, and from your not having
ligence thereof, in regard that it cannot be had, you ought not
to argue, that there are no ſuch alterations; howbeit, from the
ſeeing and obſerving of them on Earth, you well argue that
therein ſuch there are.
SIMPL. I will ſhew ſo great mutations that have befaln on
the Earth; that if any ſuch had happened in the Moon, they
might very well have been obſerved here below. We find in

very antient records, that heretofore at the Streights of Gibraltar,
the two great Mountains Abila, and Calpen, were continued
gether by certain other leſſe Mountains which there gave check
1to the Ocean: but thoſe Hills, being by ſome cauſe or other
parated, and a way being opened to the Sea to break in, it made
ſuch an inundation, that it gave occaſion to the calling of it ſince
the Mid-land Sea: the greatneſs whereof conſidered, and the
vers aſpect the ſurface of the Water and Earth then made, had it
been beheld afar off, there is no doubt but ſo great a change
might have been diſcerned by one that was then in the Moon;
as alſo to us inhabitants of the Earth, the like alterations would
be perceived in the Moon; but we find not in antiquity, that
ver there was ſuch a thing ſeen; therefore we have no cauſe to
ſay, that any of the Cœleſtial bodies are alterable, &c.
The Mediterr
an Sea made by the
ſeparation of
la and Calpen.
SALV. That ſo great alterations have hapned in the Moon, I
dare not ſay, but for all that, I am not yet certain but that ſuch
changes might occur; and becauſe ſuch a mutation could onely
repreſent unto us ſome kind of variation between the more clear,
and more obſcure parts of the Moon, I know not whether we
have had on Earth obſervant Selenographers, who have for any
conſiderable number of years, inſtructed us with ſo exact
graphy, as that we ſhould confidently conclude, that there hath
no ſuch change hapned in the face of the Moon; of the
tion of which I find no more particular deſcription, than the
ing of ſome, that it repreſents an humane face; of others, that
it is like the muzzle of a lyon; and of others, that it is Cain with
a bundle of thorns on his back: therefore, to ſay Heaven is
alterable, becauſe that in the Moon, or other Cœleſtial bodies, no
ſuch alterations are ſeen, as diſcover themſelves on Earth, is a bad
illation, and concludeth nothing.
SAGR. And there is another odd kind of ſcruple in this
ment of Simplicius, running in my mind, which I would gladly
have anſwered; therefore I demand of him, whether the Earth
before the Mediterranian inundation was generable and
ble, or elſe began then ſo to be?
SIMPL. It was doubtleſs generable and corruptible alſo
fore that time; but that was ſo vaſt a mutation, that it might
have been obſerved as far as the Moon.
SAGR. Go to; if the Earth was generable and corruptible
before that Inundation, why may not the Moon be ſo
wiſe without ſuch a change? Or why ſhould that be neceſſary
in the Moon, which importeth nothing on Earth?
SALV. It is a ſhrewd queſtion: But I am doubtfull that
plicius a little altereth the Text of Ariſtotle, and the other
patelicks, who ſay, they hold the Heavens unalterable, for that
they ſee therein no one ſtar generate or corrupt, which is
bly a leſs part of Heaven, than a City is of the Earth, and yet
innumerable of theſe have been deſtroyed, ſo as that no mark of
them hath remain'd.
1
SAGR. I verily believed otherwiſe, and conceited that
plicius diſſembled this expoſition of the Text, that he might not
charge his Maſter and Conſectators, with a notion more abſurd
than the former. And what a folly it is to ſay the Cœleſtial
part is unalterable, becauſe no ſtars do generate or corrupt
in? What then? hath any ſeen a Terreſtrial Globe corrupt, and
another regenerate in its place? And yet is it not on all hands
granted by Philoſophers, that there are very few ſtars in Heaven
leſs than the Earth, but very many that are much bigger? So

that for a ſtar in Heaven to corrupt, would be no leſs than if the
whole Terreſtrial Globe ſhould be deſtroy'd. Therefore, if for
the true proof of generation and corruption in the Univerſe, it be
neceſſary that ſo vaſt bodies as a ſtar, muſt corrupt and
rate, you may ſatisfie your ſelf and ceaſe your opinion; for I
aſſure you, that you ſhall never ſee the Terreſtrial Globe or any
other integral body of the World, to corrupt or decay ſo, that
having been beheld by us for ſo many years paſt, they ſhould ſo
diſſolve, as not to leave any footſteps of them.
Its no leſs
ble for a ſtar to
corrupt, than for
the whole
ſtrial Globe.
SALV. But to give Simplicius yet fuller ſatisfaction, and to
reclaim him, if poſſible, from his error; I affirm, that we have in

our age new accidents and obſervations, and ſuch, that I queſtion
not in the leaſt, but if Ariſtotle were now alive, they would make
him change his opinion; which may be eaſily collected from the
very manner of his diſcourſing: For when he writeth that he
ſteemeth the Heavens inalterable, &c. becauſe no new thing was
ſeen to be begot therein, or any old to be diſſolved, he ſeems
plicitely to hint unto us, that when he ſhould ſee any ſuch
dent, he would hold the contrary; and confront, as indeed it is
meet, ſenſible experiments to natural reaſon: for had he not
made any reckoning of the ſenſes, he would not then from the
not ſeeing of any ſenſible mutation, have argued immutability.
Ariſtotle would
change his opinion,
did he ſee the
velties of our age.
SIMPL. Ariſtotle deduceth his principal Argument à priori,
ſhewing the neceſſity of the inalterability of Heaven by natural,
manifeſt and clear principles; and then ſtabliſheth the ſame à
ſteriori, by ſenſe, and the traditions of the antients.
SALV. This you ſpeak of is the Method he hath obſerved in
delivering his Doctrine, but I do not bethink it yet to be that
wherewith he invented it; for I do believe for certain, that he
firſt procured by help of the ſenſes, ſuch experiments and
vations as he could, to aſſure him as much as it was poſſible, of the

concluſion, and that he afterwards ſought out the means how to
demonſtrate it: For this, the uſual courſe in demonſtrative
ces, and the reaſon thereof is, becauſe when the concluſion is
true, by help of reſolutive Method, one may hit upon ſome
poſition before demonſtrated, or come to ſome principle known
1per ſe; but if the concluſion be falſe, a man may proceed in
finitum, and never meet with any truth already known; but
ry oft he ſhall meet with ſome impoſſibility or manifeſt

ty. Nor need you queſtion but that Pythagoras along time
fore he found the demonſtration for which he offered the
tomb, had been certain, that the ſquare of the ſide ſubtending
the right angle in a rectangle triangle, was equal to the ſquare of
the other two ſides: and the certainty of the concluſion
ced not a little to the inveſtigating of the demonſtration,
derſtanding me alwayes to mean in demonſtrative Sciences. But
what ever was the method of Ariſtotle, and whether his arguing à
priori preceded ſenſe à poſteriori, or the contrary; it ſufficeth that
the ſame Ariſtotle preferreth (as hath been oft ſaid) ſenſible
periments before all diſcourſes; beſides, as to the Arugments à
priori their force hath been already examined. Now returning
to my purpoſed matter, I ſay, that the things in our times
covered in the Heavens, are, and have been ſuch, that they may
give abſolute ſatisfaction to all Philoſophers; foraſmuch as in
the particular bodies, and in the univerſal expanſion of Heaven,
there have been, and are continually, ſeen juſt ſuch accidents as
we call generations and corruptions, being that excellent
ſtronomers have obſerved many Comets generated and diſſolved
in parts higher than the Lunar Orb, beſides the two new Stars,

Anuo 1572, and Anno 1604, without contradiction much higher
than all the Planets; and in the face of the Sun it ſelf, by help

of the Teleſcope, certain denſe and obſcure ſubſtances, in
blance very like to the foggs about the Earth, are ſeen to be
produced and diſſolved; and many of theſe are ſo vaſt, that
they far exceed not only the Mediterranian Streight, but all

Affrica and Aſia alſo. Now if Ariſtotle had ſeen theſe things,
what think you he would have ſaid, and done Simplicius?
The certaixty of
the concluſion
peth by areſolutive
method to ſind the
demonstration.
Pythagoras offered
an Hecatomb for
a Geometrical
monſtration which
he found.
New ſtars
vered in Heaven.
Spots generate and
diſſolve in the face
of the Sun.
Solar spots are
bigger than all
ſia and Affrick.
SIMPL. I know not what Ariſtotle would have done or ſaid,
that was the great Maſter of all the Sciences, but yet I know in
part, what his Sectators do and ſay, and ought to do and ſay,
unleſſe they would deprive themſelves of their guide, leader, and
Prince in Philoſophy. As to the Comets, are not thoſe Modern
Aſtronomers, who would make them Cœleſtial, convinced by

the ^{*}Anti-Tycho, yea, and overcome with their own weapons, I
mean by way of Paralaxes and Calculations, every way tryed,
concluding at the laſt in favour of Aristotle, that they are all
Elementary? And this being overthrown, which was as it were
their foundation, have theſe Novelliſts any thing more
with to maintain their aſſertion?
* Aſtronomers
futed by
cho.
SALV. Hold a little, good Simplicius, this modern Author,
what ſaith he to the new Stars, Anno 1572, and 1604, and to
1the Solar ſpots? for as to the Comets, I for my own particular
little care to make them generated under or above the Moon;
nor did I ever put much ſtreſſe on the loquacity of Tycho; nor
am I hard to believe that their matter is Elementary, and that
they may elevate (ſublimate) themſelves at their pleaſure,
out meeting with any obſtacle from the impenetrability of the
Peripatetick Heaven, which I hold to be far more thin, yielding,
and ſubtil than our Air; and as to the calculations of the
rallaxes, firſt, the uncertainty whether Comets are ſubject to
ſuch accidents, and next, the inconſtancy of the obſervations,
upon which the computations are made, make me equally
pect both thoſe opinions: and the rather, for that I ſee him

you call Anti-Tycho, ſometimes ſtretch to his purpoſe, or elſe
reject thoſe obſervations which interfere with his deſign.
Anti-Tycho
ſteth Aſtronomical
obſervations to his
own parpoſe.
SIMPL. As to the new Stars, Anti-Tycho extricates himſelf
finely in three or four words; ſaying, That thoſe
dern new Stars are no certain parts of the Cœleſtial bodies, and
that the adverſaries, if they will prove alteration and
tion in thoſe ſuperior bodies, muſt ſhew ſome mutations that
have been made in the Stars deſcribed ſo many ages paſt, of
which there is no doubt but that they be Cœleſtial bodies,
which they can never be able to do: Next, as to thoſe
ters which ſome affirm, to generate and diſſipate in the face of
the Sun, he makes no mention thereof; wherefore I conclude,
that he believed them fictious, or the illuſions of the Tube, or
at moſt, ſome petty effecs cauſed by the Air, and in brief, any
thing rather than matters Cœleſtial.
SALV. But you, Simplicius, what anſwer could you give to
the oppoſition of theſe importunate ſpots which are ſtarted up
to diſturb the Heavens, and more than that, the Peripatetick
Philoſophy? It cannot be but that you, who are ſo reſolute a
Champion of it, have found ſome reply or ſolution for the
ſame, of which you ought not to deprive us.
SIMPL. I have heard ſundry opinions about this particular.
One ſaith: “They are Stars which in their proper Orbs, like as

Venus and Mervury, revolve about the Sun, and in paſſing
der it, repreſent themſelves to us obſcure; and for that they
are many, they oft happen to aggregate their parts together,
and afterwards ſeperate again. Others believe them to be
aerial impreſſions; others, the illuſions of the chryſtals; and
thers, other things: But I incline to think, yea am verily
ſwaded, That they are an aggregate of many ſeveral opacous
bodies, as it were caſually concurrent among themſelves. And
therefore we often ſee, that in one of thoſe ſpots one may
number ten or more ſuch ſmall bodies, which are of
1lar figures, and ſeem to us like flakes of ſnow, or flocks of
wooll, or moaths flying: they vary ſite amongſt themſelves,
and one while ſever, another while meet, and moſt of all
neath the Sun, about which, as about their Centre, they
tinually move. But yet, muſt we not therefore grant, that
they are generated or diſſolved, but that at ſometimes they are
hid behind the body of the Sun, and at other times, though
remote from it, yet are they not ſeen for the vicinity of the
immeaſurable light of the Sun; in regard that in the eccentrick
Orb of the Sun, there is conſtituted, as it were, an Onion,
poſed of many folds one within another, each of which, being

^{*}ſtudded with certain ſmall ſpots, doth move; and albeit their
motion at firſt ſeemeth inconſtant and irregular, yet
leſſe, it is ſaid at laſt, to be obſerved that the very ſame ſpots,
as before,” do within a determinate time return again. This
ſeemeth to me the fitteſt anſwer that hath been found to aſſigne
a reaſon of that ſame appearance, and withal to maintain the
incorruptability and ingenerability of the Heavens; and if this
doth not ſuffice; there wants not more elevated wits, which will
give you other, more convincing.
Sundry opinions
touching the Solar
ſpots.
* The Original
ſaith [tempeſtata ſi
muove] which the
Latine
on, (Miſtaking
Tempectata, aword
in Heraldry, for
Tempeſtato,)
dereth [incitata
movetur] which
ſignifieth a violent
tranſportmeut, as
in a ſtorm, that of
a Ship.
SALV. If this of which we diſpute, were ſome point of Law,

or other part of the Studies called Humanity, wherein there is
neither truth nor falſhood, if we will give ſufficient credit to
the acuteneſſe of the wit, readineſſe of anſwers, and the
ral practice of Writers, then he who moſt aboundeth in theſe,
makes his reaſon more probable and plauſible; but in Natural
Sciences, the concluſions of which are true and neceſſary, and
wherewith the judgment of men hath nothing to do, one is to
be more cautious how he goeth about to maintain any thing that
is falſe; for a man but of an ordinary wit, if it be his good
tune to be of the right ſide, may lay a thouſand Demoſthenes and
a thouſand Ariſtotles at his feet. Therefore reject thoſe hopes
and conceits, wherewith you flatter your ſelf, that there can be
any men ſo much more learned, read, and verſed in Authors,
than we, that in deſpite of nature, they ſhould be able to
make that become true, which is falſe. And ſeeing that of all
the opinions that have been hitherto alledged touching the
ſence of theſe Solar ſpots, this inſtanced in by you, is in your
judgment the trueſt, it followeth (if this be ſo) that all the reſt
are falſe; and to deliver you from this alſo, which doubtleſſe is a
moſt falſe Chimœra, over-paſſing infinite other improbabilities
that are therein, I ſhall propoſe againſt it onely two experiments;

one is, that many of thoſe ſpots are ſeen to ariſe in the midſt of
the Solar ring, and many likewiſe to diſſolve and vaniſh at a great
diſtance from the circumference of the Sun; a neceſſary
1ment that they generate and diſſolve; for if without generating
or corrrupting, they ſhould appear there by onely local motion,
they would all be ſeen to enter, and paſs out by the extreme

cumference. The other obſervation to ſuch as are not ſituate in
the loweſt degree of ignorance in Perſpective, by the mutation
of the appearing figures, and by the apparent mutations of the
velocity of motion is neceſſarily concluding, that the ſpots are
contiguous to the body of the Sun, and that touching its
cies, they move either with it or upon it, and that they in no wiſe
move in circles remote from the ſame. The motion proves

it, which towards the circumference of the Solar Circle,
appeareth very ſlow, and towards the midſt, more ſwift; the
gures of the ſpots confirmeth it, which towards the circumference

appear exceeding narrow in compariſon of that which they ſeem
to be in the parts nearer the middle; and this becauſe in the
midſt they are ſeen in their full luſter, and as they truly be; and
towards the circumference by reaſon of the convexity of the
bous ſuperficies, they ſeem more compreſſ'd: And both theſe
diminutions of figure and motion, to ſuch as know how to obſerve
and calculate them exactly, preciſely anſwer to that which ſhould
appear, the ſpots being contiguous to the Sun, and differ
cileably from a motion in circles remote, though but for ſmal
intervalls from the body of the Sun; as hath been diffuſely

monſtrated by our ^{*} Friend, in his Letters about the Solar ſpots,
to Marcus Velſerus. It may be gathered from the ſame
tion of figure, that none of them are ſtars, or other bodies of
ſpherical figure; for that amongſt all figures the ſphere never
appeareth compreſſed, nor can ever be repreſented but onely
fectly round; and thus in caſe any particular ſpot were a round
body, as all the ſtars are held to be, the ſaid roundneſs would as
well appear in the midſt of the Solar ring, as when the ſpot is near
the extreme: whereas, its ſo great compreſſion, and ſhewing its
ſelf ſo ſmall towards the extreme, and contrariwiſe, ſpatious and
large towards the middle, aſſureth us, that theſe ſpots are flat

plates of ſmall thickneſs or depth, in compariſon of their length
and breadth. Laſtly, whereas you ſay that the ſpots after their
determinate periods are obſerved to return to their former aſpect,
believe it not, Simplicius, for he that told you ſo, will deceive
you; and that I ſpeak the truth, you may obſerve them to be hid
in the face of the Sun far from the circumference; nor hath your
Obſervator told you a word of that compreſſion, which
rily argueth them to be contiguous to the Sun. That which he
tells you of the return of the ſaid ſpots, is nothing elſe but what
is read in the forementioned Letters, namely, that ſome of them
may ſometimes ſo happen that are of ſo long a duration, that
1they cannot be diſſipated by one ſole converſion about the Sun,
which is accompliſhed in leſs than a moneth.
In natural
ences, the art of
Oratory is of no
force.
An Argument
that neceſſarily
proveth the Solar
ſpots to generate
and diſſolwe.
A concluſive
monſtration, that
the ſpots are
guous to the body
of the Sun.
The motion of the
spots towards the
circumference of
the Sun appears
ſlow.
The figure of the
spots appears
row towards the
circumference of
the Suns diſcus, &
why.
* Under this word
Friend, as alſo that
of Academick, &
Common Friend,
Galilœus modeſtly
conceals himſelf
throughout theſe
Dialogues.
The Solar spots
are not ſpherical,
but flat like thin
plates.
SIMPL. I, for my part, have not made either ſo long, or ſo
exact obſervations, as to enable me to boaſt my ſelf Maſter of the
Quod ect of this matter: but I will more accurately conſider the
ſame, and make tryal my ſelf for my own ſatisfaction, whether I
can reconcile that which experience ſhews us, with that which
Ariſtotle teacheth us; for it's a certain Maxim, that two Truths
cannot be contrary to one another.
SALV. If you would reconcile that which ſenſe ſheweth you,

with the ſolider Doctrines of Ariſtotle, you will find no great
ficulty in the undertaking; and that ſo it is, doth not Ariſtotle
ſay, that one cannot treat confidently of the things of Heaven,
by reaſon of their great remoteneſs?
One cannot (ſaith
Ariſtotle) ſpeak
confidently of
ven, by reaſon of
its great diſtance.
SIMPL. He expreſly ſaith
Ariſtotle prefers
ſenſe before
cination.
SALV. And doth he not likewiſe affirm, that we ought to
fer that which ſenſe demonſtrates, before all Arguments, though
in appearance never ſo well grounded? and ſaith he not this
without the leaſt doubt or hæſitation?
SIMPL. He doth ſo.
SALV. Why then, the ſecond of theſe propoſitions, which are
both the doctrine of Ariſtotle, that ſaith, that ſenſe is to take

place of Logick, is a doctrine much more ſolid and undoubted,
than that other which holdeth the Heavens to be unalterable; and
therefore you ſhall argue more Ariſtotelically, ſaying, the
vens are alterable, for that ſo my ſenſe telleth me, than if you
ſhould ſay, the Heavens are u alterable, for that Logick ſo
ded Aristotle. Furthermore, we may diſcourſe of Cœleſtial

ters much better than Ariſtotle; becauſe, he confeſſing the
ledg thereof to be difficult to him, by reaſon of their remoteneſs
from the ſenſes, he thereby acknowledgeth, that one to whom
the ſenſes can better repreſent the ſame, may philoſophate upon
them with more certainty. Now we by help of the Teleſcope,
are brought thirty or forty times nearer to the Heavens, than ever
Ariſtotle came; ſo that we may diſcover in them an hundred
things, which he could not ſee, and amongſt the reſt, theſe ſpots
in the Sun, which were to him abſolutely inviſible; therefore
we may diſcourſe of the Heavens and Sun, with more certainty
than Ariſtolte.
Its a doctrine more
agreeing with
riſtotle, to ſay the
Heavens are
able, than that
which affirms
them inalterable.
We may by help of
the Teleſcope
courſe better of
leſtial matters,
than Ariſtot.
ſelf.
SAGR. I ſee into the heart of Simplicius, and know that he is
much moved at the ſtrength of theſe ſo convincing Arguments;
but on the other ſide, when he conſidereth the great authority
which Ariſtotle hath won with all men, and remembreth the great
number of famous Interpreters, which have made it their buſineſs
to explain his ſenſe; and ſeeth other Sciences, ſo neceſſary and
1profitable to the publick, to build a great part of their eſteem
and reputation on the credit of Ariſtotle he is much puzzled and
perplexed: and methinks I hear him ſay, To whom then ſhould

we repair for the deciſion of our controverſies, if Ariſtotle were
removed from the chair? What other Author ſhould we follow
in the Schools, Academies and Studies? What Philoſopher hath
writ all the parts of Natural Philoſophy, and that ſo methodically
without omitting ſo much as one ſingle concluſion? Shall we then
overthrow that Fabrick under which ſo many paſſengers find
ſhelter? Shall we deſtroy that Aſylum, that Prytaneum,
in ſo many Students meet with commodious harbour, where
without expoſing themſelves to the injuries of the air, with the
onely turning over of a few leaves, one may learn all the
crets of Nature? Shall we diſmantle that fort in which we are
ſafe from all hoſtile aſſaults? But I pitie him no more than I do
that Gentleman who with great expence of time and treaſure,
and the help of many hundred artiſts, erects a very
ous Pallace, and afterwards beholds it ready to fall, by reaſon
of the bad foundation; but being extremely unwilling to ſee
the Walls ſtript which are adorned with ſo many beautifull
Pictures; or to ſuffer the columns to fall, that uphold the
ly Galleries; or the gilded roofs, chimney-pieces, the freizes,
the corniſhes of marble, with ſo much coſt erected, to be
ned; goeth about with girders, props, ſhoars, butteraſſes, to
vent their ſubverſion.
The Declamation
of Simplicius.
SALV. But alaſs, Simplicius as yet fears no ſuch fall, and
I would undertake to ſecure him from that miſchief at a far
leſs charge. There is no danger that ſo great a multitude of

ſubtle and wiſe Philoſophers, ſhould ſuffer themſelves to be
Hector'd by one or two, who make a little bluſtering; nay,
they will rather, without ever turning the points of their pens
againſt them, by their ſilence onely render them the object of
univerſal ſcorn and contempt. It is a fond conceit for any one
to think to introduce new Philoſophy, by reproving this or that
Author: it will be firſt neceſſary to new-mold the brains of
men, and make them apt to diſtinguiſh truth from falſhood. A
thing which onely God can do. But from one diſcourſe to another
whither are we ſtray'd? your memory muſt help to guide me into
the way again.
Peripatetick
loſophy
able.
SIMPL. I remember very well where we left. We were
upon the anſwer of Anti-Tycho, to the objections againſt the
immutability of the Heavens, among which you inſerted this
of the Solar fpots, not ſpoke of by him; and I believe you
intended to examine his anſwer to the inſtance of the New
Stars.
1
SALV. Now I remember the reſt, and to proceed, Methinks
there are ſome things in the anſwer of Anti-Tycho, worthy of
reprehenſion. And firſt, if the two New Stars, which he can do
no leſs than place in the uppermoſt parts of the Heavens, and
which were of a long duration, but finally vaniſhed, give him no
obſtruction in maintaining the inalterability of Heaven, in that
they were not certain parts thereof, nor mutations made in the
antient Stars, why doth he ſet himſelf ſo vigorouſly and earneſtly
againſt the Comets, to baniſh them by all ways from the
ſtial Regions? Was it not enough that he could ſay of them
the ſame which he ſpoke of the New ſtars? to wit, that in
gard they were no certain parts of Heaven, nor mutations made
in any of the Stars, they could no wiſe prejudice either Heaven,
or the Doctrine of Ariſtotle? Secondly, I am not very well
fied of his meaning; when he ſaith that the alterations that ſhould
be granted to be made in the Stars, would be deſtructive to the
prerogative of Heaven; namely, its incorruptibility, &c. and
this, becauſe the Stars are Cœleſtial ſubſtances, as is manifeſt
by the conſent of every one; and yet is nothing troubled that

the ſame alterations ſhould be made ^{*} without the Stars in the reſt
of the Cœleſtial expanſion. Doth he think that Heaven is no
Cœleſtial ſubſtance? I, for my part, did believe that the Stars
were called Cœleſtial bodies, by reaſon that they were in
ven, or for that they were made of the ſubſtance of Heaven;
and yet I thought that Heaven was more Cœleſtial than they; in
like ſort, as nothing can be ſaid to be more Terreſtrial, or more
fiery than the Earth or Fire themſelves. And again, in that he
ver made any mention of the Solar ſpots, which have been
dently demonſtrated to be produced, and diſſolved, and to be
neer the Sun, and to turn either with, or about the ſame, I have
reaſon to think that this Author probably did write more for others
pleaſure, than for his own ſatisfaction; and this I affirm,
much as he having ſhewn himſelf to be skilful in the
ticks, it is impoſſible but that he ſhould have been convinced by
Demonſtrations, that thoſe ſubſtances are of neceſſity
ous with the body of the Sun, and are ſo great generations and
corruptions, that none comparable to them, ever happen in the
Earth: And if ſuch, ſo many, and ſo frequent be made in the
very Globe of the Sun, which may with reaſon be held one of the
nobleſt parts of Heaven, what ſhould make us think that others
may not happen in the other
* Ex tra Stellas.
Generability and
alteration is a
greater perfection
in the Worlds
dies than the
trary qualities.
SAGR. I cannot without great admiration, nay more,
al of my underſtanding, hear it to be attributed to natural bodies,
for a great honour and perfection that they are ^{*} impaſſible,
mutable, inalterable, &c. And on the contrary, to hear it to
1be eſteemed a great imperfection to be alterable, generable,
table, &c. It is my opinion that the Earth is very noble and

mirable, by reaſon of ſo many and ſo different alterations,
tations, generations, &c. which are inceſſantly made therein;
and if without being ſubject to any alteration, it had been all
one vaſt heap of ſand, or a maſſe of Jaſper, or that in the time
of the Deluge, the waters freezing which covered it, it had
continued an immenſe Globe of Chriſtal, wherein nothing had

ever grown, altered, or changed, I ſhould have eſteemed it a
lump of no benefit to the World, full of idleneſſe, and in a
word ſuperfluous, and as if it had never been in nature; and
ſhould make the ſame difference in it, as between a living and
dead creature: The like I ſay of the Moon, Jupiter, and all the
other Globes of the World. But the more I dive into the
ſideration of the vanity of popular diſcourſes, the more empty
and ſimple I find them. And what greater folly can there be
imagined, than to call Jems, Silver and Gold pretious; and Earth
and dirt vile? For do not theſe perſons conſider, that if there

ſhould be as great a ſcarcity of Earth, as there is of Jewels and
pretious metals, there would be no Prince, but would gladly give
a heap of Diamonds and Rubies, and many Wedges of Gold,
to purchaſe onely ſo much Earth as ſhould ſuffice to plant a
mine in a little pot, or to ſet therein a China Orange, that he might
ſee it ſprout, grow up, and bring forth ſo goodly leaves, ſo
riferous flowers, and ſo delicate fruit? It is therefore ſcarcity and

plenty that make things eſteemed and contemned by the vulgar;
who will ſay that ſame is a moſt beautiful Diamond, for that it
reſembleth a cleer water, and yet will not part with it for ten
Tun of water: Theſe men that ſo extol incorruptibility,

rability, &c. ſpeak thus I believe out of the great deſire they
have to live long, and for fear of death; not confidering, that
if men had been immortal, they ſhould have had nothing to do
in the World. Theſe deſerve to meet with a Meduſa's head,

that would transform them into Statues of Dimond and Jaſper,
that ſo they might become more perfect than they are.
* Impatible.
The Earth very
noble, by reaſon of
the many
ons made therein.
The carth
ſitable and full of
idleneſſe, its
rations taken away
The Earth more
noble than Gold
and Jewels.
Scarcity and
ty enhanſe and
baſe the price of
things.
Incorruptibility
ſteemed by the
gar out of their
fear of death.
The diſparagers of
corraptibility
ſerve to be turned
into Statua's.
SALV. And it may be ſuch a Metamorphoſis would not be
together unprofitable to them; for I am of opinion that it is
ter not to diſcourſe at all, than to argue erroniouſly.
SIMPL. There is not the leaſt queſtion to be made, but that
the Earth is much more perfect, being as it is alterable, mutable,
&c. than if it had been a maſſe of ſtone; yea although it were
one entire Diamond, moſt hard and impaſſile. But look how mueh

theſe qualifications enoble the Earth, they render the Heavenly
bodies again on the other ſide ſo much the more imperfect, in
which, ſuch conditions would be ſuperfluous; in regard that the
1Cœleſtial bodies, namely, the Sun, Moon, and the other Stars,
which are ordained for no other uſe but to ſerve the Earth, need
no other qualities for attaining of that end, ſave onely thoſe of
light and motion.
The Cœleſtial
dies deſigned to
ſerve the Earth,
need no more but
motion and light.
SAGR. How? Will you affirm that nature hath produced and
deſigned ſo many vaſt perfect and noble Cœleſtial bodies,
ſible, immortal, and divine, to no other uſe but to ſerve the
ſible, frail, and mortal Earth? to ſerve that which you call the
droſſe of the World, and ſink of all uncleanneſſe? To what
purpoſe were the Cœleſtial bodies made immortal, &c. to ſerve a
frail, &c. Take away this ſubſerviency to the Earth, and the
numerable multitude of Cœleſtial bodies become wholly

ful, and ſuperfluous, ſince they neither have nor can have any
mutual operation betwixt themſelves; becauſe they are all
terable, immutable, impaſſible: For if, for Example, the Moon
be impaſſible, what influence can the Sun or any other Star have
upon her? it would doubtleſſe have far leſſe effect upon her, than
that of one who would with his looks or imagination, lignifie a
piece of Gold. Moreover, it ſeemeth to me, that whilſt the
leſtial bodies concurre to the generation and alteration of the
Earth, they themſelves are alſo of neceſſity alterable; for
wiſe I cannot underſtand how the application of the Sun or Moon
to the Earth, to effect production, ſhould be any other than to lay
a marble Statue by a Womans ſide, and from that conjunction to
expect
Celestial bodies
want an
changeable
tion upon each
ther.
Alterability, &c.
are not in the whole
Terreſtrial Globe,
but in ſome of its
parts.
SIMPL. Corruptibility, alteration, mutation, &c. are not in
the whole Terreſtrial Globe, which as to its whole, is no leſſe
nal than the Sun or Moon, but it is generable and corruptible as to
its external parts; but yet it is alſo true that likewiſe in them
neration and corruption are perpetual, and as ſuch require the
heavenly eternal operations; and therefore it is neceſſary that
the Cœleſtial bodies be eternal.
SAGR. All this is right; but if the corruptibility of the
ficial parts of the Earth be nowiſe prejudicial to the eternity of
its whole Globe, yea, if their being generable, corruptible,
able, &c. gain them great ornament and perfection; why can­

not, and ought not you to admit alteration, generation, &c.
wiſe in the external parts of the Cœleſtial Globes, adding to
them ornament, without taking from them perfection, or
ving them of action; yea rather encreaſing their effects, by
ing not onely that they all operate on the Earth, but that they
tually operate upon each other, and the Earth alſo upon them
all?
Cœleſtial bodies
alterable in their
outward parts.
SIMPL. This cannot be, becauſe the generations, mutations,
&c. which we ſhould ſuppoſe v. g. in the Moon; would be vain
and uſeleſſe, & natura nihil fruſtra facit.
1
SAGR. And why ſhould they be vain and uſeleſſe?
SIMPL. Becauſe we cleerly ſee, and feel with our hands, that

all generations, corruptions, &c. made in the Earth, are all
ther mediately or immediately directed to the uſe, convenience,
and benefit of man; for the uſe of man are horſes brought forth,
for the feeding of horſes, the Earth produceth graſſe, and the
Clouds water it; for the uſe and nouriſhment of man, herbs, corn,
fruits, beaſts, birds, fiſhes, are brought forth; and in ſum, if
we ſhould one by one dilligently examine and reſolve all theſe
things, we ſhould find the end to which they are all directed, to be
the neceſſity, uſe, convenience, and delight of man. Now of what
uſe could the generations which we ſuppoſe to be made in the
Moon or other Planets, ever be to mankind? unleſſe you ſhould
ſay that there were alſo men in the Moon, that might enjoy the
benefit thereof; a conceit either fabulous or impious.
The generations &
mutations
ing in the Earth,
are all for the good
of Man.
SAGR. That in the Moon or other Planets, there are

ted either herbs, or plants, or animals, like to ours, or that there
are rains, winds, or thunders there, as about the Earth, I
ther know, nor believe, and much leſſe, that it is inhabited by
men: but yet I underſtand not, becauſe there are not
ted things like to ours, that therefore it neceſſarily followeth,
that no alteration is wrought therein, or that there may not be
other things that change, generate, and diſſolve, which are not

onely different from ours, but exceedingly beyond our
tion, and in a word, not to be thought of by us. And if, as I
am certain, that one born and brought up in a ſpatious Forreſt,
amongſt beaſts and birds, and that hath no knowledg at all of the
Element of Water, could never come to imagine another World

to be in Nature, different from the Eatth, full of living
tures, which without legs or wings ſwiftly move, and not upon
the ſurface onely, as beaſts do upon the Earth, but in the very
bowels thereof; and not onely move, but alſo ſtay themſelves
and ceaſe to move at their pleaſure, which birds cannot do in the
air; and that moreover men live therein, and build Palaces and
Cities, and have ſo great convenience in travailing, that without
the leaſt trouble, they can go with their Family, Houſe, and
whole Cities, to places far remote, like as I ſay, I am certain,
ſuch a perſon, though of never ſo piercing an imagination, could
never fancy to himſelf Fiſhes, the Ocean, Ships, Fleets,
do's at Sea; thus, and much more eaſily, may it happn, that in
the Moon, remote from us by ſo great a ſpace, and of a
ſtance perchance very different from the Earth, there may be
ters, and operations, not only wide off, but altogether beyond
all our imaginations, as being ſuch as have no reſemblance to
ours, and therefore wholly inexcogitable, in regard, that what we
1imagine to our ſelves, muſt neceſſarily be either a thing already
ſeen, or a compoſition of things, or parts of things ſeen at
ther time; for ſuch are the Sphinxes, Sirenes, Chimœra's,
taurs, &c.
The Moon hath
no generatings of
things, like as we
have, nor is it
habited by men.
In the Moon may
be a generation of
things different
from ours.
He that had not
heard of the
ment of Water,
could never fancy
to himſelf Ships
and Fiſhes.
SALV. I have very often let my fancy ruminate upon theſe
culations, and in the end, have thought that I had found ſome
things that neither are nor can be in the Moon; but yet I
have not found therein any of thoſe which I believe are, and may
be there, ſave onely in a very general acceptation, namely, things
that adorn it by operating, moving and living; and perhaps in a way

very different from ours; beholding and admiring the greatneſs and
beauty of the World, and of its Maker and Ruler, and with
continual Encomiums ſinging his prayſes; and in ſumme (which is
that which I intend) doing what ſacred Writers ſo frequently
firm, to wit, all the creatures making it their perpetual
ment to laud God.
There may be
ſtances in the
Moon very
rent from ours.
SAGR. Theſe are the things, which ſpeaking in general terms,
may be there; but I would gladly hear you inſtance in ſuch as you
believe neither are nor can be there; which perchance may be
more particularly named.
SALV. Take notice Sagredus that this will be the third time
that we have unawares by running from one thing to another, loſt
our principal ſubject; and if we continue theſe digreſſions, it
will be longere we come to a concluſion of our diſcourſe;
fore I ſhould judg it better to remit this, as alſo ſuch other points,
to be decided on a particular occaſion.
SAGR. Since we are now got into the Moon, if you pleaſe, let
us diſpatch ſuch things as concern her, that ſo we be not forced to
ſuch another tedious journey.
SALV. It ſhall be as you would have it. And to begin with
things more general, I believe that the Lunar Globe is far
rent from the Terreſtrial, though in ſome things they agree. I will
recount firſt their reſemblances, and next their differences. The

Moon is manifeſtly like to the Earth in figure, which undoubtedly
is ſpherical, as may be neceſſarily concluded from the aſpect of its
ſurface, which is perfectly Orbicular, and the manner of its
ceiving the light of the Sun, from which, if its ſurface were flat,
it would come to be all in one and the ſame time illuminated, and
likewiſe again in another inſtant of time obſcured, and not thoſe
parts firſt, which are ſituate towards the Sun, and the reſt
ſively, ſo that in its oppoſition, and not till then, its whole
apparent circumference is enlightned; which would happen quite
contrary, if the viſible ſurface were concave; namely, the

mination would begin from the parts oppoſite or averſe to the Sun.
Secondly ſhe is as the Earth, in her ſelf obſcure and opacous, by
which opacity it is enabled to receive, and reflect the light of the
1Sun; which were it not ſo, it could not do. Thirdly, I hold its

matter to be moſt denſe and ſolid as the Earth is, which I clearly
argue from the unevenneſs of its ſuperficies in moſt places, by means
of the many eminencies and cavities diſcovered therein by help of
the ſeleſcope: of which eminencies there are many all over it,
rectly reſembling our moſt ſharp and craggy mountains, of which
you ſhall there perceive ſome extend and run in ledges of an
dred miles long; others are contracted into rounder forms; and
there are alſo many craggy, ſolitary, ſteep and cliffy rocks. But
that of which there are frequenteſt appearances, are certain Banks
(I uſe this word, becauſe I cannot thing of another that better
preſſeth them) pretty high raiſed, which environ and incloſe fields
of ſeveral bigneſſes, and form ſundry figures, but for the moſt part
circular; many of which have in the midſt a mount raiſed pretty
high, and ſome few are repleniſhed with a matter ſomewhat
ſcure, to wit, like to the great ſpots diſcerned by the bare eye, and
theſe are of the greateſt magnitude; the number moreover of thoſe
that are leſſer and leſſer is very great, and yet almoſt all circular.

Fourthly, like as the ſurface of our Globe is diſtinguiſhed into two
principal parts, namely, into the Terreſtrial and Aquatick: ſo in
the Lunar ſurface we diſcern a great diſtinction of ſome great fields
more reſplendant, and ſome leſs: whoſe aſpect makes me believe,
that that of the Earth would ſeem very like it, beheld by any one
from the Moon, or any other the like diſtance, to be illuminated

by the Sun: and the ſurface of the ſea would appear more
ſcure, and that of the Earth more bright. Fifthly, like as we from
the Earth behold the Moon, one while all illuminated, another

while half; ſometimes more, ſometimes leſs; ſometimes horned,
ſometimes wholly inviſibly; namely, when its juſt under the Sun
beams; ſo that the parts which look towards the Earth are dark:
Thus in every reſpect, one ſtanding in the Moon would ſee the
illumination of the Earths ſurface by the Sun, with the ſame
periods to an hair, and under the ſame changes of figures.
Sixtly, -----
The Firſt
blance between the
Moon and Earth;
which is that of
figure; is proved by
the manner of
ing illuminated by
the Sun.
The Second
formity is the
Moons being
cous as the Earth.
Thirdly, The
ter of the Moon is
denſe and mo
nous as the Earth.
Fourthly, The
Moon is
guiſhed into two
different parts for
clarity and
rity, as the
strial Globe into
Sea and Land.
The ſurface of the
Sea would ſhew at
a diſtance more
ſoure than that of
the Earth.
Fiftly,
tion of ſigures in
the Earth, like to
thoſe of the Moon,
and made with the
ſame periods.
SAGR. Stay a little, Salviatus; That the illumination of
the Earth, as to the ſeveral figures, would repreſent it ſelf to a perſon
placed in the Moon, like in all things to that which we diſcover in
the Moon, I underſtand very well, but yet I cannot conceive how
it ſhall appear to be done in the ſame period; ſeeing that that
which the Suns illumination doth in the Lunar ſuperficies in a
month, it doth in the Terreſtrial in twenty four hours.
SALV. Its true, the effect of the Sun about the illuminating
theſe two bodies, and repleniſhing with its ſplendor their whole
ſurfaces, is diſpatch'd in the Earth in a Natural day, and in the
Moon in a Month; but the variation of the figures in which the
1illuminated parts of the Terreſtrial ſuperficies appear beheld from
the Moon, depends not on this alone, but on the divers aſpects
which the Moon is ſtill changing with the Sun; ſo that, if for
ſtance, the Moon punctually followed the motion of the Sun, and
ſtood, for example, always in a direct line between it and the
Earth, in that aſpect which we call Conjunction, it looking always
to the ſame Hemiſphere of the Earth which the Sun looks unto,
ſhe would behold the ſame all light: as on the contrary, if it ſhould
always ſtay in Oppoſition to the Sun, it would never behold the
Earth, of which the dark part would be continually turn'd towards
the Moon, and therefore inviſible. But when the Moon is in
Quadrature of the Sun, that half of the Terreſtrial Hemiſphere
poſed to the ſight of the Moon which is towards the Sun, is
nous; and the other towards the contrary is obſcure: and
fore the illuminated part of the Earth would repreſent it ſelf to the
Moon in a ſemi-circular figure.
SAGR. I clearly perceive all this, and underſtand very well,
that the Moon departing from its Oppoſition to the Sun, where it
ſaw no part of the illumination of the Terreſtrial ſuperficies, and
approaching day by day nearer the Sun, ſhe begins by little and
little to diſcover ſome part of the face of the illuminated Earth;
and that which appeareth of it ſhall reſemble a thin ſickle, in regard
the figure of the Earth is round: and the Moon thus acquiring by
its motion day by day greater proximity to the Sun, ſucceſſively
diſcovers more and more of the Terreſtrial Hemiſphere enlightned,
ſo that at the Quadrature there is juſt half of it viſible, inſomuch
that we may ſee the other part of her: continuing next to proceed
towards the Conjunction, it ſucceſſively diſcovers more and more
of its ſurface to be illuminated, and in fine, at the time of
ction ſeeth the whole Hemiſphere enlightned. And in ſhort, I
very well conceive, that what befalls the Inhabitants of the Earth,
in beholding the changes of the Moon, would happen to him that
from the Moon ſhould obſerve the Earth; but in a contrary order,
namely, that when the Moon is to us at her full, and in Oppoſition
to the Sun, then the Earth would be in Conjunction with the Sun,
and wholly obſcure and inviſible; on the contrary, that poſition
which is to us a Conjunction of the Moon with the Sun, and for
that cauſe a Moon ſilent and unſeen, would be there an Oppoſition
of the Earth to the Sun, and, to ſo ſpeak, Full Earth, to wit, all
enlightned. And laſtly, look what part of the Lunar ſurface
pears to us from time to time illuminated, ſo much of the Earth
in the ſame time ſhall you behold from the Moon to be obſcured:
and look how much of the Moon is to us deprived of light, ſo much
of the Earth is to the Moon illuminated. In one thing yet theſe
mutual operations in my judgment ſeem to differ, and it is, that it
1being ſuppoſed, and not granted, that ſome one being placed in the
Moon to obſerve the Earth, he would every day ſee the whole
Terreſtrial ſuperficies, by means of the Moons going about the
Earth in twenty four or twenty five hours; but we never ſee but
half of the Moon, ſince it revolves not in it ſelf, as it muſt do to
be ſeen in every part of it.
SALV. So that this, befals not contrarily, namely, that her
volving in her ſelf, is the cauſe that we ſee not the other half of
her, for ſo it would be neceſſary it ſhould be, if ſhe had the
cle. But what other difference have you behind, to exchange for
this which you have named?
SAGR. Let me ſee; Well for the preſent I cannot think of
any other.
SALV. And what if the Earth (as you have well noted) ſeeth

no more than half the Moon, whereas from the Moon one may ſee
all the Earth; and on the contrary, all the Earth ſeeth the Moon, and
but onely half of it ſeeth the Earth? For the inhabitants, to ſo ſpeak,
of the ſuperior Hemiſphere of the Moon, which is to us inviſible,
are deprived of the ſight of the Earth: and theſe haply are the
Anticthones. But here I remember a particular accident, newly
obſerved by our Academian, in the Moon, from whch are gathered

two neceſſary conſequences; one is, that we ſee ſomewhat more
than half of the Moon; and the other is, that the motion of the
Moon hath exact concentricity with the Earth: and thus he finds
the Phœnomenon and obſervation. When the Moon hath a
reſpondence and natural ſympathy with the Earth, towards which
it hath its aſpect in ſuch a determinate part, it is neceſſary that the
right line which conjoyns their centers, do paſſe ever by the ſame
point of the Moons ſuperficies; ſo that, who ſo ſhall from the
ter of the Earth behold the ſame, ſhall alwayes ſee the ſame
Diſcus or Face of the Moon punctually determined by one and
the ſame circumference; But if a man be placed upon the
ſtrial ſurface, the ray which from his eye paſſeth to the centre of the
Lunar Globe, will not paſs by the ſame point of its ſuperficies, by
which the line paſſeth that is drawn from the centre of the Earth
to that of the Moon, ſave onely when it is vertical to him: but
the Moon being placed in the Eaſt, or in the Weſt, the point of
incidence of the viſual ray, is higher than that of the line which
conjoyns the centres; and therefore the obſerver may diſcern
ſome part of the Lunar Hemiſphere towards the upper
rence, and alike part of the other is inviſible: they are
ble and undiſcernable, in reſpect of the Hemiſphere beheld from
the true centre of the Earth: and becauſe the part of the Moons
circumference, which is ſuperiour in its riſing, is nethermoſt in its
ſetting; therefore the difference of the ſaid ſuperiour and
1our parts muſt needs be very obſervable; certain ſpots and other
notable things in thoſe parts, being one while diſcernable, and
another while not. A like variation may alſo be obſerved towards
the North and South extremities of the ſame Diſcus (or Surface)
according as the Moons poſition is in one or the other Section of
its Dragon; For, if it be North, ſome of its parts towards the
North are hid, and ſome of thoſe parts towards the South are
diſcovered, and ſo on the contrary. Now that theſe

ces are really true, is verified by the Teleſcope, for there be in
the Moon two remarkable ſpots, one of which, when the Moon
is in the meridian, is ſituate to the Northweſt, and the other is
almoſt diametrically oppoſite unto it; and the firſt of theſe is
ſible even without the Teleſcope; but the other is not. That
wards the Northweſt is a reaſonable great ſpot of oval figure,
parated from the other great ones; the oppoſite one is leſſe, and
alſo ſevered from the biggeſt, and ſituate in a very cleer field; in
both theſe we may manifeſtly diſcern the foreſaid variations, and
ſee them one after another; now neer the edge or limb of the
Lunar Diſcus, and anon remote, with ſo great difference that
the diſtance betwixt the Northweſt and the circumference of the
Diſcus is more than twice as great at one time, as at the other;
and as to the ſecond ſpot (becauſe it is neerer to the
rence) ſuch mutation importeth more, than twice ſo much in the
former. Hence its manifeſt, that the Moon, as if it were drawn
by a magnetick vertue, conſtantly beholds the Terreſtrial Globe
with one and the ſame aſpect, never deviating from the ſame.
All the Earth
ſeeth half onely of
the Moon, & the
half onely of the
Moon ſeeth all the
Earth.
From the Earth
we ſee more than
half the Lunar
Globe.
Two ſpots in the
Moon, by which it
is perceived that
ſhe hath respect to
the centre of the
Earth in her
tion.
SAGR. Oh! when will there be an end put to the new
ſervations aud diſcoveries of this admirable Inſtrument?
SALV. If this ſucceed according to the progreſſe of other great
inventions, it is to be hoped, that in proceſſe of time, one may
arrive to the ſight of things, to us at preſent not to be imagined.

But returning to our firſt diſcourſe, I ſay for the ſixth reſemblance
betwixt the Moon and Earth, that as the Moon for a great part
of time, ſupplies the want of the Suns light, and makes the
nights, by the reflection of its own, reaſonable clear; ſo the
Earth, in recompence, affordeth it when it ſtands in moſt need,
by reflecting the Solar rayes, a very cleer illumination, and ſo
much, in my opinion, greater than that which cometh from her to
us, by how much the ſuperficies of the Earth is greater than that
of the Moon.
Sixthly, The
Earth and Moon
interchangeably do
illuminate.
SAGR. Hold there, Salviatus hold there, and permit me the
pleaſure of relating to you, how at this firſt hint I have penetrated
the cauſe of an accident, which I have a thouſand times thought

upon, but could never find out. You would ſay, that the
fect light which is ſeen in the Moon, eſpecially when it is horned,
1comes from the reflection of the light of the Sun on the
cies of the Earth and Sea; and that light is more clear, by how
much the horns are leſſe, for then the luminous part of the Earth,
beheld by the Moon, is greater, according to that which was
a little before proved; to wit, that the luminous part of the Earth,
expoſed to the Moon, is alway as great as the obſcure part of
the Moon, that is viſible to the Earth; whereupon, at ſuch time
as the Moon is ſharp-forked, and conſequently its tenebrous part
great, great alſo is the illuminated part of the Earth beheld from
the Moon, and its reflection of light ſo much the more potent.
Light reflected
from the Earth
to the Moon.
SALV. This is exactly the ſame with what I was about to ſay.
In a word, it is a great pleaſure to ſpeak with perſons judicious
and apprehenſive, and the rather to me, for that whileſt others
converſe and diſcourſe touching Axiomatical truths, I have
ny times creeping into my brain ſuch arduous Paradoxes, that
though I have a thouſand times rehearſed this which you at the
ry firſt, have of your ſelf apprehended, yet could I never beat
it into mens brains.
SIMPL. If you mean by your not being able to perſwade them
to it, that you could not make them underſtand the ſame, I
much wonder thereat, and am very confident that if they did
not underſtand it by your demonſtration (your way of expreſſion,
being, in my judgment, very plain) they would very hardly have
apprehended it upon the explication of any other man; but if
you mean you have not perſwaded them, ſo as to make them
lieve it, I wonder not, in the leaſt, at this; for I confeſſe my
ſelf to be one of thoſe who underſtand your diſcourſes, but
am not ſatisfied therewith; for there are in this, and ſome of
the other ſix congruities, or reſemblances, many difficulties,
which I ſhall inſtance in, when you have gone through them
all.
SALV. The deſire I have to find out any truth, in the acquiſt
whereof the objections of intelligent perſons (ſuch as your ſelf)
may much aſſiſt me, will cauſe me to be very brief in diſpatching
that which remains. For a ſeventh conformity, take their

procal reſponſion as well to injuries, as favours; whereby the
Moon, which very often in the height of its illumination, by the
interpoſure of the Earth betwixt it and the Sun, is deprived of
light, and eclipſed, doth by way of revenge; in like manner,
terpoſe it ſelf between the Earth and the Sun, and with its ſhadow
obſcureth the Earth; and although the revenge be not
able to the injury, for that the Moon often continueth, and
that for a reaſonable long time, wholly immerſed in the Earths
ſhadow, but never was the Earth wholly, nor for any long time,
eclipſed by the Moon; yet, nevertheleſſe, having reſpect to the
1ſmalneſſe of the body of this, in compariſon to the magnitude
of the other, it cannot be denied but that the will and as it
were valour of this, is very great. Thus much for their
gruities or reſemblances. It ſhould next follow that we diſcourſe
touching their diſparity; but becauſe Simplicius will favour us
with his objections againſt the former, its neceſſary that we hear
and examine them, before we proceed any farther.
Seventhly, The
Earth and Moon
do mutually eclipſe.
SAGR. And the rather, becauſe it is to be ſuppoſed that
Simplicius will not any wayes oppoſe the diſparities, and
gruities betwixt the Earth and Moon, ſince that he accounts their
ſubſtances extremely different.
SIMPL. Amongſt the reſemblances by you recited, in the
rallel you make betwixt the Earth and Moon, I find that I can
admit none confidently ſave onely the firſt, and two others; I
grant the firſt, namely, the ſpherical figure; howbeit, even in
this there is ſome kind of difference, for that I hold that of the
Moon to be very ſmooth and even, as a looking-glaſſe,
as, we find and feel this of the Earth to be extraordinary
ous and rugged; but this belonging to the inequality of
cies, it ſhall be anon conſidered, in another of thoſe
ces by you alledged; I ſhall therefore reſerve what I have to ſay
thereof, till I come to the conſideration of that. Of what you
affirm next, that the Moon ſeemeth, as you ſay in your ſecond
Reſemblance, opacous and obſcure in its ſelf, like the Earth; I
admit not any more than the firſt attribute of opacity, of which
the Eclipſes of the Sun aſſure me. For were the Moon
rent, the air in the total obſcuration of the Sun, would not
come ſo duskiſh, as at ſuch a time it is, but by means of the
tranſparency of the body of the Moon, a refracted light would
paſſe through it, as we ſee it doth through the thickeſt clouds. But
as to the obſcurity, I believe not that the Moon is wholly
ved of light, as the Earth; nay, that clarity which is ſeen in the
remainder of its Diſcus, over and above the ſmall creſcent
lightened by the Sun, I repute to be its proper and natural light,

and not a reflection of the Earth, which I eſteem unable, by
reaſon of its aſperity (craggineſſe) and obſcurity, to reflect the
raies of the Sun. In the third Parallel I aſſent unto you in one

part, and diſſent in another: I agree in judging the body of the
Moon to be moſt ſolid and hard, like the Earth, yea much more;

for if from Ariſtotle we receive that the Heavens are impenetrable,
and the Stars the moſt denſe parts of Heaven, it muſt neceſſarily
follow, that they are moſt ſolid and moſt impenetrable.
The ſecond clarity
of the Moon
ſteemed to be its
native light.
The Earth unable
to reflect the Suns
raies.
The ſubſtance of
the Heavens
netrable,
ing to Ariſtotle.
SAGR. What excellent matter would the Heavens afford us for
to make Pallaces of, if we could procure a ſubſtance ſo hard and ſo
tranſparent?
1
SALV. Rather how improper, for being by its tranſparence,
wholly inviſible, a man would not be able without ſtumbling at
the threſholds, and breaking his head againſt the Walls, to paſs
from room to room.
SAGR. This danger would not befall him, if it be true, as ſome

Peripateticks ſay, that it is intangible: and if one cannot
touch it, much leſs can it hurt him.
The ſubstance of
Heaven
ble.
SALV. This would not ſerve the turn, for though the matter
of the Heavens cannot be toucht, as wanting tangible qualities:
yet may it eaſily touch the elementary bodies; and to offend us
it is as ſufficient that it ſtrike us, nay worſe, than if we ſhould
ſtrike it. But let us leave theſe Pallaces, or, to ſay better, theſe
Caſtles in the air, and not interrupt Simplicius.
SIMPL. The queſtion which you have ſo caſually ſtarted, is one
of the moſt difficulty that is diſputed in Philoſophy; and I have
on that ſubject moſt excellent conceits of a very learned Doctor
of Padoua, but it is not now time to enter upon them. Therefore
returning to our purpoſe, I ſay that the Moon, in my opinion, is
much more ſolid than the Earth, but do not infer the ſame, as you
do, from the craggineſs and montuoſity of its ſuperficies; but

rather from the contrary, namely, from its aptitude to receive (as
we ſee it experimented in the hardeſt ſtones) a poliſh and luſtre
exceeding that of the ſmootheſt glaſs, for ſuch neceſſarily muſt
its ſuperficies be, to render it apt to make ſo lively reflection of
the Suns rays. And for thoſe appearances which you mention,
of Mountains, Cliffs, Hills, Valleys, &c. they are all illuſions:
and I have been preſent at certain publick diſputes, where I have
heard it ſtrongly maintained againſt theſe introducers of novelties,

that ſuch appearances proceed from nothing elſe, but from the
equal diſtribution of the opacous and perſpicuous parts, of which
the Moon is inwardly and outwardly compoſed: as we ſee it
often fall out in chryſtal, amber, and many other precious ſtones
of perfect luſtre; in which by reaſon of the opacity of ſome parts,
and the tranſparency of others, there doth appear ſeveral
vities and prominencies. In the fourth reſemblance, I grant, that
the ſuperficies of Terreſtrial Globe beheld from afar, would make
two different appearances, namely, one more clear, the other more
dark; but I believe that ſuch diverſity would ſucceed quite
trary to what you ſay; that is, I hold that the ſurface of the
ter would appear lucid, becauſe that it is ſmooth and tranſparent;
and that of the Earth would appear obſcure, by reaſon of its
pacity and ſcabroſity, ill accommodated for reflecting the light of
the Sun. Concernïng the fifth compariſon, I grant it wholly, and
am able, in caſe the Earth did ſhine as the Moon, to ſhow the
ſame to any one that ſhould from thence above behold it,
1ſented by figures anſwerable to thoſe which we ſee in the Moon:
I comprehend alſo, how the period of its illumination and
tion of figure, would be monthly, albeit the Sun revolves round
about it in twenty four hours: and laſtly, I do not ſcruple to
admit, that the half onely of the Moon ſeeth all the Earth, and
that all the Earth ſeeth but onely half of the Moon. For what
remains, I repute it moſt falſe, that the Moon can receive light
from the Earth, which is moſt obſcure, opacous, and utterly
apt to reflect the Suns light, as the Moon doth reflect it to us: and
as I have ſaid, I hold that that light which we ſee in the
der of the Moons face (the ſplendid creſcents ſubducted) by the
illumination, is the proper and natural light of the Moon, and no
eaſie matter would induce me to believe otherwiſe. The ſeventh,
touching the mutual Eclipſes, may be alſo admitted; howbeit
that is wont to be called the eclipſe of the Sun, which you are
pleaſed to phraſe the eclipſe of the Earth. And this is what I
have at this time to ſay in oppoſition to your ſeven congruities
or reſemblances, to which objections, if you are minded to make
any reply, I ſhall willingly hear you.
The ſuperficies of
the Moon more
ſleek than any
Looking-glaß.
The eminencies
and cavities in the
Moon are illuſions
of its opacous and
perspicuous parts.
SALV. If I have well apprehended what you have anſwered, it
ſeems to me, that there ſtill remains in controverſie between us,
tain conditions, which I made common betwixt the Moon & Earth,
and they are theſe; You eſteem the Moon to be ſmooth and poliſht,
as a Looking-glaſs, and as ſuch, able to reflect the Suns light; and
contrarily, the Earth, by reaſon of its montuoſity, unable to make
ſuch reflection: You yield the Moon to be ſolid and hard, and that
you argue from its being ſmooth and polite, and not from its being
montuous; and for its appearing montuous, you aſſign as the
cauſe, that it conſiſts of parts more and leſs opacous and
cuous. And laſtly, you eſteem that ſecondary light, to be proper
to the Moon, and not reflected from the Earth; howbeit you
ſeem not to deny the ſea, as being of a ſmooth ſurface, ſome
kind of reflection. As to the convincing you of that error, that
the reflection of the Moon is made, as it were, like that of a
Looking-glaſs, I have ſmall hope, whilſt I ſee, that what hath

been read in the ^{*} Saggiator and in the Solar Letters of our
mon Friend, hath profited nothing in your judgment, if haply
you have attentively read what he hath there written on this
ject.
* Il Saggiatore, &
Lettere Solari,
two Treatiſes of
Galilæus.
SIMPL. I have peruſed the ſame ſo ſuperficially, according to
the ſmall time of leaſure allowed me from more ſolid ſtudies;
therefore, if you think you can, either by repeating ſome of thoſe
reaſons, or by alledging others, reſolve me theſe doubts, I will
hearken to them attentively.
SALV. I will tell you what comes into my mind upon the
1inſtant, and its poſſible it may be a commixtion of my own
ceipts; and thoſe which I have ſometime read in the fore-ſaid
Books, by which I well remember, that I was then perfectly
ſatisfied, although the concluſions, at firſt ſight ſeem'd unto me
ſtrange Paradoxes. We enquire Simplicius, whether to the
king a reflection of light, like that which we receive from the
Moon, it be neceſſary that the ſuperficies from whence the
ction commeth, be ſo ſmooth and polite, as the face of a
Glaſſe, or whether a ſuperficies not ſmooth or poliſht, but rough
and uneven, be more apt for ſuch a purpoſe. Now ſuppoſing
two reflections ſhould come unto us, one more bright, the other
leſſe, from two ſuperficies oppoſite unto us, I demand of you,
which of the two ſuperficies you think would repreſent it ſelf to
our ſight, to be the cleareſt, and which the obſcureſt.
SIMPL. I am very confident, that that ſame, which moſt
cibly reflected the light upon me, would ſhew its ſelf in its aſpect
the clearer, and the other darker.
SALV. Be pleaſed to take that Glaſſe which hangs on yonder

Wall, and let us go out into the Court-yard. Come Sagredus.
Now hang the glaſſe yonder, againſt that ſame Wall, on which
the Sun ſhines, and now let us with-draw our ſelves into the ſhade.
See yonder two ſuperficies beaten by the Sun, namely, the Wall
and the Glaſſe. Tell me now which appears cleareſt unto you,
that of the Wall or that of the Glaſſe? Why do you not anſwer
me?
It is proved at
large that the
Moons ſurface is
ſharp.
SAGR. I leave the reply to Simplicius, who made the
on; but I, for my own part, am perſwaded upon this ſmall
ginning of the experiment, that the Moon muſt be of a very
poliſht ſurface.
SALV. What ſay you Simplicius, if you were to depaint that
Wall, and that Glaſſe faſtened unto it, where would you uſe
your darkeſt colours, in deſigning the Wall, or elſe in painting
the Looking-Glaſſe.
SIMPL. Much the darker in depainting the Glaſſe.
SALV. Now if from the ſuperficies, which repreſents it ſelf
more clear, there proceedeth a more powerful reflection of light,
the Wall will more forcibly reflect the raies of the Sun, than the
Glaſſe.
SIMPL. Very well, Sir, have you ever a better experiment
than this? you have placed us where the Glaſſe doth not
berate upon us; but come along with me a little this way; how,
will you not ſtir?
SAGR. You perhaps ſeek the place of the reflection, which the
Glaſſe makth.
SIMPL. I do ſo.
1
SAGR. Why look you, there it is upon the oppoſite Wall, juſt
as big as the Glaſſe, and little leſſe bright than if the Sun had
directly ſhined upon it.
SIMPL. Come hither therefore, and ſee from hence the
face of the Glaſſe, and tell me whether you think it more
ſcure than that of the Wall.
SAGR. Look on it your ſelf, for I have no mind at this time,
to dazle my eyes; and I know very well, without ſeeing it,
that it there appears as ſplendid and bright as the Sun it ſelf, or
little leſſe.
SIMPL. What ſay you therefore, is the reflection of a Glaſſe
leſſe powerful than that of a Wall? I ſee, that in this oppoſite
Wall, where the reflection of the other illuminated Wall comes,
together with that of the Glaſſe, this of the Glaſſe is much
clearer; and I ſee likewiſe, that, from this place where I ſtand,
the glaſſe it ſelf appears with much more luſtre than the Wall.
SALV. You have prevented me with your ſubtlety; for I ſtood
in need of this very obſervation to demonſtrate what remains.
You ſee then the difference which happens betwixt the two
ctions made by the two ſuperficies of the Wall and Glaſſe,
cu'ſt in the ſelf-ſame manner, by the rayes of the Sun; and you
ſee, how the reflection which comes from the Wall, diffuſeth it
ſelf towards all the parts oppoſite to it, but that of the Glaſſe
goeth towards one part onely, not at all bigger than the Glaſſe
it ſelf: you ſee likewiſe, how the ſuperficies of the Wall, beheld
from what part ſoever, alwayes ſhews it ſelf of one and the ſame
cleerneſſe, and every way, much clearer than that of the Glaſſe,
excepting only in that little place, on which the Glaſſes reflection
reverberates, for from thence indeed the Glaſſe appears much more
lucid than the Wall. By theſe ſo ſenſible, and palpable
ments, my thinks one may ſoon come to know, whether the
reflection which the Moon ſends upon us, proceed as from a
Glaſſe, or elſe, as from a Wall, that is, from a ſmooth
cies, or a rugged.
SAGR. If I were in the Moon it ſelf, I think I could not with
my hands more plainly feel the unevenneſſe of its ſuperficies, than
I do now perceive it, by apprehending your diſcourſe. The Moon
beheld in any poſture, in reſpect of the Sun and us, ſheweth us
its ſuperficies, touch't by the Suns rayes, alwayes equally clear;
an effect, which anſwers to an hair that of the Wall, which
held from what place ſoever, appeareth equally bright, and
fereth from the Glaſſe, which from one place onely appeareth
cid, and from all others obſcure. Moreover, the light which
cometh to me from the reflection of the Wall, is tollerable,
and weak, in compariſon of that of the Glaſſe, which is little
1leſſe forcible and offenſive to the ſight, than that primary and
direct light of the Sun. And thus without trouble do we behold
the face of the Moon; which were it as a Glaſſe, it appearing to
us by reaſon of its vicinity, as big as the Sun it ſelf, its ſplendor
would be abſolutely intollerable, and would ſeem as if we beheld
another Sun.
SALV. Aſcribe not, I beſeech you Sagredus, more to my
monſtration, than it produceth. I will oppoſe you with an inſtance,
which I ſee not well how you can eaſily reſolve. You inſiſt upon it
as a grand difference between the Moon and Glaſſe, that it emits
its reflection towards all parts equally, as doth the Wall;
as the Glaſſe caſts it upon one onely determinate place; and from
hence you conclude the Moon to be like to the Wall, and not to
the Glaſſe: But I muſt tell you, that that ſame Glaſſe caſts its

reflection on one place onely, becauſe its ſurface is flat, and the
reflex rayes being to depart at angles equal to thoſe of the rayes
of incidence, it muſt follow that from a plane or flat ſuperficies,
they do depart unitedly towards the ſame place; but in regard
that the ſuperficies of the Moon is not plain, but ſpherical, and
the incident rayes upon ſuch a ſuperficies, being to reflect
ſelves at angles equal to thoſe of the incidence towards all parts,
by means of the infinity of the inclinations which compoſe the
ſpherical ſuperficies, therefore the Moon may ſend forth its
on every way; and there is no neceſſity for its repercuſſion upon one
place onely, as that Glaſſe which is flat.
Flat
glaſſes caſt forth
the reflection
wards but one
place, but the
ſpherical every
way.
SIMPL. This is one of the very ſame objections, which I
tended to have made againſt him.
SAGR. If this be one, you had need have more of them; yet
I tell you, that as to this firſt, it ſeems to me to make more
gainſt you, than for you.
SIMPL. You have pronounced as a thing manifeſt, that the
ction made by that Wall, is as cleer and lucid as that which the
Moon ſends forth, and I eſteem it nothing in compariſon thereto.
“For, in this buſineſſe of the illumination, its requiſite to reſpect,
and to diſtinguiſh the Sphere of Activity; and who queſtions

but the Cœleſtial bodies have greater Spheres of activity, than
theſe our elementary, frail, and mortal ones? and that Wall,
finally, what elſe is it but a little obſcure Earth, unapt to
ſhine?”
The ſphere of
Activity greater
in the Cœleſtial
bodies than in
mentary.
SAGR. And here alſo I believe, that you very much deceive your
felf. But I come to the firſt objection moved by Salviatus; and
I conſider, that to make a body appear unto us luminous, it
ficeth not that the rayes of the illuminating body fall upon it,
but it is moreover requiſite that the reflex rayes arrive to our
eye; as is manifeſtly ſeen in the example of that Glaſſe, upon
1which, without queſtion, the illuminating rayes of the Sun do
come; yet nevertheleſſe, it appears not to us bright and ſhining,
unleſſe we ſet our eye in that particular place, where the
ction arriveth. Now let us conſider what would ſucceed, were
the glaſſe of a ſpherical figure; for without doubt, we ſhould
find, that of the reflection made by the whole ſurface
ted, that to be but a very ſmall part, which arriveth to the eye
of a particular beholder; by reaſon that that is but an
rable particle of the whole ſpherical ſuperficies, the inclination
of which caſts the ray to the particular place of the eye; whence
the part of the ſpherical ſuperficies, which ſhews it ſelf ſhining
to the eye, muſt needs be very ſmall; all the reſt being
ſented obſcure. So that were the Moon ſmooth, as a

glaſſe, a very ſmall part would be ſeen by any particular eye to
be illuſtrated by the Sun, although its whole Hemiſphere were
poſed to the Suns rayes; and the reſt would appear to the eye of
the beholder as not illuminated, and therefore inviſible; and
finally, the whole Moon would be likewiſe inviſible, for ſo much
as that particle, whence the reflection ſhould come, by reaſon of
its ſmalneſſe and remoteneſſe, would be loſt. And as it would be
inviſible to the eye, ſo would it not afford any light; for it is
together impoſſible, that a bright body ſhould take away our
darkneſſe by its ſplendor, and we not to ſee it.
The Moon if it
were ſmooth, like a
ſpherical glaſſe,
would be inviſible.
SALV. Stay good Sagredus, for I ſee ſome emotions in
the face and eyes of Simplicius, which are to me as indices that
he is not either very apprehenſive of, or ſatisfied with this which
you, with admirable proof, and abſolute truth have ſpoken.
And yet I now call to mind, that I can by another experiment
remove all ſcruple. I have ſeen above in a Chamber, a great
ſpherical Looking-glaſſe; let us ſend for it hither, and whileſt it
is in bringing, let Simplicius return to conſider, how great the
clarity is which cometh to the Wall here, under the penthouſe,
from the reflection of the flat glaſſe.
SIMPL. I ſee it is little leſſe ſhining, than if the Sun had
rectly beat upon it.
SALV. So indeed it is. Now tell me, if taking away that ſmall
flat glaſſe, we ſhould put that great ſpherical one in the ſame
place, what effect (think you) would its reflection have upon the
ſame Wall?
SIMPL. I believe that it would eject upon it a far greater and
more diffuſed light.
SALV. But if the illumination ſhould be nothing, or ſo
ſmall, that you would ſcarſe diſcern it, what would you ſay
then?
SIMPL. When I have ſeen the effect, I will bethink my ſelf
of an anſwer.
1
SALV. See here is the glaſſe, which I would have to be placed
cloſe to the other. But firſt let us go yonder towards the reflection
of that flat one, and attentively obſerve its clarity; ſee how
bright it is here where it ſhines, and how diſtinctly one may diſcern
theſe ſmall unevenneſſes in the Wall.
SIMPL. I have ſeen and very well obſerved the ſame, now place
the other glaſſe by the ſide of the firſt.
SALV. See where it is. It was placed there aſſoon as you
gan to look upon the Walls ſmall unevenneſſes, and you
ved it not, ſo great was the encreaſe of the light all over the reſt of
the Wall. Now take away the flat glaſſe. Behold now all
ction removed, though the great convex glaſſe ſtill remaineth.
Remove this alſo, and place it there again if you pleaſe, and you
ſhall ſee no alteration of light in all the Wall. See here then
monſtrated to ſenſe, that the reflection of the Sun, made upon a
ſpherical convex glaſſe, doth not ſenſibly illuminate the places neer
unto it. Now what ſay you to this experiment?
SIMPL. I am afraid that there may be ſome Leigerdemain,
uſed in this affair; yet in beholding that glaſſe I ſee it dart forth
a great ſplendor, which dazleth my eyes; and that which
ports moſt of all, I ſee it from what place ſoever I look upon it;
and I ſee it go changing ſituation upon the ſuperficies of the glaſſe,
which way ſoever I place my ſelf to look upon it; a neceſſary
gument, that the light is livelily reflected towards every ſide, and
conſequently, as ſtrongly upon all that Wall, as upon my eye.
SALV. Now you ſee how cautiouſly and reſervedly you ought
to proceed in lending your aſſent to that, which diſcourſe alone
preſenteth to you. There is no doubt but that this which you ſay,
carrieth with it probability enough, yet you may ſee, how
ble experience proves the contrary.
SIMPL. How then doth this come to paſs?
SALV. I will deliver you my thoughts thereof, but I cannot
tell how you may be pleaſ'd therewith. And firſt, that lively
ſplendor which you ſee upon the glaſs, and which you think
pieth a good part thereof, is nothing near ſo great, nay is very
ceeding ſmall; but its livelineſs occaſioneth in your eye, (by means
of the reflection made on the humidity of the extream parts of the
eye-brows, which diſtendeth upon the pupil) an adventitious
ation, like to that blaze which we think we ſee about the flame of
a candle placed at ſome diſtance; or if you will, you may
reſemble it to the adventitious ſplendor of a ſtar; for if you ſhould

compare the ſmall body v. g. of the Canicula, ſeen in the day time
with the Teleſcope, when it is ſeen without ſuch irradiation, with
the ſame ſeen by night by the eye it ſelf, you will doubtleſs
prehend that being irradiated, it appeareth above a thouſand
1times bigger than the naked and real body: and a like or greater
augmentation doth the image of the Sun make, which you ſee in
that glaſs. I ſay greater, for that it is more lively than the ſtar,
as is manifeſt from our being able to behold the ſtar with much
leſs offence, than this reflection of the glaſs. The reverberation
therefore which is to diſpere it ſelf all over this wall, cometh from
a ſmall part of that glaſs, and that which even now came from
the whole flat glaſs diſperſed and reſtrain'd it ſelf to a very ſmall
part of the ſaid wall. What wonder is it then, that the firſt
flection very lively illuminates, and that this other is almoſt
perceptible?
The ſmall body of
the ſtars fringed
round about with
rays, appeareth
ry much biggerthan
plain and naked,
and in its native
clarity.
SIMPL. I find my ſelf more perplexed than ever, and there
preſents it ſelf unto me the other difficulty, how it can be that
that wall, being of a matter ſo obſcure, and of a ſuperficies ſo
poliſh'd, ſhould be able to dart from it greater light, than a glaſs
very ſmooth and polite.
SALV. Greater light it is not, but more univerſal; for as to
the degree of brightneſs, you ſee that the reflection of that ſmall
flat glaſs, where it beamed forth yonder under the ſhadow of the
penthouſe, illuminateth very much; and the reſt of the wall which
receiveth the reflection of the wall on which the glaſs is placed,
is not in any great meaſure illuminated, as was the ſmall part on
which the reflection of the glaſs fell. And if you would
ſtand the whole of this buſineſs, you muſt conſider that the

ficies of that wall's being rough, is the ſame as if it were
ſed of innumerable ſmall ſuperficies, diſpoſed according to
numerable diverſities of inclinations: amongſt which it
rily happens, that there are many diſpoſed to ſend forth their
reflex rays from them into ſuch a place, many others into another:
and in ſum, there is not any place to which there comes not very
many rays, reflected from very many ſmall ſuperficies, diſperſed
throughout the whole ſuperficies of the rugged body, upon which
the rays of the Sun fall. From which it neceſſarily
eth, That upon any, whatſoever, part of any ſuperficies,
oppoſed to that which receiveth the primary incident rays,
there is produced reflex rays, and conſequently
nation. There doth alſo follow thereupon, That the ſame
body upon which the illuminating rays fall, beheld from
whatſoever place, appeareth all illuminated and ſhining: and
therefore the Moon, as being of a ſuperficies rugged and

not ſmooth, beameth forth the light of the Sun on every
ſide, and to all beholders appeareth equally lucid. But if
the ſurface of it, being ſpherical, were alſo ſmooth as a glaſs, it
would become wholly inviſible; foraſmuch as that ſmall part,
from which the image of the Sun ſhould be reflected unto the eye
1of a particular perſon, by reaſon of its great diſtance would be
viſible, as I have ſaid before.
The reflex light
of uneven bodies, is
more univerſal
than that of the
ſmooth, & why.
The Moon, if it
were ſmooth and
ſleek, would be
viſible.
SIMPL. I am very apprehenſive of your diſcourſe; yet
thinks I am able to reſolve the ſame with very little trouble; and
eaſily to maintain, that the Moon is rotund and polite, and that it
reflects the Suns light unto us in manner of a glaſs; nor
fore ought the image of the Sun to be ſeen in the middle of it,
aſmuch as the ſpecies of the Sun it ſelf admits not its ſmall figure
to be ſeen at ſo great a diſtance, but the light produced by the
Sun may help us to conceive that it illuminateth the whole
nar Body: a like effect we may ſee in a plate gilded and well
polliſh'd, which touch't by a luminous body, appeareth to him
that beholds it at ſome diſtance to be all ſhining; and onely near
at hand one may diſcover in the middle of it the ſmall image of
the luminous body.”
SALV. Ingenuouſly confeſſing my dullneſs of apprehenſion,
I muſt tell you, that I underſtand not any thing of this your
courſe, ſave onely what concerns the gilt plate: and if you permit
me to ſpeak freely, I have a great conceit that you alſo underſtand
not the ſame, but have learnt by heart thoſe words written by ſome
one out of a deſire of contradiction, and to ſhew himſelf more
ligent than his adverſary; but it muſt be to thoſe, which to appear
alſo more wiſe, applaud that which they do not underſtand, and
entertain a greater conceit of perſons, the leſs they are by them
underſtood: and the writer himſelf may be one of thoſe (of which
there are many) who write what they do not underſtand, and

conſequently underſtand not what they write. Therefore,
mitting the reſt, I reply, as to the gilt plate, that if it be flat and
not very big, it may appear at a diſtance very bright, whilſt a great
light beameth upon it, but yet it muſt be when the eye is in a
terminate line, namely in that of the reflex rays: and it will
pear the more ſhining, if it were v. g. of ſilver, by means of its
being burniſhed, and apt through the great denſity of the metal,
to receive a perfect poliſh. And though its ſuperficies, being very
well brightned, were not exactly plain, but ſhould have various
clinations, yet then alſo would its ſplendor be ſeen many ways;
namely, from as many places as the various reflections, made by
the ſeveral ſuperficies, do reach: for therefore are Diamonds

ground to many ſides, that ſo their pleaſing luſtre might be beheld
from many places. But if the Plate were very big, though it ſhould
be all plain, yet would it not at a diſtance appear all over ſhining:
and the better to expreſs my ſelf, Let us ſuppoſe a very large gilt
plate expoſed to the Sun, it will ſhew to an eye far diſtant, the
image of the Sun, to occupy no more but a certain part of the ſaid
plate; to wit, that from whence the reflection of the incident
1ſolar rays come: but it is true that by the vivacity of the light, the
ſaid image will appear fringed about with many rays, and ſo will
ſeem to occupie a far greater part of the plate, than really it doth.
And to ſhew that this is true, when you have noted the particular
place of the plate from whence the reflection cometh, and
ved likewiſe how great the ſhining place appeared to you, cover the
greater part of that ſame ſpace, leaving it only viſible about the
midſt; and all this ſhall not any whit diminiſh the apparent
dor to one that beholds it from afar; but you ſhall ſee it largely
diſpers'd upon the cloth or other matter, wherewith you covered
it. If therefore any one, by ſeeing from a good diſtance a ſmall
gilt plate to be all over ſhining, ſhould imagine that the ſame
would alſo even in a plate as broad as the Moon, he is no leſs
ceived, than if he ſhould believe the Moon to be no bigger than
the bottom of a tub. If again the plate were turn'd into a
rical ſuperficies, the reflection would be ſeen ſtrong in but one ſole
particle of it; but yet by reaſon of its livelineſs, it will appear
fringed about with many glittering rays: the reſt of the Ball would
appear according as it was burniſhed; and this alſo onely then

when it was not very much poliſhed, for ſhould it be perfectly
brightned, it would appear obſcure. An example of this we
have dayly before our eyes in ſilver veſſels, which whilſt they are
only boyl'd in the Argol and Salt, they are all as white as ſnow, and
do not reflect any image; but if they be in any part burniſh'd, they
become in that place preſently obſcure: and in them one may ſee the
repreſentation of any thing as in Looking-glaſſes. And that
to obſcurity, proceeds from nothing elſe but the ſmoothing and
plaining of a fine grain, which made the ſuperficies of the ſilver
rough, and yet ſuch, as that it reflected the light into all parts,
whereby it ſeemed from all parts equally illuminated: which
ſmall unevenneſſes, when they come to be exquiſitely plained by
the burniſh, ſo that the reflection of the rays of incidence are all
directed unto one determinate place; then, from that ſame place,
the burniſh'd part ſhall ſhew much more bright and ſhining than
the reſt which is onely whitened by boyling; but from all other
places it looks very obſcure. And note, that the diverſity of

ſights of looking upon burniſh'd ſuperficies, occaſioneth ſuch
difference in appearances, that to imitate and repreſent in picture,
v. g. a poliſh'd Cuirace, one muſt couple black plains with white,
one ſideways to the other, in thoſe parts of the arms where the
light falleth equally.
Some write what
they underſtand
not, and therefore
underſtand not
what they write.
Diamonds ground
to divers ſides, &
why.
Silver burniſhed
appears more
ſcuee, than the not
burniſhed, & why.
Burniſh'd Steel
beheld from one
place appears very
bright, and from
another, very
ſcure.
SAGR. If therefore theſe great Philoſophers would acquieſe
in granting, that the Moon, Venus and the other Planets, were not
of ſo bright and ſmooth a ſurface as a Looking-glaſs, but wanted
ſome ſmall matter of it, namely, were as a ſilver plate, onely boyled
1white, but not burniſhed; would this yet ſuffice to the making
of it viſible, and apt for darting forth the light of the Sun?
SALV. It would ſuffice in part; but would not give a light ſo
ſtrong, as it doth being mountainous, and in ſum, full of
eminencies and great cavities. But theſe Philoſophers will never
yield it to be leſſe polite than a glaſſe; but far more, if more it
can be imagined; for they eſteeming that to perfect bodies perfect
figures are moſt ſutable; it is neceſſary, that the ſphericity of thoſe
Cœleſtial Globes be moſt exact; beſides, that if they ſhould
grant me ſome inequality, though never ſo ſmall, I would not
ſcruple to take any other greater; for that ſuch perfection
ing in indiviſibles, an hair doth as much detract from its perfection
as a mountain.
SAGR. Here I meet with two difficulties, one is to know the
reaſon why the greater inequality of ſuperficies maketh the
ger reflection of light; the other is, why theſe Peripatetick
tlemen are for this exact figure.
SALV. I will anſwer to the firſt; and leave to Simplieius the

care of making reply to the ſecond. You muſt know therefore,
that the ſame ſuperficies happen to be by the ſame light more or leſs
illuminated, according as the rayes of illumination fall upon them

more or leſſe obliquely; ſo that the greateſt illumination is where
the rayes are perpendicular. And ſee, how I will prove it to your
ſenſe. I bend this paper, ſo, that one part of it makes an angle
upon the other: and expoſing both theſe parts to the reflection of
the light of that oppoſite Wall, you ſee how this ſide which
ceiveth the rayes obliquely, is leſſe ſhining than this other, where
the reflection fals at right angles; and obſerve, that as I by
degrees receive the illumination more obliquely, it groweth
weaker.
The more rough
ſuperficies make
greater reflection
of light, than the
leſs rough.
Perpendicular
rays illuminate
more than the
lique, and why.
SAGR. I ſee the effect, but comprehend not the cauſe.
SALV. If you thought upon it but a minute of an hour, you
would find it; but that I may not waſte the time, ſee a kind of
demonſtration thereof in Fig. 7.
SAGR. The bare ſight of this Figure hath fully ſatisfied me,
therefore proceed.
SIMPL. Pray you let me hear you out, for I am not of ſo
quick an apprehenſion.
SALV. Fancie to your ſelf, that all the paralel lines, which you
ſee to depart from the terms A. B. are the rays which fall upon the

line C. D. at right angles: then incline the ſaid C. D. till it hang
as D. O. now do not you ſee that a great part of thoſe rays which
peirce C. D. paſs by without touching D. O? If therefore D. O.
be illuminated by fewer rays, it is very reaſonable, that the light
received by it be more weak. Let us return now to the Moon,
1which being of a ſpherical figure, if its ſuperficies were ſmooth, as
this paper, the parts of its hemiſphere illuminated by the Sun,
which are towards its extremity, would receive much leſs light,
than the middle parts; the rays falling upon them moſt obliquely,
and upon theſe at right angles; whereupon at the time of full
Moon, when we ſee almoſt its whole Hemiſphere illuminated, the
parts towards the midſt, would ſhew themſelves to us with more
ſplendor, than thoſe others towards the circumference: which is
not ſo in effect. Now the face of the Moon being repreſented
to me full of indifferent high mountains, do not you ſee how their
tops and continuate ridges, being elevated above the convexity of
the perfect ſpherical ſuperficies, come to be expoſed to the view
of the Sun, and accommodated to receive its rays much leſs
liquely, and conſequently to appear as luminous as the reſt?
The more oblique
Rayes illuminate
leß, and why.
SAGR. All this I well perceive: and if there are ſuch
tains, its true, the Sun will dart upon them much more directly
than it would do upon the inclination of a polite ſuperficies: but
it is alſo true, that betwixt thoſe mountains all the valleys would
become obſcure, by reaſon of the vaſt ſhadows, which in that
time would be caſt from the mountains, whereas the parts towards
the middle, though full of valleys and hills, by reaſon they have
the Sun elevated, would appear without ſhadow, and therefore
more lucid by far than the extreme parts, which are no leſs
ſed with ſhadow than light, and yet we can perceive no ſuch
rence.
SIMPL. I was ruminating upon the like difficulty.
SALV. How much readier is Simplicius to apprehend the
jections which favour the opinions of Ariſtotle, than their
ons? I have a kind of ſuſpition, that he ſtrives alſo ſometimes to
diſſemble them; and in the preſent caſe, he being of himſelf able
to hit upon the doubt, which yet is very ingenious, I cannot
lieve but that he alſo was adviſ'd of the anſwer; wherefore I will
attempt to wreſt the ſame (as they ſay) out of his mouth.
fore tell me, Simplicius, do you think there can be any ſhadow,
where the rays of the Sun do ſhine?
SIMPL. I believe, nay I am certain that there cannot; for that
it being the grand luminary, which with its rays driveth away
neſs, it is impoſſible any tenebroſity ſhould remain where it
eth; moreover, we have the definition, that Tenebræ ſunt
tio luminis.
SALV. Therefore the Sun, beholding the Earth, Moon or
ther opacous body, never ſeeth any of its ſhady parts, it not
ving any other eyes to ſee with, ſave its rays, the conveyers of
light: and conſequently, one ſtanding in the Sun would never
ſee any thing of umbrage, foraſmuch as his viſive rays would ever
1go accompanied with thoſe illuminating beams of the Sun.
SIMPL. This is true, without any contradiction.
SALV. But when the Moon is oppoſite to the Sun, what
ference is there between the tract of the rayes of your ſight, and
that motion which the Suns rayes make?
SIMPL. Now I underſtand you; for you would ſay, that the
rayes of the ſight and thoſe of the Sun, moving by the ſame lines,
we cannot perceive any of the obſcure valleys of the Moon. Be
pleaſed to change this your opinion, that I have either ſimulation
or diſſimulation in me; for I proteſt unto you, as I am a
man, that I did not gueſſe at this ſolution, nor ſhould I have
thought upon it, without your help, or without long ſtudy.
SAGR. The reſolutions, which between you two have been
alledged touching this laſt doubt, hath, to ſpeak the truth,
ed me alſo. But at the ſame time this conſideration of the
fible rayes accompanying the rayes of the Sun, hath begotten in me
another ſcruple, about the other part, but I know not whether I
can expreſſe it right, or no: for it but juſt now comming into my
mind, I have not yet methodized it to my mind: but let us ſee if
we can, all together, make it intelligible. There is no queſtion,
but that the parts towards the circumference of that poliſh't, but not
burniſh't Hemiſphere, which is illuminated by the Sun, receiving the
rayes obliquely, receive much fewer thereof, than the
moſt parts, which receive them directly. And its poſſible, that a
tract or ſpace of v. g. twenty degrees in breadth, and which is
wards the extremity of the Hemiſphere, may not receive more rays
than another towards the middle parts, of but four degree broad:
ſo that that doubtleſs will be much more obſcure than this; and
ſuch it will appear to whoever ſhall behold them both in the face,
or (as I may ſay) in their full magnitude. But if the eye of the
beholder were conſtituted in ſuch a place, that the breadth of the
twenty degrees of the obſcure ſpace, appeared not to it longer
than one of four degrees, placed in the midſt of the Hemiſphere,
I hold it not impoſſible for it to appear to the ſaid beholder
qually clear and lucid with the other; becauſe, finally, between
two equal angles, to wit, of four degrees apiece, there come to
the eye the reflections of two equal numbers of rayes: namely,
thoſe which are reflected from the middlemoſt ſpace, four degrees
in breadth, and thoſe reflected from the other of twenty degrees,
but ſeen by compreſſion, under the quantity of four degrees: and
ſuch a ſituation ſhall the eye obtain, when it is placed between the
ſaid Hemiſphere, and the body which illuminates it; for then the
ſight and rayes move in the ſame lines. It ſeemeth not impoſſible
therefore, but that the Moon may be of a very equal ſuperficies;
and that nevertheleſſe, it may appear when it is at the full, no leſs
1light in the extremities, than in the middle parts.
SALV. The doubt is ingenious and worthy of conſideration;
and as it but juſt now came into your mind unawares, ſo I will
like wiſe anſwer with what firſt comes into my thoughts, and it may
happily fall out, that by thinking more upon it, I may ſtumble
upon a better reply. But before, that I labyrinth my ſelf any
ther, it would be neceſſary, that we aſſure our ſelves by ſome
periment, whether your objection prove in effect, what it ſeemeth
to conclude in appearance; and therefore taking once more the
ſame paper, and making it to incline, by bending a little part
thereof upon the remainder, let us try whether expoſing it to the
Sun, ſo that the rayes of light fall upon the leſſer part directly,
and upon the other obliquely; this which receiveth the rayes
ly appeareth more lucid; and ſee here by manifeſt experience,
that it is notably more clear. Now if your objection be concluſive,
it will follow, that ſtooping with our eye ſo, that in beholding
the other greater part, leſs illuminated, in compreſſion or
ſhortning, it appear unto us no bigger than the other, more ſhining;
and that conſequently, it be not beheld at a greater angle than
that; it will neceſſarily enſue, I ſay, that its light be encreaſed, ſo
that it do ſeem to us as bright as the other. See how I behold, and
look upon it ſo obliquely, that it appeareth to me narrower than
the other; but yet, notwithſtanding its obſcurity, doth not to
my perceiving, at all grow clearer. Try now if the ſame ſucceed
to you.
SAGR. I have look't upon it, and though I have ſtooped with
my eye, yet cannot I ſee the ſaid ſuperficies encreaſe in light or
clarity; nay me thinks it rather grows more dusky.
SALV. We are hitherto confident of the invalidity of the
jection; In the next place, as to the ſolution, I believe, that, by
reaſon the Superficies of this paper is little leſſe than ſmooth, the
rayes are very few, which be reflected towards the point of
dence, in compariſon of the multitude, which are reflected
wards the oppoſite parts; and that of thoſe few more and more
are loſt, the nearer the viſive rayes approach to thoſe lucid rayes
of incidence; and becauſe it is not the incident rayes, but thoſe
which are reflected to the eye, that make the object appear
minous; therefore, in ſtooping the eye, there is more loſt than got,
as you your ſelf confeſſe to have ſeen in looking upon the
rer part of the paper.
SAGR. I reſt ſatisfied with this experiment and reaſon: It
mains now, that Simplicius anſwer to my other queſtion, and tell
me what moves the Peripateticks to require this ſo exact rotundity
in the Cœleſtial bodies.
SIMPL. The Cœleſtial bodies being ingenerable, inalterable,
1paſſible, immortal, &c. they muſt needs be abſolutely perfect; and

their being abſolute perfect, neceſſarily implies that there is in them
all kinds of perfection; and conſequently, that their figure be alſo
perfect, that is to ſay, ſpherical; and abſolutely and perfectly
ſpherical, and not rough and irregular.
Perfect ſphericity
why aſcribed to
Cœlestial bodies,
by the
ticks.
SALV. And this incorruptibility, from whence do you prove
it?
SIMPL. Immediately by its freedom from contraries, and
diately, by its ſimple circular motion.
SALV. So that; by what I gather from your diſcourſe, in

king the eſſence of the Cœleſtial bodies to be incorruptible,
terable, &c, there is no need of rotundity as a cauſe, or
ſite; for if this ſhould cauſe inalterability, we might at our
ſure make wood, wax, and other Elementary matters,
tible, by reducing them to a ſpherical figure.
The Figure is not
the cauſe of
ruptibility, but of
longer duration.
SIMPL. And is it not manifeſt that a ball of Wood will better
and longer be preferved, than an oblong, or other angular
gure, made of a like quantity of the ſame wood.
SALV. This is moſt certain, but yet it doth not of corruptible
become incorruptible, but ſtill remains corruptible, though of a
much longer duration. Therefore you muſt note, that a thing

ruptible, is capable of being more or leſſe ſuch, and we may
properly ſay this is leſſe corruptible than that; as for example, the
Jaſper, than the Pietra Sirena; but incorruptibility admits not
of more, or leſſe, ſo as that it may be ſaid this is more
ble than that, if both be incorruptible and eternal. The

ſity of figure therefore cannot operate: ſave onely in matters
pable of more or leſſe duration; but in the eternal, which
not be other than equally eternal, the operation of figure ceaſeth.
And therefore, ſince the Cœleſtial matter is not incorruptible by
figure, but otherwayes no man needs to be ſo ſolicitous for this
perfect ſphericity; for if the matter be incorruptible, let it have
what figure it will, it ſhall be alwayes ſuch.
Corruptibility
mits of more or
leſſe; ſo doth noe
incorruptibiliiy.
The perfection of
figure, operateth
in corruptible
dies, but not in the
eternal.
SAGR. But I am conſidering another thing, and ſay, that if

we ſhould grant the ſpherical figure a faculty of conferring
ruptibility, all bodies of whatſoever figure, would be
ble; foraſmuch as if the rotund body be incorruptible,
bility would then ſubſiſt in thoſe parts which alter the perfect
tundity; as for inſtance, there is in a Die a body perfectly round,
and, as ſuch, incorruptible; therefore it remaineth that thoſe
gles be corruptible which cover and hide the rotundity; ſo that
the moſt that could happen, would be, that thoſe angles, and
(to ſo ſpeak) excreſcencies, would corrupt. But if we proceed to a
more inward conſideration, that in thoſe parts alſo towards the
angles, there are compriſed other leſſer bals of the ſame matter;
1and therefore they alſo, as being round, muſt be alſo
tible; and likewife in the remainders, which environ theſe eight
leſſer Spheres, a man may underſtand that there are others: ſo
that in the end, reſolving the whole Die into innumerable balls,
it muſt neceſſarily be granted incorruptible. And the ſame
courſe and reſolution may be made in all other figures.
If the ſpherical
gure conferreth
ternity, all bodies
would be eternal.
SALV. Your method in making the concluſion, for if v. g. a
round Chryſtal were, by reaſon of its figure, incorruptible; namely,
received from thence a faculy of reſiſting all internal and external
alterations, we ſhould not find, that the joyning to it other
ſtal, and reducing it v. g. into a Cube, would any whit alter it
within, or without; ſo as that it would thereupon become leſſe
apt to reſiſt the new ambient, made of the ſame matter, than it
was to reſiſt the other, of a matter different; and eſpecially, if
it be true, that corruption is generated by contraries, as
ſtotle ſaith; and with what can you encloſe that ball of Cryſtal,
that is leſſe contrary to it, than Cryſtal it ſelf? But we are not
ware how time flies away; and it will be too late before we come
to an end of our diſpute, if we ſhould make ſo long diſcourſes,
upon every particular; beſides our memories are ſo confounded
in the multiplicity of notions, that I can very hardly recal to
mind the Propotſiions, which I propoſed in order to Simplicius,
for our conſideration.
SIMPL. I very well remember them: And as to this particular
queſtion of the montuoſity of the Moon, there yet remains
anſwered that which I have alledged, as the cauſe, (and which
may very well ſerve for a ſolution) of that Phænomenon, ſaying,
that it is an illuſion proceeding from the parts of the Moon,
ing unequally opacous, and perſpicuous.
SAGR. Even now, when Simplicius aſcribed the apparent
tnberancies or unevenneſſes of the Moon (according to the opinion
of a certain Peripatetick his friend) to the diverſly opacous, and

perſpicuous parts of the ſaid Moon, conformable to which the like
illuſions are ſeen in Cryſtal, and Jems of divers kinds, I bethought
my ſelf of a matter much more commodious for the repreſenting
ſuch effects; which is ſuch, that I verily believe, that that
pher would give any price for it; and it is the mother of Pearl, which
is wrought into divers figures, and though it be brought to an
treme evenneſſe, yet it ſeemeth to the eye in ſeveral parts, ſo
ouſly hollow and knotty, that we can ſcarce credit our feeling of
their evenneſſe.
Mother of Pearl
accommodated to
imitate the
rent unevenneſſes
of the Moons
face.
SALV. This invention is truly ingenious; and that which hath
not been done already, may be done in time to come; and if
there have been produced other Jems, and Cryſtals, which have
nothing to do with the illuſions of the mother of Pearl, theſe may
1be produced alſo; in the mean time, that I may not prevent any
one, I will ſuppreſſe the anſwer which might be given, and onely
for this time betake my ſelf to ſatisfie the objections brought by
Simplicius. I ſay therefore, that this reaſon of yours is too
neral, and as you apply it not to all the appearances one by one;
which are ſeen in the Moon, and for which my ſelf and others
are induced to hold it mountainous, I believe you will not find
any one that will be ſatisfied with ſuch a doctrine; nor can I think,
that either you, or the Author himſelf, find in it any greater
quietude, than in any other thing wide from the purpoſe. Of the

very many ſeveral appearances which are ſeen night by night in
the courſe of Moon, you cannot imitate ſo much as one, by making
a Ball at your choice, more or leſs opacous and perſpicuous, and
that is of a polite ſuperficies; whereas on the contrary, one may

make Balls of any ſolid matter whatſoever, that is not tranſparent,
which onely with eminencies and cavities, and by receiving the
lumination ſeveral ways, ſhall repreſent the ſame appearances and
mutations to an hair, which from hour to hour are diſcovered in

the Moon. In them you ſhall ſee the ledges of Hills expoſed to
the Suns light, to be very ſhining, and after them the projections
of their ſhadows very obſcure; you ſhall ſee them greater and leſs,
according as the ſaid eminencies ſhall be more or leſs diſtant from
the confines which diſtinguiſh the parts of the Moon illuminated,
from the obſcure: you ſhall ſee the ſame term and confine, not
equally diftended, as it would be if the Ball were poliſh'd, but
craggie and rugged. You ſhall ſee beyond the ſame term, in the
dark parts of the Moon many bright prominencies, and diſtinct
from the reſt of the illuminations: you ſhall ſee the ſhadows
foreſaid, according as the illumination gradually riſeth, to
niſh by degrees, till they wholly diſappear; nor are there any of
them to be ſeen when the whole Hemiſphere is enlightned.
gain on the contrary, in the lights paſſage towards the other
miſphere of the Moon, you ſhall again obſerve the ſame
cies that were marked, and you ſhall ſee the projections of their
ſhadows to be made a contrary way, and to decreaſe by degrees:
of which things, once more I ſay, you cannot ſhew me ſo much as
one in yours that are opacous and perſpicuous.
The apparent
evenneſſes of the
Moon cannot be
mitated by way of
more and leſs
city & perſpicuity.
The various
ſpects of the Moon,
imitable with any
opacous matter.
Various appear
ces from which the
Moons montuoſity
is argued.
SAGR. One of them certainly he may imitate, namely, that of
the Full-Moon, when by reaſon of its being all illuminated, there
is not to be ſeen either ſhadow, or other thing, which receiveth
any alteration from its eminencies and cavities. But I beſeech
you, Salviatus, let us ſpend no more time on this Argument, for
a perſon that hath had but the patience to make obſervation of but
one or two Lunations, and is not ſatisfied with this moſt ſenſible
truth, may well be adjudged void of all judgment; and upon
1ſuch why ſhould we throw away our time and breath in vain?
SIMPI. I muſt confeſs I have not made the obſervations, for
that I never had ſo much curioſity, or the Inſtruments proper for
the buſineſs; but I will not fail to do it. In the mean time, we
may leave this queſtion in ſuſpenſe, and paſs to that point which
follows, producing the motives inducing you to think that the
Earth may reflect the light of the Sun no leſs forceably than the
Moon, for it ſeems to me ſo obſcure and opacous, that I judg ſuch
an effect altogether impoſſible.
SALV. The cauſe for which you repute the Earth unapt for
illumination, may rather evince the contrary: And would it not
be ſtrange, Simplicius, if I ſhould apprehend your diſcourſes
ter than you your ſelf?
SIMPL. Whether I argue well or ill, it may be, that you may
better underſtand the ſame than I; but be it ill or well that I
diſcourſe, I ſhall never believe that you can penetrate what I mean
better than I my ſelf.
SALV. Well, I will make you believe the ſame preſently. Tell
me a little, when the Moon is near the Full, ſo that it may be ſeen
by day, and alſo at midnight, at what do you think it more
did, by day or by night?
SIMPL. By night, without all compariſon. And methinks

the Moon reſembleth that pillar of Clouds and pillar of Fire,
which guided the Iſraelites; which at the preſence of the Sun,
appeared like a Cloud, but in the night was very glorious. Thus

I have by day obſerved the Moon amidſt certain ſmall Clouds,
juſt as if one of them had been coloured white, but by night it
ſhines with much ſplendor.
The Moon
pears brighter by
night than by day.
The Moon
held in the day
time, is like to a
little cloud.
SALV. So that if you had never happened to ſee the Moon,
ſave onely in the day time, you would not have thought it more
ſhining than one of thoſe Clouds.
SIMPL. I verily believe I ſhould not.
SALV. Tell me now; do you believe that the Moon is really
more ſhining in the night than day, or that by ſome accident it
ſeemeth ſo?
SIMPL. I am of opinion, that it reſplends in it ſelf as much in
the day as night, but that its light appears greater by night,
cauſe we behold it in the dark mantle of Heaven; and in the day
time, the whole Atmoſphere being very clear, ſo that ſhe little
exceedeth it in luſtre, ſhe ſeems to us much leſs bright.
SALV. Now tell me; have you ever at midnight ſeen the
reſtrial Globe illuminated by the Sun?
SIMPL. This ſeemeth to me a queſtion not to be ask'd, unleſs
in jeſt, or of ſome perſon known to be altogether void of ſenſe.
SALV. No, no; I eſteem you to be a very rational man, and
1do ask the queſtion ſeriouſly; and therefore anſwer me: and if
afterwards you ſhall think that I ſpeak impertinently, I will be
content to be the ſenſeleſs man: for he is much more a fool who
interrogates ſimply, than he to whom the queſtion is put.
SIMPL. If then you do not think me altogether ſimple, take
it for granted that I have anſwered you already, and ſaid, that it
is impoſſible, that one that is upon the Earth, as we are, ſhould ſee
by night that part of the Earth where it is day, namely, that is
luminated by the Sun.
SALV. Therefore you have never ſeen the Earth enlightned,
ſave onely by day; but you ſee the Moon to ſhine alſo in the
dead of night. And this is the cauſe, Simplicius, which makes
you believe that the Earth doth not ſhine like the Moon; but if
you could ſee the Earth illuminated, whilſt you were in ſome dark
place, like our night, you would ſee it ſhine brighter than the
Moon. Now if you deſire that the compariſon may proceed
well, you muſt compare the light of the Earth, with that of the
Moon ſeen in the day time, and not with the ſame by night: for
it is not in our power to ſee the Earth illuminated, ſave onely in
the day. Is it not ſo?
SIMPL. So it ought to be.
SALV. And foraſmuch as you your ſelf have already confeſſed
to have ſeen the Moon by day among ſome little white Clouds,
and very nearly, as to its aſpect, reſembling one of them; you did

thereby grant, that thoſe Clouds, which yet are Elementary
matters, are as apt to receive illumination, as the Moon, yea
more, if you will but call to mind that you have ſometimes ſeen
ſome Clouds of vaſt greatneſs, and as perfect white as the Snow;
and there is no queſtion, but that if ſuch a Cloud could be
tinued ſo luminous in the deep of night, it would illuminate the
places near about it, more than an hundred Moons. If therefore
we were aſſured that the Earth is illuminated by the Sun, like one
of thoſe Clouds, it would be undubitable, but that it would be no
leſs ſhining than the Moon. But of this there is no queſtion to
be made, in regard we ſee thoſe very Clouds in the abſence of
the Sun, to remain by night, as obſcure as the Earth: and that
which is more, there is not any one of us, but hath ſeen many
times ſome ſuch Clouds low, and far off, and queſtioned whether
they were Clouds or Mountains: an evident ſign that the
tains are no leſs luminous than thoſe
Clouds are no leſs
apt than the Moon
to be illuminated
by the Sun.
A wall
ted by the Sun,
compared to the
Moon ſhineth no
leſs than it.
SAGR. But what needs more diſcourſe? See yonder the Moon
is riſen, and more than half of it illuminated; ſee there that wall,
on which the Sun ſhineth; retire a little this way, ſo that you ſee
the Moon ſideways with the wall: look now; which of them
ſhews more lucid? Do not you ſee, that if there is any advantage,
1the wall hath it? The Sun ſhineth on that wall; from thence it

is reverberated upon the wall of the Hall, from thence it's
cted upon that chamber, ſo that it falls on it at the third reflection:
and I am very certain, that there is in that place more light, than
if the Moons light had directly faln upon it.
The third
ction of a Wall
minates more than
the firſt of the
Moon.
SIMPL. But this I cannot believe; for the illumination of the
Moon, eſpecially when it is at the full, is very great.
SAGR. It ſeemeth great by reaſon of the circumjacent dark

places; but abſolutely it is not much, and is leſs than that of the
twilight half an hour after the Sun is ſet; which is manifeſt,
cauſe you ſee not the ſhadows of the bodies illuminated by the
Moon till then, to begin to be diſtinguiſhed on the Earth.
ther, again, that third reflection upon that chamber, illuminates
more than the firſt of the Moon, may be known by going thether,
and reading a Book, and afterwards ſtanding there in the night
by the Moons light, which will ſhew by which of them lights one
may read more or leſs plainly, but I believe without further tryal,
that one ſhould ſee leſs diſtinctly by this later.
The light of the
Moon weaker than
that of the
light.
SALV. Now, Simplicius, (if haply you be ſatisfied) you may
conceive, as you your ſelf know very well, that the Earth doth
ſhine no leſs than the Moon; and the only remembring you of ſome
things, which you knew of your ſelf, and learn'd not of me, hath
aſſured you thereof: for I taught you not that the Moon ſhews
lighter by night than by day, but you underſtood it of your ſelf;
as alſo you could tell me that a little Cloud appeareth as lucid as
the Moon: you knew alſo, that the illumination of the Earth
not be ſeen by night; and in a word, you knew all this, without
knowing that you knew it. So that you have no reaſon to be
pulous of granting, that the dark part of the Earth may illuminate
the dark part of the Moon, with no leſs a light than that
with the Moon illuminates the obſcurities of the night, yea rather
ſo much the greater, inaſmuch as the Earth is forty times bigger
than the Moon.
SIMPL. I muſt confeſs that I did believe, that that ſecondary
light had been the natural light of the Moon.
SALV. And this alſo you know of your ſelf, and perceive not
that you know it. Tell me, do not you know without teaching,
that the Moon ſhews it ſelf more bright by night than by day, in

reſpect of the obſcurity of the ſpace of the ambient? and
quently, do you not know in genere, that every bright body ſhews
the clearer, by how much the ambient is obſcurer?
Luminous bodies
appear the brighter
in an obſcurer
bient.
SIMPL. This I know very well.
SALV. When the Moon is horned, and that ſecondary light
ſeemeth to you very bright, is it not ever nigh the Sun, and
ſequently, in the light of the crepuſculum, (twilight?)
1
SIMPL. It is ſo; and I have oftentimes wiſh'd that the Air
would grow thicker, that I might be able to ſee that ſame light
more plainly; but it ever diſappeared before dark night.
SALV. You know then very certainly, that in the depth of
night, that light would be more conſpicuous.
SIMPL. I do ſo; and alſo more than that, if one could but
take away the great light of the creſcent illuminated by the Sun,
the preſence of which much obſcureth the other leſſer.
SALV. Why, doth it not ſometimes come to paſs, that one may
in a very dark night ſee the whole face of the Moon, without
ing at all illuminated by the Sun?
SIMPL. I know not whether this ever happeneth, ſave onely
in the total Ecclipſes of the Moon.
SALV. Why, at that time this its light would appear very
clear, being in a moſt obſcure medium, and not darkned by the
clarity of the luminous creſcents: but in that poſition, how light
did it appear to you?
SIMPL. I have ſometimes ſeen it of the colour of braſs, and a
little whitiſh; but at other times it hath been ſo obſcure, that I
have wholly loſt the ſight of it.
SALV. How then can that light be ſo natural, which you ſee ſo
cleer in the cloſe of the twilight, notwithſtanding the impediment
of the great and contiguous ſplendor of the creſcents; and which
again, in the more obſcure time of night, all other light removed,
appears not at all?
SIMPL. I have heard of ſome that believed that ſame light to
be participated to theſe creſcents from the other Stars, and in
ticular from Venus, the Moons neighbour.
SALV. And this likewiſe is a vanity; becauſe in the time of
its total obſcuration, it ought to appear more ſhining than ever;
for you cannot ſay, that the ſhadow of the Earth intercepts the
ſight of Venus, or the other Stars. But to ſay true, it is not at
that inſtant wholly deprived thereof, for that the Terreſtrial
miſphere, which in that time looketh towards the Moon, is that
where it is night, that is, an intire privation of the light of the Sun.
And if you but diligently obſerve, you will very ſenſibly perceive,
that like as the Moon, when it is ſharp-horned, doth give very little
light to the Earth; and according as in her the parts
nated by the Suns light do encreaſe: ſo likewiſe the ſplendor to
our ſeeming encreaſeth, which from her is reflected towards us;
thus the Moon, whilſt it is ſharp-forked, and that by being between
the Sun and the Earth, it diſcovereth a very great part of the

reſtrial Hemiſphere illuminated, appeareth very clear: and
ing from the Sun, and paſſing towards the ^{*}Quadrature, you
may ſee the ſaid light by degrees to grow dim; and after the
1Quadrature, the ſame appears very weak, becauſe it continually
loſeth more and more of the view of the luminous part of the
Earth: and yet it ſhould ſucceed quite contrary, if that light were
its own, or communicated to it from the Stars; for then we ſhould
ſee it in the depth of night, and in ſo very dark an ambient.
*By the Moons two
Quadratures you
are to underſtand
its firſt and last
quarters, as
ſtrologers call them
SIMPL. Stay a little; for I juſt now remember, that I have
read in a little modern tract, full of many novelties; “That this
ſecondary light is not derived from the Stars, nor innate in the
Moon, and leaſt of all communicated by the Earth, but that it is

received from the ſame illumination of the Sun, which, the
ſtance of the Lunar Globe being ſomewhat tranſparent,
trateth thorow all its body; but more livelily illuminateth the
ſuperficies of the Hemiſphere expoſed to the rays of the Sun:
and its proſundity imbuing, and (as I may ſay) ſwallowing that
light, after the manner of a cloud or chryſtal, tranſmits it, and
renders it viſibly lucid. And this (if I remember aright) he
proveth by Authority, Experience and Reaſon; citing Cleomedes,
Vitellion, Macrobius, and a certain other modern Author: and
adding, That it is ſeen by experience to ſhine moſt in the days
neareſt the Conjunction, that is, when it is horned, and is chiefly
bright about its limb. And he farther writes, That in the Solar
Ecclipſes, when it is under the Diſcus of the Sun, it may be ſeen
tranſlucid, and more eſpecially towards its utmoſt Circle. And
in the next place, for Arguments, as I think, he ſaith, That it not
being able to derive that light either from the Earth, or from the
Stars, or from it ſelf, it neceſſarily follows, that it cometh from
the Sun. Beſides that, if you do but grant this ſuppoſition, one
may eaſily give convenient reaſons for all the particulars that
occur. For the reaſon why that ſecundary light ſhews more
lively towards the outmoſt limb, is, the ſhortneſs of the ſpace
that the Suns rays hath to penetrate, in regard that of the lines
which paſs through a circle, the greateſt is that which paſſeth
through the centre, and of the reſt, thoſe which are fartheſt from
it, are always leſs than thoſe that are nearer. From the ſame
principle, he ſaith, may be ſhewn why the ſaid light doth not
much diminiſh. And laſtly, by this way the cauſe is aſſigned
whence it comes, that that ſame more ſhining circle about the
utmoſt edge of the Moon, is ſeen at the time of the Solar
clipſe, in that part which lyeth juſt under the Diſcus of the Sun,
but not in that which is beſide the Diſcus: which happeneth
becauſe the rays of the Sun paſs directly to our eye, through the
parts of the Moon underneath: but as for the parts which are
beſides it, they fall beſides the eye.”
The ſecondary
light of the Moon
cauſed by the Sun,
according to ſome.
SALV. If this Philoſopher had been the firſt Author of this
pinion, I would not wonder that he ſhould be ſo affectionate to it,
1as to have received it for truth; but borrowing it from others, I
cannot find any reaſon ſufficient to excuſe him for not perceiving
its fallacies; and eſpecially after he had heard the true cauſe of
that effect, and had it in his power to ſatisfie himſelf by a thouſand
experiments, and manifeſt circumſtances, that the ſame proceeded
from the reflection of the Earth, and from nothing elſe: and the more
this ſpeculation makes ſomething to be deſired, in the judgment of
this Author, and of all thoſe who give no credit to it: ſo much the
more doth their not having underſtood and remembred it, excuſe
thoſe more receſs Antients, who, I am very certain, did they now
underſtand it, would without the leaſt repugnance admit thereof.
And if I may freely tell you what I think, I cannot believe but
that this Modern doth in his heart believe it; but I rather think,
that the conceit he ſhould not be the firſt Author thereof, did a
little move him to endeavour to ſuppreſſe it, or to diſparage it at
leaſt amongſt the ſimple, whoſe number we know to be very
great; and many there are, who much more affect the
rous applauds of the people, than the approbation of a few not
vulgar judgments.
SAGR. Hold good Salviatus, for me thinks, I ſee that you
go not the way to hit the true mark in this your diſcourſe, for theſe
that ^{*} confound all propriety, know alſo how to make themſelves

Authors of others inventions, provided they be not ſo ſtale,
and publick in the Schools and Market-places, as that they are more
then notorious to every one.
* Tendono le
te al commune.
SALV. Ha! well aimed, you blame me for roving from the
point in hand; but what have you to do with Schools and

kets? Is it not all one whether opinions and inventions be new to
men, or the men new to them? If you ^{*} contend about the
ſteem of the Founders of Sciences, which in all times do ſtart up,

you may make your ſelf their inventor, even to the Alphabet it
ſelf, and ſo gain admiration amongſt that illiterate rabble; and
though in proceſſe of time your craft ſhould be perceived, that
would but little prejudice your deſigne; for that others would
ſucceed them in maintaining the number of your fautors; but let
us return to prove to Simplicius the invalidity of the reaſons of his
modern Author, in which there are ſeveral falſities,

cies, and incredible Paradoxes. And firſt, it is falſe that this
condary light is clearer about the utmoſt limb than in the middle
parts, ſo as to form, as it were, a ring or circle more bright than
the reſt of its ſpace or contence. True it is, indeed, that looking
on the Moon at the time of twilight, at firſt ſight there is the
ſemblance of ſuch a circle, but by an illuſion ariſing from the
verſity of confines that bound the Moons Diſcus, which are
fuſed by means of this ſecondary light; foraſmuch as on the part
1towards the Sun it is bounded by the lucid horns of the Moon,
and on the other part, its confining term is the obſcure tract of the
twilight; whoſe relation makes us think the candor of the Moons
Diſcus to be ſo much the clearer; the which happens to be
fuſcated in the oppoſite part, by the greater clarity of the
cents; but if this modern Author had eſſaied to make an

poſition between the eye and the primary ſplendor, by the ridg of
ſome houſe, or ſome other ſcreen, ſo as to have left viſible only
the groſe of the Moon, the horns excluded, he might have ſeen
it all alike luminous.
Its all one
ther opinions be
new to men, or men
new to opinions.
* Conteſtare falſly
rendered in the
Latine Tranſlation
content are.
The ſecondary
light of the Moon
appears in form of
a Ring, that is to
ſay, bright in the
extreme
rence, and not in
the midſt, and why.
The may to
ſerve the
ry light of the
Moon.
SIMPL, I think, now I remember, that he writes of his
making uſe of ſuch another Artifice, to hide from us the falſe
Incidum.
SALV. Oh! how is this (as I believed) inadvertency of his,
changed into a lie, bordering on raſhneſſe; for that every one
may frequently make proof of the contrary. That in the next

place, at the Suns Eclipſe, the Moons Diſcus is ſeen otherwayes
than by privation, I much doubt, and ſpecially when the
clipſe is not total, as thoſe muſt neceſſarily have been, which
were obſerved by the Author; but if alſo he ſhould have
red ſomewhat of light, this contradicts not, rather favoureth our
opinion; for that at ſuch a time, the whole Terreſtrial
ſphere illuminated by the Sun, is oppoſite to the Moon, ſo that
although the Moons ſhadow doth obſcure a part thereof, yet this
is very ſmall in compariſon of that which remains illuminated.
That which he farther adds, that in this caſe, the part of the
limb, lying under the Sun, doth appear very lucid, but that
which lyeth beſides it, not ſo; and that to proceed from the
ming of the ſolar rayes directly through that part to the eye, but
not through this, is really one of thoſe fopperies, which diſco
ver the other fictions, of him which relates them: For if it be
requiſite to the making a ſecondary light viſible in the lunar
cus, that the rayes of the Sun came directly through it to our
eyes, doth not this pitiful Philoſopher perceive, that we ſhould
ver ſee this ſame ſecondary light, ſave onely at the Eclipſe of the
Sun? And if a part onely of the Moon, far leſſe than half a
gree, by being remote from the Suns Diſcus, can deflect or
viate the rayes of the Sun, ſo that they arrive not at our eye;
what ſhall it do when it is diſtant twenty or thirty degrees, as it is
at its firſt apparition? and what courſe ſhall the rayes of the Sun
keep, which are to paſſe thorow the body of the Moon, that

they may find out our eye? This man doth go ſucceſſively
dering what things ought to be, that they may ſerve his purpoſe,
but doth not gradually proceed, accommodating his conceits to
the things, as really they are. As for inſtance, to make the light
1of the Sun capable to penetrate the ſubſtance of the Moon, he
makes her in part diaphanous, as is v. g. the tranſparence of a cloud,
or cryſtal: but I know not what he would think of ſuch a
ſparency, in caſe the ſolar rayes were to paſſe a depth of clouds
of above two thouſand miles; but let it be ſuppoſed that he
ſhould boldly anſwer, that might well be in the Cœleſtial, which
are quite other things from theſe our Elementary, impure, and
feculent bodies; and let us convict his error by ſuch wayes, as
admit him no reply, or (to ſay better) ſubter-fuge. If he will
maintain, that the ſubſtance of the Moon is diaphanous, he
muſt ſay that it is ſo, whileſt that the rayes of the Sun are to
netrate its whole profundity, that is, more than two thouſand
miles; but that if you oppoſe unto them onely one mile, or
leſſe, they ſhould no more penetrate that, than they penetrate
one of our mountains.
The Moons
cus in a ſolar
clipſe can be ſeen
onely by privation.
The Author of the
Book of
ons, accommodates
the things to his
purpoſes, and not
his purpoſes to the
things.
SAGR. You put me in mind of a man, who would have ſold

me a ſecret how to correſpond, by means of a certain ſympathy of
magnetick needles, with one, that ſhould be two or three
ſand miles diſtant; and I telling him, that I would willingly buy
the ſame, but that I deſired firſt to ſee the experiment thereof,
and that it did ſuffice me to make it, I being in one Chamber, and
he in the next, he anſwered me, that in ſo ſmall a diſtance one
could not ſo well perceive the operation; whereupon I turn'd him
going, telling him, that I had no mind, at that time, to take a
journey unto Grand Cairo, or to Muſcovy, to make the
ment; but that, if he would go himſelf, I would perform the
other part, ſtaying in Venice. But let us hear whither the
ction of our Author tendeth, and what neceſſity there is, that he
muſt grant the matter of the Moon to be moſt perforable by the
rayes of the Sun, in a depth of two thouſand miles, but more
opacous than one of our mountains, in a thickneſſe of one mile
onely.
A jeſt put upon one
that would ſell a
certain ſecret for
holding
dency with a perſon
a thouſand miles
off
SALV. The very mountains of the Moon themſelves are a
proof thereof, which percuſſed on one ſide of the Sun, do caſt
on the contrary ſide very dark ſhadows, terminate, and more
ſtinct by much, than the ſhadows of ours; but had theſe
tains been diaphanous, we could never have come to the
ledg of any unevenneſſe in the ſuperficies of the Moon, nor have
ſeen thoſe luminous montuoſities diſtinguiſhed by the terms which
ſeparate the lucid parts from the dark: much leſſe, ſhould we ſee
this ſame term ſo diſtinct, if it were true, that the Suns light did
penetrate the whole thickneſſe of the Moon; yea rather,
ing to the Authors own words, we ſhould of neceſſity diſcern the
paſſage, and confine, between the part of the Sun ſeen, and the
part not ſeen, to be very confuſed, and mixt with light and
1darkneſſe; for that that matter which admits the paſſage of the
Suns rayes thorow a ſpace of two thouſand miles, muſt needs be
ſo tranſparent, that it would very weakly reſiſt them in a
dredth, or leſſer part of that thickneſſe; nevertheleſſe, the term
which ſeparateth the part illuminated from the obſcure, is
dent, and as diſtinct, as white is diſtinct from black; and
ſpecially where the Section paſſeth through the part of the Moon,
that is naturally more clear and montanous; but where the old
ſpots do part, which are certain plains, that by means of their
ſpherical inclination, receive the rayes of the Sun obliquely,
there the term is not ſo diſtinct, by reaſon of the more dimme
lumination. That, laſtly, which he ſaith, how that the ſecondary
light doth not diminiſh and languiſh, according as the Moon
creaſeth, but conſerveth it ſelf continually in the ſame efficacy;
is moſt falſe; nay it is hardly ſeen in the quadrature, when, on
the contrary, it ſhould appear more ſplendid, and be viſible after
the crepuſculum in the dark of night. Let us conclude therefore,
that the Earths reflection is very ſtrong upon the Moon; and that,
which you ought more to eſteem, we may deduce from thence
other admirable congruity between the Moon and Earth;

ly, that if it be true, the Planets operate upon the Earth by their
motion and light, the Earth may probably be no leſſe potent in
operating reciprocally upon them with the ſame light, and
venture, motion alſo. And though it ſhould not move, yet may
it retain the ſame operation; becauſe, as it hath been proved
ready, the action of the light is the ſelf ſame, I mean of the light
of the Sun reflected; and motion doth nothing, ſave only vary
the aſpects, which fall out in the ſame manner, whether we make
the Earth move, and the Sun ſtand ſtill, or the contrary.
The Earth may
ciprocally operate
upon Cœleſtial
dies, with its light.
SIMPL. None of the Philoſophers are found to have ſaid, that
theſe inferiour bodies operate on the Cœleſtial, nay, Ariſtotle
firmes the direct contrary.
SALV. Aristotle and the reſt, who knew not that the Earth and
Moon mutually illuminated each other, are to be excuſed; but
they would juſtly deſerve our cenſure, if whileſt they deſire that
we ſhould grant and believe with them, that the Moon operateth
upon the Earth with light, they ſhould deny to us, who have
taught them that the Earth illuminates the Moon, the operation
the Earth hath on the Moon.
SIMPL. In ſhort, I find in my ſelf a great unwillingneſſe to
admit this commerce, which you would perſwade me to be
twixt the Earth and Moon, placing it, as we ſay, amongſt the
number of the Stars; for if there were nothing elſe, the great
ſeparation and diſtance between it and the Cœleſtial bodies, doth
in my opinion neceſſarily conclude a vaſt diſparity between them.
1
SALV. See Simplicius what an inveterate affection and
ted opinion can do, ſince it is ſo powerful, that it makes you think
that thoſe very things favour you, which you produce againſt
your ſelf. For if ſeparation and diſtance are accidents ſufficient to
perſwade with you a great diverſity of natures, it mnſt follow that

proximity and contiguity import ſimilitude. Now how much more
neerer is the Moon to the Earth, than to any other of the Cœleſtial
Orbs? You muſt acknowledg therefore, according to your own
ceſſion (and you ſhall have other Philoſophers bear you company)
that there is a very great affinity betwixt the Earth and Moon.
Now let us proceed, and ſee whether any thing remains to be
ſidered, touching thoſe objections which you made againſt the
ſemblances that are between theſe two bodies.
Affinity between
he Earth & Moon
in reſpect of their
vicinity.
SIMPL. It reſts, that we ſay ſomething touching the ſolidity of
the Moon, which I argued from its being exquiſite ſmooth and
polite, and you from its montuoſity. There is another ſcruple
ſo comes into my mind, from an opinion which I have, that the
Seas reflection ought by the equality of its ſurface, to be rendered
ſtronger than that of the Earth, whoſe ſuperficies is ſo rough and
opacous.
SALV. As to the firſt objection; I ſay, that like as among the
parts of the Earth, which all by their gravity ſtrive to approach the

neareſt they can poſſible to the center, ſome of them alwayes are
more remote from it than the reſt, as the mountains more than
the valleys, and that by reaſon of their ſolidity and firmneſſe
(for if they were of fluid, they would be even) ſo the ſeeing ſome
parts of the Moon to be elevated above the ſphericity of the
er parts, argueth their hardneſſe; for it is probable that the
ter of the Moon is reduced into a ſpherical form by the
ous conſpiration of all its parts to the ſame ſentenſe. Touching
the ſecond doubt, my thinks that the particulars already obſerved
to happen in the Looking-glaſſes, may very well aſſure us, that the
reflection of light comming from the Sea, is far weaker than that

which cometh from Land; underſtanding it alwayes of the
univerſal reflection; for as to that particular, on which the
ter being calm, caſteth upon a determinate place, there is no
doubt, but that he who ſhall ſtand in that place, ſhall ſee a very
great reflection in the water, but every way elſe he ſhall ſee the
ſurface of the Water more obſcure than that of the Land; and to

prove it to your ſenſes, let us go into yonder Hall, and power
forth a little water upon the Pavement. Tell me now, doth not
this wet brick ſhew more dull than the other dry ones?
leſſe it doth, and will ſo appear, from what place ſoever you
hold it, except one onely, and this is that way which the light
cometh, that entereth in at yonder window; go backwards
therefore by a little and a little.
1
Solidity of the
Lunar Globe
ed from its being
montainous.
The Seas
ction of light much
weaker than that
of the Earth.
An experiment
to prove the
ction of the Water
leſſe clear than
that of the Land.
SIMPL. Here I ſee the weſt part ſhine more than all the reſt of
the pavement, and I ſee that it ſo hapneth, becauſe the
ction of the light which entereth in at the window, cometh
wards me.
SALV. That moiſture hath done no more but filled thoſe little
cavities which are in the brick with water, and reduced its
ficies to an exact eveneſſe; whereupon the reflex rayes iſſue
unitedly towards one and the ſame place; but the reſt of the
pavement which is dry, hath its protuberances, that is, an
merable variety of inclinations in its ſmalleſt particles;
on the reflections of the light ſcatter towards all parts, but more
weakly than if they had gone all united together; and therefore,
the ſame ſheweth almoſt all alike, beheld ſeveral wayes, but far
leſſe clear than the moiſtned brick. I conclude therefore, that the
ſurface of the Sea, beheld from the Moon, in like manner, as it
would appear moſt equal, (the Iſlands and Rocks deducted) ſo it
would ſhew leſſe clear than that of the Earth, which is montanous
and uneven. And but that I would not ſeem, as the ſaying is,
to harp too much on one ſtring, I could tell you that I have
ſerved in the Moon that ſecondary light which I told you came to
her from the reflection of the Terreſtrial Globe, to be notably

more clear two or three dayes before the conjunction, than after,
that is, when we ſee it before break of day in the Eaſt, than
when it is ſeen at night after Sun-ſet in the Weſt; of which
ference the cauſe is, that the Terreſtrial Hemiſphere, which looks
towards the Eaſtern Moon, hath little Sea, and much Land, to
wit, all Aſia, whereas, when it is in the Weſt, it beholds very
great Seas, that is, the whole Atlantick Ocean as far as America:
An Argument ſufficiently probable that the ſurface of the water
appears leſſe ſplendid than that of the Earth.
The ſecondary
light of the Moon
clearer before the
conjunction, than
after.
SIMPL. So that perhaps you believe, thoſe great ſpots
vered in the face of the Moon, to be Seas, and the other clearer
parts to be Land, or ſome ſuch thing?
SALV. This which you ask me, is the beginning of thoſe
congruities which I eſteem to be between the Moon and the
Earth, out of which it is time to diſ-ingage our ſelves, for we
have ſtayed too long in the Moon. I ſay therefore, that if there
were in nature but one way onely, to make two ſuperficies
ted by the Sun, to appear one more clear than the other, and
that this were by the being of the one Earth, and the other
ter; it would be neceſſary to ſay that the ſurface of the Moon
were part earthy and part aquatick; but becauſe we know many
wayes to produce the ſame effect (and others there may be which
we know not of;) therefore I dare not affirm the Moon to
ſiſt of one thing more than another: It hath been ſeen already
1that a ſilver plate boiled, being toucht with the Burniſher,
cometh of white obſcure; that the moiſt part of the Earth ſhews
more obſcure than the dry; that in the tops of Hills, the woody
parts appear more gloomy than the naked and barren; which
hapneth becauſe there falleth very much ſhadow among the Trees,
but the open places are illuminated all over by the Sun. And this
mixtion of ſhadow hath ſuch operation, that in tuſted velvet, the
ſilk which is cut, is of a far darker colour than that which is not
cut, by means of the ſhadows diffuſed betwixt thred and thred,
and a plain velvet ſhews much blacker than a Taffata, made of the
ſame ſilk. So that if there were in the Moon things which ſhould
look like great Woods, their aſpect might repreſent unto us the
ſpots which we diſcover; alike difference would be occaſioned, if
there were Seas in her: and laſtly, nothing hindreth, but that thoſe
ſpots may really be of an obſcurer colour than the reſt; for thus
the ſnow makes the mountains ſhew brighter. That which is

ly obſerved in the Moon is, that its moſt obſcure parts are all
plains, with few riſes and bancks in them; though ſome there be;
the reſt which is of a brighter colour, is all full of rocks,
tains, hillocks of ſpherical and other figures; and in particular, round
about the ſpots are very great ledges of mountains. That the

ſpots be plain ſuperficies, we have aſſuredproof, in that we ſee,
how that the term which diſtinguiſheth the part illuminated from
the obſcure, in croſſing the ſpots makes the interſection even, but
in the clear parts it ſhews all craggy and ſhagged. But I know not
as yet whether this evenneſſe of ſuperficies may be ſufficient of it
ſelf alone, to make the obſcurity appear, and I rather think not.
Beſides, I account the Moon exceeding different from the Earth;
for although I imagine to my ſelf that thoſe are not idle and dead
Regions, yet I affirm not, that there are in them motion and life,

much leſs that there are bred plants, animals or other things like
to ours; but, if ſuch there be, they ſhould nevertheleſs be very
different, and remote from our imagination. And I am induced ſo
to think, becauſe in the firſt place, I eſteem that the matter of the
Lunar Globe conſiſts not of Earth and Water; and this alone
ſufficeth to take away the generations and alterations reſembling
ours: but now ſuppoſing that there were in the Moon, Water and

Earth, yet would they not produce plants and animals like to
ours; and this for two principal reaſons: The firſt is, that unto our

productions there are required ſo many variable aſpects of the Sun,
that without them they would all miſcarry: now the habitudes of
the Sun towards the Earth are far different from thoſe towards
the Moon. We as to the diurnal illumination, have, in the greater
part of the Earth, every twenty four hours part day, and part
night, which effect in the Moon is monethly: and that annual
1nation and elevation of the Sun in the Zodiack, by which it

duceth diverſity of Seaſons, and inequality of dayes and nights,
are finiſhed in the Moon in a moneth; and whereas the Sun to us

riſeth and declineth ſo much, that from the greateſt to the leaſt
titude, there is a difference of almoſt 47 degrees, for ſo much is
the diſtance from one to the other Tropick; this is in the Moon
but ten degrees only, or little more; namely, as much as the
teſt Latitudes of the Dragon on each ſide the Ecliptick. Now
conſider what effect the Sun would have in the torrid Zone, ſhould
it continually for fifteen dayes together beam forth its Rayes upon
it; which without all queſtion would deſtroy plants, herbs,
and living creatures: and if it ſhould chance that there were any
production, it would be of herbs, plants, and creatures very

rent from thoſe which are now there. Secondly, I verily believe
that in the Moon there are no rains, for if Clouds ſhould gather
in any part thereof, as they do about the Earth, they would
upon hide from our ſight ſome of thoſe things, which we with the
Teleſcope behold in the Moon, and in a word, would ſome way or
other change its Phœnomenon, an effect which I could never by long
and diligent obſervations diſcover; but alwayes beheld it in a
even and pure ſerenity.
The obſcurer
parts of the Moon
are plains, and the
more bright
tainous.
Long ledges of
mountaixs about
the ſpots of the
Moon.
There are not
generated in the
Moon things like
to ours, but if
there be any
ductions, they are
very different.
The Moon not
compoſed of Water
and Earth.
Thoſe aſpects of
the Sun neceſſary
for our
ons, are not ſo in
the Moon.
Natural dayas
in the Moon are of
a Moneth long.
To the Moon
the Sun aſeondeth
and declineth with
a difference of ten
degrees, and to the
Earth of forty
ven degrees.
There are no
rains in the Moon.
SAGR. To this may be anſwered, either that there might be
great miſts, or that it might rain in the time of their night, that is,
when the Sun doth not illuminate it.
SALV. If other paſſages did but aſſure us, that there were
nerations in it like to ours, and that there was onely wanting the
concourſe of rains, we might find out this, or ſome other
rament to ſerve inſtead thereof, as it happens in Egypt by the
undation of Nile: but not meeting with any accident, which
reſponds with ours, of many that have been ſought out for the
duction of the like effects, we need not trouble our ſelves to
duce one alone; and that alſo, not becauſe we have certain
vation of it, but for a bare non-repugnance that we find therein.
Moreover, if I was demanded what my firſt apprehenſion, and pure
natural reaſon dictated to me concerning the production of things
like or unlike there above, I would alwayes reply, that they are
moſt different, and to us altogether unimaginable, for ſo me thinks
the riches of Nature, and the omnipotence of our Creator and
Governour, do require.
SAGR. I ever accounted extraordinary madneſſe that of thoſe,
who would make humane comprehenſion the meaſure of what
ture hath a power or knowledge to effect; whereas on the

trary there is not any the leaſt effect in Nature, which can be fully
underſtood by the moſt ſpeculative wits in the world. This their
ſo vain preſumption of knowing all, can take beginning from
1thing, unleſſe from their never having known any thing; for if
one hath but once onely experienced the perfect knowledg of one
onely thing, and but truly taſted what it is to know, he ſhall
ceive that of infinite other concluſions, he underſtands not ſo much
as one.
The having a
perfect knowledg
of nothing, maketh
ſome believe they
underſtand all
things.
SALV. Your diſcourſe is very concluding; in confirmation of
which we have the example of thoſe who underſtand, or have
known ſome thing, which the more knowing they are, the more
they know, and freely confeſſe that they know little; nay, the
wiſeſt man in all Greece, and for ſuch pronounced by the Oracle,
openly profeſſed to know that he knew nothing.
SIMPL. It muſt be granted therefore, either that Socrates or
that the Oracle it ſelf was a lyar, that declaring him to be moſt
wiſe, and he confeſſing that he knew himſelf to be moſt
norant.
SALV. Neither one nor the other doth follow, for that both

the aſſertions may be true. The Oracle adjudged Socrates the
ſeſt of all men, whoſe knowledg is limited; Socrates
ledgeth that he knew nothing in relation to abſolute wiſdome,
which is infinite; and becauſe of infinite, much is the ſame part,
as is little, and as is nothing (for to arrive v. g. to the infinite
number, it is all one to accumulate thouſands, tens, or ciphers,)
therefore Socrates well perceived his wiſdom to be nothing, in
compariſon of the infinite knowledg which he wanted. But yet,
becauſe there is ſome knowledg found amongſt men, and this
not equally ſhared to all, Socrates might have a greater ſhare
thereof than others, and therefore verified the anſwer of the
Oracle.
The anſwer of
the Oracle true in
judging Socrates
the wiſeft of his
time.
SAGR. I think I very well underſtand this particular amongſt
men, Simplicius there is a power of operating, but not equally
diſpenſed to all; and it is without queſtion, that the power of an
Emperor is far greater than that of a private perſon; but, both
this and that are nothing in compariſon of the Divine
tence. Amongſt men, there are ſome that better underſtand
Agriculture than many others; but the knowledg of planting a
Vine in a trench, what hath it to do with the knowledg of
king it to ſprout forth, to attract nouriſhment, to ſelect this good
part from that other, for to make thereof leaves, another to make
ſprouts, another to make grapes, another to make raiſins,
ther to make the huskes of them, which are the works of moſt
wiſe Nature? This is one only particular act of the innumerable,
which Nature doth, and in it alone is diſcovered an infinite

dom, ſo that Divine Wiſdom may be concluded to be infinitely
infinite.
Divine Wiſdom
infinitely infinise.
SALV. Take hereof another example. Do we not ſay that the
1judicious diſcovering of a moſt lovely Statua in a piece of Marble,

hath ſublimated the wit of Buonarruotti far above the vulgar wits
of other men? And yet this work is onely the imitation of a
meer aptitude and diſpoſition of exteriour and ſuperficial
bers of an immoveable man; but what is it in compariſon of a
man made by nature, compoſed of as many exteriour and
riour members, of ſo many muſcles, tendons, nerves, bones,
which ſerve to ſo many and ſundry motions? but what ſhall we
ſay of the ſenſes, and of the powers of the ſoul, and laſtly, of
the underſtanding? May we not ſay, and that with reaſon, that
the ſtructure of a Statue fals far ſhort of the formation of a living
man, yea more of a contemptible worm?
Buonarruotti, a
ſtatuary of
rable ingenuity.
SAGR. And what difference think you, was there betwixt the
Dove of Architas, and one made by Nature?
SIMPL. Either I am none of theſe knowing men, or elſe
there is a manifeſt contradiction in this your diſcourſe. You
count underſtanding amongſt the greateſt (if you make it not the
chief of the) Encomiums aſcribed to man made by Nature, and
a little before you ſaid with Socrates, that he had no knowledg at
all; therefore you muſt ſay, that neither did Nature underſtand
how to make an underſtanding that underſtandeth.
SALV. You argue very cunningly, but to reply to your
ction I muſt have recourſe to a Philoſophical diſtinction, and ſay
that the underſtanding is to be taken too ways, that is intenſivè, or

extenſivè; and that extenſive, that is, as to the multitude of
ligibles, which are infinite, the underſtanding of man is as
thing, though he ſhould underſtand a thouſand propoſitions; for
that a thouſand, in reſpect of infinity is but as a cypher: but taking
the underſtanding intenſive, (in as much as that term imports)
tenſively, that is, perfectly ſome propoſitions, I ſay, that humane
dom underſtandeth ſome propoſitions ſo perfectly, and is as
lutely certain thereof, as Nature her ſelf; and ſuch are the pure
Mathematical ſciences, to wit, Geometry and Arithmetick: in which
Divine Wiſdom knows infinite more propoſitions, becauſe it knows
them all; but I believe that the knowledge of thoſe few
hended by humane underſtanding, equalleth the divine, as to the
certainty objectivè, for that it arriveth to comprehend the
ſity thereof, than which there can be no greater certainty.
Man
eth very well
tenſivè, but little
extenſivè.
SIMPL. This ſeemeth to me a very bold and raſh expreſſion.
SALV. Theſe are common notions, and far from all umbrage
of temerity, or boldneſs, and detract not in the leaſt from the
jeſty of divine wiſdom; as it nothing diminiſheth the omnipotence
thereof to ſay, that God cannot make what is once done, to be
done: but I doubt, Simplicius, that your ſcruple ariſeth from an
pinion you have, that my words are ſomewhat equivocal;
1fore the better to expreſs my ſelf I ſay, that as to the truth, of
which Mathematical demonſtrations give us the knowledge, it is
the ſame, which the divine wiſdom knoweth; but this I muſt grant
you, that the manner whereby God knoweth the infinite

ſitions, of which we underſtand ſome few, is highly more excellent
than ours, which proceedeth by ratiocination, and paſſeth from

cluſion to concluſion, whereas his is done at one ſingle thought or
intuition; and whereas we, for example, to attain the knowledg
of ſome paſſion of the Circle, which hath infinite, beginning
from one of the moſt ſimple, and taking that for its definition,
do proceed with argumentation to another, and from that to a
third, and then to a fourth, &c. the Divine Wiſdom, by the
apprehenſion of its eſſence comprehends, without temporary
ocination, all theſe infinite paſſions; which notwithſtanding, are
in effect virtually compriſed in the definitions of all things; and, to

conclude, as being infinite, perhaps are but one alone in their nature,
and in the Divine Mind; the which neither is wholly unknown to
humane underſtanding, but onely be-clouded with thick and

groſſe miſts; which come in part to be diſſipated and clarified,
when we are made Maſters of any concluſions, firmly
ſtrated, and ſo perfectly made ours, as that we can ſpeedily run
through them; for in ſum, what other, is that propoſition, that
the ſquare of the ſide ſubtending the right angle in any triangle,
is equal to the ſquares of the other two, which include it, but
onely the Paralellograms being upon common baſes, and between
parallels equal amongſt themſelves? and this, laſtly, is it not the
ſame, as to ſay that thoſe two ſuperficies are equal, of which
equal parts applyed to equal parts, poſſeſſe equal place? Now

theſe inferences, which our intellect apprehendeth with time and a
gradual motion, the Divine Wiſdom, like light, penetrateth in
an inſtant, which is the ſame as to ſay, hath them alwayes
ſent: I conclude therefore, that our underſtanding, both as to
the manner and the multitude of the things comprehended by us,
is infinitely ſurpaſt by the Divine Wiſdom; but yet I do not ſo
vilifie it, as to repute it abſolutely nothing; yea rather, when I
conſider how many and how great miſteries men have underſtood,
diſcovered, and contrived, I very plainly know and underſtand
the mind of man to be one of the works, yea one of the moſt
cellent works of God.
Gods manner of
knowing different
from that of men.
Humane
ſtanding done by
raciocination.
Definitions
tein virtually all
the paſſions of the
things defined.
Infinite Paſſions
are perhaps but
one onely.
The diſcourſes
which humane
reaſon makes in a
certain time, the
Divine Wiſdom
ſolveth in a
ment; that is, hath
them alwayes
ſent.
SAGR. I have oft times conſidered with my ſelf, in purſuance

of that which you ſpeak of, how great the wit of man is; and
whil'ſt I run thorow ſuch and ſo many admirable inventions found
out by him, as well in the Arts, as Sciences; and again reflecting
upon my own wit, ſo far from promiſing me the diſcovery of any
thing new, that I deſpair of comprehending what is already
1covered, confounded with wonder, and ſurpriſed with
tion, I account my ſelf little leſſe than miſerable. If I behold a
Statue of ſome excellent Maſter, I ſay with my ſelf; When wilt
thou know how to chizzle away the refuſe of a piece of Marble,
and diſcover ſo lovely a figure, as lyeth hid therein? When wilt
thou mix and ſpread ſo many different colours upon a Cloth, or
Wall, and repreſent therewith all viſible objects, like a Michael
Angelo, a Raphaello, or a Tizvano? If I behold what inventions
men have in comparting Muſical intervals, in eſtabliſhing
cepts and Rules for the management thereof with admirable
light to the ear: When ſhall I ceaſe my aſtoniſhment? What
ſhall I ſay of ſuch and ſo various Inſtruments of that Art? The
reading of excellent Poets, with what admiration doth it ſwell
any one that attentively conſidereth the invention of conceits,
and their explanation? What ſhall we ſay of Architecture?

What of Navigation? But, above all other ſtupendious
ons, what ſublimity of mind was that in him, that imagined to
himſelf to find out a way to communicate his moſt ſecret thoughts
to any other perſon, though very far diſtant from him either in
time, or place, ſpeaking with thoſe that are in the India's;
ing to thoſe that are not yet born, nor ſhall be this thouſand, or
ten thouſand years? and with how much facility? but by the

rious collocation of ^{*} twenty little letters upon a paper? Let this
be the Seal of all the admirable inventions of man, and the cloſe
of our Diſcourſe for this day: For the warmer hours being paſt,
I ſuppoſe that Salviatus hath a deſire to go and take the air in his
Gondelo; but too morrow we will both wait upon you, to
tinue the Diſcourſes we have begun, &c.
The wit of man
admirably acute.
The invention of
writing ſtupendious
above all others.
* For of ſo many
only the Italian
Alphabet conſiſts.
11[Figure 1]2[Figure 2]3[Figure 3]4[Figure 4]5[Figure 5]6[Figure 6]7[Figure 7]
Place this Plate
at the end of
the first
Dialogue
1
[Empty page]
1
GALILÆUS
Galilæus Lyncæus,
HIS
SYSTEME
OF THE
WORLD.
The Second Dialogue.
INTERLOCVTORS.
SALVIATUS, SAGREDUS, and SIMPLICIUS.
SALV. The yeſter-dayes diverſions which led us
out of the path of our principal diſcourſe,
were ſuch and ſo many, that I know not
how I can without your aſſiſtance
ver the track in which I am to proceed.
SAGR. I wonder not, that you, who
have your fancy charged and laden with
both what hath been, and is to be
ken, do find your ſelf in ſome
on; but I, who as being onely an Auditor, have nothing to
then my memory withal, but ſuch things as I have heard, may
happily by a ſuccinct rehearſal of them, recover the firſt thred
of our Diſcourſe. As far therefore as my memory ſerves me, the
ſum of yeſterdayes conferences were an examination of the
1ciples of Ptolomy and Copernicus, and which of their opinions is
the more probable and rational; that, which affirmeth the
ſtance of the Cœleſtial bodies to be ingenerable, incorruptible,
alterable, impaſſible, and in a word, exempt from all kind of change,
ſave that of local, and therefore to be a fifth eſſence, quite different
from this of our Elementary bodies, which are generable,
tible, alterable, &c. or elſe the other, which taking away ſuch
deformity from the parts of the World, holdeth the Earth to
joy the ſame perfections as the other integral bodies of the
verſe; and eſteemeth it a moveable and erratick Globe, no leſſe
than the Moon, Jupiter, Venus, or any other Planet: And laſtly,
maketh many particular parallels betwixt the Earth and Moon;
and more with the Moon, than with any other Planet;
ly by reaſon we have greater and more certain notice of it, as
being leſſe diſtant from us. And having, laſtly, concluded this
ſecond opinion to have more of probability with it than the firſt,
I ſhould think it beſt in the ſubſequent diſcourſes to begin to
mine whether the Earth be eſteemed immoveable, as it hath
been till now believed by moſt men, or elſe moveable, as ſome
ancient Philoſophers held, and others of not very receſſe times,
were of opinion; and if it be moveable, to enquire of what
kind its motion may be?
SALV. I ſee already what way I am to take; but before we
offer to proceed any farther, I am to ſay ſomething to you
ing thoſe laſt words which you ſpake, how that the opinion which
holds the Earth to be endued with the ſame conditions that the
Cœleſtial bodies enjoy, ſeems to be more true than the
ry; for that I affirmed no ſuch thing, nor would I have any of the
Propoſitions in controverſie, be made to ſpeak to any definitive
ſenſe: but I onely intended to produce on either part, thoſe
ſons and anſwers, arguments and ſolutions, which have been
therto thought upon by others, together with certain others,
which I have ſtumbled upon in my long ſearching thereinto,
wayes remitting the deciſion thereof to the judgment of others.
SAGR. I was unawares tranſported by my own ſenſe of the
thing; and believing that others ought to judg as I did, I made
that concluſion univerſal, which ſhould have been particular; and
therefore confeſſe I have erred, and the rather, in that I know
not what Simplicius his judgment is in this particular.
SIMPL. I muſt confeſſe, that I have been ruminating all this
night of what paſt yeſterday, and to ſay the truth, I meet
in with many acute, new, aud plauſible notions; yet nevertheleſs,
I find my ſelf over-perſwaded by the authority of ſo many great
Writers, and in particular -------&c. I ſee you ſhake your
head Sagredus, and ſmile to your ſelf, as if I had uttered ſome
great abſurdity.
1
SAGR. I not onely ſmile, but to tell you true, am ready to
burſt with holding in my ſelf from laughing outright, for you
have put me in mind of a very pretty paſſage, that I was a
neſſe of, not many years ſince, together with ſome others of
my worthy friends, which I could yet name unto you.
SALV. It would be well that you told us what it was, that ſo
Simplicius may not ſtill think that he gave you the occaſion of
laughter.
SAGR. I am content. I found one day, at home in his houſe, at
Venice, a famous Phiſician, to whom ſome flockt for their ſtudies,
and others out of curioſity, ſometimes came thither to ſee certain
natomies diſſected by the hand of a no leſſe learned, than careful
and experienced Anatomiſt. It chanced upon that day, when I was

there, that he was in ſearch of the original and riſe of the Nerves,
about which there is a famous controverſie between the Galeniſts
and Peripateticks; and the Anatomiſt ſhewing, how that the great
number of Nerves departing from the Brain, as their root, and
paſſing by the nape of the Neck, diſtend themſelves afterwards
along by the Back-bone, and branch themſelves thorow all the
Body; and that a very ſmall filament, as fine as a thred went to
the Heart; he turned to a Gentleman whom he knew to be a
ripatetick Philoſopher, and for whoſe ſake he had with
dinary exactneſſe, diſcovered and proved every thing, and
ed of him, if he was at length ſatisfied and perſwaded that the
nal of the Nerves proceeded from the Brain, and not from the
Heart? To which the Philoſopher, after he had ſtood muſing a

while, anſwered; you have made me to ſee this buſineſſe ſo
plainly and ſenſibly, that did not the Text of Ariſtotle aſſert the
contrary, which poſitively affirmeth the Nerves to proceed from
the Heart, I ſhould be conſtrained to confeſſe your opinion to be
true.
The original of
the Nerv s.
cording to
tle, and according
to Phiſicians.
The ridiculus
anſwer of a
ſopher,
ning the original of
the Nerves.
SIMPL. I would have you know my Maſters, that this
verſie about the original of the Nerves is not yet ſo proved and
decided, as ſome may perhaps perſwade themſelves.
SAGR. Nor queſtionleſſe ever ſhall it be, if it find ſuch like
contradictors; but that which you ſay, doth not at all leſſen the
extravagance of the anſwer of that Peripatetick, who againſt
ſuch ſenſible experience produced not other experiments, or
ſons of Ariſtotle, but his bare authority and pure ipſe dixit.
SIMPL. Ariſtotle had not gained ſo great authority, but for
the force of his Demonſtrations, and the profoundneſſe of his
arguments; but it is requiſite that we underſtand him, and not
onely underſtand him, but have ſo great familiarity with his
Books, that we form a perfect Idea thereof in our minds, ſo as
that every ſaying of his may be alwayes as it were, preſent in our
1memory for he did not write to the vulgar, nor is he obliged to
ſpin out his Sillogiſmes with the trivial method of diſputes; nay
rather, uſing a freedome, he hath ſometimes placed the proof
of one Propoſition amongſt Texts, which ſeem to treat of quite

another point; and therefore it is requiſite to be maſter of all
that vaſt Idea, and to learn how to connect this paſſage with that,
and to combine this Text with another far remote from it; for it
is not to be queſtioned but that he who hath thus ſtudied him,
knows how to gather from his Books the demonſtrations of every
knowable deduction, for that they contein all things.
Requiſites to fit
a man to
phate well after
the manner of
riſtotle.
SAGR. But good Simplicius, like as the things ſcattered here
and there in Ariſtotle, give you no trouble in collecting them,
but that you perſwade your ſelf to be able by comparing and

connecting ſeveral ſmall ſentences to extract thence the juice of
ſome deſired concluſion, ſo this, which you and other
ous Philoſophers do with the Text of Ariſtotle, I could do by the

verſes of Virgil, or of Ovid, compoſing thereof ^{*} Centones, and
therewith explaining all the affairs of men, and ſecrets of
ture. But what talk I of Virgil, or any other Poet? I have a
tle Book much ſhorter than Ariſtotle and Ovid, in which are
teined all the Sciences, and with very little ſtudy, one may gather
out of it a moſt perfect Idea, and this is the Alphabet; and there
is no doubt but that he who knows how to couple and diſpoſe
aright this and that vowel, with thoſe, or thoſe other conſonants,
may gather thence the infallible anſwers to all doubts, and
duce from them the principles of all Sciences and Arts, juſt in the
ſame manner as the Painter from divers ſimple colours, laid
rally upon his Pallate, proceedeth by mixing a little of this and
a little of that, with a little of a third, to repreſent to the life
men, plants, buildings, birds, fiſhes, and in a word,
ing what ever object is viſible, though there be not on the Pallate
all the while, either eyes, or feathers, or fins, or leaves, or ſtones.
Nay, farther, it is neceſſary, that none of the things to be
ted, or any part of them, be actually among colours, if you
would be able therewith to repreſent all things; for ſhould there
be amongſt them v. gr. feathers, theſe would ſerve to repreſent
nothing ſave birds, and plumed creatures.
A cunning way
to gather
phy out of any book
whatſoever.
* A word
ing works
ſed of many
ments of verſes
collected out of the
Poets.
SALV. And there are certain Gentlemen yet living, and in health,
who were preſent, when a Doctor, that was Profeſſor in a

mous Academy, hearing the deſcription of the Teleſcope, by him
not ſeen as then, ſaid, that the invention was taken from
ſtotle, and cauſing his works to be fetch't, he turned to a place
where the Philoſopher gives the reaſon, whence it commeth, that
from the bottom of a very deep Well, one may ſee the ſtars in
Heaven, at noon day; and, addreſſing himſelf to the company,
1ſee here, ſaith he, the Well, which repreſenteth the Tube, ſee
here the groſs vapours, from whence is taken the invention of
the Cryſtals, and ſee here laſtly the ſight fortified by the paſſage
of the rays through a diaphanous, but more denſe and obſcure
medium.
Invention of the
Teleſcope taken
from Ariſtotle.
SAGR. This is a way to comprehend all things knowable, much
like to that wherewith a piece of marble conteineth in it one, yea,
a thouſand very beautiful Statua's, but the difficulty lieth in
ing able to diſcover them; or we may ſay, that it is like to the
propheſies of Abbot Joachim, or the anſwers of the Heathen
Oracles, which are not to be underſtood, till after the things
fore-told are come to paſſe.
SALV. And why do you not adde the predictions of the
nethliacks, which are with like cleerneſſe ſeen after the event, in
their Horoſcopes, or, if you will, Configurations of the Heavens.
SAGR. In this manner the Chymiſts find, being led by their

melancholly humour, that all the ſublimeſt wits of the World
have writ of nothing elſe in reality, than of the way to make
Gold; but, that they might tranſmit the ſecret to poſterity
out diſcovering it to the vulgar, they contrived ſome one way, and
ſome another how to conceal the ſame under ſeveral maskes; and
it would make one merry to hear their comments upon the ancient
Poets, finding out the important miſteries, which lie hid under
their Fables; and the ſignification of the Loves of the Moon,
and her deſcending to the Earth for Endimion; her diſpleaſure
againſt Acteon, and what was meant by Jupiters turning himſelf
into a ſhowre of Gold; and into flames of fire; and what great
ſecrets of Art are conteined in that Mercury the Interpreter; in
thoſe thefts of Pluto; and in thoſe Branches of Gold.
Chymiſts
pret the Eables of
the Poets to be
crets for making of
Gold.
SIMPL. I believe, and in part know, that there want not in the
World very extravagant heads, the vanities of whom ought not to
redound to the prejudice of Ariſtotle, of whom my thinks you
ſpeak ſometimes with too little reſpect, and the onely antiquity
and bare name that he hath acquired in the opinions of ſo many
famous men, ſhould ſuffice to render him honourable with all
that profeſſe themſelves learned.
SALV. You ſtate not the matter rightly, Simplicius; There
are ſome of his followers that fear before they are in danger,
who give us occaſion, or, to ſay better, would give us cauſe to
eſteem him leſſe, ſhould we conſent to applaud their Capricio's.

And you, pray you tell me, are you for your part ſo ſimple, as
not to know that had Arictotle been preſent, to have heard the
Doctor that would have made him Author of the Teleſcope, he
would have been much more diſpleaſed with him, than with thoſe,
who laught at the Doctor and his Comments? Do you queſtion
1whether Ariſtotle, had he but ſeen the novelties diſcovered in
ven, would not have changed his opinion, amended his Books,
and embraced the more ſenſible Doctrine; rejecting thoſe ſilly
Gulls, which too ſcrupulouſly, go about to defend what ever he
hath ſaid; not conſidering, that if Ariſtotle were ſuch a one as
they fancy him to themſelves, he would be a man of an
ble wit, an obſtinate mind, a barbarous ſoul, a ſtubborn will,
that accounting all men elſe but as ſilly ſheep, would have his
Oracles preferred before the Senſes, Experience, and Nature her
ſelf? They are the Sectators of Aristotle that have given him this
Authority, and not he that hath uſurped or taken it upon him;
and becauſe it is more eaſie for a man to ſculk under anothers
ſhield than to ſhew himſelf openly, they tremble, and are affraid
to ſtir one ſtep from him; and rather than they will admit ſome
alterations in the Heaven of Ariſtotle, they will impertinently
ny thoſe they behold in the Heaven of Nature.
Some of
tles Sectators
pare the reputation
of their Maſter, in
going about to
hanſe it.
SAGR. Theſe kind of Drolleries put me in mind of that

ary which having reduced a great piece of Marble to the Image of
an Hercules, or a thundring Jupiter, I know not whether, and
given it with admirable Art ſuch a vivacity and threatning fury,
that it moved terror in as many as beheld it; he himſelf began
alſo to be affraid thereof, though all its ſprightfulneſſe, and life
was his own workmanſhip; and his affrightment was ſuch, that
he had no longer the courage to affront it with his Chizzels and
Mallet.
A ridiculous
paſſage of a certain
Statuary.
SALV. I have many times wondered how theſe nice
ers of what ever fell from Ariſtotle, are not aware how great a
judice they are to his reputation and credit; and how that the
more they go about to encreaſe his Authority, the more they
diminiſh it; for whileſt I ſee them obſtinate in their attempts
to maintain thoſe Propoſitions which I palpably diſcover to
be manifeſtly falſe; and in their deſires to perſwade me that
ſo to do, is the part of a Philoſopher; and that Ariſtotle himſelf
would do the ſame, it much abates in me of the opinion that he
hath rightly philoſophated about other concluſions, to me more
abſtruſe: for if I could ſee them concede and change opinion in
a manifeſt truth, I would believe, that in thoſe in which they
ſhould perſiſt, they may have ſome ſolid demonſtrations to me
known, and unheard of.
SAGR. Or when they ſhould be made to ſee that they have
zarded too much of their own and Ariſtotle's repuatation in
feſſing, that they had not underſtood this or that concluſion found
out by ſome other man; would it not be a leſs evil for them to
ſeek for it amongſt his Texts, by laying many of them together,
according to the art intimated to us by Simplicius? for if his
1works contain all things knowable, it muſt follow alſo that they
may be therein diſcovered.
SALV. Good Sagredus, make no jeſt of this advice, which me
thinks you rehearſe in too Ironical a way; for it is not long ſince
that a very eminent Philoſopher having compoſed a Book de animà,
wherein, citing the opinion of Ariſtotle, about its being or not
ing immortal, he alledged many Texts, (not any of thoſe
fore quoted by Alexander ab Alexandro: for in thoſe he ſaid, that
Ariſtotle had not ſo much as treated of that matter, much leſs
termined any thing pertaining to the ſame, but others) by himſelf
found out in other more abſtruſe places, which tended to an
roneous ſenſe: and being adviſed, that he would find it an hard
matter to get a Licence from the Inquiſitors, he writ back unto

his friend, that he would notwithſtanding, with all expedition
procure the ſame, for that if no other obſtacle ſhould interpoſe,
he would not much ſcruple to change the Doctrine of Ariſtotle,
and with other expoſitions, and other Texts to maintain the
trary opinion, which yet ſhould be alſo agreeable to the ſenſe of
Ariſtotle.
A brave
tion of a certain
Peripatetick
loſopher.
SAGR. Oh moſt profound Doctor, this! that can command
me that I ſtir not a ſtep from Ariſtotle, but will himſelf lead
him by the noſe, and make him ſpeak as he pleaſeth. See how
much it importeth to learn to take Time by the Fore-top. Nor
is it ſeaſonable to have to do with Hercules, whil'ſt he is
raged, and amongſt the Furies, but when he is telling merry tales
amongſt the Meonion Damoſels. Ah, unheard of ſordidneſſe of

ſervile ſouls! to make themſelves willing ſlaves to other mens
nions; to receive them for inviolable Decrees, to engage
ſelves to ſeem ſatisfied and convinced by arguments, of ſuch
cacy, and ſo manifeſtly concludent, that they themſelves
not certainly reſolve whether they were really writ to that
poſe, or ſerve to prove that aſſumption in hand, or the contrary.
But, which is a greater madneſſe, they are at variance amongſt
themſelves, whether the Author himſelf hath held the affirmative
part, or the negative. What is this, but to make an Oracle of a
Log, and to run to that for anſwers, to fear that, to reverence
and adore that?
The ſervile
rit of ſome of
ſtotles followers.
SIMPL. But in caſe we ſhould recede from Aristotle, who have
we to be our Guid in Philoſophy? Name you ſome Author.
SALV. We need a Guid in unknown and uncouth wayes, but
in champion places, and open plains, the blind only ſtand in need
of a Leader; and for ſuch, it is better that they ſtay at home.
But he that hath eyes in his head, and in his mind, him ſhould
a man chooſe for his Guid. Yet miſtake me not, thinking that I

ſpeak this, for that I am againſt hearing of Ariſtotle; for on the
1contrary, I commend the reading, and diligently ſtudying of him;
and onely blame the ſervile giving ones ſelf up a ſlave unto him,
ſo, as blindly to ſubſcribe to what ever he delivers, and without
ſearch of any farther reaſon thereof, to receive the ſame for an
violable decree. Which is an abuſe, that carrieth with it
ther great inconvenience, to wit, that others will no longer take
pains to underſtand the validity of his Demonſtrations. And
what is more ſhameful, than in the middeſt of publique diſputes,
whileſt one perſon is treating of demonſtrable concluſions, to
hear aother interpoſe with a paſſage of Ariſtotle, and not
dome writ to quite another purpoſe, and with that to ſtop the
mouth of his opponent? But if you will continue to ſtudy in this
manner, I would have you lay aſide the name of Philoſophers;

and call your ſelves either Hiſtorians or Doctors of Memory, for
it is not ſit, that thoſe who never philoſophate, ſhould uſurp
the honourable title of Philoſophers. But it is beſt for us to
turn to ſhore, and not lanch farther into a boundleſſe Gulph, out
of which we ſhall not be able to get before night. Therefore
Simplicius, come either with arguments and demonſtrations of
your own, or of Ariſtotle, and bring us no more Texts and

ked authorities, for our diſputes are about the Senſible World,
and not one of Paper. And foraſmuch as in our diſcourſes
day, we retrein'd the Earth from darkneſſe, and expoſed it to the
open skie, ſhewing, that the attempt to enumerate it amongſt
thoſe which we call Cœleſtial bodies, was not a poſition ſo foil'd,
and vanquiſh't, as that it had no life left in it; it followeth next,
that we proceed to examine what probability there is for holding
of it fixt, and wholly immoveable, ſcilicet as to its entire Globe,
what likelyhood there is for making it moveable with ſome motion,
and of what kind that may be. And foraſmuch as in this ſame
queſtion I am ambiguous, and Simplicius is reſolute, as likewiſe
Ariſtotle for the opinion of its immobility, he ſhall one by one
produce the arguments in favour of their opinion, and I will
ledge the anſwers and reaſons on the contrary part; and next
gredus ſhall tell us his thoughts, and to which ſide he finds
ſelf inclined.
Too cloſe
ring to Ariſtotle is
blameable.
It is not juſt, that
thoſe who never
philoſophate, ſhould
uſurp the title of
Philoſophers.
The Senſible
World.
SAGR. Content; provided alwayes that I may reſerve the
berty to my ſelf of alledging what pure natural reaſon ſhall
times dictate to me.
SALV. Nay more, it is that which I particularly beg of you;
for, amongſt the more eaſie, and, to ſo ſpeak, material
tions, I believe there are but few of them that have been
ted by Writers, ſo that onely ſome of the more ſubtle, and
mote can be deſired, or wanting; and to inveſtigate theſe, what
other ingenuity can be more ſit than that of the moſt acute and
piercing wit of Sagredus?
1
SAGR. I am what ever pleaſeth Salviatus, but I pray you,
let us not ſally out into another kind of digreſſion complemental;
for at this time I am a Philoſopher, and in the Schools, not in the
Court.
SALV. Let our contemplation begin therefore with this
deration, that whatſoever motion may be aſcribed to the Earth,
it is neceſſary that it be to us, (as inhabitants upon it, and
quently partakers of the ſame) altogether imperceptible, and as if
it were not at all, ſo long as we have regard onely to terreſtrial
things; but yet it is on the contrary, as neceſſary that the ſame

motion do ſeem common to all other bodies, and viſible
jects, that being ſeparated from the Earth, participate not of the
ſame. So that the true method to find whether any kind of motion
may be aſcribed to the Earth, and that found, to know what it
is, is to conſider and obſerve if in bodies ſeparated from the
Earth, one may diſcover any appearance of motion, which

qually ſuiteth to all the reſt; for a motion that is onely ſeen, v. gr.
in the Moon, and that hath nothing to do with Venus or Jupiter,
or any other Stars, cannot any way belong to the Earth, or to
any other ſave the Moon alone. Now there is a moſt general and
grand motion above all others, and it is that by which the Sun,

the Moon, the other Planets, and the Fixed Stars, and in a word,
the whole Univerſe, the Earth onely excepted, appeareth in our
thinking to move from the Eaſt towards the Weſt, in the ſpace of
twenty four hours; and this, as to this firſt appearance, hath no
obſtacle to hinder it, that it may not belong to the Earth alone,
as well as to all the World beſides, the Earth excepted; for the
ſame aſpects will appear in the one poſition, as in the other.
Hence it is that Ariſtotle and Ptolomy, as having hit upon this

ſideration, in going about to prove the Earth to be immoveable,
argue not againſt any other than this Diurnal Motion; ſave onely
that Ariſtotle hinteth ſomething in obſcure terms againſt another
Motion aſcribed to it by an Ancient, of which we ſhall ſpeak in
its place.
The motions of
the Earth are
perceptible to its
inhabitants.
The Earth can
have no other
tions, than thoſe
which to us appear
commune to all the
rest of the
verſe, the Earth
excepted.
The Diurnal
tion, ſeemeth
mune to all the
niverſe, ſave onely
the Earth excepted.
Ariſtotle and
Ptolomy argue
gainſt the
nal Motion
buted to the Earth.
SAGR. I very well perceive the neceſſity of your illation: but
I meet with a doubt which I know not how to free my ſelf from,
and this it is, That Copernicus aſſigning to the Earth another
tion beſide the Diurnal, which, according to the rule even now laid
down, ought to be to us, as to appearance, imperceptible in the
Earth, but viſible in all the reſt of the World; me thinks I may
neceſſarily infer, either that he hath manifeſtly erred in aſſigning
the Earth a motion, to which there appears not a general
ſpondence in Heaven; or elſe that if there be ſuch a congruity
therein, Ptolomy on the other hand hath been deficient in not
futing this, as he hath done the other.
1
SALV. You have good cauſe for your doubt: and when we
come to treat of the other Motion, you ſhall ſee how far
nicus excelled Ptolomey in clearneſs and ſublimity of wit, in that
he ſaw what the other did not, I mean the admirable harmony
wherein that Motion agreed with all the other Cœleſtial Bodies.
But for the preſent we will ſuſpend this particular, and return to
our firſt conſideration; touching which I will proceed to propoſe
(begining with things more general) thoſe reaſons which ſeem to
favour the mobility of the Earth, and then wait the anſwers which

Simplicius ſhall make thereto. And firſt, if we conſider onely
the immenſe magnitude of the Starry Sphere, compared to the
ſmalneſs of the Terreſtrial Globe, contained therein ſo many
lions of times; and moreover weigh the velocity of the motion
which muſt in a day and night make an entire revolution thereof,
I cannot perſwade my ſelf, that there is any man who believes it
more reaſonable and credible, that the Cœleſtial Sphere turneth
round, and the Terreſtrial Globe ſtands ſtill.
Why the diurnal
motion more
bably ſhould belong
to the Earth, than
to the reſt of the
Vniverſe.
SAGR. If from the univerſality of effects, which may in nature
have dependence upon ſuch like motions, there ſhould
ly follow all the ſame conſequences to an hair, aſwell in one
theſis as in the other; yet I for my part, as to my firſt and general
apprehenſion, would eſteem, that he which ſhould hold it more
tional to make the whole Univerſe move, and thereby to ſalve the
Earths mobility, is more unreaſonable than he that being got to
the top of your Turret, ſhould deſire, to the end onely that he
might behold the City, and the Fields about it, that the whole
Country might turn round, that ſo he might not be put to the
trouble to ſtir his head. And yet doubtleſs the advantages would
be many and great which the Copernican Hypotheſis is attended
with, above thoſe of the Ptolomaique, which in my opinion
ſembleth, nay ſurpaſſeth that other folly; ſo that all this makes
me think that far more probable than this. But haply Ariſtotle,
Ptolomey, and Simplicius may find the advantages of their
ſteme, which they would do well to communicate to us alſo, if
any ſuch there be; or elſe declare to me, that there neither are or
can be any ſuch things.
SALV. For my part, as I have not been able, as much as I have
thought upon it, to find any diverſity therein; ſo I think I have
found, that no ſuch diverſity can be in them: in ſo much that I

eſteem it to no purpoſe to ſeek farther after it. Therefore
ſerve: Motion is ſo far Motion, and as Motion operateth, by how
far it hath relation to things which want Motion: but in thoſe
things which all equally partake thereof it hath nothing to do, and
is as if it never were. And thus the Merchandiſes with which a
ſhip is laden, ſo far move, by how far leaving London, they paſs
1by France, Spain, Italy, and ſail to Aleppo, which London, France,
Spain &c. ſtand ſtill, not moving with the ſhip: but as to the
Cheſts, Bales and other Parcels, wherewith the ſhip is ſtow'd and
and laden, and in reſpect of the ſhip it ſelf, the Motion from
don to Syria is as much as nothing; and nothing-altereth the
lation which is between them: and this, becauſe it is common to
all, and is participated by all alike: and of the Cargo which is in
the ſhip, if a Bale were romag'd from a Cheſt but one inch onely,
this alone would be in that Cargo, a greater Motion in reſpect of
the Cheſt, than the whole Voyage of above three thouſand miles,
made by them as they were ſtived together.
Motion, as to the
things that equally
move thereby, is as
of it never were, &
ſo far operates as it
hath relation to
things deprived of
motion.
SIMPL. This Doctrine is good, ſound, and altogether
patetick.
SALV. I hold it to be much more antient: and ſuſpect that A-

riſtotle in receiving it from ſome good School, did not fully
ſtand it, and that therefore, having delivered it with ſome
tion, it hath been an occaſion of confuſion amongſt thoſe, who
would defend whatever he ſaith. And when he writ, that
ſoever moveth, doth move upon ſomething immoveable, I ſuppoſe
that he equivocated, and meant, that whatever moveth, moveth
in reſpect to ſomething immoveable; which propoſition admitteth
no doubt, and the other many.
A propoſition
ken by Ariſtotle
from the Antients,
but ſomewhat
tered by him.
SAGR. Pray you make no digreſſion, but proceed in the
ſertation you began.
SALV. It being therefore manifeſt, that the motion which is

common to many moveables, is idle, and as it were, null as to the
relation of thoſe moveables between themſelves, becauſe that
mong themſelves they have made no change: and that it is
rative onely in the relation that thoſe moveables have to other
things, which want that motion, among which the habitude is
changed: and we having divided the Univerſe into two parts, one
of which is neceſſarily moveable, and the other immoveable; for
the obtaining of whatſoever may depend upon, or be required
from ſuch a motion, it may as well be done by making the Earth
alone, as by making all the reſt of the World to move: for that
the operation of ſuch a motion conſiſts in nothing elſe, ſave in
the relation or habitude which is between the Cœleſtial Bodies,
and the Earth, the which relation is all that is changed. Now if
for the obtaining of the ſame effect ad unguem, it be all one
ther the Earth alone moveth, the reſt of the Univerſe ſtanding
ſtill; or that, the Earth onely ſtanding ſtill, the whole Univerſe

moveth with one and the ſame motion; who would believe, that
Nature (which by common conſent, doth not that by many things,
which may be done by few) hath choſen to make an innumerable
number of moſt vaſt bodies move, and that with an unconceivable
1velocity, to perform that, which might be done by the moderate
motion of one alone about its own Centre?
The firſt diſcourſe
to prove that the
diurnal motion
longs to the Earth.
Nature never
doth that by many
things, which may
be done by a few.
SIMPL. I do not well underſtand, how this grand motion
niſieth nothing as to the Sun, as to the Moon, as to the other
nets, and as to the innumerable multitude of fixed ſtars: or why
you ſhould ſay that it is to no purpoſe for the Sun to paſs from one
Meridian to another; to riſe above this Horizon, to ſet beneath
that other; to make it one while day, another while night: the
like variations are made by the Moon, the other Planets, and the
fixed ſtars themſelves.
SALV. All theſe alterations inſtanced by you, are nothing, ſave
onely in relation to the Earth: and that this is true, do but

magine the Earth to move, and there will be no ſuch thing in the
World as the riſing or ſetting of the Sun or Moon, nor Horizons,
nor Meridians, nor days, nor nights; nor, in a word, will ſuch a
motion cauſe any mutation between the Moon and Sun, or any
other ſtar whatſoever, whether fixed or erratick; but all theſe
changes have relation to the Earth: which all do yet in ſum
import no other than as if the Sun ſhould ſhew it ſelf now to
China, anon to Perſia, then to Egypt, Greece, France, Spain,
merica, &c. and the like holdeth in the Moon, and the reſt of the
Cœleſtial Bodies: which ſelf ſame effect falls out exactly in the
ſame manner, if, without troubling ſo great a part of the Univerſe,

the Terreſtrial Globe be made to revolve in it ſelf. But we will
augment the difficulty by the addition of this other, which is a
very great one, namely, that if you will aſcribe this Great Motion to
Heaven, you muſt of neceſſity make it contrary to the particular
motion of all the Orbs of the Planets, each of which without
controverſie hath its peculiar motion from the Weſt towards the
Eaſt, and this but very eaſie and moderate: and then you make
them to be hurried to the contrary part, i. e. from Eaſt to Weſt,
by this moſt furious diurnal motion: whereas, on the contrary,
making the Earth to move in it ſelf, the contrariety of motions is
taken away, and the onely motion from Weſt to Eaſt is
modated to all appearances, and exactly ſatisfieth every
menon.
The diurnal
tion cauſeth no
mutation amongſt
the Cœleſtial
dies, but all
ges have relation
to the Earth.
A ſccond
firmation that the
diurnal motion
longs to the Earth.
SIMPL. As to the contrariety of Motions it would import

tle, for Ariſtotle demonſtrateth, that circular motions, are not
trary to one another; and that theirs cannot be truly called
trariety.
Circular
ons are not
ry, according to
Ariſtotle.
SALV. Doth Ariſtotle demonſtrate this, or doth he not rather
barely affirm it, as ſerving to ſome certain deſign of his? If
traries be thoſe things, that deſtroy one another, as he himſelf
affirmeth, I do not ſee how two moveables that encounter each
other in a circular line, ſhould leſſe prejudice one another, than if
they interfered in a right line.
1
SAGR. Hold a little, I pray you. Tell me Simplicius, when
two Knights encounter each other, tilting in open field, or when
two whole Squadrons, or two Fleets at Sea, make up to grapple,
and are broken and ſunk, do you call theſe encounters contrary to
one another?
SIMPL. Yes, we ſay they are contrary.
SAGR. How then, is there no contrariety in circular motions.
Theſe motions, being made upon the ſuperſicies of the Earth or
Water, which are, as you know, ſpherical, come to be circular.
Can you tell, Simplicius, which thoſe circular motions be, that
are not contrary to each other? They are (if I miſtake not) thoſe
of two circles, which touching one another without, one thereof
being turn'd round, naturally maketh the other move the
ry ^{*} way; but if one of them ſhall be within the other, it is

poſſible that their motion being made towards different points,
they ſhould not juſtle one another.
As you ſee in a
Mill, wherein the
implicated cogs ſet
the wheels on
ving.
SALV. But be they contrary, or not contrary, theſe are but
alterations of words; and I know, that upon the matter, it would
be far more proper and agreeable with Nature, if we could ſalve
all with one motion onely, than to introduce two that are (if you
will not call them contrary) oppoſite; yet do I not cenſure this
introduction (of contrary motions) as impoſſible; nor pretend I
from the denial thereof, to inferre a neceſſary Demonſtration,
but onely a greater probability, of the other. A third reaſon

which maketh the Ptolomaique Hypotheſis leſſe probable is, that it
moſt unreaſonably confoundeth the order, which we aſſuredly
ſee to be amongſt thoſe Cœleſtial Bodies, the circumgyration of
which is not queſtionable, but moſt certain. And that Order is,

that according as an Orb is greater, it finiſheth its revolution in a
longer time, and the leſſer, in ſhorter. And thus Saturn
bing a greater Circle than all the other Planets, compleateth the
ſame in thirty yeares: Jupiter finiſheth his; that is leſſe, in
twelve years: Mars in two: The Moon runneth thorow hers, ſo
much leſſe than the reſt, in a Moneth onely. Nor do we leſſe
ſenſibly ſee that of the Medicean Stars, which is neareſt to Ju-

piter, to make its revolution in a very ſhort time, that is, in four
and forty hours, or thereabouts, the next to that in three dayes and
an half, the third in ſeven dayes, and the moſt remote in ſixteen.
And this rate holdeth well enough, nor will it at all alter, whileſt
we aſſign the motion of 24 hours to the Terreſtrial Globe, for it
to move round its own center in that time; but if you would have
the Earth immoveable, it is neceſſary, that when you have paſt
from the ſhort period of the Moon, to the others ſucceſſively
bigger, until you come to that of Mars in two years, and from
thence to that of the bigger Sphere of Jupiter in twelve years, and
1from this to the other yet bigger of Saturn, whoſe period is of
thirty years, it is neceſſary, I ſay, that you paſſe to another
Sphere incomparably greater ſtill than that, and make this to

compliſh an entire revolution in twenty four hours. And this yet is
the leaſt diſorder that can follow. For if any one ſhould paſſe
from the Sphere of Saturn to the Starry Orb, and make it ſo
much bigger than that of Saturn, as proportion would require, in
reſpect of its very ſlow motion, of many thouſands of years, then
it muſt needs be a Salt much more abſurd, to skip from this to
another bigger, and to make it convertible in twenty four hours.
But the motion of the Earth being granted, the order of the
riods will be exactly obſerved, and from the very ſlow Sphere of
Saturn, we come to the fixed Stars, which are wholly

ble, and ſo avoid a fourth difficulty, which we muſt of neceſſity
mit, if the Starry Sphere be ſuppoſed moveable, and that is the

immenſe diſparity between the motions of thoſe ſtars themſelves;
of which ſome would come to move moſt ſwiftly in moſt vaſt
cles, others moſt ſlowly in circles very ſmall, according as thoſe
or theſe ſhould be found nearer, or more remote from the Poles;
which ſtill is accompanied with an inconvenience, as well becauſe
we ſee thoſe, of whoſe motion there is no queſtion to be made,
to move all in very immenſe circles; as alſo, becauſe it ſeems to
be an act done with no good conſideration, to conſtitute bodies,
that are deſigned to move circularly, at immenſe diſtances from
the centre, and afterwards to make them move in very ſmall
cles. And not onely the magnitudes of the circles, and
quently the velocity of the motions of theſe Stars, ſhall be moſt

different from the circles and motions of thoſe others, but
(which ſhall be the fifth inconvenience) the ſelf-ſame Stars
ſhall ſucceſſively vary its circles and velocities: For that

thoſe, which two thouſand years ſince were in the Equinoctial,
and conſequently did with their motion deſcribe very vaſt
cles, being in our dayes many degrees diſtant from thence, muſt
of neceſſity become more ſlow of motion, and be reduced to
move in leſſer circles, and it is not altogether impoſſible but that
a time may come, in which ſome of them which in aforetime had
continually moved, ſhall be reduced by uniting with the Pole, to
a ſtate of reſt, and then after ſome time of ceſſation, ſhall return
to their motion again; whereas the other Stars, touching whoſe
motion none ſtand in doubt, do all deſcribe, as hath been ſaid,
the great circle of their Orb, and in that maintain themſelves
without any variation. The abſurdity is farther enlarged (which

let be the ſixth inconvenience) to him that more ſeriouſly
neth the thing, in that no thought can comprehend what ought to
be the ſolidity of that immenſe Sphere, whoſe depth ſo ſtedfaſtly
1holdeth faſt ſuch a multitude of Stars, which without ever
ing fite among themſelves, are with ſo much concord carried
bout, with ſo great diſparity of motions. Or elſe, ſuppoſing the
Heavens to be fluid, as we are with more reaſon to believe, ſo
as that every Star wandereth to and fro in it, by wayes of its
own, what rules ſhall regulate their motions, and to what
poſe, ſo, as that being beheld from the Earth, they appear as if
they were made by one onely Sphere? It is my opinion, that they
might ſo much more eaſily do that, and in a more commodious
manner, by being conſtituted immoveable, than by being made
errant, by how much more facile it is to number the quarries in the
Pavement of a Piazza, than the rout of boyes which run up and
down upon them. And laſtly, which is the ſeventh inſtance, if

we atribute the Diurnal Motion to the higheſt Heaven, it muſt be
conſtituted of ſuch a force and efficacy, as to carry along with
it the innumerable multitude of fixed Stars, Bodies all of vaſt
magnitude, and far bigger than the Earth; and moreover all the
Spheres of the Planets; notwithſtanding that both theſe and thoſe
of their own nature move the contrary way. And beſides all this,
it muſt be granted, that alſo the Element of Fire, and the
er part of the Air, are likewiſe forcibly hurried along with the
reſt, and that the ſole little Globe of the Earth pertinaciouſly
ſtands ſtill, and unmoved againſt ſuch an impulſe; a thing, which
in my thinking, is very difficult; nor can I ſee how the Earth, a
pendent body, and equilibrated upon its centre, expoſed

ferently to either motion or reſt, and environed with a liquid
bient, ſhould not yield alſo as the reſt, and be carried about.
But we find none of theſe obſtacles in making the Earth to move;
a ſmall body, and inſenſible, compared to the Univerſe, and
therefore unable to offer it any violence.
A third
mation of the ſame
Doctrine.
The greater Orbs
make their
ſions in greater
times.
The times of the
Medicean Planets
converſions.
The motion of
24 hours aſcribed
to the higheſt
Sphere diſorders
the period of the
inferiour.
The fourth
firmation.
Great diſparity
amongſt the
ons of the
lar fixed ſtars, if
their Sphere be
moveable.
The fifth
firmation.
The motions of
the fixed ſtars
would accelerate
and grow ſlow in
divers times, if the
ſtarry Sphere were
moueable.
The ſixth
firmatiox.
The Seventh
firmation.
The Earth a
pendent Body, and
equilibrated in a
fluid Medium
ſeems unable to
reſiſt the rapture
of the Diurnal
Motion.
SAGR. I find my fancy diſturbed with certain conjectures ſo
fuſedly ſprung from your later diſcourſes; that, if I would be
bled to apply my ſelf with atention to what followeth, I muſt of
ceſſity attempt whether I can better methodize them, and gather
thence their true conſtruction, if haply any can be made of them;
and peradventure, the proceeding by interrogations may help me
the more eaſily to expreſſe my ſelf. Therefore I demand firſt of
plicius, whether he believeth, that divers motions may
ly agree to one and the ſame moveable body, or elſe that it be
requiſite its natural and proper motion be onely one.
SIMPL. To one ſingle moveable, there can naturally agree

but one ſole motion, and no more; the reſt all happen
tally and by participation; like as to him that walketh upon the
Deck of a Ship, his proper motion is that of his walk, his motion
by participation that which carrieth him to his Port, whither he
1would never with his walking have arrived, if the Ship with its
motion had not wafted him thither.
A ſingle
able hath but onely
one natural
on, and all the
reſt are by
pation.
SAGR. Tell me ſecondly. That motion, which is
cated to any moveable by participation, whileſt it moveth by it
ſelf, with another motion different from the participated, is it
neceſſary, that it do reſide in ſome certain ſubject by it ſelf, or
elſe can it ſubſiſt in nature alone, without other ſupport.
SIMPL. Ariſtotle giveth you an anſwer to all theſe queſtions,

and tels you, that as of one ſole moveable the motion is but one;
ſo of one ſole motion the moveable is but one; and
ly, that without the inherence in its ſubject, no motion can
ther ſubſiſt, or be imagined.
Motion cannot
be made without
its moveable
ject.
SAGR. I would have you tell me in the third place, whether
you beblieve that the Moon and the other Planets and Cœleſtial
bodies, have their proper motions, and what they are.
SIMPL. They have ſo, and they be thoſe according to which
they run through the Zodiack, the Moon in a Moneth, the Sun
in a Year, Mars in two, the Starry Sphere in thoſe ſo many
ſand. And theſe are their proper, or natural motions.
SAGR. But that motion wherewith I ſee the fixed Stars, and
with them all the Planets go unitedly from Eaſt to Weſt, and
turn round to the Eaſt again in twenty four hours, how doth it
agree with them?
SIMPL. It ſuiteth with them by participation.
SAGR. This then reſides not in them, and not reſiding in
them, nor being able to ſubſiſt without ſome ſubject in which it
is reſident, it muſt of force be the proper and natural motion of
ſome other Sphere.
SIMPL. For this purpoſe Aſtronomers, and Philoſophers have
found another high Sphere, above all the reſt, without Stars, to
which Natural agreeth the Diurnal Motion; and this they call
the Primum mobile; the which carrieth along with it all the
feriour Spheres, contributing and imparting its motion to
them.
SAGR. But when, without introducing other Spheres unknown
and hugely vaſt, without other motions or communicated raptures,
with leaving to each Sphere its ſole and ſimple motion, without
intermixing contrary motions, but making all turn one way, as
it is neceſſary that they do, depending all upon one ſole principle,
all things proceed orderly, and correſpond with moſt perfect
mony, why do we reject this Phœnomenon, and give our aſſent to
thoſe prodigious and laborious conditions?
SIMPL. The difficulty lyeth in finding out this ſo natural and
expeditious way.
1
SAGR. In my judgment this is found. Make the Earth the
Primum mobile, that is, make it turn round its own axis in twenty
four hours, and towards the ſame point with all the other Spheres;
and without participating this ſame motion to any other Planet or
Star, all ſhall have their riſings, ſettings, and in a word, all their
other appearances.
SIMPL. The buſineſs is, to be able to make the Earth move
without athouſand inconveniences.
SALV. All the inconveniences ſhall be removed as faſt as you
propound them: and the things ſpoken hitherto are onely the
primary and more general inducements which give us to believe
that the diurnal converſion may not altogether without
lity be applyed to the Earth, rather than to all the reſt of the
niverſe: the which inducements I impoſe not upon you as
lable Axioms, but as hints, which carry with them ſomewhat of
likelihood. And in regard I know very well, that one ſole

periment, or concludent demonſtration, produced on the contrary
part, ſufficeth to batter to the ground theſe and a thouſand other
probable Arguments; therefore it is not fit to ſtay here, but proceed
forwards and hear what Simplicius anſwereth, and what greater
probabilities, or ſtronger arguments he alledgeth on the contrary.
One ſingle
periment, or ſound
demonſtration
tereth down all
guments meerly
probable.
SIMPL. I will firſt ſay ſomething in general upon all theſe
ſiderations together, and then I will deſcend to ſome particulars.
It ſeems that you univerſally bottom all you ſay upon the greater
ſimplicity and facility of producing the ſame effects, whilſt you
hold, that as to the cauſing of them, the motion of the Earth
lone, ſerveth as well as that of all the reſt of the World, the Earth
deducted: but as to the operations, you eſteem that much eaſier
than this. To which I reply, that I am alſo of the ſame opinion,
ſo long as I regard my own not onely finite, but feeble power;
but having a reſpect to the ſtrength of the Mover, which is
finite, its no leſſe eaſie to move the Univerſe, than the Earth,
yea than a ſtraw. And if his power be infinite, why ſhould he not

rather exerciſe a greater part thereof than a leſſe? Therefore,
I hold that your diſcourſe in general is not convincing.
Of an infinite
power one would
think a greater
part ſhould rather
be imploy'd than a
leſſe.
SALV. If I had at any time ſaid, that the Univerſe moved not
for want of power in the Mover, I ſhould have erred, and your
reproof would have been ſeaſonable; and I grant you, that to
an infinite power, it is as eaſie to move an hundred thouſand, as
one. But that which I did ſay, concerns not the Mover, but
ly hath reſpect to the Moveables; and in them, not onely to
their reſiſtance, which doubtleſſe is leſſer in the Earth, than in
the Univerſe; but to the many other particulars, but even now
conſidered. As to what you ſay in the next place, that of an
finite power it is better to exerciſe a great part than a ſmall: I
1ſwer, that of infinite one part is not greater than another, ſince

both are infinite; nor can it be ſaid, that of the infinite number,
an hundred thouſand is a greater part than two, though that be
fifty thouſand times greater than this; and if to the moving of
the Univerſe there be required a finite power, though very great
in compariſon of that which ſufficeth to move the Earth onely;
yet is there not implied therein a greater part of the infinite power,
nor is that part leſſe infinite which remaineth unimploy'd. So that
to apply unto a particular effect, a little more, or a little leſſe
power, importeth nothing; beſides that the operation of ſuch
vertue, hath not for its bound or end the Diurnal Motion onely;
but there are ſeveral other motions in the World, which we
know of, and many others there may be, that are to us unknown.
Therefore if we reſpect the Moveables, and granting it as out of
queſtion, that it is a ſhorter and eaſier way to move the Earth,
than the Univerſe; and moreover, having an eye to the ſo many
other abreviations, and facilities that onely this way are to be
tained, an infallible Maxime of Ariſtotle, which he teacheth us,
that, fruſtra fit per plura, quod poteſt fieri per pauciora,
dereth it more probable that the Diurnal Motion belongs to the
Earth alone, than to the Univerſe, the Earth ſubducted.
Of infinity one
part is no bigger
than auother,
though they are
comparatively
equal.
SIMPL. In reciting that Axiom, you have omitted a ſmall
clauſe, which importeth as much as all the reſt, eſpecially in our
caſe, that is to ſay, the words æquè bene. It is requiſite therefore
to examine whether this Hypotheſis doth equally well ſatisfie in all
particulars, as the other.
SALV. The knowledg whether both theſe poſitions do æquè
bene, ſatisfie, may be comprehended from the particular
nation of the appearances which they are to ſatisfie; for hitherto
we have diſcourſed, and will continue to argue ex hypotheſi,
namely, ſuppoſing, that as to the ſatisfaction of the appearances,

both the aſſumptions are equally accomodated. As to the clauſe
which you ſay was omitted by me, I have more reaſon to ſuſpect
that it was ſuperfluouſly inſerted by you. For the expreſſion æquè
bene, is a relative that neceſſarily requireth two terms at leaſt,
for a thing cannot have relation to its ſelf, nor do we ſay, v. gr.
reſt to be equally good, as reſt. And becauſe, when we ſay, that
is done in vain by many means, which may be done with fewer,
we mean, that that which is to be done, ought to be the ſame
thing, not two different ones; and becauſe the ſame thing
not be ſaid to be done as well as its ſelf; therefore, the addition
of the Phraſe æquè bene is ſuperfluous, and a relation, that hath
but one term onely.
In the Axiome
Fruſtra fit per
ra, &c. the
tion of æque benè,
is ſuperfluous.
SAGR. Unleſſe you will have the ſame befal us, as did
day, let us return to our matter in hand; and let Simplicius
1gin to produce thoſe difficulties that ſeem in his opinion, to thwart
this new diſpoſition of the World.
SIMPL. That diſpoſition is not new, but very old, and that
you may ſee it is ſo, Ariſtotle confuteth it; and his confutations
are theſe: “Firſt if the Earth moveth either in it felf about its

own Centre, or in an Excentrick Circle, it is neceſſary that that
ſame motion be violent; for it is not its natural motion, for
if it were, each of its parts would partake thereof; but each
of them moveth in a right line towards its Centre. It being
therefore violent and pteternatural, it could never be
al: But the order of the World is perpetual. Therefore, &c.
Secondly, all the other moveables that move circularly, ſeem
to ^{*} ſtay behind, and to move with more than one motion, the

Primum Mobile excepted: Whence it would be neceſſary that
the Earth alſo do move with two motions; and if that ſhould
be ſo, it would inevitably follow, that mutations ſhould be
made in the Fixed Stars, the which none do perceive; nay
without any variation, the ſame Stars alwayes riſe from towards
the ſame places, and in the ſame places do ſet. Thirdly, the
tion of the parts is the ſame with that of the whole, and
ly tendeth towards the Centre of the Univerſe; and for the ſame
cauſe reſt, being arrived thither. He thereupon moves the
ſtion whether the motion of the parts hath a tendency to the
centre of the Univerſe, or to the centre of the Earth; and
deth that it goeth by proper inſtinct to the centre of the Univerſe,
and per accidence to that of the Earth; of which point we largely
diſcourſed yeſterday. He laſtly confirmeth the ſame with a fourth
argument taken from the experiment of grave bodies, which
ing from on high, deſcend perpendicularly unto the Earthsſurface;
and in the ſame manner Projections ſhot perpendicularly upwards,
do by the ſame lines return perpendicularly down again, though
they were ſhot to a very great height. All which arguments
ſarily prove their motion to be towards the Centre of the Earth,
which without moving at all waits for, and receiveth them. He
intimateth in the laſt place that the Aſtronomers alledg other
reaſons in confirmation of the ſame concluſions, I mean of the
Earths being in the Centre of the Univerſe, and immoveable;
and inſtanceth onely in one of them, to wit, that all the
nomena or appearances that are ſeen in the motions of the Stars,
perfectly agree with the poſition of the Earth in the Centre;
which would not be ſo, were the Earth ſeated otherwiſe.
The reſt produced by Ptolomy and the other Aſtronomers, I can
give you now if you pleaſe, or after you have ſpoken what you
have to ſay in anſwer to theſe of Ariſtotle.”
Ariſtotles
guments for the
Earths quieſſence.
* Reſtino indietzo,
which is meant
here of that
on which a bowl
makes when its
born by its by as to
one ſide or other,
and ſo hindered in
its direct motion.
SALV. The arguments which are brought upon this occaſion
1are of two kinds: ſome have reſpect to the accidents Terreſtrial,

without any relation to the Stars, and others are taken from the
Phænomena and obſervations of things Cœleſtial. The arguments
of Ariſtotle are for the moſt part taken from things neer at hand,
and he leaveth the others to Aſtronomers; and therefore it is the
beſt way, if you like of it, to examine theſe taken from
ments touching the Earth, and then proceed to thoſe of the other
kind. And becauſe Ptolomy, Tycho, and the other Aſtronomers

and Philoſophers, beſides the arguments of Ariſtotle by them
med, confirmed, and made good, do produce certain others; we
will put them all together, that ſo we may not anſwer twice to
the ſame, or the like objections. Therefore Simplicius, chooſe
whether you will recite them your ſelf, or cauſe me to eaſe you of
this task, for I am ready to ſerve you.
Two kindes of
Arguments
ching the Earths
motion or rest.
Arguments of
Ptolomy and
cho, and other
ſons, over and
bove thoſe of
ſtotle.
SIMPL. It is better that you quote them, becauſe, as having
taken more pains in the ſtudy of them, you can produce them with
more readineſſe, and in greater
The firſt
ment taken from
grave bodies
ling from on high
to the ground.
SALV. All, for the ſtrongeſt reaſon, alledge that of grave
dies, which falling downwards from on high, move by a right line,
that is perpendicular to the ſurface of the Earth, an argument
which is held undeniably to prove that the Earth is immoveable:
for in caſe it ſhould have the diurnal motion, a Tower, from the
top of which a ſtone is let fall, being carried along by the
ſion of the Earth, in the time that the ſtone ſpends in falling, would
be tranſported many hundred yards Eaſtward, and ſo far diſtant
from the Towers foot would the ſtone come to ground. The
which effect they back with another experiment; to wit, by let­

ting a bullet of lead fall from the round top of a Ship, that lieth at
anchor, and obſerving the mark it makes where it lights, which they
find to be neer the ^{*} partners of the Maſt; but if the ſame bullet

be let fall from the ſame place when the ſhip is under ſail, it ſhall
light as far from the former place, as the ſhip hath run in the time
of the leads deſcent; and this for no other reaſon, than becauſe
the natural motion of the ball being at liberty is by a right line

wards the centre of the Earth. They fortiſie this argument with
the experiment of a projection ſhot on high at a very great
ſtance; as for example, a ball ſent out of a Cannon, erected
pendicular to the horizon, the which ſpendeth ſo much time in
cending and falling, that in our parallel the Cannon and we both
ſhould be carried by the Earth many miles towards the Eaſt, ſo
that the ball in its return could never come neer the Peece, but

would fall as far Weſt, as the Earth had run Eaſt. They againe
adde a third, and very evident experiment, ſcilicet, that ſhooting a
bullet point blank (or as Gunners ſay, neither above nor under
tal) out of a Culverin towards the Eaſt, and afterwards another,
1with the ſame charge, and at the ſame elevation or diſport towards
the Weſt, the range towards the Weſt ſhould be very much
ter then the other towards the Eaſt: for that whil'ſt the ball goeth
Weſtward, and the Peece is carried along by the Earth Eaſtward,
the ball will fall from the Peece as far diſtant as is the aggregate of
the two motions, one made by it ſelf towards the Weſt, and the
other by the Peece carried about by the Earth towards the Eaſt;
and on the contrary, from the range of the ball ſhot Eaſtward you
are to ſubſtract the ſpace the Peece moved, being carried after it.
Now ſuppoſe, for example, that the range of the ball ſhot Weſt
were five miles, and that the Earth in the ſame parallel and in the
time of the Bals ranging ſhould remove three miles, the Ball in this
caſe would fall eight miles diſtant from the Culverin, namely, its
own five Weſtward, and the Culverins three miles Eaſtward: but
the range of the ſhot towards the Eaſt would be but two miles
long, for ſo much is the remainder, after you have ſubſtracted
from the five miles of the range, the three miles which the Peece
had moved towards the ſame part. But experience ſheweth the
Ranges to be equal, therefore the Culverin, and conſequently the
Earth are immoveable. And the ſtability of the Earth is no leſfe

confirmed by two other ſhots made North and South; for they
would never hit the mark, but the Ranges would be alwayes wide,
or towards the Weſt, by meanes of the remove the mark would
make, being carried along with the Earth towards the Eaſt, whil'ſt
the ball is flying. And not onely ſhots made by the Meridians,

but alſo thoſe aimed Eaſt or Weſt would prove uncertain; for
thoſe aim'd Eaſt would be too high, and thoſe directed Weſt too
low, although they were ſhot point blank, as I ſaid. For the
Range of the Ball in both the ſhots being made by the Tangent,
that is, by a line parallel to the Horizon, and being that in the
urnal motion, if it be of the Earth, the Horizon goeth continually
deſcending towards the Eaſt, and riſing from the Weſt (therefore
the Oriental Stars ſeem to riſe, and the Occidental to decline) ſo
that the Oriental mark would deſcend below the aime, and
upon the ſhot would fly too high, and the aſcending of the
ern mark would make the ſhot aimed that way range too low; ſo
that the Peece would never carry true towards any point; and for
that experience telleth us the contrary, it is requiſite to ſay, that
the Earth is immoveable.
Which is
med by the
ment of a body let
fall from the round
top of a Ship.
* That is, at the
foot of the Maſt,
upon the upper
deck.
The ſecond
gument taken from
a Projection ſhot
very high.
The third
ment taken from
the ſhots of a
non, towards the
Eaſt, and towards
the West.
This argument
is confirmed by two
ſhots towards the
South and towards
the North.
And it is
wiſe confirmed by
two ſhots towards
the Eaſt, and
wards the Weſt.
SIMPL. Theſe are ſolid reaſons, and ſuch as I believe no man
can anſwer.
SALV. Perhaps they are new to you?
SIMPL. Really they are; and now I ſee with how many
mirable experiments Nature is pleaſed to favour us, wherewith to
aſſiſt us in the knowledge of the Truth. Oh! how exactly one
1truth agreeth with another, and all conſpire to render each other
inexpugnable!
SAGR. What pity it is that Guns were not uſed in Ariſtotles
age, he would with help of them have eaſily battered down
norance, and ſpoke without hæſitation of theſe mundane points.
SALV. I am very glad that theſe reaſons are new unto you, that
ſo you may not reſt in the opinion of the major part of
ticks, who believe, that if any one forſakes the Doctrine of
ſtotle, it is becauſe they did not underſtand or rightly apprehend
his demonſtrations. But you may expect to hear of other

ties, and you ſhall ſee the followers of this new Syſteme produce
gainſt themſelves obſervations, experiences, and reaſons of farre
greater force than thoſe alledged by Aristotle, Ptolomy, and other
oppoſers of the ſame concluſions, and by this means you ſhall come
to aſcertain your ſelf that they were not induced through want of
knowledge or experience to follow that opinion.
Copernicus his
followers are not
moved through
nor ance of the
guments on the
ther part.
SAGR. It is requiſite that upon this occaſion I relate unto you
ſome accidents that befell me, ſo ſoon as I firſt began to hear ſpeak
of this new doctrine. Being very young, and having ſcarcely
niſhed my courſe of Philoſophy, which I left off, as being ſet upon
other employments, there chanced to come into theſe parts a
tain Foreigner of Roſtock, whoſe name, as I remember, was Chri-

ſtianus Vurſtitius, a follower of Copernicus, who in an Academy
made two or three Lectures upon this point, to whom many flock't
as Auditors; but I thinking they went more for the novelty of the
ſubject than otherwiſe, did not go to hear him: for I had
ded with my ſelf that that opinion could be no other than a ſolemn
madneſſe. And queſtioning ſome of thoſe who had been there, I
perceived they all made a jeſt thereof, execpt one, who told me
that the buſineſſe was not altogether to be laugh't at, and becauſe
this man was reputed by me to be very intelligent and wary, I
pented that I was not there, and began from that time forward as
oft as I met with any one of the Copernican perſwaſion, to demand
of them, if they had been alwayes of the ſame judgment; and of as
many as I examined, I found not ſo much as one, who told me not
that he had been a long time of the contrary opinion, but to have
changed it for this, as convinced by the ſtrength of the reaſons
ving the ſame: and afterwards queſtioning them, one by one; to
ſee whether they were well poſſeſt of the reaſons of the other ſide;

I found them all to be very ready and perfect in them; ſo that I
could not truly ſay, that they had took up this opinion out of
norance, vanity, or to ſhew the acuteneſſe of their wits. On the
contrary, of as many of the Peripateticks and Ptolomeans as I
have asked (and out of curioſity I have talked with many) what
pains they had taken in the Book of Copernicus, I found very
1few that had ſo much as ſuperficially peruſed it; but of thoſe
whom, I thought, had underſtood the ſame, not one; and
over, I have enquired amongſt the followers of the Peripatetick
Doctrine, if ever any of them had held the contrary opinion, and
likewiſe found none that had. Whereupon conſidering that there
was no man who followed the opinion of Copernicus, that had
not been firſt on the contrary ſide, and that was not very well
quainted with the reaſons of Ariſtotle and Ptolomy; and, on the
contrary, that there is not one of the followers of Ptolomy that
had ever been of the judgment of Copernicus, and had left that,
to imbrace this of Ariſtotle, conſidering, I ſay, theſe things, I
began to think, that one, who leaveth an opinion imbued with
his milk, and followed by very many, to take up another owned
by very few, and denied by all the Schools, and that really
ſeems a very great Paradox, muſt needs have been moved, not
to ſay forced, by more powerful reaſons. For this cauſe, I am
become very curious to dive, as they ſay, into the bottom of this
buſineſſe, and account it my great good fortune that I have met
you two, from whom I may without any trouble, hear all that
hath been, and, haply, can be ſaid on this argument, aſſuring
my ſelf that the ſtrength of your reaſons will reſolve all ſcruples,
and bring me to a certainty in this ſubject.
Chriſtianus
ſtitius read certain
Lectures touching
the opinion of
pernicus, & what
enſued thereupon.
The followers of
Copernicus were
all firſt againſt
that opinion, but
the Sectators of
Ariſtotle &
lomy, were never
of the other ſide.
SIMPL. But its poſſible your opinion and hopes may be
pointed, and that you may find your ſelves more at a loſſe in the
end than you was at firſt.
SAGR. I am very confident that this can in no wiſe befal
me.
SIMPL. And why not? I have a manifeſt example in my ſelf,
that the farther I go, the more I am confounded.
SAGR. This is a ſign that thoſe reaſons that hitherto ſeemed
concluding unto you, and aſſured you in the truth of your
nion, begin to change countenance in your mind, and to let you
by degrees, if not imbrace, at leaſt look towards the contrary
nent; but I, that have been hitherto indifferent, do greatly hope
to acquire reſt and ſatisfaction by our future diſcourſes, and you
will not deny but I may, if you pleaſe but to hear what
deth me to this expectation.
SIMPL. I will gladly hearken to the ſame, and ſhould be no
leſſe glad that the like effect might be wrought in me.
SAGR. Favour me therefore with anſwering to what I ſhall ask
you. And firſt, tell me, Simplicius, is not the concluſion, which
we ſeek the truth of, Whether we ought to hold with Ariſtotle
and Ptolomy, that the Earth onely abiding without motion in the
Centre of the Univerſe, the Cœleſtial bodies all move, or elſe,
Whether the Starry Sphere and the Sun ſtanding ſtill in the Centre,
1the Earth is without the ſame, and owner of all thoſe motions that
in our ſeeming belong to the Sun and fixed Stars?
SIMPL. Theſe are the concluſions which are in diſpute.
SAGR. And theſe two concluſions, are they not of ſuch a
ture, that one of them muſt neceſſarily be true, and the other
falſe?
SIMPL. They are ſo. We are in a Dilemma, one part of which
muſt of neceſſity be true, and the other untrue; for between
tion and Reſt, which are contradictories, there cannot be inſtanced
a third, ſo as that one cannot ſay the Earth moves not, nor ſtands
ſtill; the Sun and Stars do not move, and yet ſtand not ſtill.
SAGR. The Earth, the Sun, and Stars, what things are they in
nature? are they petite things not worth our notice, or grand and
worthy of conſideration?
SIMPL They are principal, noble, integral bodies of the
verſe, moſt vaſt and conſiderable.
SAGR. And Motion, and Reſt, what accidents are they in

Motion and reſt
principal accidents
in nature.
SIMPL. So great and principal, that Nature her ſelf is defined
by them.
SAGR. So that moving eternally, and the being wholly
veable are two conditions very conſiderable in Nature, and
cate very great diverſity; and eſpecially when aſcribed to the
principal bodies of the Univerſe, from which can enſue none but
very different events.
SIMPL. Yea doubtleſſe.
SAGR. Now anſwer me to another point. Do you believe that
in Logick, Rhethorick, the Phyſicks, Metaphyſicks, Mathematicks,
and finally, in the univerſality of Diſputations there are arguments
ſufficient to perſwade and demonſtrate to a perſon the fallacious,
no leſſe then the true concluſions?
Vntruths cannot
be demonstrated,
as Truths are.
SIMPL. No Sir; rather I am very confident and certain, that
for the proving of a true and neceſſary concluſion, there are in

nature not onely one, but many very powerfull demonſtrations:
and that one may diſcuſſe and handle the ſame divers and ſundry
wayes, without ever falling into any abſurdity; and that the more
any Sophiſt would diſturb and muddy it, the more clear would its
certainty appear: And that on the contrary to make a falſe
tion paſſe for true, and to perſwade the belief thereof, there
not be any thing produced but fallacies, Sophiſms, Paralogiſmes,
Equivocations, and Diſcourſes vain, inconſiſtant, and full of
pugnances and contradictions.
For proof of true
concluſions, many
ſolid arguments
may be produced,
but to prove a
ſity, none.
SAGR. Now if eternal motion, and eternal reſt be ſo
pal accidents of Nature, and ſo different, that there can depend
on them only moſt different conſequences, and eſpecially when
1applyed to the Sun, and to the Earth, ſo vaſt and famous bodies
of the Univerſe; and it being, moreover, impoſſible, that one of
two contradictory Propoſitions, ſhould not be true, and the other
falſe; and that for proof of the falſe one, any thing can be
duced but fallacies; but the true one being perſwadeable by all
kind of concluding and demonſtrative arguments, why ſhould
you think that he, of you two, who ſhall be ſo fortunate as to
maintain the true Propoſition ought not to perſwade me? You
muſt ſuppoſe me to be of a ſtupid wit, perverſe judgment, dull
mind and intellect, and of a blind reaſon, that I ſhould not be
able to diſtinguiſh light from darkneſſe, jewels from coals, or
truth from falſhood.
SIMPL. I tell you now, and have told you upon other
occaſions, that the beſt Maſter to teach us how to diſcern
phiſmes, Paralogiſmes, and other fallacies, was Ariſtotle, who
in this particular can never be deceived.
SAGR. You inſiſt upon Aristotle, who cannot ſpeak. Yet I
tell you, that if Ariſtotle were here, he would either yield

ſelf to be perſwaded by us, or refuting our arguments, convince
us by better of his own. And you your ſelf, when you heard the
experiments of the Suns related, did you not acknowledg and
admire them, and confeſſe them more concludent than thoſe of
Ariſtotle? Yet nevertheleſſe I cannot perceive that Salviatus,
who hath produced them, examined them, and with exquiſite
care ſcan'd them, doth confeſſe himſelf perſwaded by them; no
nor by others of greater force, which he intimated that he was
about to give us an account of. And I know not on what grounds
you ſhould cenſure Nature, as one that for many Ages hath
been lazie, and forgetful to produce ſpeculative wits; and
that knoweth not how to make more ſuch, unleſſe they be ſuch
kind of men as ſlaviſhly giving up their judgments to Ariſtotle, do
underſtand with his brain, and reſent with his ſenſes. But let us
hear the reſidue of thoſe reaſons which favour his opinion, that
we may thereupon proceed to ſpeak to them; comparing and
weighing them in the ballance of impartiality.
Ariſtotle would
either refute his
adverſaries
ments, or would
alter his opinion.
SALV. Before I proceed any farther, I muſt tell Sagredus, that
in theſe our Diſputations, I perſonate the Copernican,, and
tate him, as if I were his Zany; but what hath been effected in
my private thoughts by theſe arguments which I ſeem to alledg in
his favour, I would not have you to judg by what I ſay, whil'ſt
I am in the heat of acting my part in the Fable; but after I have
laid by my diſguiſe, for you may chance to find me different
from what you ſee me upon the Stage. Now let us go on.
Ptolomy and his followers produce another experiment like to

that of the Projections, and it is of things that being ſeparated
1from the Earth, continue a good ſpace of time in the Air, ſuch
as are the Clouds, Birds of flight; and as of them it cannot be
ſaid that they are rapt or tranſparted by the Earth, having no
heſion thereto, it ſeems not poſſible, that they ſhould be able to
keep pace with the velocity thereof; nay it ſhould rather ſeem
to us, that they all ſwiftly move towards the Weſt: And if
being carried about by the Earth, paſſe our parallel in twenty
four hours, which yet is at leaſt ſixteen thouſand miles, how can
Birds follow ſuch a courſe or revolution? Whereas on the
trary, we ſee them fly as well towards the Eaſt, as towards the
Weſt, or any other part, without any ſenſible difference.

over, if when we run a Horſe at his ſpeed, we feel the air beat
vehemently againſt our face, what an impetuous blaſt ought we
perpetually to feel from the Eaſt, being carried with ſo rapid a
courſe againſt the wind? and yet no ſuch effect is perceived. Take
another very ingenious argument inferred from the following

periment. The circular motion hath a faculty to extrude and
ſipate from its Centre the parts of the moving body, whenſoever
either the motion is not very ſlow, or thoſe parts are not very
well faſtened together; and therefore, if v. g. we ſhould turn
one of thoſe great wheels very faſt about, wherein one or more
men walking, crane up very great weights, as the huge maſſie
ſtone, uſed by the Callander for preſſing of Cloaths; or the
fraighted Barks which being haled on ſhore, are hoiſted out of
one river into another; in caſe the parts of that ſame Wheel ſo
ſwiftly turn'd round, be not very well joyn'd and pin'd together,
they would all be ſhattered to pieces; and though many ſtones or
other ponderous ſubſtances, ſhould be very faſt bound to its outward
Rimme, yet could they not reſiſt the impetuoſity, which with
great violence would hurl them every way far from the Wheel,
and conſequently from its Centre. So that if the Earth did move
with ſuch and ſo much greater velocity, what gravity, what
city of lime or plaiſter would keep together Stones, Buildings, and
whole Cities, that they ſhould not be toſt into the Air by ſo
cipitous a motion? And both men and beaſts, which are not
ſtened to the Earth, how could they reſiſt ſo great an impetus?
Whereas, on the other ſide, we ſee both theſe, and far leſſe
ſiſtances of pebles, ſands, leaves reſt quietly on the Earth, and
to return to it in falling, though with a very ſlow motion. See
here, Simplicius, the moſt potent arguments, taken, to ſo ſpeak,
from things Terreſtrial; there remain thoſe of the other kind,
namely, ſuch as have relation to the appearances of Heaven,
which reaſons, to confeſſe the truth, tend more to prove the
Earth to be in the centre of the Univerſe, and conſequently, to
deprive it of the annual motion about the ſame, aſcribed unto it
1by Copernicus. Which arguments, as being of ſomewhat a
rent nature, may be produced, after we have examined the
ſtrength of theſe already propounded.
An argument
taken from the
Clouds, and from
Birds.
An argument
taken from the air
which we feel to
beat upon us when
we run a Horſe at
full ſpeed.
An argument
taken from the
whirling of
lar motion, which
hath a faculty to
extrude and
pate.
SAGR. What ſay you Simplicius? do you think that Salviatus
is Maſter of, and knoweth how to unfold the Ptolomean and
ſtotelian arguments? Or do you think that any Peripatetick is
qually verſt in the Copernican demonſtrations?
SIMPL. Were it not for the high eſteem, that the paſt
ſes have begot in me of the learning of Salviatus, and of the
cuteneſſe of Sagredus, I would by their good leave have gone my
way without ſtaying for their anſwers; it ſeeming to me a thing
impoſſible, that ſo palpable experiments ſhould be contradicted;
and would, without hearing them farther, conſirm my ſelf in my
old perſwaſion; for though I ſhould be made to ſee that it was
roneous, its being upheld by ſo many probable reaſons, would
der it excuſeable. And if theſe are fallacies, what true
tions were ever ſo fair?
SAGR. Yet its good that we hear the reſponſions of Salviatus;
which if they be true, muſt of neceſſity be more fair, and that by
inſinite degrees; and thoſe muſt be deformed, yea moſt deformed,
if the Metaphy ſical Axiome hold, That true and fair are one and

the ſame thing; as alſo falſe and deformed. Therefore Salviatus
let's no longer loſe time.
True and fair
are one and the
ſame, as alſo falſe
and deformed.
SALV. The firſt Argument alledged by Simplicius, if I well
member it, was this. The Earth cannot move circularly, becauſe
ſuch motion would be violent to the ſame, and therefore not
petual: that it is violent, the reaſon was: Becauſe, that had it been
natural, its parts would likewiſe naturally move round, which is
impoſſible, for that it is natural for the parts thereof to move with a
right motion downwards. To this my reply is, that I could
ly wiſh, that Ariſtotle had more cleerly expreſt himſelf, where he

ſaid; That its parts would likewiſe move circularly; for this
ving circularly is to be underſtood two wayes, one is, that every
particle or atome ſeparated from its Whole would move circularly
about its particular centre, deſcribing its ſmall Circulets; the other
is, that the whole Globe moving about its centre in twenty four
hours, the parts alſo would turn about the ſame centre in four and
twenty hours. The firſt would be no leſſe an impertinency, than
if one ſhould ſay, that every part of the circumference of a Circle
ought to be a Circle; or becauſe that the Earth is Spherical, that
therefore every part thereof be a Globe, for ſo doth the Axiome
require: Eadem eſt ratio totius, & partium. But if he took it in
the other ſenſe, to wit, that the parts in imitation of the Whole
ſhould move naturally round the Centre of the whole Globe in
twenty four hours, I ſay, that they do ſo; and it concerns you,
1inſtead of Ariſtotle, to prove that they do not.
The anſwer to
Ariſtotles firſt
gument.
SIMPL. This is proved by Ariſtotle in the ſame place, when he
ſaith, that the natural motion of the parts is the right motion
downwards to the centre of the Univerſe; ſo that the circular
motion cannot naturally agree therewith.
SALV. But do not you ſee, that thoſe very words carry in them
a confutation of this ſolution?
SIMPL. How? and where?
SALV. Doth not he ſay that the circular motion of the Earth
would be violent? and therefore not eternal? and that this is
ſurd, for that the order of the World is eternal?
SIMPL. He ſaith ſo.
SALV. But if that which is violent cannot be eternal, then by

converſion, that which cannot be eternal, cannot be natural: but
the motion of the Earth downwards cannot be otherwiſe eternal;
therefore much leſſe can it be natural: nor can any other motion
be natural to it, ſave onely that which is eternal. But if we make
the Earth move with a circular motion, this may be eternal to it,
and to its parts, and therefore natural.
That which is
violent, cannot be
eternal, and that
which cannot be
ternal, cannot be
natural.
SIMPL. The right motion is moſt natural to the parts of the
Earth, and is to them eternal; nor ſhall it ever happen that they
move not with a right motion; alwayes provided that the
diments be removed.
SALV. You equivocate Simplicius; and I will try to free you
from the equivoke. Tell me, therefore, do you think that a
Ship which ſhould ſail from the Strait of Gibralter towards
ſtina can eternally move towards that Coaſt? keeping alwayes an
equal courſe?
SIMPL. No doubtleſſe.
SALV. And why not?
SIMPL. Becauſe that Voyage is bounded and terminated
tween the Herculean Pillars, and the ſhore of the Holy-land; and
the diſtance being limited, it is paſt in a finite time, unleſſe one by
returning back ſhould with a contrary motion begin the ſame
age anew; but this would be an interrupted and no continued
motion.
SALV. Very true. But the Navigation from the Strait of
galanes by the Pacifick Ocean, the Moluccha's, the Cape di buona
Speranza, and from thence by the ſame Strait, and then again by
the Pacifick Ocean, &c. do you believe that it may be
tuated?
SIMPL. It may; for this being a circumgyration, which
turneth about its ſelf, with infinite replications, it may be
ated without any interruption.
SALV. A Ship then may in this Voyage continue ſailing
nally.
1
SIMPL. It may, in caſe the Ship were incorruptible, but the
Ship decaying, the Navigation muſt of neceſſity come to an end.
SALV. But in the Mediterrane, though the Veſſel were
ruptible, yet could ſhe not ſail perpetually towards Paleſtina, that

Voyage being determined. Two things then are required, to the
end a moveable may without intermiſſion move perpetually; the
one is, that the motion may of its own nature be indeterminate and
infinite; the other, that the moveable be likewiſe incorruptible
and eternal.
Two things
quiſite to the end a
motion may
petuate it ſelf; an
unlimited ſpace,
and an
ble moveable.
SIMPL. All this is neceſſary.
SALV. Therefore you may ſee how of your own accord you
have confeſſed it impoſſible that any moveable ſhould move
nally in a right line, in regard that right motion, whether it be

wards, or downwards, is by you your ſelf bounded by the
ference and centre; ſo that if a Moveable, as ſuppoſe the Earth
be eternal, yet foraſmuch as the right motion is not of its own
ture eternall, but moſt ^{*}terminate, it cannot naturally ſuit with

the Earth. Nay, as was ſaid ^{*} yeſterday, Ariſtotle himſelf is

conſtrained to make the Terreſtrial Globe eternally immoveable.
When again you ſay, that the parts of the Earth evermore move
downwards, all impediments being removed, you egregiouſly
vocate; for then, on the other ſide they muſt be impeded,
ried, and forced, if you would have them move; for, when they
are once fallen to the ground, they muſt be violently thrown
wards, that they may a ſecond time fall; and as to the
ments, theſe only hinder its arrival at the centre; but if there were
a Well, that did paſſe thorow and beyond the centre, yet would not
a clod of Earth paſſe beyond it, unleſſe inaſmuch as being
ported by its impetus, it ſhould paſſe the ſame to return thither
gain, and in the end there to reſt. As therefore to the defending,
that the motion by a right line doth or can agree naturally neither
to the Earth, nor to any other moveable, whil'ſt the Univerſe
taineth its perfect order, I would have you take no further paines
bout it, but (unleſſe you will grant them the circular motion)
your beſt way will be to defend and maintain their immobility.
Right motion
cannot be eternal,
and conſequently
cannot be natural
to the Earth.
* Terminatiſſimo.
* By this
on he every where
means the
ding Dialogue, or
Giornata.
SIMPL. As to their immoveableneſſe, the arguments of
ſtotle, and moreover thoſe alledged by your ſelf ſeem in my
on neceſſarily to conclude the ſame, as yet; and I conceive it will
be a hard matter to refute them.
SALV. Come we therefore to the ſecond Argument, which was,
That thoſe bodies, which we are aſſured do move circularly, have

more than one motion, unleſſe it be the Primum Mobile; and
therefore, if the Earth did move circularly, it ought to have two
motions; from which alterations would follow in the riſing and
ſetting of the Fixed Stars: Which effect is not perceived to enſue.
1Therefore, &c. The moſt proper and genuine anſwer to this
gation is contained in the Argument it ſelf; and even Aristotle
puts it in our mouths, which it is impoſſible, Simplicius, that you
ſhould not have ſeen.
The anſwer to
the ſecond
ment.
SIMPL. I neither have ſeen it, nor do I yet apprehend it.
SALV. This cannot be, ſure, the thing is ſo very plain.
SIMPL. I will with your leave, caſt an eye upon the Text.
SAGR. We will command the Text to be brought forthwith.
SIMPL. I alwayes carry it about with me: See here it is, and
I know the place perfectly well, which is in lib. 2. De Cælo, cap.
16. Here it is, Text 97. Preterea omnia, quæ feruntur latione
circulari ſubdeficere videntur, ac moveri pluribus una latione,
præter primam Sphæram; quare & Terram neceſſariam eſt, ſive
circa medium, ſive in medio poſita feratur, duabus moveri
lationibus. Si autem hoc acciderit, neceſſariam eſt fieri
tiones, ac converſiones fixorum aſtrorum. Hoc autem non
tur ficri, ſed ſemper eadem, apud eadem loca ipſius, &
tur, & occidunt. [In Engliſh thus:] Furthermore all that are

carried with circular motion, ſeem to ^{*} foreſlow, and to move
with more than one motion, except the firſt Sphere; wherefore
it is neceſſary that the Earth move with two motions, whether

it be carried about the ^{*} middle, or placed in the middle. But
if it be ſo, there would of neceſſity be alterations and
ons made amongſt the fixed Stars. But no ſuch thing is ſeen to
be done, but the ſame Star doth alwayes riſe and ſet in the ſame
place. In all this I find not any falacy, and my thinks the
ment is very forcible.
* Subdeſicere.
* Or Centre.
SALV. And this new reading of the place hath confirmed me
in the fallacy of the Sillogiſme, and moreover, diſcovered
ther falſity. Therefore obſerve. The Poſitions, or if you will,
Concluſions, which Ariſtotle endeavours to oppoſe, are two; one
is that of thoſe, who placing the Earth in the midſt of the World,
do make it move in it ſelf about its own centre. The other is of
thoſe, who conſtituting it far from the middle, do make it
volve with a circular motion about the middle of the Univerſe.
And both theſe Poſitions he conjointly impugneth with one and
the ſame argument. Now I affirm that he is out in both the one
and the other impugnation; and that his error againſt the firſt
Poſition is an Equivoke or Paralogiſme; and his miſtake

ing the ſecond is a falſe conſequence. Let us begin with the firſt
Aſſertion, which conſtituteth the Earth in the midſt of the
World, and maketh it move in it ſelf about its own centre; and

let us confront it with the objection of Ariſtotle; ſaying, All
moveables, that move circularly, ſeem to ^{*} foreſlow, and move
with more than one Byas, except the firſt Sphere (that is the pri-
1mum mobile) therefore the Earth moving about its own centre,
being placed in the middle, muſt of neceſſity have two byaſſes,
and foreſlow. But if this were ſo, it would follow, that there
ſhould be a variation in the riſing and ſetting of the fixed Stars,
which we do not perceive to be done: Therefore the Earth doth
not move, &c. Here is the Paralogiſme, and to diſcover it, I will
argue with Ariſtotle in this manner. Thou ſaiſt, oh Ariſtotle,
that the Earth placed in the middle of the World, cannot move
in it ſelf (i. e. upon its own axis) for then it would be requiſite
to allow it two byaſſes; ſo that, if it ſhould not be neceſſary to
allow it more than one Byas onely, thou wouldeſt not then hold
it impoſſible for it to move onely with that one; for thou would'ſt
unneceſſarily have conſined the impoſſibility to the plurality of
byaſſes, if in caſe it had no more but one, yet it could not move
with that. And becauſe that of all the moveables in the World,
thou makeſt but one alone to move with one ſole byas; and all
the reſt with more than one; and this ſame moveable thou
firmeſt to be the firſt Sphere, namely, that by which all the
ed and erratick Stars ſeem harmoniouſly to move from Eaſt to
Weſt, if in caſe the Earth may be that firſt Sphere, that by
ving with one by as onely, may make the Stars appear to move
from Eaſt to Weſt, thou wilt not deny them it: But he that
firmeth, that the Earth being placed in the midſt of the World,
moveth about its own Axis, aſcribes unto it no other motion,
ſave that by which all the Stars appear to move from Eaſt to Weſt;
and ſo it cometh to be that firſt Sphere, which thou thy ſelf
knowledgeſt to move with but one by as onely. It is therefore
ceſſary, oh Ariſtotle, if thou wilt conclude any thing, that thou
demonſtrate, that the Earth being placed in the midſt of the
World, cannot move with ſo much as one by as onely; or elſe,
that much leſſe can the firſt Sphere have one ſole motion; for
therwiſe thou doeſt in thy very Sillogiſme both commit the falacy,
and detect it, denying, and at that very time proving the ſame
thing. I come now to the ſecond Poſition, namely, of thoſe
who placing the Earth far from the midſt of the Univerſe, make
it moveable about the ſame; that is, make it a Planet and
tick Star; againſt which the argument is directed, and as to
form is concludent, but faileth in matter. For it being granted,
that the Earth doth in that manner move, and that with two
aſſes, yet doth it not neceſſarily follow that though it were ſo,
it ſhould make alterations in the riſings and ſettings of the fixed
Stars, as I ſhall in its proper place declare. And here I could
gladly excuſe Ariſtotle; rather I could highly applaud him for
ving light upon the moſt ſubtil argument that could be produced
againſt the Copernican Hypotheſis; and if the objection be
1nious, and to outward appearance moſt powerful, you may ſee
how much more acute and ingenious the ſolution muſt be, and
not to be found by a wit leſſe piercing than that of Copernicus;
and again from the difficulty in underſtanding it, you may argue
the ſo much greater difficulty in finding it. But let us for the
ſent ſuſpend our anſwer, which you ſhall underſtand in due time
and place, after we have repeated the objection of Ariſtotle, and
that in his favour, much ſtrengthened. Now paſſe we to Ari-

ſtotles third Argument, touching which we need give no farther
reply, it having been ſufficiently anſwered betwixt the diſcourſes
of yeſterday and to day: In as much as he urgeth, that the
tion of grave bodies is naturally by a right line to the centre; and
then enquireth, whether to the centre of the Earth, or to that
of the Univerſe, and concludeth that they tend naturally to the
centre of the Univerſe, but accidentally to that of the Earth.

Therefore we may proceed to the fourth, upon which its requiſite
that we ſtay ſome time, by reaſon it is founded upon that
riment, from whence the greater part of the remaining
ments derive all their ſtrength. Ariſtotle ſaith therefore, that it is
a moſt convincing argument of the Earths immobility, to ſee
that projections thrown or ſhot upright, return perpendicularly
by the ſame line unto the ſame place from whence they were ſhot
or thrown. And this holdeth true, although the motion be of a
very great height; which could never come to paſſe, did the
Earth move: for in the time that the projected body is moving
upwards and downwards in a ſtate of ſeparation from the Earth,
the place from whence the motion of the projection began, would
be paſt, by means of the Earths revolution, a great way
wards the Eaſt, and look how great that ſpace was, ſo far from
that place would the projected body in its deſcent come to the
ground. So that hither may be referred the argument taken from
a bullet ſhot from a Canon directly upwards; as alſo that other
uſed by Ariſtotle and Ptolomy, of the grave bodies that falling
from on high, are obſerved to deſcend by a direct and
lar line to the ſurface of the Earth. Now that I may begin to untie
theſe knots, I demand of Simplicius that in caſe one ſhould deny
to Ptolomy and Ariſtotle that weights in falling freely from on
high, deſcend by a right and perpendicular line, that is, directly
to the centre, what means he would uſe to prove it?
Ariſtotles
ment againſt the
Earths motion, is
defective in two
things
* The ſame word
which a little above
I tendred ſtay
hind, as a bowle
when it meets with
ruls.
The anſwer to
the third
ment.
The anſwer to
the fourth
ment.
SIMPL. The means of the ſenſes; the which aſſureth us, that
that Tower or other altitude, is upright and perpendicular, and
ſheweth us that that ſtone, or other grave body, doth ſlide along
the Wall, without inclining a hairs breadth to one ſide or
ther, and light at the foot thereof juſt under the place from whence
it was let fall.
1
SALV. But if it ſhould happen that the Terreſtrial Globe did
move round, and conſequently carry the Tower alſo along with
it, and that the ſtone did then alſo grate and ſlide along the ſide of
the Tower, what muſt its motion be then?
SIMPL. In this caſe we may rather ſay its motions: for it
would have one wherewith to deſcend from the top of the Tower
to the bottom, and ſhould neceſſarily have another to follow the
courſe of the ſaid Tower.
SALV. So that its motion ſhould be compounded of two, to
wit, of that wherewith it meaſureth the Tower, and of that
ther wherewith it followeth the ſame: From which compoſition
would follow, that the ſtone would no longer deſcribe that ſimple
right and perpendicular line, but one tranſverſe, and perhaps not
ſtreight.
SIMPL. I can ſay nothing of its non-rectitude, but this I know
very well, that it would of neceſſity be tranſverſe, and different
from the other directly perpendicular, which it doth deſcribe, the
Earth ſtanding ſtill.
SALV. You ſee then, that upon the meer obſerving the falling
ſtone to glide along the Tower, you cannot certainly affirm that
it deſcribeth a line which is ſtreight and perpendicular, unleſs you
firſt ſuppoſe that the Earth ſtandeth ſtill.
SIMPL. True; for if the Earth ſhould move, the ſtones
tion would be tranſverſe, and not perpendicular.
SALV. Behold then the Paralogiſm of Ariſtotle and Ptolomey

to be evident and manifeſt, and diſcovered by you your ſelf,
wherein that is ſuppoſed for known, which is intended to be
monſtrated.
The Paralogiſm
of Ariſtotle and
Ptolomey in
poſing that for
known, which is in
queſtion.
SIMPL. How can that be? To me it appeareth that the
Syllogiſm is rightly demonſtrated without petitionem principii.
SALV. You ſhall ſee how it is; anſwer me a little. Doth he
not lay down the concluſion as unknown?
SIMPL. Unknown; why otherwiſe the demonſtrating it would
be ſuperfluous.
SALV. But the middle term, ought not that to be known?
SIMPL. Its neceſſary that it ſhould; for otherwiſe it would be
a proving ignotum per æquè ignotum.
SALV. Our concluſion which is to be proved, and which is
known, is it not the ſtability of the Earth?
SIMPL. It is the ſame.
SALV. The middle term, which ought to be known, is it not the
ſtreight and perpendicular deſcent of the ſtone?
SIMPL. It is ſo.
SALV. But was it not juſt now concluded, that we can have
no certain knowledg whether that ſame ſhall be direct and
1dicular, unleſs we firſt know that the Earth ſtands ſtill? Therefore
in your Syllogiſm the certainty of the middle term is aſſumed
from the uncertainty of the concluſion. You may ſee then, what
and how great the Paralogiſm is.
SAGR. I would, in favour of Simplicius, defend Ariſtotle if it
were poſſible, or at leaſt better ſatisfie my ſelf concerning the
ſtrength of your illation. You ſay, that the ſeeing the ſtone rake
along the Tower, is not ſufficient to aſſure us, that its motion is
perpendicular (which is the middle term of the Syllogiſm) unleſs
it be preſuppoſed, that the Earth ſtandeth ſtill, which is the
cluſion to be proved: For that if the Tower did move together
with the Earth, and the ſtone did ſlide along the ſame, the motion
of the ſtone would be tranſverſe, and not perpendicular. But I
ſhall anſwer, that ſhould the Tower move, it would be impoſſible
that the ſtone ſhould fall gliding along the ſide of it; and
fore from its falling in that manner the ſtability of the Earth is
ferred.
SIMPL. It is ſo; for if you would have the ſtone in
ing to grate upon the Tower, though it were carried round by
the Earth, you muſt allow the ſtone two natural motions, to wit,
the ſtraight motion towards the Centre, and the circular about
the Centre, the which is impoſſible.
SALV. Ariſtotles defenſe then conſiſteth in the impoſſibilitie,
or at leaſt in his eſteeming it an impoſſibility, that the ſtone ſhould
move with a motion mixt of right and circular: for if he did
not hold it impoſſible that the ſtone could move to the Centre,
and about the Centre at once, he muſt have underſtood, that it
might come to paſs that the cadent ſtone might in its deſcent, race
the Tower as well when it moved as when it ſtood ſtill; and
ſequently he muſt have perceived, that from this grating nothing
could be inferred touching the mobility or immobility of the
Earth. But this doth not any way excuſe Aristotle; aſwell
cauſe he ought to have expreſt it, if he had had ſuch a conceit, it
being ſo material a part of his Argument; as alſo becauſe it can
neither be ſaid that ſuch an effect is impoſſible, nor that Ariſtotle
did eſteem it ſo. The firſt cannot be affirmed, for that by and
by I ſhall ſhew that it is not onely poſſible, but neceſſary: nor

much leſs can the ſecond be averred, for that Ariſtotle himſelf
granteth fire to move naturally upwards in a right line, and to
move about with the diurnal motion, imparted by Heaven to the
whole Element of Fire, and the greater part of the Air: If
fore he held it not impoſſible to mix the right motion upwards,
with the circular communicated to the Fire and Air from the
cave of the Moon, much leſs ought he to account impoſſible the
mixture of the right motion downwards of the ſtone, with the
1circular which we preſuppoſe natural to the whole Terreſtrial
Globe, of which the ſtone is a part.
Ariſtotle
teth that the Fire
moveth directly
upwards by
ture, and round
bout by
tion.
SIMPL. I ſee no ſuch thing: for if the element of Fire
volve round together with the Air, it is a very eaſie, yea a neceſſary
thing, that a ſpark of fire which from the Earth mounts upwards,
in paſſing thorow the moving air, ſhould receive the ſame motion,
being a body ſo thin, light, and eaſie to be moved: but that a
very heavy ſtone, or a Canon bullet, that deſcendeth from on
high, and that is at liberty to move whither it will, ſhould ſuffer
it ſelf to be tranſported either by the air or any other thing, is
altogether incredible. Beſides that, we have the Experiment,
which is ſo proper to our purpoſe, of the ſtone let fall from the
round top of the Maſt of a ſhip, which when the ſhip lyeth ſtill,
falleth at the Partners of the Maſt; but when the ſhip ſaileth, falls
ſo far diſtant from that place, by how far the ſhip in the time of
the ſtones falling had run forward; which will not be a few
thoms, when the ſhips courſe is ſwift.
SALV. There is a great diſparity between the caſe of the Ship

and that of the Earth, if the Terreſtrial Globe be ſuppoſed to have
a diurnal motion. For it is a thing very manifeſt, that the
tion of the Ship, as it is not natural to it, ſo the motion of all thoſe
things that are in it is accidental, whence it is no wonder that the
ſtone which was retained in the round top, being left at liberty,
deſcendeth downwards without any obligation to follow the
tion of the Ship. But the diurnal converſion is aſcribed to the
Terreſtrial Globe for its proper and natural motion, and
quently, it is ſo to all the parts of the ſaid Globe; and, as being
impreſs'd by nature, is indelible in them; and therefore that ſtone
that is on the top of the Tower hath an intrinſick inclination of
revolving about the Centre of its Whole in twenty four hours, and
this ſame natural inſtinct it exerciſeth eternally, be it placed in any
ſtate whatſoever. And to be aſſured of the truth of this, you
have no more to do but to alter an antiquated impreſſion made
in your mind; and to ſay, Like as in that I hitherto holding it to
be the property of the Terreſtrial Globe to reſt immoveable about
its Centre, did never doubt or queſtion but that all whatſoever
particles thereof do alſo naturally remain in the ſame ſtate of reſt:
So it is reaſon, in caſe the Terreſtrial Globe did move round by
natural inſtinct in twenty four hours, that the intrinſick and
ral inclination of all its parts ſhould alſo be, not to ſtand ſtill, but

to follow the ſame revolution. And thus without running into
any inconvenience, one may conclude, that in regard the motion
conferred by the force of ^{*}Oars on the Ship, and by it on all the
things that are contained within her, is not natural but forreign, it
is very reaſonable that that ſtone, it being ſeparated from the ſhip,
1do reduce its ſelf to its natural diſpoſure, and return to exerciſe

its pure ſimple inſtinct given it by nature. To this I add, that
it's neceſſary, that at leaſt that part of the Air which is beneath the
greater heights of mountains, ſhould be tranſported and carried
round by the roughneſs of the Earths ſurface; or that, as being
mixt with many Vapours, and terrene Exhalations, it do
turally follow the diurnal motion, which occurreth not in the
Air about the ſhip rowed by Oars: So that your arguing
from the ſhip to the Tower hath not the force of an illation;
becauſe that ſtone which falls from the round top of the Maſt,
entereth into a medium, which is unconcern'd in the motion
of the ſhip: but that which departeth from the top of the Tower,
finds a medium that hath a motion in common with the whole
reſtrial Globe; ſo that without being hindred, rather being aſſiſted
by the motion of the air, it may follow the univerſal courſe of the
Earth.
The diſparity
tween the fall of a
ſtone from the
round top of a ſhip,
and from the top
of a tower.
*That you may not
ſuſpect my
tion, or wonder
what Oars have to
do with a ſhip, you
are to know that
the Author intends
the Gallies uſed in
the Mediterrane.
The part of the
Air inferiour to
the higher
tains doth follow
the motion of the
Earth.
SIMPL. I cannot conceive that the air can imprint in a very

great ſtone, or in a groſs Globe of Wood or Ball of Lead, as
ſuppoſe of two hundred weight, the motion wherewith its ſelf is
moved, and which it doth perhaps communicate to feathers, ſnow,
and other very light things: nay, I ſee that a weight of that
ture, being expoſed to any the moſt impetuous wind, is not
by removed an inch from its place; now conſider with your ſelf
whether the air will carry it along therewith.
The motion of the
Air apt to carry
with it light things
but not heavy.
SALV. There is great difference between your experiment and
our caſe. You introduce the wind blowing againſt that ſtone,
ſuppoſed in a ſtate of reſt, and we expoſe to the air, which already
moveth, the ſtone which doth alſo move with the ſame velocity;
ſo that the air is not to conferr a new motion upon it, but onely
to maintain, or to ſpeak better, not to hinder the motion already
acquired: you would drive the ſtone with a ſtrange and
natural motion, and we deſire to conſerve it in its natural. If
you would produce a more pertinent experiment, you ſhould ſay,
that it is obſerved, if not with the eye of the forehead, yet with
that of the mind, what would evene, if an eagle that is carried by
the courſe of the wind, ſhould let a ſtone fall from its talons;
which, in regard that at its being let go, it went along with the
wind, and after it was let fall it entered into a medium that
ved with equal velocity, I am very confident that it would not be
ſeen to deſcend in its fall perpendicularly, but that following the
courſe of the wind, and adding thereto that of its particular
vity, it would move with a tranſverſe motion.
SIMPI. But it would firſt be known how ſuch an experiment
may be made; and then one might judg according to the event.
In the mean time the effect of the ſhip doth hitherto incline to
vour our opinion.
1
SALV. Well ſaid you hitherto, for perhaps it may anon change
countenance. And that I may no longer hold you in ſuſpenſe,
tell me, Simplicius, do you really believe, that the Experiment of
the ſhip ſquares ſo very well with our purpoſe, as that it ought to
be believed, that that which we ſee happen in it, ought alſo to
evene in the Terreſtrial Globe?
SIMPL. As yet I am of that opinion; and though you have
alledged ſome ſmall diſparities, I do not think them of ſo great
moment, as that they ſhould make me change my judgment.
SALV. I rather deſire that you would continue therein, and
hold for certain, that the effect of the Earth would exactly anſwer
that of the ſhip: provided, that when it ſhall appear prejudicial to
your cauſe, you would not be humorous and alter your thoughts.
You may haply ſay, Foraſmuch as when the ſhip ſtands ſtill, the
ſtone falls at the foot of the Maſt, and when ſhe is under ſail, it
lights far from thence, that therefore by converſion, from the ſtones
falling at the foot is argued the ſhips ſtanding ſtill, and from its
falling far from thence is argued her moving; and becauſe that
which occurreth to the ſhip, ought likewiſe to befall the Earth:
that therefore from the falling of the ſtone at the foot of the
er is neceſſarily inferred the immobility of the Terreſtrial Globe.
Is not this your argumentation?
SIMPL. It is; and reduced into that conciſeneſs, as that it is
become moſt eaſie to be apprehended.
SALV. Now tell me; if the ſtone let fall from the
top, when the ſhip is in a ſwift courſe, ſhould fall exactly in
the ſame place of the ſhip, in which it falleth when the ſhip is at
anchor, what ſervice would theſe experiments do you, in order to
the aſcertaining whether the veſſel doth ſtand ſtill or move?
SIMPL. Juſt none: Like as, for exemple, from the beating of
the pulſe one cannot know whether a perſon be aſleep or awake,
ſeeing that the pulſe beateth after the ſame manner in ſleeping as
in waking.
SALV. Very well. Have you ever tryed the experiment of the
Ship?
SIMPL. I have not; but yet I believe that thoſe Authors
which alledg the ſame, have accurately obſerved it; beſides that
the cauſe of the diſparity is ſo manifeſtly known, that it admits
of no queſtion.
SALV. That it is poſſible that thoſe Authors inſtance in it,
without having made tryal of it, you your ſelf are a good
mony, that without having examined it, alledg it as certain, and in
a credulous way remit it to their authority; as it is now not onely
poſſible, but very probable that they likewiſe did; I mean, did
remit the ſame to their Predeceſſors, without ever arriving at one
1that had made the experiment: for whoever ſhall examine the
ſame, ſhall find the event ſucceed quite contrary to what hath
been written of it: that is, he ſhall ſee the ſtone fall at all times
in the ſame place of the Ship, whether it ſtand ſtill, or move with
any whatſoever velocity. So that the ſame holding true in the

Earth, as in the Ship, one cannot from the ſtones falling
dicularly at the foot of the Tower, conclude any thing touching
the motion or reſt of the Earth.
The stone falling
from the Mast of
a ſhip lights in the
ſame place,
ther the ſhip doth
move or ly still.
SIMPL. If you ſhould refer me to any other means than to
experience, I verily believe our Diſputations would not come to
an end in haſte; for this ſeemeth to me a thing ſo remote from all
humane reaſon, as that it leaveth not the leaſt place for credulity
or probability.
SALV. And yet it hath left place in me for both.
SIMPL. How is this? You have not made an hundred, no nor
one proof thereof, and do you ſo confidently affirm it for true?
I for my part will return to my incredulity, and to the confidence
I had that the Experiment hath been tried by the principal
thors who made uſe thereof, and that the event ſucceeded as they
affirm.
SALV. I am aſſured that the effect will enſue as I tell you; for ſo
it is neceſſary that it ſhould: and I farther add, that you know your
ſelf that it cannot fall out otherwiſe, however you feign or ſeem to
feign that you know it not. Yet I am ſo good at taming of wits,
that I will make you confeſs the ſame whether you will or no. But
Sagredus ſtands very mute, and yet, if I miſtake not, I ſaw him
make an offer to ſpeak ſomewhat.
SAGR. I had an intent to ſay ſomething, but to tell you true, I
know not what it was; for the curioſity that you have moved in me,
by promiſing that you would force Simplicius to diſcover the
knowledg which he would conceal from us, hath made me to
poſe all other thoughts: therefore I pray you to make good your
vaunt.
SALV. Provided that Simplicius do conſent to reply to what I
ſhall ask him, I will not fail to do it.
SIMPL. I will anſwer what I know, aſſured that I ſhall not be
much put to it, for that of thoſe things which I hold to be falſe,
I think nothing can be known, in regard that Science reſpecteth
truths and not falſhoods.
SALV. I deſire not that you ſhould ſay or reply, that you know
any thing, ſave that which you moſt aſſuredly know. Therefore
tell me; If you had here a flat ſuperficies as polite as a
glaſs, and of a ſubſtance as hard as ſteel, and that it were not
ralel to the Horizon, but ſomewhat inclining, and that upon it
you did put a Ball perfectly ſpherical, and of a ſubſtance grave and
1hard, as ſuppoſe of braſs; what think you it would do being let
go? do not you believe (as for my part I do) that it would lie
ſtill?
SIMPL. If that ſuperficies were inclining?
SALV. Yes; for ſo I have already ſuppoſed.
SIMPL. I cannot conceive how it ſhould lie ſtill: nay, I am
confident that it would move towards the declivity with much
penſneſs.
SALV. Take good heed what you ſay, Simplicius, for I am
confident that it would lie ſtill in what ever place you ſhould lay
it.
SIMPL. So long as you make uſe of ſuch ſuppoſitions,
viatus, I ſhall ceaſe to wonder if you inferr moſt abſurd
cluſions.
SALV. Are you aſſured, then, that it would freely move
wards the declivity?
SIMPL. Who doubts it?
SALV. And this you verily believe, not becauſe I told you ſo,
(for I endeavoured to perſwade you to think the contrary) but of
your ſelf, and upon your natural judgment.
SIMPL. Now I ſee what you would be at; you ſpoke not this
as really believing the ſame; but to try me, and to wreſt matter
out of my own mouth wherewith to condemn me.
SALV. You are in the right. And how long would that Ball
move, and with what velocity? But take notice that I inſtanced
in a Ball exactly round, and a plain exquiſitely poliſhed, that all
external and accidental impediments might be taken away. And
ſo would I have you remove all obſtructions cauſed by the Airs
ſiſtance to diviſion, and all other caſual obſtacles, if any other
there can be.
SIMPL. I very well underſtand your meaning, and as to your
demand, I anſwer, that the Ball would continue to move in
finitum, if the inclination of the plain ſhould ſo long laſt, and
tinually with an accelerating motion; for ſuch is the nature of
ponderous moveables, that vires acquirant eundo: and the
er the declivity was, the greater the velocity would be.
SALV. But if one ſhould require that that Ball ſhould move
upwards on that ſame ſuperficies, do you believe that it would
ſo do?
SIMPL. Not ſpontaneouſly; but being drawn, or violently
thrown, it may.
SALV. And in caſe it were thruſt forward by the impreſſion of
ſome violent impetus from without, what and how great would
its motion be?
SIMPL. The motion would go continually decreaſing and
1tarding, as being contrary to nature; and would be longer or
ſhorter, according to the greater or leſs impulſe, and according to
the greater or leſs acclivity.
SALV. It ſeems, then, that hitherto you have explained to me
the accidents of a moveable upon two different Planes; and that
in the inclining plane, the grave moveable doth ſpontaneouſly
ſcend, and goeth continually accelerating, and that to retain it in
reſt, force muſt be uſed therein: but that on the aſcending plane,
there is required a force to thruſt it forward, and alſo to ſtay it in
reſt, and that the motion impreſſed goeth continually diminiſhing,
till that in the end it cometh to nothing. You ſay yet farther,
that in both the one and the other caſe, there do ariſe differences
from the planes having a greater or leſs declivity or acclivity; ſo
that the greater inclination is attended with the greater velocity;
and contrariwiſe, upon the aſcending plane, the ſame moveable
thrown with the ſame force, moveth a greater diſtance, by how
much the elevation is leſs. Now tell me, what would befall the
ſame moveable upon a ſuperficies that had neither acclivity nor
declivity?
SIMPL. Here you muſt give me a little time to conſider of an
anſwer. There being no declivity, there can be no natural
nation to motion: and there being no acclivity, there can be no
reſiſtance to being moved; ſo that there would ariſe an
rence between propenſion and reſiſtance of motion; therefore,
methinks it ought naturally to ſtand ſtill. But I had forgot my
ſelf: it was but even now that Sagredus gave me to underſtand
that it would ſo do.
SALV. So I think, provided one did lay it down gently: but
if it had an impetus given it towards any part, what would
low?
SIMP. There would follow, that it ſhould move towards that
part.
SALV. But with what kind of motion? with the continually
accelerated, as in declining planes; or with the ſucceſſively
tarded, as in thoſe aſcending.
SIMP. I cannot tell how to diſcover any cauſe of acceleration,
or retardation, there being no declivity or acclivity.
SALV. Well: but if there be no cauſe of retardation, much
leſs ought there to be any cauſe of reſt. How long therefore
would you have the moveable to move?
SIMP. As long as that ſuperficies, neither inclined nor
ned ſhall laſt.
SALV. Therefore if ſuch a ſpace were interminate, the motion
upon the ſame would likewiſe have no termination, that is, would
be perpetual.
1
SIMP. I think ſo, if ſo be the moveable be of a matter
durable.
SALV. That hath been already ſuppoſed, when it was ſaid,
that all external and accidental impediments were removed, and
the brittleneſſe of the moveable in this our caſe, is one of thoſe
impediments accidental. Tell me now, what do you think is the
cauſe that that ſame Ball moveth ſpontaneouſly upon the inclining
plane, and not without violence upon the erected?
SIMP. Becauſe the inclination of grave bodies is to move
wards the centre of the Earth, and onely by violence upwards
wards the circumference; and the inclining ſuperficies is that
which acquireth vicinity to the centre, and the aſcending one,
remoteneſſe.
SALV. Therefore a ſuperficies, which ſhould be neither
clining nor aſcending, ought in all its parts to be equally
ſtant from the centre. But is there any ſuch ſuperficies in the
World?
SIMP. There is no want thereof: Such is our Terreſtrial
Globe, if it were more even, and not as it is rough and
nous; but you have that of the Water, at ſuch time as it is calm
and ſtill.
SALV. Then a ſhip which moveth in a calm at Sea, is one of
thoſe moveables, which run along one of thoſe ſuperficies that
are neither declining nor aſcending, and therefore diſpoſed, in
caſe all obſtacles external and accidental were removed, to move
with the impulſe once imparted inceſſantly and uniformly.
SIMPL. It ſhould ſeem to be ſo.
SALV. And that ſtone which is on the round top, doth not it
move, as being together with the ſhip carried about by the
cumference of a Circle about the Centre; and therefore
quently by a motion in it indelible, if all extern obſtacles be
removed? And is not this motion as ſwift as that of the ſhip.
SIMPL. Hitherto all is well. But what followeth?
SALV. Then in good time recant, I pray you, that your laſt
concluſion, if you are ſatisfied with the truth of all the
miſes.
SIMPL. By my laſt concluſion, you mean, That that ſame
ſtone moving with a motion indelibly impreſſed upon it, is not to
leave, nay rather is to follow the ſhip, and in the end to light in
the ſelf ſame place, where it falleth when the ſhip lyeth ſtill; and
ſo I alſo grant it would do, in caſe there were no outward
diments that might diſturb the ſtones motion, after its being let
go, the which impediments are two, the one is the moveables
inability to break through the air with its meer impetus onely, it
being deprived of that of the ſtrength of Oars, of which it had
1been partaker, as part of the ſhip, at the time that it was upon
the Maſt; the other is the new motion of deſcent, which alſo
muſt needs be an hinderance of that other progreſſive motion.
SALV. As to the impediment of the Air, I do not deny it
you; and if the thing falling were a light matter, as a feather,
or a lock of wool, the retardation would be very great, but in
an heavy ſtone is very exceeding ſmall. And you your ſelf but
even now did ſay, that the force of the moſt impetuous wind
ſufficeth not to ſtir a great ſtone from its place; now do but
ſider what the calmer air is able to do, being encountred by a
ſtone no more ſwift than the whole ſhip. Nevertheleſſe, as I ſaid
before, I do allow you this ſmall effect, that may depend upon
ſuch an impediment; like as I know, that you will grant to me,
that if the air ſhould move with the ſame velocity that the ſhip
and ſtone hath, then the impediment would be nothing at all.
As to the other of the additional motion downwards; in the firſt
place it is manifeſt, that theſe two, I mean the circular, about
the centre, and the ſtreight, towards the centre, are not
ries, or deſtructive to one another, or incompatible. Becauſe that
as to the moveable, it hath no repugnance at all to ſuch motions,
for you your ſelf have already confeſt the repugnance to be
gainſt the motion which removeth from the centre, and the
nation to be towards the motion which approacheth to the centre.
Whence it doth of neceſſity follow, that the moveable hath
ther repugnance, nor propenſion to the motion which neither
proacheth, nor goeth from the centre, nor conſequently is there
any cauſe for the diminiſhing in it the faculty impreſſed. And
aſmuch as the moving cauſe is not one alone, which it hath
tained by the new operation of retardation; but that they are
two, diſtinct from each other, of which, the gravity attends
ly to the drawing of the moveable towards the centre, and the
vertue impreſs't to the conducting it about the centre, there
maineth no occaſion of impediment.
SIMPL. Your argumentation, to give you your due, is very
probable; but in reality it is invelloped with certain intricacies,
that are not eaſie to be extricated. You have all along built upon

a ſuppoſition, which the Peripatetick Schools will not eaſily grant
you, as being directly contrary to Aristotle, and it is to take for
known and manifeſt, That the project ſeparated from the
cient, continueth the motion by vertue impreſſed on it by the
ſaid projicient, which vertue impreſſed is a thing as much
ſted in Peripatetick Philoſophy, as the paſſage of any accident
from one ſubject into another. Which doctrine doth hold, as I
believe it is well known unto you, that the project is carried by
the medium, which in our caſe happeneth to be the Air. And
1therefore if that ſtone let fall from the round top, ought to
low the motion of the ſhip, that effect ſhould be aſcribed to the
Air, and not to the vertue impreſſed. But you preſuppoſe that
the Air doth not follow the motion of the ſhip, but is tranquil.
Moreover, he that letteth it fall, is not to throw it, or to give
it impetus with his arm, but ought barely to open his hand and let
it go; and by this means, the ſtone, neither through the vertue
impreſſed by the projicient, nor through the help of the Air,
ſhall be able to follow the ſhips motion, and therefore ſhall be
left behind.
The project
cording to
tle, is not moved by
vertue impreſſed,
but by the medium.
SALV. I think then that you would ſay, that if the ſtone be
not thrown by the arm of that perſon, it is no longer a
jection.
SIMPL. It cannot be properly called a motion of projection.
SALV. So then that which Ariſtotle ſpeaks of the motion, the
moveable, and the mover of the projects, hath nothing to do
with the buſineſſe in hand; and if it concern not our purpoſe,
why do you alledg the ſame?
SIMP. I produce it on the oceaſion of that impreſſed vertue,
named and introduced by you, which having no being in the
World, can be of no force; for non-entium nullæ ſunt
nes; and therefore not onely of projected, but of all other
ternatural motions, the moving cauſe ought to be aſcribed to the
medium, of which there hath been no due conſideration had;
and therefore all that hath been ſaid hitherto is to no purpoſe.
SALV. Go to now, in good time. But tell me, ſeeing that
your inſtance is wholly grounded upon the nullity of the vertue
impreſſed, if I ſhall demonſtrate to you, that the medium hath
nothing to do in the continuation of projects, after they are
patated from the projicient, will you admit of the impreſſed
tue, or will you make another attempt to overthrow it?
SIMP. The operation of the medium being removed, I ſee not
how one can have recourſe to any thing elſe ſave the faculty
preſſed by the mover.
SALV. It would be well, for the removing, as much as is
poſſible, the occaſions of multiplying contentions, that you
would explain with as much diſtinctneſſe as may be, what is that
operation of the medium in continuing the motion of the
Operation of the
medium in
ing the motion of
the project.
SIMP. The projicient hath the ſtone in his hand, and with
force and violence throws his arm, with which jactation the
ſtone doth not move ſo much as the circumambient Air; ſo that
when the ſtone at its being forſaken by the hand, findeth it ſelf
in the Air, which at the ſame time moveth with impetouſity, it
is thereby born away; for, if the air did not operate, the ſtone
would fall at the foot of the projicient or thrower.
1
Many
ments, and
ſons againſt the
cauſe of the
on of projects,
ſigned by Ariſtotle.
SALV. And was you ſo credulous, as to ſuffer your ſelf to be
perſwaded to believe theſe fopperies, ſo long as you had your
ſenſes about you to confute them, and to underſtand the
truth thereof? Therefore tell me, that great ſtone, and that
Canon bullet, which but onely laid upon a table, did continue
immoveable againſt the moſt impetuous winds, according as you a
little before did affirm, if it had been a ball of cork or other light
ſtuffe, think you that the wind would have removed it from its
place?
SIMP. Yes, and I am aſſured that it would have blown it
quite away, and with ſo much more velocity, by how much the
matter was lighter, for upon this reaſon we ſee the clouds to be
tranſported with a velocity equal to that of the wind that drives
them.
SALV. And what is the Wind?
SIMP. The Wind is defined to be nothing elſe but air moved.
SALV. Then the moved air doth carry light things more
ſwiftly, and to a greater diſtance, then it doth heavy.
SIMP. Yes certainly.
SALV. But if you were to throw with your arm a ſtone, and a
lock of cotton wool, which would move ſwiſteſt and fartheſt?
SIMP. The ſtone by much; nay the wool would fall at my
feet.
SALV. But, if that which moveth the projected ſubſtance,
ter it is delivered from the hand, be no other than the air moved
by the arm, and the moved air do more eaſily bear away light
than grave matters, how cometh it that the project of wool flieth
not farther, and ſwifter than that of ſtone? Certainly it
eth that the ſtone hath ſome other impulſe beſides the motion of
the air. Furthermore, if two ſtrings of equal length did hang
at yonder beam, and at the end of one there was faſtened a
let of lead, and a ball of cotton wool at the other, and both
were carried to an equal diſtance from the perpendicular, and
then let go; it is not to be doubted, but that both the one and
the other would move towards the perpendicular, and that being
carried by their own impetus, they would go a certain ſpace
yond it, and afterwards return thither again. But which of theſe
two pendent Globes do you think, would continue longeſt in
tion, before that it would come to reſt in its perpendicularity?
SIMP. The ball of lead would ſwing to and again many times,
and that of wool but two or three at the moſt.
SALV. So that that impetus and that mobility whatſoever is
the cauſe thereof, would conſerve its ſelf longer in grave
ſtances, than light; I proceed now to another particular, and
mand of you, why the air doth not carry away that Lemon
which is upon that ſame Table?
1
SIMP. Becauſe that the air it ſelf is not moved
SALV. It is requiſite then, that the projicient do confer
tion on the Air, with which it afterward moveth the project. But
if ſuch a motion cannot be impreſſed [i. e. imparted] it being im­
poſſible to make an accident paſſe out of one ſubject into another,
how can it paſſe from the arm into the Air? Will you ſay that the
Air is not a ſubject different from the arm?
SIMP. To this it is anſwered that the Air, in regard it is
ther heavy nor light in its own Region, is diſpoſed with facility to
receive every impulſe, and alſo to retain the ſame.
SALV. But if thoſe penduli even now named, did prove
unto us, that the moveable, the leſſe it had of gravity, the leſſe
apt it was to conſerve its motion, how can it be that the Air
which in the Air hath no gravity at all, doth of it ſelf alone
tain the motion acquired? I believe, and know that you by this
time are of the ſame opinion, that the arm doth not ſooner
turn to reſt, than doth the circumambient Air. Let's go into the
Chamber, and with a towel let us agitate the Air as much as we
can, and then holding the cloth ſtill, let a little candle be
brought, that was lighted in the next room, or in the ſame place
let a leaf of beaten Gold be left at liberty to flie any wav, and you
ſhall by the calm vagation of them be aſſured that the Air is
diately reduced to tranquilty. I could alledg many other
ments to the ſame purpoſe, but if one of theſe ſhould not
fice, I ſhould think your folly altogether incurable.
SAGR. When an arrow is ſhot againſt the Wind, how
ble a thing is it, that that ſame ſmall filament of air, impelled by
the bow-ſtring, ſhould in deſpite of fate go along with the arrow?
But I would willingly know another particular of Ariſtotle, to
which I intreat Simplicius would vouchſafe me an anſwer.
poſing that with the ſame Bow there were ſhot two arrows, one
juſt after the uſual manner, and the other ſide-wayes, placing it
long-wayes upon the Bow-ſtring, and then letting it flie, I would
know which of them would go fartheſt. Favour me, I pray you
with an anſwer, though the queſtion may ſeem to you rather
ridiculous than otherwiſe; and excuſe me, for that I, who am, as
you ſee, rather blockiſh, than not, can reach no higher with my
ſpeculative faculty.
SIMPL. I have never ſeen an arrow ſhot in that manner, yet
nevertheleſſe I believe, that it would not flie ſide-long, the
twentieth part of the ſpace that it goeth end-wayes.
SAGR. And for that I am of the ſame opinion, hence it is, that
I have a doubt riſen in me, whether Aristotle doth not contradict
experience. For as to experience, if I lay two arrows upon this
Table, in a time when a ſtrong Wind bloweth, one towards
1the courſe of the wind, and the other ſidelong, the wind will
quickly carry away this later, and leave the other where it was;
and the ſame to my ſeeming, ought to happen, if the Doctrine of
Ariſtotle were true, of thoſe two ſhot out of a Bow: foraſmuch
as the arrow ſhot ſideways is driven by a great quantity of Air,
moved by the bowſtring, to wit by as much as the ſaid ſtring is
long, whereas the other arrow receiveth no greater a quantity of
air, than the ſmall circle of the ſtrings thickneſs. And I cannot
imagine what may be the reaſon of ſuch a difference, but would
fain know the ſame.
SIMP. The cauſe ſeemeth to me ſufficiently manifeſt; and it
is, becauſe the arrow ſhot endways, hath but a little quantity of
air to penetrate, and the other is to make its way through a
tity as great as its whole length.
SALV. Then it ſeems the arrows ſhot, are to penetrate the air?
but if the air goeth along with them, yea, is that which carrieth
them, what penetration can they make therein? Do you not ſee
that, in this caſe, the arrow would of neceſſity move with greater
velocity than the air? and this greater velocity, what doth confer
it on the arrow? Will you ſay the air giveth them a velocity
greater than its own? Know then, Simplicius, that the buſineſs
proceeds quite contrary to that which Ariſtotle ſaith, and that the

medium conferreth the motion on the project, is as falſe, as it is
true, that it is the onely thing which procureth its obſtruction; and
having known this, you ſhall underſtand without finding any thing
whereof to make queſtion, that if the air be really moved, it doth
much better carry the dart along with it longways, than endways,
for that the air which impelleth it in that poſture, is much, and in
this very little. But ſhooting with the Bow, foraſmuch as the air
ſtands ſtill, the tranſverſe arrow, being to force its paſſage through
much air, comes to be much impeded, and the other that was nock't
eaſily overcometh the obſtruction of the ſmall quantity of air,
which oppoſeth it ſelf thereto.
The medium doth
impede and not
fer the motion of
projects.
SALV. How many Propoſitions have I obſerved in Ariſtotle,
(meaning ſtill in Natural Philoſophy) that are not onely falſe,
but falſe in ſuch ſort, that its diametrical contrary is true, as it
happens in this caſe. But purſuing the point in hand, I think that
Simplicius is perſwaded, that, from ſeeing the ſtone always to fall
in the ſame place, he cannot conjecture either the motion or
bility of the Ship: and if what hath been hitherto ſpoken,
ſhould not ſuffice, there is the Experiment of the medium which
may thorowly aſſure us thereof; in which experiment, the moſt
that could be ſeen would be, that the cadent moveable might be
left behind, if it were light, and that the air did not follow the
motion of the ſhip: but in caſe the air ſhould move with equal
1velocity, no imaginable diverſity could be found either in this,
or any other experiment whatſoever, as I am anon to tell you.
Now if in this caſe there appeareth no difference at all, what can
be pretended to be ſeen in the ſtone falling from the top of the
Tower, where the motion in gyration is not adventitious, and
cidental, but natural and eternal; and where the air exactly
loweth the motion of the Tower, and the Tower that of the
reſtrial Globe? have you any thing elſe to ſay, Simplicius, upon
this particular?
SIMP. No more but this, that I ſee not the mobility of the
Earth as yet proved.
SALV. Nor have I any intention at this time, but onely to
ſhew, that nothing can be concluded from the experiments
ed by our adverſaries for convincing Arguments: as I think I
ſhall prove the others to be.
SAGR. I beſeech you, Salviatus, before you proceed any
ther, to permit me to ſtart certain queſtions, which have been
rouling in my fancy all the while that you with ſo much patience
and equanimity, was minutely explaining to Simplicius the
riment of the Ship.
SALV. We are here met with a purpoſe to diſpute, and it's fit
that every one ſhould move the difficulties that he meets withall,
for this is the way to come to the knowledg of the truth.
Therefore ſpeak freely.
SAGR. If it be true, that the impetus wherewith the ſhip moves,
doth remain indelibly impreſſ'd in the ſtone, after it is let fall from
the Maſt; and if it be farther true, that this motion brings no
pediment or retardment to the motion directly downwards,
tural to the ſtone: it's neceſſary, that there do an effect enſue of

a very wonderful nature. Let a Ship be ſuppoſed to ſtand ſtill,
and let the time of the falling of a ſtone from the Maſts Round-top
to the ground, be two beats of the pulſe; let the Ship afterwards
be under ſail, and let the ſame ſtone depart from the ſame place,
and it, according to what hath been premiſed, ſhall ſtill take up
the time of two pulſes in its fall, in which time the ſhip will have
run, ſuppoſe, twenty yards; To that the true motion of the ſtone
will be a tranſverſe line, conſiderably longer than the firſt ſtraight
and perpendicular line, which is the length of the ^{*} Maſt, and yet

nevertheleſs the ^{*} ſtone will have paſt it in the ſame time. Let
it be farther ſuppoſed, that the Ships motion is much more
rated, ſo that the ſtone in falling ſhall be to paſs a tranſverſe line
much longer than the other; and in ſum, increaſing the Ships

locity as much as you will, the falling ſtone ſhall deſcribe its
verſe lines ſtill longer and longer, and yet ſhall paſs them all in
thoſe ſelf ſame two pulſes. And in this faſhion, if a Canon were
1level'd on the top of a Tower, and ſhots were made therewith
point blank, that is, paralel to the Horizon, let the Piece have a
greater or leſs charge, ſo as that the ball may fall ſometimes a
thouſand yards diſtant, ſometimes four thouſand, ſometimes ſix,
ſometimes ten, &c. and all theſe ſhots ſhall curry or finiſh their
ranges in times equal to each other, and every one equal to the
time which the ball would take to paſs from the mouth of the
Piece to the ground, being left, without other impulſe, to fall
ſimply downwards in a perpendicular line. Now it ſeems a very
admirable thing, that in the ſame ſhort time of its falling
dicularly down to the ground, from the height of, ſuppoſe, an
hundred yards, the ſame ball, being thruſt violently out of the
Piece by the Fire, ſhould be able to paſs one while four hundred,
another while a thouſand, another while four, another while ten
thouſand yards, ſo as that the ſaid ball in all ſhots made point
blank, always continueth an equal time in the air.
An admirable
accident in the
tion of projects.
*By the length of
the maſt he means
the diſtance
tween the
deck and
top.
* La palla.
SALV. The conſideration for its novelty is very pretty, and if
the effect be true, very admirable: and of the truth thereof, I
make no queſtion: and were it not for the accidental impediment
of the air, I verily believe, that, if at the time of the balls going
out of the Piece, another were let fall from the ſame height
rectly downwards, they would both come to the ground at the
ſame inſtant, though that ſhould have curried ten thouſand
miles in its range, and this but an hundred onely: preſuppoſing
the ſurface of the Earth to be equal, which to be aſſured of, the
experiment may be made upon ſome lake. As for the impediment
which might come from the air, it would conſiſt in retarding the
extreme ſwift motion of the ſhot. Now, if you think fit, we will
proceed to the ſolution of the other Objections, ſeeing that
plicius (as far as I can ſee) is convinc'd of the nullity of this firſt,
taken from things falling from on high downwards.
SIMP. I find not all my ſcruples removed, but it may be the
fault is my own, as not being of ſo eaſie and quick an apprehenſion
as Sagredus. And it ſeems to me, that if this motion, of which
the ſtone did partake whilſt it was on the Round-top of the Ships
Maſt, be, as you ſay, to conſerve it ſelf indelibly in the ſaid ſtone,
even after it is ſeparated from the Ship, it would follow, that
wiſe in caſe any one, riding a horſe that was upon his ſpeed, ſhould
let a bowl drop out of his hand, that bowl being fallen to the
ground would continue its motion and follow the horſes ſteps,
without tarrying behind him: the which effect, I believe, is not
to be ſeen, unleſs when he that is upon the horſe ſhould throw it
with violence that way towards which he runneth; but otherwiſe,
I believe it will ſtay on the ground in the ſame place where it
fell.
1
SALV. I believe that you very much deceive your ſelf, and am
certain, that experience will ſhew you the contrary, and that the ball
being once arrived at the ground, will run together with the horſe,
not ſtaying behind him, unleſs ſo far as the aſperity and
neſs of the Earth ſhall hinder it. And the reaſon ſeems to me
very manifeſt: for if you, ſtanding ſtill, throw the ſaid ball
long the ground, do you think it would not continue its motion
even after you had delivered it out of your hand? and that for ſo
much a greater ſpace, by how much the ſuperficies were more
ſmooth, ſo that v. g. upon ice it would run a great way?
SIMP. There is no doubt of it, if I give it impetus with my
arm; but in the other caſe it is ſuppoſed, that he who is upon the
horſe, onely drops it out of his hand:
SALV. So I deſire that it ſhould be: but when you throw it
with your arm, what other remaineth to the ball being once gone
out of your hand, than the motion received from your arm, which
motion being conſerved in the boul, it doth continue to carry it
forward? Now, what doth it import, that that impetus be
ferred on the ball rather from the arm than from the horſe? Whilſt
you were on horſeback, did not your hand, and conſequently the
ball run as faſt as the horſe it ſelf? Doubtleſs it did: therefore
in onely opening of the hand, the ball departs with the motion
ready conceived, not from your arm, by your particular motion,
but from the motion dependant on the ſaid horſe, which cometh to
be communicated to you, to your arm, to your hand, and laſtly to
the ball. Nay, I will tell you farther, that if the rider upon his
ſpeed fling the ball with his arm to the part contrary to the courſe,
it ſhall, after it is fallen to the ground, ſometimes (albeit thrown to
the contrary part) follow the courſe of the horſe, and ſometimes lie
ſtill on the ground; and ſhall onely move contrary to the ſaid
courſe, when the motion received from the arm, ſhall exceed that
of the carrier in velocity. And it is a vanity, that of ſome, who
ſay that a horſeman is able to caſt a javelin thorow the air, that
way which the horſe runs, and with the horſe to follow and
take the ſame; and laſtly, to catch it again. It is, I ſay, a vanity,
for that to make the project return into the hand, it is requiſite to
caſt it upwards, in the ſame manner as if you ſtood ſtill. For, let
the carrier be never ſo ſwift, provided it be uniform, and the
ject not over-light, it ſhall always fall back again into the hand of
the projicient, though never ſo high thrown.
SAGR. By this Doctrine I come to know ſome Problems very

curious upon this ſubject of projections; the firſt of which muſt
ſeem very ſtrange to Simplicius. And the Problem is this; I
firm it to be poſſible, that the ball being barely dropt or let fall,
by one that any way runneth very ſwiftly, being arrived at the
1Earth, doth not onely follow the courſe of that perſon, but doth
much out go him. Which Problem is connexed with this, that
the moveable being thrown by the projicient above the plane of
the Horizon, may acquire new velocity, greater by far than that
confer'd upon it by the projicient. The which effect I have with
admiration obſerved, in looking upon thoſe who uſe the ſport of
tops, which, ſo ſoon as they are ſet out of the hand, are ſeen to
move in the air with a certain velocity, the which they afterwards
much encreaſe at their coming to the ground; and if whipping
them, they rub at any uneven place that makes them skip on high,
they are ſeen to move very ſlowly through the air, and falling
gain to the Earth, they ſtill come to move with a greater velocity:
But that which is yet more ſtrange, I have farther obſerved, that
they not onely turn always more ſwiftly on the ground, than in
the air, but of two ſpaces both upon the Earth, ſometimes a
tion in the ſecond ſpace is more ſwift than in the firſt. Now what
would Simplicius ſay to this?
Sundry curious
Problems,
ing the motions of
projects.
SIMP. He would ſay in the firſt place, that he had never made
ſuch an obſervation. Secondly, he would ſay, that he did not
lieve the ſame. He would ſay again, in the third place, that if
you could aſſure him thereof, and demonſtratively convince him of
the ſame, he would account you a great Dæmon.
SAGR. I hope then that it is one of the Socratick, not infernal
ones. But that I may make you underſtand this particular, you
muſt know, that if a perſon apprehend not a truth of himſelf, it
is impoſſible that others ſhould make him underſtand it: I may
deed inſtruct you in thoſe things which are neither true nor falſe;
but the true, that is, the neceſſary, namely, ſuch as it is impoſſible
ſhould be otherwiſe, every common capacity either comprehendeth
them of himſelf, or elſe it is impoſſible he ſhould ever know them.
And of this opinion I am confident is Salviatus alſo: and
fore I tell you, that the reaſons of the preſent Problems are known
by you, but it may be, not apprehended.
SIMP. Let us, for the preſent, paſs by that controverſie, and
permit me to plead ignorance of theſe things you ſpeak of, and try
whether you can make me capable of underſtanding theſe
blems.
SAGR. This firſt dependeth upon another, which is, Whence
cometh it, that ſetting a top with the laſh, it runneth farther, and
conſequently with greater force, than when its ſet with the
gers?
SIMP. Ariſtotle alſo makes certain Problems about theſe kinds
of projects.
SALV. He doth ſo; and very ingenious they are:
ly, That, Whence it cometh to paſs that round tops run better than
the ſquare?
1
SAGR. And cannot you, Simplicius, give a reaſon for this,
without others prompting you?
SIMP. Very good, I can ſo; but leave your jeering.
SAGR. In like manner you do know the reaſon of this other
alſo. Tell me therefore; know you that a thing which moveth,
being impeded ſtands ſtill?
SIMP. I know it doth, if the impediment be ſo great as to
ſuffice.
SAGR. Do you know, that moving upon the Earth is a greater
impediment to the moveable, than moving in the air, the Earth
ing rough and hard, and the air ſoft and yielding?
SIMP. And knowing this, I know that the top will turn faſter
in the air, than on the ground, ſo that my knowledg is quite
trary to what you think it.
SAGR. Fair and ſoftly, Simplicius. You know that in the
parts of a moveable, that turneth about its centre, there are found
motions towards all ſides; ſo that ſome aſcend, others deſcend;
ſome go forwards, others backwards?
SIMP. I know it, and Aristotle taught me the ſame.
SAGR. And with what demonſtration, I pray you?
SIMP. With that of ſenſe.
SAGR. Ariſtotle, then, hath made you ſee that which without
him you would not have ſeen? Did he ever lend you his eyes?
You would ſay, that Ariſtotle hath told, advertiſed, remembered
you of the ſame; and not taught you it. When then a top,
out changing place, turns round, (or in the childrens phraſe,
eth) not paralel, but erect to the Horizon, ſome of its parts aſcend,
and the oppoſite deſcend; the ſuperiour go one way, the
riour another. Fancie now to your ſelf, a top, that without
ging place, ſwiftly turns round in that manner, and ſtands
ded in the air, and that in that manner turning, it be let fall to the
Earth perpendicularly, do you believe, that when it is arrived at
the ground, it will continue to turn round in the ſame manner,
without changing place, as before?
SIMP. No, Sir.
SAGR. What will it do then?
SIMP. It will run along the ground very faſt.
SAGR. And towards what part?
SIMP. Towards that, whither its ^{*}reeling carrieth
* Vertigine.
SAGR. In its reeling there are parts, that is the uppermoſt, which
do move contrary to the inferiour; therefore you muſt inſtance
which it ſhall obey: for as to the parts aſcending and deſcending,
the one kind will not yield to the other; nor will they all go
downwards, being hindered by the Earth, nor upwards as being
heavy.
1
SIMP. The top will run reeling along the floor towards that
part whither its upper parts encline it.
SAGR. And why not whither the contrary parts tend, namely,
thoſe which touch the ground?
SIMP. Becauſe thoſe upon the ground happen to be impeded
by the roughneſs of the touch, that is, by the floors unevenneſs;
but the ſuperiour, which are in the tenuous and flexible air, are
hindred very little, if at all; and therefore the top will obey their
inclination.
SAGR. So that that taction, if I may ſo ſay, of the neither
parts on the floor, is the cauſe that they ſtay, and onely the upper
parts ſpring the top forward.
SALV. And therefore, if the top ſhould fall upon the ice, or
other very ſmooth ſuperficies, it would not ſo well run forward, but
might peradventure continue to revolve in it ſelf, (or ſleep)
out acquiring any progreſſive motion.
SAGR. It is an eaſie thing for it ſo to do; but yet
leſs, it would not ſo ſpeedily come to ſleep, as when it falleth on
a ſuperficies ſomewhat rugged. But tell me, Simplicius, when
the top turning round about it ſelf, in that manner, is let fall, why
doth it not move forwards in the air, as it doth afterwards when it
is upon the ground?
SIMP. Becauſe having air above it, and beneath, neither thoſe
parts, nor theſe have any where to touch, and not having more
caſion to go forward than backward, it falls perpendicularly.
SAGR. So then the onely reeling about its ſelf, without other
impetus, can drive the top forward, being arrived at the ground,
very nimbly. Now proceed we to what remains. That laſh,
which the driver tyeth to his Top-ſtick, and with which, winding
it about the top, he ſets it (i. e. makes it go) what effect hath it on
the ſaid top?
SIMP. It conſtrains it to turn round upon its toe, that ſo it may
free it ſelf from the Top-laſh.
SAGR. So then, when the top arriveth at the ground, it cometh
all the way turning about its ſelf, by means of the laſh. Hath it
not reaſon then to move in it ſelf more ſwiftly upon the ground,
than it did whilſt it was in the air?
SIMP. Yes doubtleſs; for in the air it had no other impulſe
than that of the arm of the projicient; and if it had alſo the
ing, this (as hath been ſaid) in the air drives it not forward at all:
but arriving at the floor, to the motion of the arm is added the
progreſſion of the reeling, whereby the velocity is redoubled. And
I know already very well, that the top skipping from the ground,
its velocity will deminiſh, becauſe the help of its circulation is
wanting; and returning to the Earth will get it again, and by that
1means move again faſter, than in the air. It onely reſts for me to
underſtand, whether in this ſecond motion on the Earth it move
more ſwiftly, than in the firſt; for then it would move in
tum, alwayes accelerating.
SAGR. I did not abſolutely affirm, that this ſecond motion is
more ſwift than the firſt; but that it may happen ſo to be
times.
SIMP. This is that, which I apprehend not, and which I
deſire to know.
SAGR. And this alſo you know of your ſelf. Therefore tell
me: When you let the top fall out of your hand, without
king it turn round (i. e. ſetting it) what will it do at its coming to
the ground?
SIMP. Nothing, but there lie ſtill.
SAGR. May it not chance, that in its fall to the ground it may
acquire a motion? Think better on it.
SIMP. Unleſſe we let it fall upon ſome inclining ſtone, as
children do playing at ^{*} Chioſa, and that falling ſide-wayes upon

the ſame, it do acquire the motion of turning round upon its toe,
wherewith it afterwards continueth to move progreſſively on the
floor, I know not in what other manner it can do any thing but
lie ſtill where it falleth.
* A Game in Italy,
which is, to glide
bullets down an
inclining ſtone,
&c.
SAGR. You ſee then that in ſome caſe it may acquire a new
revolution. When then the top jerked up from the ground, falleth
down again, why may it not caſually hit upon the declivity of
ſome ſtone fixed in the floor, and that hath an inclination that
way towards which it moveth, and acquiring by that ſlip a new
whirle over and above that conferred by the laſh, why may it
not redouble its motion, and make it ſwifter than it was at its
firſt lighting upon the ground?
SIMP. Now I ſee that the ſame may eaſily happen. And I
am thinking that if the top ſhould turn the contrary way, in
riving at the ground, it would work a contrary effect, that is,
the motion of the accidental whirl would retard that of the
jicient.
SAGR. And it would ſometimes wholly retard and ſtop it, in
caſe the revolution of the top were very ſwift. And from hence
riſeth the reſolution of that ſlight, which the more skilful Tennis
Players uſe to their advantage; that is, to gull their adverſary by
cutting (for ſo is their Phraſe) the Ball; which is, to return it
with a ſide Rachet, in ſuch a manner, that it doth thereby
quire a motion by it ſelf contrary to the projected motion, and ſo
by that means, at its coming to the ground, the rebound, which
if the ball did not turn in that manner, would be towards the
adverſary, giving him the uſual time to toſſe it back again, doth
1fail, and the ball runs tripping along the ground, or rebounds leſſe
than uſual, and breaketh the time of the return. Hence it is

that you ſee, thoſe who play at ^{*} Stool-ball, when they play in
a ſtony way, or a place full of. holes and rubs that make the ball
trip an hundred ſeveral wayes, never ſuffering it to come neer the
mark, to avoid them all, they do not trundle the ball upon the
ground, but throw it, as if they were to pitch a quait. But
cauſe in throwing the ball, it iſſueth out of the hand with ſome
roling conferred by the fingers, when ever the hand is under the
ball, as it is moſt commonly held; whereupon the ball in its lighting
on the ground neer to the mark, between the motion of the
jicient and that of the roling, would run a great way from the
ſame: To make the ball ſtay, they hold it artificially, with their
hand uppermoſt, and it undermoſt, which in its delivery hath
a contrary twirl or roling conferred upon it by the fingers, by
means whereof in its coming to the ground neer the mark it ſtays
there, or runs very very little forwards. But to return to our
principal problem which gave occaſion for ſtarting theſe others; I
ſay it is poſſible that a perſon carried very ſwiftly, may let a ball
drop out of his hand, that being come to the Earth, ſhall not
onely follow his motion, but alſo out-go it, moving with a
er velocity. And to ſee ſuch an effect, I deſire that the courſe
may be that of a Chariot, to which on the out-ſide let a
ning board be faſtened; ſo as that the neither part may be towards
the horſes, and the upper towards the hind Wheel. Now, if in
the Chariots full career, a man within it, let a ball fall gliding
long the declivity of that board, it ſhall in roling downward
quire a particular vertigo or turning, the which added to the
motion impreſſed by the Chariot, will carrie the ball along the
ground much faſter than the Chariot. And if one accommodate
another declining board over againſt it, the motion of the
riot may be qualified ſo, that the ball, gliding downwards along
the board, in its coming to the ground ſhall reſt immoveable,
and alſo ſhall ſometimes run the contrary way to the Chariot. But
we are ſtrayed too far from the purpoſe, therefore if Simplicius
be ſatisfied with the reſolution of the firſt argnment againſt the
Earths mobility, taken from things falling perpendicularly, we
may paſſe to the reſt
*A Game in Italy,
wherein they ſtrive
who ſhall trundle
or throw a wooden
bowle neereſt to an
aſſigned mark.
SALV. The digreſſions made hitherto, are not ſo alienated
from the matter in hand, as that one can ſay they are wholly
ſtrangers to it. Beſides theſe argumentations depend on thoſe
things that ſtart up in the fancy not of one perſon, but of three,
that we are: And moreover we diſcourſe for our pleaſure, nor
are we obliged to that ſtrictneſſe of one who ex profeſſo treateth
methodically of an argument, with an intent to publiſh the ſame.
1I will not conſent that our Poem ſhould be ſo confined to that
unity, as not to leave us fields open for Epſody's, which every
ſmall connection ſhould ſuffice to introduce; but with almoſt as
much liberry as if we were met to tell ſtories, it ſhall be lawful
for me to ſpeak, what ever your diſcourſe brings into my mind.
SAGR. I like this motion very well; and ſince we are at this
liberty, let me take leave, before we paſſe any farther to ask of
you Salviatus, whether you did ever conſider what that line may
be that is deſcribed by the grave moveable naturally falling down
from the top of a Tower; and if you have reflected on it, be
pleaſed to tell me what you think thereof.
SALV. I have ſometimes conſidered of it, and make no
ſtion, that if one could be certain of the nature of that motion
wherewith the grave body deſcendeth to approach the centre of
the Terreſtrial Globe, mixing it ſelf afterwards with the common
circular motion of the diurnal converſion; it might be exactly
found what kind of line that is, that the centre of gravity of the
moveable deſcribeth in thoſe two motions.
SAGR. Touching the ſimple motion towards the centre
pendent on the gravity, I think that one may confidently,
out error, believe that it is by a right line, as it would be, were
the Earth immoveable.
SALV. As to this particular, we may not onely believe it, but
experience rendereth us certain of the ſame.
SAGR. But how doth experience aſſure us thereof, if we
ver ſee any motions but ſuch as are compoſed of the two, circular
and deſcending.
SALV. Nay rather Sagredus we onely ſee the ſimple motion of
deſcent; ſince that other circular one common to the Earth, the
Tower and our ſelves remains imperceptible, and as if it never
were, and there remaineth perceptible to us that of the ſtone,
ly not participated by us, and for this, ſenſe demonſtrateth that
it is by a right line, ever parallel to the ſaid Tower, which is
built upright and perpendicular upon the Terreſtrial ſurface.
SAGR. You are in the right; and this was but too plainly
monſtrated to me even now, ſeeing that I could not remember ſo
eaſie a thing; but this being ſo manifeſt, what more is it that you
ſay you deſire, for underſtanding the nature of this motion
downwards?
SALV. It ſufficeth not to know that it is ſtreight, but its
ſite to know whether it be uniform, or irregular; that is,
ther it maintain alwayes one and the ſame velocity, or elſe goeth
retarding or accelerating.
SAGR. It is already clear, that it goeth continually
rating.
1
SALV. Neither doth this ſuffice, but its requiſite to know
cording to what proportion ſuch accelleration is made; a
blem, that I believe was never hitherto underſtood by any
loſopher or Mathematician; although Philoſophers, and
larly the Peripateticks, have writ great and entire Volumes,
touching motion.
SIMP. Philoſophers principally buſie themſelves about
ſals; they find the definitions and more common ſymptomes,
mitting certain ſubtilties and niceties, which are rather
ſities to the Mathematicians. And Aristotle did content himſelf
to deſine excellently what motion was in general; and of the
cal, to ſhew the principal qualities, to wit, that one is natural,
another violent; one is ſimple, another compound; one is
equal, another accellerate; and concerning the accelerate,
tents himſelf to give the reaſon of acceleration, remitting the
finding out of the proportion of ſuch acceleration, and other
particular accidents to the Mechanitian, or other inferiour
Artiſt.
SAGR. Very well Simplicius. But you Salviatus, when you
deſcend ſometimes from the Throne of Peripatetick Majeſty,
have you ever thrown away any of your hours in ſtudying to find
this proportion of the acceleration of the motion of deſcending
grave bodies?
SALV. There was no need that I ſhould ſtudy for it, in regard
that the Academick our common friend, heretofore ſhewed me a
Treatiſe of his ^{*} De Motu, where this, and many other

dents were demonſtrated. But it would be too great a digreſſion,
if for this particular, we ſhould interrupt our preſent diſcourſe,
(which yet it ſelf is alſo no better than a digreſſion) and make as
the Saying is, a Comedy within a Comedy.
This is that
cellent tract which
we give the firſt
place in our ſecond
Volume.
SAGR. I am content to excuſe you from this narration for the
preſent, provided that this may be one of the Propoſitions
ved to be examined amongſt the reſt in another particular meeting,
for that the knowledg thereof is by me very much deſired; and
in the mean time let us return to the line deſcribed by the grave
body in its fall from the top of the Tower to its baſe.
SALV. If the right motion towards the centre of the Earth was
uniforme, the circular towards the Eaſt being alſo uniforme, you
would ſee compoſed of them both a motion by a ſpiral line, of
that kind with thoſe defined by Archimedes in his Book Dc
libus; which are, when a point moveth uniformly upon a right
line, whileſt that line in the mean time turneth uniformly about
one of its extreme points fixed, as the centre of his gyration.
But becauſe the right motion of grave bodies falling, is
ally accelerated, it is neceſſary, that the line reſulting of the
1compoſition of the two motions do go alwayes receding with
greater and greater proportion from the circumference of that
cle, which the centre of the ſtones gravity would have deſigned,
if it had alwayes ſtaid upon the Tower; it followeth of neceſſity
that this receſſion at the firſt be but little, yea very ſinall, yea,
more, as ſmall as can be imagined, ſeeing that the deſcending
grave body departing from reſt, that is, from the privation of
motion, towards the bottom and entring into the right motion
downwards, it muſt needs paſſe through all the degrees of
ty, that are betwixt reſt, and any aſſigned velocity; the which
degrees are infinite; as already hath been at large diſcourſed and
proved.
It being ſuppoſed therefore, that the progreſſe of the
ration being after this manner, and it being moreover true, that
the deſcending grave body goeth to terminate in the centre of the
Earth, it is neceſſary that the line of its mixt motion be ſuch, that

it go continually receding with greater and greater proportion
from the top of the Tower, or to ſpeak more properly, from
the circumference of the circle deſcribed by the top of the Tower,
by means of the Earths converſion; but that ſuch receſſions be
leſſer and leſſer in infinitum; by how much the moveable finds it
ſelf to be leſſe and leſſe removed from the firſt term where it
reſted. Moreover it is neceſſary, that this line of the
ed motion do go to terminate in the centre of the Earth. Now
having preſuppoſed theſe two things, I come to deſcribe about
the centre A [in Fig. 1. of this ſecond Dialogue;] with the ſemi­
diameter A B, the circle B I, repreſenting to me the Terreſtrial
Globe, and prolonging the ſemidiameter A B to C, I have
ſcribed the height of the Tower B C; the which being carried
about by the Earth along the circumference B I, deſcribeth with
its top the arch C D: Dividing, in the next place, the line C A
in the middle at E; upon the centre E, at the diſtance E C, I
ſcribe the ſemicircle C I A: In which, I now affirm, that it is very
probable that a ſtone falling from the top of the Tower C, doth
move, with a motion mixt of the circular, which is in common,
and of its peculiar right motion. If therefore in the circumference
C D, certain equal parts C F, F G, G H, H L, be marked, and
from the points F, G, H, L, right lines be drawn towards the
centre A, the parts of them intercepted between the two
cumferences C D and B I, ſhall repreſent unto us the ſame
Tower C B, tranſported by the Terreſtrial Globe towards D I;
in which lines the points where they come to be interſected by the
arch of the ſemicircle C I, are the places by whichfrom time to
time the falling ſtone doth paſſe; which points go continually
with greater and greater proportion receding from the top of the
1Tower. And this is the cauſe why the right motion made along
the ſide of the Tower appeareth to us more and more accelerate.
It appeareth alſo, how by reaſon of the infinite acuteneſſe of
the contact of thoſe two circles D C, C I, the receſſion of the
cadent moveable from the circumference C F D; namely, from
the top of the Tower, is towards the beginning extream ſmall,
which is as much as if one ſaid its motion downwards is very ſlow,
and more and more ſlow in infinitum, according to its vicinity to
the term C, that is to the ſtate of reſt. And laſtly it is ſeen how
in the end this ſame motion goeth to terminate in the centre of the
Earth A.
The line
bed by a moveable
in its natural
ſcent, the motion
of the Earth
bout its own centre
being preſuppoſed,
would probably be
the circumference
of a circle.
SAGR. I underſtand all this very well, nor can I perſwade my
ſelf that the falling moveable doth deſcribe with the centre of its
gravity any other line, but ſuch an one as this.
SALV. But ſtay a little Sagredus, for I am to acquaint you
alſo with three Obſervations of mine, that its poſſible will not

pleaſe you. The firſt of which is, that if we do well conſider, the
moveable moveth not really with any more than onely one motion
ſimply circular, as when being placed upon the Tower, it moved
with one ſingle and circular motion. The ſecond is yet more

ſant; for, it moveth neither more nor leſſe then if it had ſtaid
tinually upon the Tower, being that to the arches C F, F G, G H,
&c. that it would have paſſed continuing alwayes upon the Tower,
the arches of the circumference C I are exactly equal, anſwering
under the ſame C F, F G, G H, &c. Whence followeth the third

wonder, That the true and real motion of the ſtone is never
lerated, but alwayes even and uniforme, ſince that all the equal
ches noted in the circumference C D, and their reſpondent ones
marked in the circumference C I, are paſt in equal times; ſo that
we are left at liberty to ſeek new cauſes of acceleration, or of
ther motions, ſeeing that the moveable, as well ſtanding upon the
Tower, as deſcending thence, alwayes moveth in the ſame faſhion,
that is, circularly, with the ſame velocity, and with the ſame
formity. Now tell me what you think of this my fantaſtical
jecture.
A moveable
ting from the top of
the Tower, moveth
in the
rence of a circle.
It moveth neither
more nor leſſe, than
if it had ſtaid
wayes there.
It moveth with
an uniform, not
an accelerate
tion.
SAGR. I muſt tell you, that I cannot with words ſufficiently
expreſſe how admirable it ſeemeth to me; and for what at
ſent offereth it ſelf to my underſtanding, I cannot think that the
buſineſs happeneth otherwiſe; and would to God that all the
demonſtrations of Philoſophers were but half ſo probable as this.
However for my perfect ſatisfaction I would gladly hear how you
prove thoſe arches to be equal.
SALV. The demonſtration is moſt eaſie. Suppoſe to your ſelf
a line drawn from I to E. And the Semidiameter of the circle CD,
that is, the line C A, being double the Semidiameter C E of the
1circle C I, the circumference ſhall be double to the circumference,
and every arch of the greater circle double to every like arch of
the leſſer; and conſequently, the half of the arch of the greater
circle, equal to the whole arch of the leſſe. And becauſe the
gle C E I made in the centre E of the leſſer circle, and which
ſteth upon the arch C I, is double the angle C A D, made in the
centre A of the greater circle, to which the arch C D ſubtendeth;
therefore the arch C D is half of the arch of the greater circle like
to the arch C I, and therefore the two arches C D and C I are
qual; and in the ſame manner we may demonſtrate of all their
parts. But that the buſineſs, as to the motion of deſcending grave
bodies, proceedeth exactly thus, I will not at this time affirm; but
this I will ſay, that if the line deſcribed by the cadent moveable
be not exactly the ſame with this, it doth extream neerly reſemble
the ſame.
SAGR. But I, Salviatus, am juſt now conſidering another

ticular very admirable; and this it is; That admitting theſe
ſiderations, the right motion doth go wholly ^{*} mounting, and that

Nature never makes uſe thereof, ſince that, even that that uſe,
which was from the beginning granted to it, which was of
cing the parts of integral bodies to their place, when they were
ſeparated from their whole, and therefore conſtituted in a
ved diſpoſition, is taken from it, and aſſigned to the circular
motion.
Right motion
ſeemeth wholly
cluded in nature.
* Vadia del tutto a
monte, rendered in
the Latixe
no peſſum eat.
SALV. This would neceſſarily follow, if it were concluded
that the Terreſtrial Globe moveth circularly; a thing, which I
pretend not to be done, but have onely hitherto attempted, as I
ſhall ſtill, to examine the ſtrength of thoſe reaſons, which have
been alledged by Philoſophers to prove the immobility of the
Earth, of which this firſt taken from things falling
larly, hath begat the doubts, that have been mentioned; which
I know not of what force they may have ſeemed to Simplicius;
and therefore before I paſſe to the examination of the remaining
arguments, it would be convenient that he produce what he hath
to reply to the contrary.
SIMP. As to this firſt, I confeſſe indeed that I have heard
ſundry pretty notions, which I never thought upon before, and
in regard they are new unto me, I cannot have anſwers ſo ready
for them, but this argument taken from things falling
cularly, I eſteem it not one of the ſtrongeſt proofs of the
lity of the Earth; and I know not what may happen touching the
ſhots of great Guns, eſpecially thoſe aimed contrary to the
nal motion.
SAGR. The flying of the birds as much puzzleth me as the
objection of the Gun-ſhot, and all the other experiments above
1alledged. For theſe birds which at their pleaſure flie
wards and backwards, and wind to and again in a thouſand
faſhions, and, which more importeth, lie whole hours upon the
wing, theſe I ſay do not a little poſe me, nor do I ſee, how
mongſt ſo many circumgyrations, they ſhould not loſe the motion
of the Earth, and how they ſhould be able to keep pace with
ſo great a velocity as that which they ſo far exceed with their flight.
SALV. To ſpeak the truth, your ſcruple is not without reaſon,
and its poſſible Copernicus himſelf could not find an anſwer for it,
that was to himſelf entirely ſatisfactory; and therefore haply paſt
it over in ſilence albeit he was, indeed, very brief in examining
the other allegations of his adverſaries, I believe through his
height of wit, placed on greater aud ſublimer contemplations,
like as Lions are not much moved at the barking of little Dogs.
We will therefore reſerve the inſtance of birds to the laſt place,
and for the preſent, ſee if we can give Simplicius ſatisfaction in
the others, by ſhewing him in our wonted manner, that he
ſelf hath their anſwers at hand, though upon firſt thoughts he doth
not diſcover them. And to begin with the ſhots made at randome,
with the ſelf ſame piece, powder, and ball, the one towards the Eaſt,
the other towards the Weſt, let him tell me what it is that perſwades
him to think that the Range towards the Weſt (if the diurnal
verſion belonged to the Earth) ought to be much longer than that
towards the
The reaſon why
a Gun ſhould ſiem
to carry farther
wards the Weſt
than towards the
Eaſt.
SIMP. I am moved ſo to think; becauſe in the ſhot made
wards the Eaſt, the ball whil'ſt it is out of the piece, is
ed by the ſaid piece, the which being carried round by the Earth,
runneth alſo with much velocity towards the ſame part,
upon the fall of the ball to the ground, cometh to be but little
diſtant from the piece. On the contrary in the ſhot towards the
Weſt, before that the ball falleth to the ground, the piece is
tired very far towards the Eaſt, by which means the ſpace
tween the ball and the piece, that is Range, will appear longer
than the other, by how much the piece, that is the Earth, had
run in the time that both the bals were in the air.
SALV. I could wiſh, that we did know ſome way to make an
experiment correſponding to the motion of theſe projects, as that
of the ſhip doth to the motion of things perpendicularly falling
from on high; and I am thinking how it may be done.
The experiment
of a running
riot to find out the
difference of
ges.
SAGR. I believe, that it would be a very oppoſite proof, to
take an open Chariot, and to accomodate therein a ^{*}Stock-bow
at half elevation, to the end the flight may prove the greateſt

that my be, and whil'ſt the horſes ſhall run, to ſhoot firſt towards
the part whither you drive, and then another backwards towards
the contrary part, cauſing ſome one to mark diligently where
the Chariot was in that moment f time when the ſhaft came to
1the ground, as well in the one ſhot as in the other: for thus you
may ſee exactly how much one ſhaft flew farther than the other.
* Baleſtrone da
zoni.
SIMP. In my thoughts this experiment is very proper: and I
do not doubt but that the flight, that is, the ſpace between the
ſhaft and the place where the chariot was at the ſhafts fall, will be
leſs by much when one ſhooteth towards the chariots courſe, than
when one ſhooteth the contrary way. For an example, let the
flight of it ſelf be three hundred yards, and the courſe of the
riot in the time whilſt the ſhaft ſtayeth in the air, an hundred
yards, therefore ſhooting towards the courſe, of the three hundred
yards of the flight, the chariot will have gone one hundred; ſo
then at the ſhafts coming to the ground, the ſpace between it and
the chariot, ſhall be but two hundred yards onely; but on the
contrary, in the other ſhoot, the chariot running contrary to the
ſhaft, when the ſhaft ſhall have paſſed its three hundred yards, and
the chariot its other hundred the contrary way, the diſtance
poſing ſhall be found to be four hundred yards.
SALV. Is there any way to ſhoot ſo that theſe flights may be
equal?
SIMP. I know no other way, unleſs by making the chariot to
ſtand ſtill.
SALV. This we know; but I mean when the chariot runneth
in full carreer.
SIMP. In that caſe you are to draw the Bow higher in
ing forwards, and to ſlack it in ſhooting the contrary way.
SALV. Then you ſee that there is one way more. But how
much is the bow to be drawn, and how much ſlackened?
SIMP. In our caſe, where we have ſuppoſed that the bow
ried three hundred yards, it would be requiſite to draw it ſo, as
that it might carry four hundred, and in the other to ſlacken it ſo,
as that it might carry no more than two hundred. For ſo each
of the flights would be but three hundred in relation to the chariot,
the which, with its courſe of an hundred yards which it ſubſtracts
from the ſhoot of four hundred, and addeth to that of two
dred, would reduce them both to three hundred.
SALV. But what effect hath the greater or leſs intenſneſs of the
bow upon the ſhaft?
SIMP. The ſtiffer bow carrieth it with greater velocity, and the
weaker with leſs; and the ſame ſhaft flieth ſo much farther at one
time than another, with how much greater velocity it goeth out of
the tiller at one time, than another.
SALV. So that to make the ſhaft ſhot either way, to flie at
qual diſtance from the running chariot, it is requiſite, that if in the
firſt ſhoot of the precedent example, it goeth out of the tiller with
v. g. four degrees of velocity, that then in the other ſhoot it
1part but with two onely: but if the ſame bow be uſed, it always
receiveth thence three degrees.
SIMP. It doth ſo; and for this reaſon, ſhooting with the
ſame bow in the chariots courſe, the ſhoots cannot be equal.
SALV. I had forgot to ask, with what velocity it is ſuppoſed in
this particular experiment, that the chariot runneth.
SIMP. The velocity of the chariot muſt be ſuppoſed to be one
degree in compariſon to that of the bow, which is three,
SALV. Very right, for ſo computation gives it. But tell me,
when the chariot moveth, doth not all things in the ſame move
with the ſame velocity?
SIMP. Yes doubtleſs.
SALV. Then ſo doth the ſhaft alſo, and the bow, and the ſtring,
upon which the ſhaft is nock't.
SIMP. They do ſo.
SALV. Why then, in diſcharging the ſhaft towards the courſe
of the chariot, the bow impreſſeth its three degrees of velocity on
a ſhaft that had one degree of velocity before, by means of the
chariot which tranſported it ſo faſt towards that part; ſo that in
its going off it hath four degrees of velocity. On the contrary,
in the other ſhoot, the ſame bow conferreth its ſame three degrees
of velocity on a ſhaft that moveth the contrary way, with one
gree; ſo that in its departing from the bow-ſtring, it hath no more
left but onely two degrees of velocity. But you your ſelf have
already ſaid, that the way to make the ſhoots equal, is to cauſe
that the ſhaft be let flie the firſt time with four degrees of velocity,
and the ſecond time with two. Therefore without changing the
bow, the very courſe of the chariot is that which adjuſteth the

flights, and the experiment doth ſo repreſent them to any one who
is not either wilfully or naturally incapable of reaſon. Now
apply this diſcourſe to Gunnery, and you ſhall find, that whether the
Earth move or ſtand ſtill, the ſhots made with the ſame force, will
always curry equal ranges, to what part ſoever aimed. The error
of Ariſtotle, Ptolomey, Iycho, your ſelf, and all the reſt, is
ed upon that fixed and ſtrong perſuaſion, that the Earth ſtandeth
ſtill, which you have not judgment nor power to depoſe, no not
when you have a deſire to argue of that which would enſue,
ſuppoſing the Earth to move. And thus, in the other argument,
not conſidering that whil'ſt the ſtone is upon the Tower, it doth,
as to moving or not moving, the ſame that the Terreſtrial Globe
doth, becauſe you have concluded with your ſelf, that the Earth
ſtands ſtill, you always diſcourſe touching the fall of the ſtone, as
if it were to depart from reſt: whereas it behooveth to ſay, that
if the Earth ſtandeth ſtill, the ſtone departeth from reſt, and
ſcendeth perpendicularly; but if the Earth do move, the ſtone
1likewiſe moveth with like velocity, nor doth it depart from reſt,
but from a motion equal to that of the Earth, wherewith it
mixeth the ſupervenient motion of deſcent, and of thoſe two
poſeth a third which is tranſverſal or ſide-ways.
The ſolution of
the argument
ken from
Guns ſhot towards
the East & Weſt.
SIMP. But for Gods ſake, if it move tranſverſly, how is it that
I behold it to move directly and perpendicularly? This is no
ter than the denial of manifeſt ſenſe; and if we may not believe
ſenſe, at what other door ſhall we enter into diſquiſitions of
ſophy?
SALV. In reſpect to the Earth, to the Tower, and to our ſelves,
which all as one piece move with the diurnal motion together with
the ſtone, the diurnal motion is as if it never had been, and
eth inſenſible, imperceptible, and without any action at all; and
the onely motion which we can perceive, is that of which we
take not, that is the deſcent gliding along the ſide of the Tower:
You are not the firſt that hath felt great repugnance in
ding this non-operating of motion upon things to which it is
mon.
SAGR. Now I do remember a certain conceipt, that came one

day into my fancy, whilſt I ſailed in my voyage to Aleppo, whither
I went Conſul for our Countrey, and poſſibly it may be of ſome
uſe, for explaining this nullity of operation of common motion,
and being as if it never were to all the partakers thereof. And if
it ſtand with the good liking of Simplicius, I will reaſon with
him upon that which then I thought of by my ſelf alone.
A notable caſe
of Sagredus, to ſhew
the non-operating
of common motion.
SIMP. The novelty of the things which I hear, makes me not
ſo much a patient, as a greedy and curious auditor: therefore go
on.
SAGR. If the neb of a writing pen, that I carried along with
me in the ſhip, through all my navigation from Venice to ^{*} Scan-

deron, had had a facultie of leaving viſible marks of its whole
age, what ſigns, what marks, what lines would it have left?
* Aleſſandretta.
SIMP. It would have left a line diſtended from Venice thither,
not perfectly ſtreight, or to ſay better, diſtended in a perfect arch
of a circle, but in ſome places more, in ſome leſs curved, according
as the veſſel had gone more or leſs fluctuating; but this its
cting in ſome places a fathom or two to the right hand or to the
left, upwards or downwards, in a length of many hundred miles,
would have brought but little alteration to the intire tract of the
line, ſo that it would have been hardly ſenſible; and without any
conſiderable error, might have been called the part of a perfect
arch.
SAGR. So that the true and moſt exact motion of the neb of
my pen would have alſo been an arch of a perfect circle, if the
veſſels motion, the fluctuation of the billows ceaſing, had been
1calm and tranquill. And if I had continually held that pen in
my hand, and had onely moved it ſometimes an inch or two this
way or that way, what alteration ſhould I have made in that its
principal, and very long tract or ſtroke?
SIMP. Leſs than that which the declining in ſeveral places from
abſolute rectitude, but the quantity of a flea's eye makes in a right
line of a thouſand yards long.
SAGR. If a Painter, then, at our launching from the Port, had
began to deſign upon a paper with that pen, and continued his
work till he came to Scanderon, he would have been able to have
taken by its motion a perfect draught of all thoſe figures perfectly
interwoven and ſhadowed on ſeveral ſides with countreys,
ings, living creatures, and other things; albeit all the true, real,
and eſſential motion traced out by the neb of that pen, would
have been no other than a very long, but ſimple line: and as to
the proper operation of the Painter, he would have delineated the
ſame to an hair, if the ſhip had ſtood ſtill. That therefore of the
huge long motion of the pen there doth remain no other marks,
than thoſe tracks drawn upon the paper, the reaſon thereof is
cauſe the grand motion from Venice to Scanderon, was common to
the paper, the pen, and all that which was in the ſhip: but the petty
motions forwards and backwards, to the right, to the left,
municated by the fingers of the Painter unto the pen, and not to
the paper, as being peculiar thereunto, might leave marks of it ſelf
upon the paper, which did not move with that motion. Thus it
is likewiſe true, that the Earth moving, the motion of the ſtone in
deſcending downwards, was really a long tract of many hundreds
and thouſands of yards, and if it could have been able to have
lineated in a calm air, or other ſuperficies, the track of its courſe,
it would have left behind an huge long tranſverſe line. But that
part of all this motion which is common to the ſtone, the Tower,
and our ſelves, is imperceptible to us, and as if it had never been,
and that part onely remaineth obſervable, of which neither the
Tower nor we are partakers, which is in fine, that wherewith the
ſtone falling meaſureth the Tower.
SALV. A moſt witty conceipt to clear up this point, which was
not a little difficult to many capacities. Now if Simplicius will
make no farther reply, we may paſs to the other experiments, the
unfolding of which will receive no ſmall facility from the things
already declared.
SIMP. I have nothing more to ſay: and I was well-nigh
ported with that delineation, and with thinking how thoſe ſtrokes
drawn ſo many ways, hither, thither, upwards, downwards,
wards, backwards, and interwoven with thouſands of turnings, are
not eſſentially or really other, than ſmall pieces of one ſole line
1drawn all one way, and the ſame without any other alteration ſave
the declining the direct rectitude, ſometimes a very inſenſible
ter towards one ſide or another, and the pens moving its neb one
while ſofter, another while ſlower, but with very ſmall inequality.
And I think that it would in the ſame manner write a letter, and
that thoſe frollike penmen, who to ſhew their command of hand,
without taking their pen from the paper in one ſole ſtroke, with
infinite turnings draw a pleaſant knot, if they were in a boat that
did tide it along ſwiftly they would convert the whole motion
of the pen, which in reality is but one ſole line, drawn all towards
one and the ſame part, and very little curved, or declining from
perfect rectitude, into a knot or flouriſh. And I am much pleaſed
that S agredus hath helped me to this conceit: therefore let us go
on, for the hope of meeting with more of them, will make me the
ſtricter in my attention.
SAGR. If you have a curioſity to hear ſuch like ſubtilties, which

occurr not thus to every one, you will find no want of them,
cially in this particular of Navigation; and do you not think that a
witty conceit which I met with likewiſe in the ſame voyage, when I
obſerved that the maſt of the ſhip, without either breaking or
ing, had made a greater voyage with its round-top, that is with its
top-gallant, than with its foot; for the round top being more diſtant
from the centre of the Earth than the foot is, it had deſcribed the
arch of a circle bigger than the circle by which the foot had paſſed.
Subtilties
ently inſipid,
cally, ſpoken and
taken from a
tain Encyclopædia.
SIMP. And thus when a man walketh he goeth farther with
his head than with his feet.
SAGR. You have found out the matter your ſelf by help of
your own mother-wit: But let us not interrupt Salviatus.
SALV. It pleaſeth me to ſee Simplicius how he ſootheth up
himſelf in this conceit, if happly it be his own, and that he hath not
borrowed it from a certain little pamphlet of concluſions, where
there are a great many more ſuch fancies no leſs pleaſant & witty.
It followeth that we ſpeak of the peice of Ordinance mounted

pendicular to the Horizon, that is, of a ſhot towards our vertical
point, and to conclude, of the return of the ball by the ſame line
unto the ſame peice, though that in the long time which it is
parated from the peice, the earth hath tranſported it many miles
towards the Eaſt; now it ſeemeth, that the ball ought to fall a like
diſtance from the peice towards the Weſt; the which doth not
happen: therefore the peice without having been moved did ſtay
expecting the ſame. The anſwer is the ſame with that of the

ſtone falling from the Tower; and all the fallacy, and
on conſiſteth in ſuppoſing ſtill for true, that which is in queſtion;
for the Opponent hath it ſtill fixed in his conceit that the
ball departs from its reſt, being diſcharged by the fire
1from the piece; and the departing from the ſtate of reſt, cannot
be, unleſſe the immobility of the Terreſtrial Globe be
ſed, which is the concluſion of that was in diſpute; Therefore,
I reply, that thoſe who make the Earth moveable, anſwer, that
the piece, and the ball that is in it, partake of the ſame motion
with the Earth; nay that they have this together with her from
nature; and that therefore the ball departs in no other manner
from its quieſcence, but conjoyned with its motion about the
tre, the which by its projection upwards, is neither taken away,
nor hindered; and in this manner following, the univerſal motion
of the Earth towards the Eaſt, it alwayes keepeth perpendicular
over the ſaid piece, as well in its riſe as in its return. And the
ſame you ſee to enſue, in making the experiment in a ſhip with
a bullet ſhot upwards perpendicularly with a Croſſe-bow, which
returneth to the ſame place whether the ſhip doth move, or ſtand

An inſtance
gainst the diurnal
motion of the earth,
taken from the ſhot
of a Peece of
nance
larly.
The anſwer to the
objection, ſhewing
the equivoke.
Another anſwer
to the ſame
on.
SAGR. This ſatisfieth very well to all; but becauſe that I have
ſeen that Simplicius taketh pleaſure with certain ſubtilties to
puzzle his companions, I will demand of him whether,
ſing for this time that the Earth ſtandeth ſtill, and the piece
cted upon it perpendicularly, directed to our Zenith, he do at all
queſtion that to be the true perpendicular ſhot, and that the ball
in departing, and in its return is to go by the ſame right line,
ſtill ſuppoſing all external and accidental impediments to be
moved?
SIMP. I underſtand that the matter ought to ſucceed exactly
in that manner.
SAGR. But if the piece were placed, not perpendicularly, but
inclining towards ſome place, what would the motion of the ball
be? Would it go haply, as in the other ſhot, by the
cular line, and return again by the ſame?
SIMP. It would not ſo do; but iſſuing out of the piece, it
would purſue its motion by a right line which prolongeth the
rect perpendicularity of the concave cylinder of the piece, unleſſe
ſo far as its own weight would make it decline from that erection
towards the Earth.
SAGR. So that the mounture of the cylinder is the regulator of
the motion of the ball, nor doth it, or would it move out of that
line, if its own gravity did not make it decline downwards. And

therefore placing the cylinder perpendicularly, and ſhooting the
ball upwards, it returneth by the ſame right line downwards;
cauſe the motion of the ball dependent on its gravity is
ward, by the ſame perpendicular. The journey therefore of the
ball out of the piece, continueth or prolongeth the rectitude or
perpendicularity of that ſmall part of the ſaid journey, which it
made within the ſaid piece; is it not ſo?
1
Projects
nue their motion
by the right line
that followeth the
direction of the
motion, made
gether with the
projicient, whil'ſt
they were conjoin'd
therewith.
SIMP. So it is, in my opinion.
SAGR. Now imagine the cylinder to be erected, and that the
Earth doth revolve about with a diurnal motion, carrying the
piece along with it, tell me what ſhall be the motion of the ball
within the cylinder, having given fire?
SIMP. It ſhall be a ſtreight and perpendicular motion, the
der being erected perpendicularly.
SAGR. Conſider well what you ſay: for I believe that it will
not be perpendicular. It would indeed be perpendicular, if the
Earth ſtood ſtill, for ſo the ball would have no other motion but
that proceeding from the fire. But in caſe the Earth turns round,

the ball that is in the piece, hath likewiſe a diurnal motion, ſo
that there being added to the ſame the impulſe of the fire, it
veth from the breech of the piece to the muzzle with two motions,
from the compoſition whereof it cometh to paſſe that the motion
made by the centre of the balls gravity is an inclining line. And
for your clearer underſtanding the ſame, let the piece A C [in
Fig. 2.] be erected, and in it the ball B; it is manifeſt, that the
piece ſtanding immoveable, and fire being given to it, the ball
will make its way out by the mouth A, and with its centre,
ſing thorow the the piece, ſhall have deſcribed the perpendicular
line B A, and it ſhall purſue that rectitude when it is out of the
piece, moving toward the Zenith. But in caſe the Earth ſhould
move round, and conſequently carry the piece along with it, in
the time that the ball driven out of the piece ſhall move along
the cylinder, the piece being carried by the Earth, ſhall paſſe
to the ſituation D E, and the ball B, in going off, would be at
the corniſh D, and the motion of the bals centre, would have
been according to the line B D, no longer perpendicular, but
clining towards the Eaſt; and the ball (as hath been concluded)
being to continue its motion through the air, according to the
direction of the motion made in the piece, the ſaid motion ſhall
continue on according to the inclination of the line B D, and ſo
ſhall no longer be perpendicular, but inclined towards the Eaſt,
to which part the piece doth alſo move; whereupon the ball may
follow the motion of the Eerth, and of the piece. Now Simplicius,
you ſee it demonſtrated, that the Range which you took to be
perpendicular, is not ſo.
The revolution
of the Earth
poſed, the ball in
the piece erected
perpendicularly,
doth not move by a
perpendicular, but
an inclined line.
SIMP. I do not very well underſtand this buſineſs; do you,
Salviatus?
SALV. I apprehend it in part; but I have a certain kind of
ſcruple, which I wiſh I knew how to expreſs. It ſeems to me, that
according to what hath been ſaid, if the Piece be erected
dicular, and the Earth do move, the ball would not be to fall, as
Ariſtotle and Tycho will have it, far from the Piece towards the
1Weſt, nor as you would have it, upon the Piece, but rather far
diſtant towards the Eaſt. For according to your explanation, it
would have two motions, the which would with one conſent carry
it thitherward, to wit, the common motion of the Earth, which
carrieth the Piece and the ball from C A towards E D; and the
fire which carrieth it by the inclined line B D, both motions
wards the Eaſt, and therefore they are ſuperiour to the motion of
the Earth.
SAGR. Not ſo, Sir. The motion which carrieth the ball
wards the Eaſt, cometh all from the Earth, and the fire hath no
part at all therein: the motion which mounteth the ball upwards,
is wholly of fire, wherewith the Earth hath nothing to do. And
that it is ſo, if you give not fire, the ball will never go out of the
Piece, nor yet riſe upwards a hairs breadth; as alſo if you make
the Earth immoveable, and give fire, the ball without any
nation ſhall go perpendicularly upwards. The ball therefore
ving two motions, one upwards, and the other in gyration, of both
which the tranſverſe line B D is compounded, the impulſe upward
is wholly of fire, the circular cometh wholly from the Earth, and
is equal to the Earths motion: and being equal to it, the ball
maintaineth it ſelf all the way directly over the mouth of the
Piece, and at laſt falleth back into the ſame: and becauſe it
ways obſerveth the erection of the Piece, it appeareth alſo
nually over the head of him that is near the Piece, and therefore
it appeareth to mount exactly perpendicular towards our Zenith,
or vertical point.
SIMP. I have yet one doubt more remaining, and it is, that in
regard the motion of the ball is very ſwift in the Piece, it ſeems
not poſſible, that in that moment of time the tranſpoſition of the
Piece from C A to A D ſhould confer ſuch an inclination upon
the tranſverſe line C D, that by means thereof, the ball when it
cometh afterwards into the air ſhould be able to follow the courſe
of the Earth.
SAGR. You err upon many accounts; and firſt, the inclination
of the tranſverſe line C D, I believe it is much greater than you
take it to be, for I verily think that the velocity of the Earths
tion, not onely under the Equinoctial, but in our paralel alſo, is
greater than that of the ball whilſt it moveth in the Piece; ſo that
the interval C E would be abſolutely much bigger than the whole
length of the Piece, and the inclination of the tranſverſe line
ſequently bigger than half a right angle: but be the velocity of
the Earth more, or be it leſs, in compariſon of the velocity of the
fire, this imports nothing; for if the velocity of the Earth be ſmall,
and conſequently the inclination of the tranſverſe line be little
alſo; there is then alſo need but of little inclination to make the
1ball ſuſpend it ſelf in its range directly over the Piece. And in a
word, if you do but attentively conſider, you will comprehend,
that the motion of the Earth in transferring the Piece along with
it from C A to E D, conferreth upon the tranſverſe line C D, ſo
much of little or great inclination, as is required to adjuſt the
range to its perpendicularity. But you err, ſecondly, in that you
referr the faculty of carrying the ball along with the Earth to the
impulſe of the fire, and you run into the ſame error, into which
Salviatus, but even now ſeemed to have fallen; for the faculty
of following the motion of the Earth, is the primary and perpetual
motion, indelibly and inſeparably imparted to the ſaid ball, as to a
thing terreſtrial, and that of its own nature doth and ever ſhall
poſſeſs the ſame.
SALV. Let us yield, Simplicius, for the buſineſs is juſt as he

ſaith. And now from this diſcourſe let us come to underſtand the
reaſon of a Venatorian Problem, of thoſe Fowlers who with their
guns ſhoot a bird flying; and becauſe I did imagine, that in regard
the bird flieth a great pace, therefore they ſhould aim their ſhot far
from the bird, anticipating its flight for a certain ſpace, and more
or leſs according to its velocity and the diſtance of the bird, that
ſo the bullet haſting directly to the mark aimed at, it might come
to arrive at the ſelf ſame time in the ſame point with its motion,
and the bird with its flight, and by that means one to encounter
the other: and asking one of them, if their practiſe was not ſo
to do; He told me, no; but that the ſlight was very eaſie and
certain, and that they took aim juſt in the ſame manner as if they
had ſhot at a bird that did ſit ſtill; that is, they made the flying
bird their mark, and by moving their fowling-piece they followed
her, keeping their aim ſtill full upon her, till ſuch time as they let
fly, and in this manner ſhot her as they did others ſitting ſtill. It is
neceſſary therefore that that motion, though ſlow, which the
ing-piece maketh in turning and following after the flight of the
bird do communicate it ſelf to the bullet alſo, and that it be joyned
with that of the fire; ſo that the ball hath from the fire the
tion directly upwards, and from the concave Cylinder of the barrel
the declination according to the flight of the Bird, juſt as was ſaid
before of the ſhot of a Canon; where the ball receiveth from the
fire a virtue of mounting upwards towards the Zenith, and from
the motion of the Earth its winding towards the Eaſt, and of both
maketh a compound motion that followeth the courſe of the
Earth, and that to the beholder ſeemeth onely to go directly
wards, and return again downwards by the ſame line. The
ing therefore of the gun continually directed towards the mark,
maketh the ſhoot hit right, and that you may keep your gun
rected to the mark, in caſe the mark ſtands ſtill, you muſt alſo hold
1your gun ſtill; and if the mark ſhall move, the gun muſt be kept upon
the mark by moving. And upon this dependeth the proper anſwer

to the other argument taken from the ſhot of a Canon, at the
mark placed towards the South or North: wherein is alledged,
that if the Earth ſhould move, the ſhots would all range
ward of the mark, becauſe that in the time whilſt the ball, being
forc'd out of the Piece, goeth through the air to the mark, the ſaid
mark being carried toward the Eaſt, would leave the ball to the
Weſtward. I anſwer therefore, demanding whether if the
non be aimed true at the mark, and permitted ſo to continue, it
will conſtantly hit the ſaid mark, whether the Earth move or ſtand
ſtill? It muſt be replied, that the aim altereth not at all, for if
the mark doth ſtand ſtill, the Piece alſo doth ſtand ſtill, and if it,
being tranſported by the Earths motion, doth move, the Piece doth
alſo move at the ſame rate, and, the aim maintained, the ſhot
proveth always true, as by what hath been ſaid above, is
feſt.
The manner how
Fowlers ſhoot birds
flying.
The anſwer to
the objection tak n
from the ſhots of
great Guns made
towards the North
and South.
SAGR. Stay a little, I entreat you, Salviatus, till I have
pounded a certain conceit touching theſe ſhooters of birds flying,
whoſe proceeding I believe to be the ſame which you relate, and
believe the effect of hitting the bird doth likewiſe follow: but yet
I cannot think that act altogether conformable to this of ſhooting
in great Guns, which ought to hit as well when the piece and mark
moveth, as when they both ſtand ſtill; and theſe, in my opinion,
are the particulars in which they diſagree. In ſhooting with a
great Gun both it and the mark move with equal velocity, being
both tranſported by the motion of the Terreſtrial Globe: and
beit ſometimes the piece being planted more towards the Pole,
than the mark, and conſequently its motion being ſomewhat
er than the motion of the mark, as being made in a leſſer circle,
ſuch a difference is inſenſible, at that little diſtance of the piece
from the mark: but in the ſhot of the Fowler the motion of the
Fowling-piece wherewith it goeth following the bird, is very ſlow
in compariſon of the flight of the ſaid bird; whence me thinks it
ſhould follow, that that ſmall motion which the turning of the
Birding-piece conferreth on the bullet that is within it, cannot,
when it is once gone forth of it, multiply it ſelf in the air, untill it
come to equal the velocity of the birds flight, ſo as that the ſaid bullet
ſhould always keep direct upon it: nay, me thinketh the bird
would anticipate it and leave it behind. Let me add, that in this
act, the air through which the bullet is to paſs, partaketh not of the
motion of the bird: whereas in the caſe of the Canon, both it,
the mark, and the intermediate air, do equally partake of the
mon diurnal motion. So that the true cauſe of the Marks-man
his hitting the mark, as it ſhould ſeem, moreover and beſides the
1following the birds flight with the piece, is his ſomewhat
ting it, taking his aim before it; as alſo his ſhooting (as I believe)
not with one bullet, but with many ſmall balls (called ſhot) the
which ſcattering in the air poſſeſs a great ſpace; and alſo the
treme velocity wherewith theſe ſhot, being diſcharged from the
Gun, go towards the bird.
SALV. See how far the winged wit of Sagredus anticipateth,
and out-goeth the dulneſs of mine; which perhaps would have

light upon theſe diſparities, but not without long ſtudie. Now
turning to the matter in hand, there do remain to be conſidered
by us the ſhots at point blank, towards the Eaſt and towards the
Weſt; the firſt of which, if the Earth did move, would always
happen to be too high above the mark, and the ſecond too low;
foraſmuch as the parts of the Earth Eaſtward, by reaſon of the
urnal motion, do continually deſcend beneath the tangent paralel
to the Horizon, whereupon the Eaſtern ſtars to us appear to aſcend;
and on the contrary, the parts Weſtward do more and more
cend, whereupon the Weſtern ſtars do in our ſeeming deſcend:
and therefore the ranges which are leveled according to the ſaid
tangent at the Oriental mark, (which whilſt the ball paſſeth
along by the tangent deſcendeth) ſhould prove too high, and the
Occidental too low by means of the elevation of the mark, whilſt
the ball paſſeth along the tangent. The anſwer is like to the reſt:
for as the Eaſtern mark goeth continually deſcending, by reaſon
of the Earths motion, under a tangent that continueth
able; ſo likewiſe the piece for the ſame reaſon goeth continually
inclining, and with its mounture purſuing the ſaid mark: by
which means the ſhot proveth true.
The anſwer to the
Argument taken
from the ſhots at
point blanck
wards the Eaſt &
Weſt.
But here I think it a convenient opportunity to give notice of

certain conceſſions, which are granted perhaps over liberally by
the followers of Copernicus unto their Adverſaries: I mean of
yielding to them certain experiments for ſure and certain, which
yet the Adverſaries themſelves had never made tryal of: as for
example, that of things falling from the round-top of a ſhip whilſt
it is in motion, and many others; amongſt which I verily believe,
that this of experimenting whether the ſhot made by a Canon
wards the Eaſt proveth too high, and the Weſtern ſhot too low,
is one: and becauſe I believe that they have never made tryal
thereof, I deſire that they would tell me what difference they
think ought to happen between the ſaid ſhots, ſuppoſing the Earth
moveable, or ſuppoſing it moveable; and let Simplieius for this
time anſwer for them.
The followers of
Copernicus too
freely admit
tain propoſitions for
true, which are
very doubtfull.
SIMP. I will not undertake to anſwer ſo confidently as another
more intelligent perhaps might do; but ſhall ſpeak what thus upon
the ſudden I think they would reply; which is in effect the ſame
1with that which hath been ſaid already, namely, that in caſe the
Earth ſhould move, the ſhots made Eaſtward would prove too
high, &c. the ball, as it is probable, being to move along the
gent.
SALV. But if I ſhould ſay, that ſo it falleth out upon triall,
how would you cenſure me?
SIMP. It is neceſſary to proceed to experiments for the
ving of it.
SALV. But do you think, that there is to be found a Gunner ſo
skilful, as to hit the mark at every ſhoot, in a diſtance of v.g. five
hundred paces?
SIMP. No Sir; nay I believe that there is no one, how good a
marks-man ſoever that would promiſe to come within a pace of
the mark,
SALV. How can we then, with ſhots ſo uncertain, aſſure our
ſelves of that which is in diſpute?
SIMP. We may be aſſured thereof two wayes; one, by
king many ſhots; the other, becauſe in reſpect of the great
city of the Earths motion, the deviation from the mark would in
my opinion be very great.
SALV. Very great, that is more than one pace; in regard that
the varying ſo much, yea and more, is granted to happen ordinarily
even in the Earths mobility.
SIMP. I verily believe the variation from the mark would be
more than
A Computation
how much the
ges of great ſhot
ought to vary from
the marke, the
Earths motion
ing granted.
SALV. Now I deſire that for our ſatisfaction we do make thus
in groſſe a ſlight calculation, if you conſent thereto, which will
ſtand us in ſtead likewiſe (if the computation ſucceed as I expect)
for a warning how we do in other occurrences ſuffer our ſelves, as
the ſaying is, to be taken with the enemies ſhouts, and ſurrender
up our belief to what ever firſt preſents it ſelf to our fancy. And
now to give all advantages to the Peripateticks and Tychonicks,
let us ſuppoſe our ſelves to be under the Equinoctial, there to ſhoot
a piece of Ordinance point blank Eaſtwards at a mark five
dred paces off. Firſt, let us ſee thus (as I ſaid) in a level, what
time the ſhot after it is gone out of the Piece taketh to arrive at
the mark; which we know to be very little, and is certainly no
more than that wherein a travailer walketh two ſteps, which alſo
is leſs than the ſecond of a minute of an hour; for ſuppoſing
that the travailer walketh three miles in an hour, which are nine
thouſand paces, being that an hour containes three thouſand, ſix
hundred ſecond minutes, the travailer walketh two ſteps and an
half in a ſecond, a ſecond therefore is more than the time of the
balls motion. And for that the diurnal revolution is twenty four
hours, the Weſtern horizon riſeth fifteen degrees in an hour, that
1is, fifteen firſt minutes of a degree, in one firſt minute of an hour;
that is, fifteen ſeconds of a degree, in one ſecond of an hour; and
becauſe one ſecond is the time of the ſhot, therefore in this time
the Weſtern horizon riſeth fifteen ſeconds of a degree, and ſo
much likewiſe the mark; and therefore fifteen ſeconds of that
cle, whoſe ſemidiameter is five hundred paces (for ſo much the
ſtance of the mark from the Piece was ſuppoſed.) Now let us
look in the table of Arches and Chords (ſee here is Copernicus his
book) what part is the chord of fifteen ſeconds of the
ter, that is, five hundred paces. Here you ſee the chord (or
tenſe) of a firſt minute to be leſs than thirty of thoſe parts, of
which the ſemidiameter is an hundred thouſand. Therefore the
chord of a ſecond minute ſhall be leſs then half of one of thoſe
parts, that is leſs than one of thoſe parts, of whichthe
ter is two hundred thouſand; and therefore the chord of fifteen
conds ſhall be leſs than fifteen of thoſe ſame two hundred thouſand
parts; but that which is leſs than (a) fifteen parts of two hun­

dred thouſand, is alſo more than that which is four centeſmes of
five hundred; therefore the aſcent of the mark in the time of the
balls motion is leſſe than four centeſmes, that is, than one twenty
fifth part of a pace; it ſhall be therefore (b) about two inches:
And ſo much conſequently ſhall be the variation of each Weſtern
ſhot, the Earth being ſuppoſed to have a diurnal motion. Now if I
ſhall tell you, that this variation (I mean of falling two inches ſhort
of what they would do in caſe the Earth did not move) upon

all doth happen in all ſhots, how will you convince me Simplicius,
ſhewing me by an experiment that it is not ſo? Do you not ſee
that it is impoſſible to confute me, unleſs you firſt find out a way
to ſhoot at a mark with ſo much exactneſſe, as never to miſſe an
hairs bredth? For whilſt the ranges of great ſhot conſiſt of
rent numbers of paces, as de facto they do, I will affirm that in
each of thoſe variations there is contained that of two inches
ſed by the motion of the Earth.
(a) That is, in
plainer termes the
fraction 15/200000, is
more than the
ction 4/50000, for
viding the
nators by their
minators, and the
firſt produceth
13333 1/3 the other
but 12500.
(b) It ſhall be
neer 2 2/5 inches,
counting the pace
to be Geometrical,
containing 5 foot.
SAGR. Pardon me, Salviatus, you are too liberal. For I would

tell the Peripateticks, that though every ſhot ſhould hit the very
centre of the mark, that ſhould not in the leaſt diſprove the motion
of the Earth. For the Gunners are ſo conſtantly imployed in
velling the ſight and gun to the mark, as that they can hit the ſame,
notwithſtanding the motion of the Earth. And I ſay, that if the
Earth ſhould ſtand ſtill, the ſhots would not prove true; but the
Occidental would be too low, and the Oriental too high: now let
Simplicius diſprove me if he can.
It is
ted with great
tilty, that the
Earths motion
poſed, Canon ſhot
ought not to vary
more than in reſt.
SALV. This is a ſubtilty worthy of Sagredus: But whether
this variation be to be obſerved in the motion, or in the reſt of the
Earth, it muſt needs be very ſmall, it muſt needs be ſwallowed up
1in thoſe very great ones which ſundry accidents continually

duce. And all this hath been ſpoken and granted on good grounds
to Simplicius, and only with an intent to advertiſe him how much
it importeth to be cautious in granting many experiments for true
to thoſe who never had tried them, but only eagerly alledged them
juſt as they ought to be for the ſerving their purpoſe: This is
ken, I ſay, by way of ſurpluſſage and Corollary to Simplicius, for

the real truth is, that as concerning theſe ſhots, the ſame ought
actly to befall aſwell in the motion as in the reſt of the Terreſtrial
Globe; as likewiſe it will happen in all the other experiments
that either have been or can be produced, which have at firſt bluſh
ſo mnch ſemblance of truth, as the antiquated opinion of the
Earths motion hath of equivocation.
It is requiſite to
be very cautious in
admitting
ments for true, to
thoſe who never
tried them.
Experiments and
arguments againſt
the Earths motion
ſeem ſo far
cluding, as they lie
hid under
vokes.
SAGR. As for my part I am fully ſatisfied, and very well
derſtand that who ſo ſhall imprint in his fancy this general
munity of the diurnal converſion amongſt all things Terreſtrial,
to all which it naturally agreeth, aſwell as in the old conceit of its
reſt about the centre, ſhall doubtleſſe diſcern the fallacy and
voke which made the arguments produced ſeem eoncluding.
There yet remains in me ſome hæſitancy (as I have hinted
fore) touching the flight of birds; the which having as it were an
animate faculty of moving at their pleaſure with a thouſand
tions, and to ſtay long in the Air ſeparated from the Earth, and
therein with moſt irregular windings to go fluttering to and again,
I cannot conceive how amongſt ſo great a confuſion of motions,
they ſhould be able to retain the firſt commune motion; and in
what manner, having once made any ſtay behind, they can get
it up again, and overtake the ſame with flying, and kcep pace
with the Towers and trees which hurry with ſo precipitant a courſe
towards the Eaſt; I ſay ſo precipitant, for in the great circle of
the Globe it is little leſſe than a thouſand miles an hour, whereof
the flight of the ſwallow I believe makes not fifty.
SALV. If the birds were to keep pace with the courſe of the
trees by help of their wings, they would oſ neceſſity flie very faſt;
and if they were deprived of the univerſal converſion, they would
lag as far behind; and their flight would ſeem as furious towards
the Weſt, and to him that could diſcern the ſame, it would
much exceed the flight of an arrow; but I think we could not be
able to perceive it, no more than we ſee a Canon bullet, whil'ſt
driven by the fury of the fire, it flieth through the Air: But the
truth is that the proper motion of birds, I mean of their flight,
hath nothing to do with the univerſal motion, to which it is
ther an help, nor an hinderance; and that which maintaineth
the ſaid motion unaltered in the birds, is the Air it ſelf, thorough
which they flie, which naturally following the Vertigo of the
1Earth, like as it carrieth the clouds along with it, ſo it tranſporteth
birds and every thing elſe which is pendent in the ſame; in ſo much
that as to the buſineſſe of keeping pace with the Earth, the birds
need take no care thereof, but for that work might ſleep
tually.
SAGR. That the Air can carry the clouds along with it, as
being matters eaſie for their lightneſſe to be moved and deprived
of all other contrary inclination, yea more, as being matters that
partake alſo of the conditions and properties of the Earth; I
prehend without any difficulty; but that birds, which as having
life, may move with a motion quite contrary to the diurnal, once
having ſurceaſed the ſaid motion, the Air ſhould reſtore them to
it, ſeems to me a little ſtrange, and the rather for that they are ſolid
and weighty bodies; and withal, we ſee; as hath been ſaid, ſtones
and other grave bodies to lie unmoved againſt the impetus of the
air; and when they ſuffer themſelves to be overcome thereby,
they never acquire ſo much velocity as the wind which carrieth
them.
SALV. We aſcribe not ſo little force, Sagredus, to the moved
Air, which is able to move and bear before it ſhips full fraught,
to tear up trees by the roots, and overthrow Towers when it
moveth ſwiftly; and yet we cannot ſay that the motion of the
Air in theſe violent operations is neer ſo violent, as that of the
diurnal revolution.
SIMP. You ſee then that the moved Air may alſo cotinue the
motion of projects, according to the Doctrine of Ariſtotle; and
it ſeemed to me very ſtrange that he ſhould have erred in this
particular.
SALV. It may without doubt, in caſe it could continue it ſelf,
but lik as when the wind ceaſing neither ſhips go on, nor trees are
blown down, ſo the motion in the Air not continuing after the
ſtone is gone out of the hand, and the Air ceaſing to move, it
followeth that it muſt be ſomething elſe beſides the Air that
keth the projects to move.
SIMP. But how upon the winds being laid, doth the ſhip ceaſe
to move? Nay you may ſee that when the wind is down, and
the ſails furl'd, the veſſel continueth to run whole miles.
SALV. But this maketh againſt your ſelf Simplicius, for that
the wind being laid that filling the ſails drove on the ſhip, yet
vertheleſſe doth it without help of the medium continue its
courſe.
SIMP. It might be ſaid that the water was the medium which
carried forward the ſhip, and maintain'd it in motion.
SALV. It might indeed be ſo affirmed, if you would ſpeak
quite contrary to truth; for the truth is, that the water, by
1ſon of its great reſiſtance to the diviſion made by the hull of the
ſhip, doth with great noiſe reſiſt the ſame; nor doth it permit it
of a great while to acquire that velocity which the wind would
confer upon it, were the obſtacle of the water removed.
haps Simplicius you have never conſidered with what fury the
water beſets a bark, whil'ſt it forceth its way through a ſtanding
water by help of Oars or Sails: for if you had ever minded that
effect, you would not now have produced ſuch an abſurdity.
And I am thinking that you have hitherto been one of thoſe who
to find out how ſuch things ſucceed, and to come to the
ledg of natural effects, do not betake themſelves to a Ship, a
Croſſe-bow, or a piece of Ordinance, but retire into their
dies, and turn over Indexes and Tables to ſee whether Aristotle
hath ſpoken any thing thereof, and being aſſured of the true
ſenſe of the Text, neither deſire nor care for knowing any

The great
city for which they
are much to be
vied who perſwade
themſelves that
they know every
thing.
SAGR. This is a great felicity, and they are to be much
vied for it. For if knowledg be deſired by all, and if to be wiſe,
be to think ones ſelf ſo, they enjoy a very great happineſſe, for
that they may perſwade themſelves that they know and underſtand
all things, in ſcorn of thoſe who knowing, that they underſtand
not what theſe think they underſtand, and conſequently ſeeking
that they know not the very leaſt particle of what is knowable,
kill themſelves with waking and ſtudying, and conſume their days
in experiments and obſervations. But pray you let us return to
our birds; touching which you have ſaid, that the Air being
ved with great velocity, might reſtore unto them that part of the
diurnal motion which amongſt the windings of their flight they
might have loſt; to which I reply, that the agitated Air ſeemeth
unable to confer on a ſolid and grave body, ſo great a velocity as
its own: And becauſe that of the Air is as great as that of the
Earth, I cannot think that the Air is able to make good the loſſe
of the birds retardation in flight.
SALV. Your diſcourſe hath in it much of probability, and to
ſtick at trivial doubts is not for an acute wit; yet nevertheleſſe the
probability being removed, I believed that it hath not a jot more
force than the others already conſidered and reſolved.
SAGR. It is moſt certain that if it be not neceſſatily
dent, its efficacy muſt needs be juſt nothing at all, for it is
onely when the concluſion is neceſſary that the opponent hath
thing to alledg on the contrary.
SALV. Your making a greater ſcruple of this than of the other
inſtances dependeth, if I miſtake not, upon the birds being
mated, and thereby enabled to uſe their ſtrength at pleaſure
gainſt the primary motion in-bred in terrene bodies: like as for
1example, we ſee them whil'ſt they are alive to fly upwards, a thing
altogether impoſſible for them to do as they are grave bodies;
whereas being dead they can onely fall downwards; and
fore you hold that the reaſons that are of force in all the kinds of
projects above named, cannot take place in birds: Now this is
very true; and becauſe it is ſo, Sagredus, that doth not appear
to be done in thoſe projects, which we ſee the birds to do. For if

from the top of a Tower you let fall a dead bird and a live one,
the dead bird ſhall do the ſame that a ſtone doth, that is, it ſhall
firſt follow the general motion diurnal, and then the motion of
deſcent, as grave; but if the bird let fall, be a live, what ſhall
hinder it, (there ever remaining in it the diurnal motion) from
ſoaring by help of its wings to what place of the Horizon it ſhall
pleaſe? and this new motion, as being peculiar to the bird, and
not participated by us, muſt of neceſſity be viſible to us; and if
it be moved by help of its wings towards the Weſt, what ſhall
hinder it from returning with a like help of its wings unto the
Tower. And, becauſe, in the laſt place, the birds wending its
flight towards the Weſt was no other than a withdrawing from
the diurnal motion, (which hath, ſupppoſe ten degrees of velocity)
one degree onely, there did thereupon remain to the bird whil'ſt
it was in its flight nine degrees of velocity, and ſo ſoon as it did
alight upon the the Earth, the ten common degrees returned to it,
to which, by flying towards the Eaſt it might adde one, and with
thoſe eleven overtake the Tower. And in ſhort, if we well
ſider, and more narrowly examine the effects of the flight of
birds, they differ from the projects ſhot or thrown to any part of
the World in nothing, ſave onely that the projects are moved by an
external projicient, and the birds by an internal principle. And

here for a final proof of the nullity of all the experiments before
alledged, I conceive it now a time and place convenient to
demonſtrate a way how to make an exact trial of them all.
Shut your ſelf up with ſome friend in the grand Cabbin between
the decks of ſome large Ship, and there procure gnats, flies, and
ſuch other ſmall winged creatures: get alſo a great tub (or
other veſſel) full of water, and within it put certain fiſhes; let
alſo a certain bottle be hung up, which drop by drop letteth forth
its water into another bottle placed underneath, having a narrow
neck: and, the Ship lying ſtill, obſerve diligently how thoſe ſmall
winged animals fly with like velocity towards all parts of the
bin; how the fiſhes ſwim indifferently towards all ſides; and how
the diſtilling drops all fall into the bottle placed underneath. And
caſting any thing towards your friend, you need not throw it with
more force one way then another, provided the diſtances be equal:
and leaping, as the ſaying is, with your feet cloſed, you will reach
1as far one way as another. Having obſerved all theſe particulars,
though no man doubteth that ſo long as the veſſel ſtands ſtill, they
ought to ſucceed in this manner; make the Ship to move with
what velocity you pleaſe; for (ſo long as the motion is uniforme,
and not fluctuating this way and that way) you ſhall not diſcern
any the leaſt alteration in all the forenamed effects; nor can you
gather by any of them whether the Ship doth move or ſtand ſtill.
In leaping you ſhall reach as far upon the floor, as before; nor for
that the Ship moveth ſhall you make a greater leap towards the
poop than towards the prow; howbeit in the time that you ſtaid
in the Air, the floor under your feet ſhall have run the contrary way
to that of your jump; and throwing any thing to your companion
you ſhall not need to caſt it with more ſtrength that it may reach
him, if he ſhall be towards the prow, and you towards the poop,
then if you ſtood in a contrary ſituation; the drops ſhall all diſtill
as before into the inferiour bottle and not ſo much as one ſhall
fall towards the poop, albeit whil'ſt the drop is in the Air, the Ship
ſhall have run many feet; the Fiſhes in their water ſhall not ſwim
with more trouble towards the fore-part, than towards the hinder
part of the tub; but ſhall with equal velocity make to the bait
placed on any ſide of the tub; and laſtly, the flies and gnats
ſhall continue their flight indifferently towards all parts; nor
ſhall they ever happen to be driven together towards the ſide of
the Cabbin next the prow, as if they were wearied with
lowing the ſwift courſe of the Ship, from which through their
ſuſpenſion in the Air, they had been long ſeparated; and if
burning a few graines of incenſe you make a little ſmoke,
you ſhall ſee it aſcend on high, and there in manner of a cloud
ſuſpend it ſelf, and move indifferently, not inclining more to one
ſide than another: and of this correſpondence of effects the cauſe
is for that the Ships motion is common to all the things contained
in it, and to the Air alſo; I mean if thoſe things be ſhut up in the
Cabbin: but in caſe thoſe things were above deck in the open Air,
and not obliged to follow the courſe of the Ship, differences more
or leſſe notable would be obſerved in ſome of the fore-named
fects, and there is no doubt but that the ſmoke would ſtay behind
as much as the Air it ſelf; the flies alſo, and the gnats being
dered by the Air would not be able to follow the motion of the
Ship, if they were ſeparated at any diſtance from it. But keeping
neer thereto, becauſe the Ship it ſelf as being an unfractuous
brick, carrieth along with it part of its neereſt Air, they would
follow the ſaid Ship without any pains or difficulty. And for the
like reaſon we ſee ſometimes in riding poſt, that the troubleſome
flies and ^{*} hornets do follow the horſes flying ſometimes to one,

ſometimes to another part of the body, but in the falling drops
1the difference would be very ſmall; and in the ſalts, and
ons of grave bodies altogether imperceptible.
The anſwer to
the argument
ken from the flight
of birds contrary
to the motion of the
Earth.
An experiment
with which alone
is ſhewn the nullity
of all the
ons produced
gainst the motion
of the Earth.
* Tafaris,
flyes.
SAGR. Though it came not into my thoughts to make triall of
theſe obſervations, when I was at Sea, yet am I confident that they
will ſucceed in the ſame manner, as you have related; in
tion of which I remember that being in my Cabbin I have asked
an hundred times whether the Ship moved or ſtood ſtill; and
ſometimes I have imagined that it moved one way, when it ſteered
quite another way. I am therefore as hitherto ſatisfied and
vinced of the nullity of all thoſe experiments that have been
duced in proof of the negative part. There now remains the
jection founded upon that which experience ſhews us, namely, that
a ſwift Vertigo or whirling about hath a faculty to extrude and
diſperſe the matters adherent to the machine that turns round;
whereupon many were of opinion, and Ptolomy amongſt the reſt,
that if the Earth ſhould turn round with ſo great velocity, the
ſtones and creatures upon it ſhould be toſt into the Skie, and
that there could not be a morter ſtrong enough to faſten buildings
ſo to their foundations, but that they would likewiſe ſuffer a like
extruſion.
SALV. Before I come to anſwer this objection, I cannot but
take notice of that which I have an hundred times obſerved, and
not without laughter, to come into the minds of moſt men ſo ſoon
as ever they hear mention made of this motion of the Earth, which
is believed by them ſo fixt and immoveable, that they not only
ver doubted of that reſt, but have ever ſtrongly believed that all
other men aſwell as they, have held it to be created immoveable,
and ſo to have continued through all ſucceeding ages: and being

ſetled in this perſwaſion, they ſtand amazed to hear that any one
ſhould grant it motion, as if, after that he had held it to be
veable, he had fondly thought it to commence its motion then
(and not till then) when Pythagoras (or whoever elſe was the firſt
hinter of its mobility) ſaid that it did move. Now that ſuch a
liſh conceit (I mean of thinking that thoſe who admit the motion
of the Earth, have firſt thought it to ſtand ſtill from its creation,
untill the time of Pythagoras, and have onely made it moveable
after that Pythagor as eſteemed it ſo) findeth a place in the mindes
of the vulgar, and men of ſhallow capacities, I do not much
der; but that ſuch perſons as Ariſtotle and Ptolomy ſhould alſo
run into this childiſh miſtake, is to my thinking a more admirable
and unpardonable folly.
The ſtupidity of
ſome that think the
Earth to have
gun to move, when
Pythagoras began
to affirme that it
did ſo.
SAGR. You believe then, Salviatus, that Ptolomy thought, that
in his Diſputation he was to maintain the ſtability of the Earth
againſt ſuch perſons, as granting it to have been immoveable,
till the time of Pythagoras, did affirm it to have been but then
1made moveable, when the ſaid Pythagoras aſcribed unto it
tion.
SALV. We can think no other, if we do but conſider the way

he taketh to confute their aſſertion; the confutation of which
conſiſts in the demolition of buildings, and the toſſing of ſtones,
living creatures and men themſelves up into the Air. And
cauſe ſuch overthrows and extruſions cannot be made upon
dings and men, which were not before on the Earth, nor can men
be placed, nor buildings erected upon the Earth, unleſſe when it
ſtandeth ſtill; hence therefore it is cleer, that Ptolomy argueth
gainſt thoſe, who having granted the ſtability of the Earth for
ſome time, that is, ſo long as living creatures, ſtones, and Maſons
were able to abide there, and to build Palaces and Cities, make it
afterwards precipitately moveable to the overthrow and
of Edifices, and living creatures, &c. For if he had undertook to
diſpute againſt ſuch as had aſcribed that revolution to the Earth
from its firſt creation, he would have confuted them by ſaying,
that if the Earth had alwayes moved, there could never have been
placed upon it either men or ſtones; much leſs could buildings
have been erected, or Cities founded, &c.
Ariſtotle and
Ptolomy ſeem to
confute the
ty of the Earth
gainſt thoſe who
thought that it
ving a long time
ſtood still, did
gin to move in the
time of Pythagoras
SIMP. I do not well conceive theſe Ariſtotelick and
maick inconveniences.
SALV. Ptolomey either argueth againſt thoſe who have
ed the Earth always moveable; or againſt ſuch as have held that
it ſtood for ſome time ſtill, and hath ſince been ſet on moving.
If againſt the firſt, he ought to ſay, that the Earth did not always
move, for that then there would never have been men, animals, or
edifices on the Earth, its vertigo not permitting them to ſtay
thereon. But in that he arguing, ſaith that the Earth doth not
move, becauſe that beaſts, men, and houſes before plac'd on the
Earth would precipitate, he ſuppoſeth the Earth to have been once
in ſuch a ſtate, as that it did admit men and beaſts to ſtay, and
build thereon; the which draweth on the conſequence, that it
did for ſome time ſtand ſtill, to wit, was apt for the abode of
nimals and erection of buildings. Do you now conceive what I
would ſay?
SIMP. I do, and I do not: but this little importeth to the
merit of the cauſe; nor can a ſmall miſtake of Ptolomey,
mitted through inadvertencie be ſufficient to move the Earth,
when it is immoveable. But omitting cavils, let us come to the
ſubſtance of the argument, which to me ſeems unanſwerable.
SALV. And I, Simplicius, will drive it home, and re-inforce it,
by ſhewing yet more ſenſibly, that it is true that grave bodies
turn'd with velocity about a ſettled centre, do acquire an impetus
of moving, and receding to a diſtance from that centre, even
1then when they are in a ſtate of having a propenſion of moving
naturally to the ſame. Tie a bottle that hath water in it, to
the end of a cord, and holding the other end faſt in your hand,
and making the cord and your arm the ſemi-diameter, and the
knitting of the ſhoulder the centre, ſwing the bottle very faſt
bout, ſo as that it may deſcribe the circumference of a circle,
which, whether it be parallel to the Horizon, or perpendicular to
it, or any way inclined, it ſhall in all caſes follow, that the
ter will not fall out of the bottle: nay, he that ſhall ſwing it,
ſhall find the cord always draw, and ſtrive to go farther from the
ſhoulder. And if you bore a hole in the bottom of the bottle,
you ſhall ſee the water ſpout forth no leſs upwards into the skie,
than laterally, and downwards to the Earth; and if inſtead of
ter, you ſhall put little pebble ſtones into the bottle, and ſwing it
in the ſame manner, you ſhall find that they will ſtrive in the like
manner againſt the cord. And laſtly, we ſee boys throw ſtones
a great way, by ſwinging round a piece of a ſtick, at the end of
which the ſtone is let into a ſlit (which ſtick is called by them a
ſling;) all which are arguments of the truth of the concluſion,
to wit, that the vertigo or ſwing conferreth upon the moveable,
a motion towards the circumference, in caſe the motion be ſwift:
and therefore if the Earth revolve about its own centre, the
tion of the ſuperficies, and eſpecially towards the great circle,
as being incomparably more ſwift than thoſe before named, ought
to extrude all things up into the air.
SIMP. The Argument ſeemeth to me very well proved and
inforced; and I believe it would be an hard matter to anſwer and
overthrow it.
SALV. Its ſolution dependeth upon certain notions no leſs
known and believed by you, than by my ſelf: but becauſe they
come not into your mind, therefore it is that you perceive not the
anſwer; wherefore, without telling you it (for that you know the
ſame already) I ſhall with onely aſſiſting your memory, make you
to refute this argument.
SIMP. I have often thought of your way of arguing, which
hath made me almoſt think that you lean to that opinion of Pla-

to, Quòd noſtrum ſcire ſit quoddam reminiſci; therefore I intreat
you to free me from this doubt, by letting me know your
ment.
Our krowledg is
a kind of
cence according to
Plato.
SALV. What I think of the opinion of Plato, you may gather
from my words and actions. I have already in the precedent
ferences expreſly declared my ſelf more than once; I will purſue
the ſame ſtyle in the preſent caſe, which may hereafter ſerve you
for an example, thereby the more eaſily to gather what my
nion is touching the attainment of knowledg, when a time ſhall
1offer upon ſome other day: but I would not have Sagredus
fended at this digreſſion.
SAGR. I am rather very much pleaſed with it, for that I
member that when I ſtudied Logick, I could never comprehend that
ſo much cry'd up and moſt potent demonſtration of Ariſtotle.
SALV. Let us go on therefore; and let Simplicius, tell me
what that motion is which the ſtone maketh that is held faſt in the
ſlit of the ſling, when the boy ſwings it about to throw it a great
way?
SIMP. The motion of the ſtone, ſo long as it is in the ſlit, is
circular, that is, moveth by the arch of a circle, whoſe ſtedfaſt
centre is the knitting of the ſhoulder, and its ſemi-diameter the arm
and ſtick.
SALV. And when the ſtone leaveth the ſling, what is its
tion? Doth it continue to follow its former circle, or doth it go
by another line?
SIMP. It will continue no longer to ſwing round, for then it
would not go farther from the arm of the projicient, whereas
we ſee it go a great way off.
SALV. With what motion doth it move then?
SIMP. Give me a little time to think thereof; For I have
ver conſidered it before.
SALV. Hark hither, Sagredus; this is the Quoddam reminiſci
in a ſubject well underſtood. You have pauſed a great while,
Simplicius.
SIMP. As far as I can ſee, the motion received in going out of
the ſling, can be no other than by a right line; nay, it muſt
ceſſarily be ſo, if we ſpeak of the pure adventitious impetus. I
was a little puzled to ſee it make an arch, but becauſe that arch
bended all the way upwards, and no other way, I conceive that

that incurvation cometh from the gravity of the ſtone, which
turally draweth it downwards. The impreſſed impetus, I ſay,
without reſpecting the natural, is by a right line.
The motion
preſſed by the
jicient is onely by a
right line.
SALV. But by what right line? Becauſe infinite, and towards
every ſide may be produced from the ſlit of the ſling, and from the
point of the ſtones ſeparation from the ſling.
SIMP. It moveth by that line which goeth directly from the
motion which the ſtone made in the ſling.
SALV. The motion of the ſtone whilſt it was in the ſlit, you
have affirmed already to be circular; now circularity oppoſeth
directneſs, there not being in the circular line any part that is
rect or ſtreight.
SIMP I mean not that the projected motion is direct in
ſpect of the whole circle, but in reference to that ultimate point,
where the circular motion determineth. I know what I would
1ſay, but do not well know how to expreſs my ſelf.
SALV. And I alſo perceive that you underſtand the buſineſs,
but that you have not the proper terms, wherewith to expreſs the
ſame. Now theſe I can eaſily teach you; teach you, that is, as
to the words, but not as to the truths, which are things. And that
you may plainly ſee that you know the thing I ask you, and onely
want language to expreſs it, tell me, when you ſhoot a bullet out
of a gun, towards what part is it, that its acquired impetus
eth it?
SIMP. Its acquired impetus carrieth it in a right line, which
continueth the rectitude of the barrel, that is, which inclineth
ther to the right hand nor to the left, nor upwards not
wards.
SALV. Which in ſhort is aſmuch as to ſay, it maketh no angle
with the line of ſtreight motion made by the ſling.
SIMP. So I would have ſaid.
SALV. If then the line of the projects motion be to continue
without making an angle upon the circular line deſcribed by it,
whilſt it was with the projicient; and if from this circular motion it
ought to paſs to the right motion, what ought this right line to be?
SIMP. It muſt needs be that which toucheth the circle in the
point of ſeparation, for that all others, in my opinion, being
longed would interſect the circumference, and by that means make
ſome angle therewith.
SALV. You have argued very well, and ſhewn your ſelf half a
Geometrician. Keep in mind therefore, that your true opinion
is expreſt in theſe words, namely, That the project acquireth an
impetus of moving by the Tangent, the arch deſcribed by the
motion of the projicient, in the point of the ſaid projects
tion from the projicient.
SIMP. I underſtand you very well, and this is that which I
would ſay.
SALV. Of a right line which toucheth a circle, which of its
points is the neareſt to the centre of that circle?
SIMP. That of the contact without doubt: for that is in the
circumference of a circle, and the reſt without: and the points of
the circumference are all equidiſtant from the centre.
SALV. Therefore a moveable departing from the contact, and
moving by the ſtreight Tangent, goeth continually farther and
farther from the contact, and alſo from the centre of the circle.
SIMP. It doth ſo doubtleſs.
SALV. Now if you have kept in mind the propoſitions, which
you have told me, lay them together, and tell me what you gather
from them.
SIMP. I think I am not ſo forgetful, but that I do remember
1
them. From the things premiſed I gather that the project ſwiftly
ſwinged round by the projicient, in its ſeparating from it, doth
tain an impetus of continuing its motion by the right line, which
toucheth the circle deſcribed by the motion of the projicient in
the point of ſeparation, by which motion the project goeth
tinually receding from the centre of the circle deſcribed by the
motion of the projicient.
The project
veth by the
gent of the circle of
the motion
dent in the point of
ſeparation.
SALV. You know then by this time the reaſon why grave
dies ſticking to the rim of a wheele, ſwiftly moved, are extruded
and thrown beyond the circumference to yet a farther diſtance
from the centre.
SIMP. I think I underſtand this very well; but this new
ledg rather increaſeth than leſſeneth my incredulity that the Earth
can turn round with ſo great velocity, without extruding up into
the sky, ſtones, animals, &c.
SALV. In the ſame manner that you have underſtood all this,
you ſhall, nay you do underſtand the reſt: and with recollecting
your ſelf, you may remember the ſame without the help of
thers: but that we may loſe no time, I will help your memory
therein. You do already know of your ſelf, that the circular
tion of the projicient impreſſeth on the project an impetus of
ving (when they come to ſeparate) by the right Tangent, the
circle of the motion in the point of ſeparation, and continuing
long by the ſame the motion ever goeth receding farther and
ther from the projicient: and you have ſaid, that the project
would continue to move along by that right line, if there were not
by its proper weight an inclination of deſcent added unto it; from
which the incurvation of the line of motion is derived. It ſeems
moreover that you knew of your ſelf, that this incurvation
ways bended towards the centre of the Earth, for thither do all
grave bodies tend. Now I proceed a little farther, and ask you,
ther the moveable after its ſeparation, in continuing the right
tion goeth always equally receding from the centre, or if you will,
from the circumference of that circle, of which the precedent
tion was a part; which is as much as to ſay, Whether a moveable,
that forſaking the point of a Tangent, and moving along by the
ſaid Tangent, doth equally recede from the point of contact, and
from the circumference of the circle?
SIMP. No, Sir: for the Tangent near to the point of contact,
recedeth very little from the circumference, wherewith it keepeth
a very narrow angle, but in its going farther and farther
off, the diſtance always encreaſeth with a greater proportion; ſo
that in a circle that ſhould have v. g. ten yards of diameter, a point
of the Tangent that was diſtant from the contact but two palms,
would be three or four times as far diſtant from the circumference
1of the circle, as a point that was diſtant from the contaction one
palm, and the point that was diſtant half a palm, I likewiſe believe
would ſcarſe recede the fourth part of the diſtance of the ſecond:
fo that within an inch or two of the contact, the ſeparation of the
Tangent from the circumference is ſcarſe diſcernable.
SALV. So that the receſſion of the project from the
rence of the precedent circular motion is very ſmall in the
ing?
SIMP. Almoſt inſenſible.
SALV. Now tell me a little; the project, which from the
tion of the projicient receiveth an impetus of moving along the
Tangent in a right line, and that would keep unto the ſame, did
not its own weight depreſs it downwards, how long is it after the
ſeparation, ere it begin to decline downwards.
SIMP. I believe that it beginneth preſently; for it not
ving any thing to uphold it, its proper gravity cannot but

A grave project,
as ſoon as it is
parated from the
projicient begineth
to decline.
SALV. So that, if that ſame ſtone, which being extruded from
that wheel turn'd about very faſt, had as great a natural
ſion of moving towards the centre of the ſaid wheel, as it hath to
move towards the centre of the Earth, it would be an eaſie
ter for it to return unto the wheel, or rather not to depart from it;
in regard that upon the begining of the ſeparation, the receſſion
ing ſo ſinall, by reaſon of the infinite acuteneſs of the angle of
contact, every very little of inclination that draweth it back
wards the centie of the wheel, would be ſufficient to retain it
on the rim or circumference.
SIMP. I queſtion not, but that if one ſuppoſe that which
ther is, nor can be, to wit, that the inclination of thoſe grave
dies was to go towards the centre of the wheel, they would never
come to be extruded or ſhaken off.
SALV. But I neither do, nor need to ſuppoſe that which is not;
for I will not deny but that the ſtones are extruded. Yet I ſpeak
this by way of ſuppoſition, to the end that you might grant me
the reſt. Now fancy to your ſelf, that the Earth is that great
wheel, which moved with ſo great velocity is to extrude the ſtones.
You could tell me very well even now, that the motion of
ction ought to be by that right line which toucheth the Earth in
the point of ſeparation: and this Tangent, how doth it notably
recede from the ſuperficies of the Terreſtrial Globe?
SIMP. I believe, that in a thouſand yards, it will not recede
from the Earth an inch.
SALV. And did you not ſay, that the project being drawn by
its own weight, declineth from the Tangent towards the centre of
the Earth?
1
SIMP. I ſaid ſo, and alſo confeſſe the reſt: and do now plainly
underſtand that the ſtone will not ſeparate from the Earth, for
that its receſſion in the beginning would be ſuch, and ſo ſmall,
that it is a thouſand times exceeded by the inclination which the
ſtone hath to move towards the centre of the Earth, which
tre in this caſe is alſo the centre of the wheel. And indeed it muſt
be confeſſed that the ſtones, the living creatures, and the other
grave bodies cannot be extruded; but here again the lighter things
beget in me a new doubt, they having but a very weak propenſion
of deſcent towards the centre; ſo that there being wanting in
them that faculty of withdrawing from the ſuperficies, I ſee not,
but that they may be extruded; and you know the rule, that ad
deſtruendum ſufficit unum.
SAVL. We will alſo give you ſatisfaction in this. Tell me
therefore in the firſt place, what you underſtand by light matters,
that is, whether you thereby mean things really ſo light, as that
they go upwards, or elſe not abſolutely light, but of ſo ſmall
vity, that though they deſcend downwards, it is but very ſlowly;
for if you mean the abſolutely light, I will be readier than your
ſelf to admit their extruſion.
SIMP. I ſpeak of the other ſort, ſuch as are feathers, wool,
ton, and the like; to lift up which every ſmall force ſufficeth:
yet nevertheleſſe we ſee they reſt on the Earth very quietly.
SALV. This pen, as it hath a natural propenſion to deſcend
wards the ſuperficies of the Earth, though it be very ſmall, yet I
muſt tell you that it ſufficeth to keep it from mounting upwards:
and this again is not unknown to you your ſelf; therefore tell me
if the pen were extruded by the Vertigo of the Earth, by what
line would it move?
SIMP. By the tangent in the point of ſeparation.
SALV. And when it ſhould be to return, and re-unite it ſelf to
the Earth, by what line would it then move?
SIMP. By that which goeth from it to the centre of the
Earth.
SALV. So then here falls under our conſideration two
ons; one the motion of projection, which beginneth from the
point of contact, and proceedeth along the tangent; and the
ther the motion of inclination downwards, which beginneth from
the project it ſelf, and goeth by the ſecant towards the centre; and
if you deſire that the projection follow, it is neceſſary that the
petus by the tangent overcome the inclination by the ſecant: is it
not ſo?
SIMP. So it ſeemeth to me.
SALV. But what is it that you think neceſſary in the motion
of the projicient, to make that it may prevail over that
1tion, from which enſueth the ſeparation and elongation of the
pen from the Earth?
SIMP. I cannot tell.
SALV. How, do you not know that? The moveable is here
the ſame, that is, the ſame pen; now how can the ſame moveable
ſuperate and exceed it ſelf in motion?
SIMP. I do not ſee how it can overcome or yield to it ſelf in
motion, unleſſe by moving one while faſter, and another while
ſlower.
SALV. You ſee then, that you do know it. If therefore the
projection of the pen ought to follow, and its motion by the
gent be to overcome its motion by the ſecant, what is it requiſite
that their velocities ſhould be?
SIMP. It is requiſite that the motion by the tangent be greater
than that other by the ſecant. But wretch that I am! Is it not
only many thouſand times greater than the deſcending motion of
the pen, but than that of the ſtone? And yet like a ſimple fellow
I had ſuffered my ſelf to be perſwaded, that ſtones could not be
extruded by the revolution of the Earth. I do therefore revoke
my former ſentence, and ſay, that if the Earth ſhould move,
ſtones, Elephants, Towers, and whole Cities would of neceſſity be
toſt up into the Air; and becauſe that that doth not evene, I
clude that the Earth doth not move.
SALV. Softly Simplicius, you go on ſo faſt, that I begin to be
more afraid for you, than for the pen. Reſt a little, and obſerve what
I am going to ſpeap. If for the reteining of the ſtone or pen
nexed to the Earths ſurface it were neceſſary that its motion of
deſcent were greater, or as much as the motion made by the
gent; you would have had reaſon to ſay, that it ought of neceſſity
to move as faſt, or faſter by the ſecant downwards, than by the
tangent Eaſtwards: But did not you tell me even now, that a
thouſand yards of diſtance by the tangent from the contact, do
remove hardly an inch from the circumference? It is not
ent therefore that the motion by the tangent, which is the ſame
with that of the diurnall Vertigo, (or haſty revolution) be fimply
more ſwift than the motion by the ſecant, which is the ſame with
that of the pen in deſcending; but it is requiſite that the ſame be
ſo much more ſwift as that the time which ſufficeth for the pen
to move v.g. a thouſand yards by the tangent, be inſufficient for
it to move one ſole inch by the ſecant. The which I tell you ſhall
never be, though you ſhould make that motion never ſo ſwift,
and this never ſo ſlow.
SIMP. And why might not that by the tangent be ſo ſwift, as
not to give the pen time to return to the ſurface of the Earth?
SALV. Try whether you can ſtate the caſe in proper termes,
1and I will give you an anſwer. Tell me therefore, how much do
you think ſufficeth to make that motion ſwifter than this?
SIMP. I will ſay for example, that if that motion by the
gent were a million of times ſwifter than this by the ſecant, the
pen, yea, and the ſtone alſo would come to be extruded.
SALV. You ſay ſo, and ſay that which is falſe, onely for
want, not of Logick, Phyſicks, or Metaphyſicks, but of
try; for if you did but underſtand its firſt elements, you would
know, that from the centre of a circle a right line may be drawn
to meet the tangent, which interſecteth it in ſuch a manner, that
the part of the tangent between the contact and the ſecant, may
be one, two, or three millions of times greater than that part of
the ſecant which lieth between the tangent and the circumference,
and that the neerer and neerer the ſecant ſhall be to the contact,
this proportion ſhall grow greater and greater in infinitum; ſo
that it need not be feared, though the vertigo be ſwift, and the
motion downwards ſlow, that the pen or other lighter matter can
begin to riſe upwards, for that the inclination downwards always
exceedeth the velocity of the projection.
SAGR. I do not perfectly apprehend this buſineſſe.
SALV. I will give you a moſt univerſal yet very eaſie demon­

ſtration thereof. Let a proportion be given between B A [in Fig.
3.] and C: And let B A be greater than C at pleaſure. And let
there be deſcribed a circle, whoſe centre is D. From which it is
required to draw a ſecant, in ſuch manner, that the tangent may
be in proportion to the ſaid ſecant, as B A to C. Let A I be
ſuppoſed a third proportional to B A and C. And as B I is to
I A, ſo let the diameter F E be to E G; and from the point G,
let there be drawn the tangent G H. I ſay that all this is done as
was required; and as B A is to C, ſo is H G to G E. And in
gard that as B I is to I A, ſo is F E to E G; therefore by
ſition, as B A is to A I; ſo ſhall F G be to G E. And becauſe C
is the middle proportion between B A and A I; and G H is a
middle term between F G and G E; therefore, as B A is to C,
ſo ſhall F G be to G H; that is H G to G E, which was to be
demonſtrated.
A geometrical
demonſtration to
prove the
bility of extruſion
by means of the
terreſtrial vertigo.
SAGR. I apprehend this demonſtration; yet nevertheleſſe, I
am not left wholly without hæſitation; for I find certain
ſed ſcruples role to and again in my mind, which like thick and
dark clouds, permit me not to diſcern the cleerneſſe and neceſſity
of the concluſion with that perſpicuity, which is uſual in
matical Demonſtrations. And that which I ſtick at is this. It is
true that the ſpaces between the tangent and the circumference do
gradually diminiſh in infinitum towards the contact; but it is alſo
true on the contrary, that the propenſion of the moveable to
1deſcending groweth leſs & leſs in it, the nearer it is to the firſt term
of its deſcent; that is, to the ſtate of reſt; as is manifeſt from that
which you declare unto us, demonſtrating that the deſcending grave
body departing from reſt, ought to paſſe thorow all the degrees of
tardity comprehended between the ſaid reſt, & any aſſigned degree
of velocity, the which grow leſs and leſs in infinitum. To which may
be added, that the ſaid velocity and propenſion to motion, doth for
another reaſon diminiſh to infinity; and it is becauſe the gravity of
the ſaid moveable may infinitely diminiſh. So that the cauſes which
diminiſh the propenſion of aſcending, and conſequently favour
the projection, are two; that is, the levity of the moveable, and its
vicinity to the ſtate of reſt; both which are augmentable in infinit.
and theſe two on the contrary being to contract but with one ſole
cauſe of making the projection, I cannot conceive how it alone,
though it alſo do admit of infinite augmentation, ſhould be able to
remain invincible againſt the union & confederacy of the others, w^{ch}
are two, and are in like manner capable of infinite augmentation.
SALV. This is a doubt worthy of Sagredus; and to explain it ſo as
that we may more cleerly apprehend it, for that you ſay that you
your ſelf have but a confuſed Idea of it, we will diſtinguiſh of the
ſame by reducing it into figure; which may alſo perhaps afford us
ſome caſe in reſolving the ſame. Let us therefore [in Fig. 4.] draw
a perpendicular line towards the centre, and let it be AC, and to it
at right angles let there be drawn the Horizontal line A B, upon
which the motion of the projection ought to be made; now the
ject would continue to move along the ſame with an even motion, if
ſo be its gravity did not incline it downwards. Let us ſuppoſe from
the point A a right line to be drawn, that may make any angle at
pleaſure with the line A B; which let be A E, and upon AB let us
mark ſome equal ſpaces AF, FH, HK, and from them let us let fall
the perpendiculars FG, HI, K L, as far as AE. And becauſe, as al
ready hath been ſaid, the deſcending grave body departing from reſt,
goeth from time to time acquiring a greater degree of velocity,
according as the ſaid time doth ſucceſſively encreaſe; we may
ceive the ſpaces AF, FH, HK, to repreſent unto us equal times; and
the perpendiculars FG, HI, KL, degrees of velocity acquired in the
ſaid times; ſo that the degree of velocity acquired in the whole time
A K, is as the line K L, in reſpect to the degree H I, acquired in the
time AH, and the degree FG in the time AF; the which degrees KL,
HI, FG, are (as is manifeſt) the ſame in proportion, as the times K A,
HA, F A, and if other perpendiculars were drawn from the points
marked at pleaſure in the line F A, one might ſucceſſively find
grees leſſe and leſſe in infinitum, proceeding towards the point A,
repreſenting the firſt inſtant of time, and the firſt ſtate of reſt. And
this retreat towards A, repreſenteth the firſt propenſion to the
1motion of deſcent, diminiſhed in infinitum by the approach of
the moveable to the firſt ſtate of reſt, which approximation is
augmentable in infinitum. Now let us find the other diminution
of velocity, which likewiſe may proceed to infinity, by the
minution of the gravity of the moveable, and this ſhall be
ſented by drawing other lines from the point A, which contein
angles leſſe than the angle B A E, which would be this line A D,
the which interſecting the parallels K L, H I, F G, in the points
M, N, and O, repreſent unto us the degrees F O, H N, K M,
acquired in the times A F, A H, A K, leſſe than the other
grees F G, H I, K L, acquired in the ſame times; but theſe
latter by a moveable more ponderous, and thoſe other by a
moveable more light. And it is manifeſt, that by the retreat of
the line E A towards A B, contracting the angle E A B (the
which may be done in infinitum, like as the gravity may in
nitum be diminiſhed) the velocity of the cadent moveable may
in like manner be diminiſhed in infinitum, and ſo conſequently
the cauſe that impeded the projection; and therefore my thinks
that the union of theſe two reaſons againſt the projection,
niſhed to infinity, cannot be any impediment to the ſaid
ction. And couching the whole argument in its ſhorteſt terms, we
will ſay, that by contracting the angle E A B, the degrees of
locity L K, I H, G F, are diminiſhed; and moreover by the
treat of the parallels K L, H I, F G, towards the angle A, the
fame degrees are again diminiſhed; and both theſe diminutions
extend to infinity: Therefore the velocity of the motion of
ſcent may very well diminiſh ſo much, (it admitting of a twoſold
diminution in infinitum) as that it may not ſuffice to reſtore the
moveable to the circumference of the wheel, and thereupon may
occaſion the projection to be hindered and wholly obviated.
Again on the contrary, to impede the projection, it is
ſary that the ſpaces by which the project is to deſcend for the
reuniting it ſelf to the Wheel, be made ſo ſhort and cloſe
ther, that though the deſcent of the moveable be retarded, yea
more, diminiſhed in infinitum, yet it ſufficeth to reconduct it thither:
and therefore it would be requiſite, that you find out a
on of the ſaid ſpaces, not only produced to infinity, but to ſuch an
infinity, as that it may ſuperate the double infinity that is made in
the diminution of the velocity of the deſcending moveable. But
how can a magnitude be diminiſhed more than another, which
hath a twofold diminution in infinitum? Now let Simplicius
ſerve how hard it is to philoſophate well in nature, without
metry. The degrees of velocity diminiſhed in infinitum, as well
by the diminution of the gravity of the moveable, as by the
proxination to the firſt term of the motion, that is, to the ſtate
1of reſt, are alwayes determinate, and anſwer in proportion to the
parallels comprehended between two right lines that concur in
an angle, like to the angle B A E, or B A D, or any other
infinitely more acute, alwayes provided it be
But the diminution of the ſpaces thorow which the moveable is
to be conducted along the circumference of the wheel, is
tionate to another kind of diminution, comprehended between
lines that contain an angle infinitely more narrow and acute, than
any rectilineal angle, how acute ſoever, which is that in our
ſent caſe. Let any point be taken in the perpendicular A C, and
making it the centre, deſcribe at the diſtance C A, an arch A M P,
the which ſhall interſect the parallels that determine the degrees of
velocity, though they be very minute, and comprehended within
a moſt acute rectilineal angle; of which parallels the parts that
lie between the arch and the tangent A B, are the quantities of
the ſpaces, and of the returns upon the wheel, alwayes leſſer (and
with greater proportion leſſer, by how much neerer they approach
to the contact) than the ſaid parallels of which they are parts.
The parallels comprehended between the right lines in retiring
wards the angle diminiſh alwayes at the ſame rate, as v.g. A H
ing divided in two equal parts in F, the parallel H I ſhall be
ble to F G, and ſub-dividing F A, in two equal parts, the
lel produced from the point of the diviſion ſhall be the half of
F G; and continuing the ſub-diviſion in infinitum, the ſubſequent
parallels ſhall be alwayes half of the next preceding; but it doth
not ſo fall out in the lines intercepted between the tangent and
the circumference of the circle: For if the ſame ſub-diviſion be
made in F A; and ſuppoſing for example, that the parallel which
cometh from the point H, were double unto that which commeth
from F, this ſhall be more then double to the next following, and
continually the neerer we come towards the contact A, we ſhall
find the precedent lines contein the next following three, four,
ten, an hundred, a thouſand, an hundred thouſand, an hundred
millions of times, and more in infinitum. The brevity therefore of
ſuch lines is ſo reduced, that it far exceeds what is requiſite to make
the project, though never ſo light, return, nay more, continue
unremoveable upon the circumference.
SAGR. I very well comprehend the whole diſcourſe, and upon
what it layeth all its ſtreſſe, yet nevertheleſſe methinks that he
that would take pains to purſue it, might yet ſtart ſome further
queſtions, by ſaying, that of thoſe two cauſes which render the
deſcent of the moveable ſlower and ſlower in infinitum, it is
feſt, that that which dependeth on the vicinity to the firſt term of
the deſcent, increaſeth alwayes in the ſame proportion, like as the
parallels alwayes retain the ſame proportion to each other, &c.
1but that the diminution of the ſame velocity, dependent on the
diminution of the gravity of the moveable (which vvas the ſecond
cauſe) doth alſo obſerve the ſame proportion, doth not ſo plainly
appear, And vvho ſhall aſſure us that it doth not proceed
ding to the proportion of the lines intercepted between the ſecant,
and the circumference; or vvhether vvith a greater proportion?
SALV. I have aſſumed for a truth, that the velocities of
bles deſcending naturally, vvill follovv the proportion of their
vities, with the favour of Simplicius, and of Ariſtotle, who doth
in many places affirm the ſame, as a propoſition manifeſt: You,
in favour of my adverſary, bring the ſame into queſtion, and ſay
that its poſſible that the velocity increaſeth with greater
tion, yea and greater in infinitum than that of the gravity; ſo that
all that hath been ſaid falleth to the ground: For maintaining
whereof, I ſay, that the proportion of the velocities is much leſſe
than that of the gravities; and thereby I do not onely ſupport
but confirme the premiſes. And for proof of this I appeal unto
experience, which will ſhew us, that a grave body, howbeit thirty
or fourty times bigger then another; as for example, a ball of
lead, and another of ſugar, will not move much more than twice
as faſt. Now if the projection would not be made, albeit the
locity of the cadent body ſhould diminiſh according to the
portion of the gravity, much leſſe would it be made ſo long as the
velocity is but little diminiſhed, by abating much from the
ty. But yet ſuppoſing that the velocity diminiſheth with a
tion much greater than that wherewith the gravity decreaſeth, nay
though it were the ſelf-ſame wherewith thoſe parallels conteined
between the tangent and circumference do decreaſe, yet cannot I
ſee any neceſſity why I ſhould grant the projection of matters of
never ſo great levity; yea I farther averre, that there could no ſuch
projection follow, meaning alwayes of matters not properly and
abſolutely light, that is, void of all gravity, and that of their own
natures move upwards, but that deſcend very ſlowly, and
have very ſmall gravity. And that which moveth me ſo to think
is, that the diminution of gravity, made according to the
tion of the parallels between the tangent and the circumference,
hath for its ultimate and higheſt term the nullity of weight, as thoſe
parallels have for their laſt term of their diminution the contact it
ſelf, which is an indiviſible point: Now gravity never diminiſheth
ſo far as to its laſt term, for then the moveable would ceaſe to be
grave; but yet the ſpace of the reverſion of the project to the
circumference is reduced to the ultimate minuity, which is when
the moveable reſteth upon the circumference in the very point of
contact; ſo as that to return thither it hath no need of ſpace:
and therefore let the propenſion to the motion of deſcent be
1ver ſo ſmall, yet is it alwayes more than ſufficient to reconduct the
moveable to the circumference, from which it is diſtant but its leaſt
ſpace, that is, nothing at all.
SAGR. Your diſcourſe, I muſt confeſs, is very accurate; and
yet no leſs concluding than it is ingenuous; and it muſt be
ted that to go about to handle natural queſtions, without
try, is to attempt an impoſſibility.
SALV. But Simplicius will not ſay ſo; and yet I do not think
that he is one of thoſe Peripateticks that diſſwade their Diſciples
from ſtudying the Mathematicks, as Sciences that vitiate the
ſon, and render it leſſe apt for contemplation.
SIMP. I would not do ſo much wrong to Plato, but yet I may
truly ſay with Aristotle, that he too much loſt himſelf in, and too
much doted upon that his Geometry: for that in concluſion theſe
Mathematical ſubtilties Salviatus are true in abſtract, but applied
to ſenſible and Phyſical matter, they hold not good. For the
Mathematicians will very well demonſtrate for example, that
Sphæratangit planum in puncto; a poſition like to that in diſpute,
but when one cometh to the matter, things ſucceed quite another
way. And ſo I may ſay of theſe angles of contact, and theſe
proportions; which all evaporate into Air, when they are applied
to things material and ſenſible.
SALV. You do not think then, that the tangent toucheth the
ſuperficies of the terreſtrial Globe in one point only?
SIMP. No, not in one ſole point; but I believe that a right
line goeth many tens and hundreds of yards touching the ſurface
not onely of the Earth, but of the water, before it ſeparate from
the ſame.
SALV. But if I grant you this, do not you perceive that it
keth ſo much the more againſt your cauſe? For if it be ſuppoſed
that the tangent was ſeparated from the terreſtrial ſuperficies, yet
it hath been however demonſtrated that by reaſon of the great
cuity of the angle of contingence (if happily it may be call'd an
angle) the project would not ſeparate from the ſame; how much
leſſe cauſe of ſeparation would it have, if that angle ſhould be
wholly cloſed, and the ſuperficies and the tangent become all one?

Perceive you not that the Projection would do the ſame thing
on the ſurface of the Earth, which is aſmuch as to ſay, it would
do juſt nothing at all? You ſee then the power of truth, which
while you ſtrive to oppoſe it, your own aſſaults themſelves uphold
and defend it. But in regard that you have retracted this errour,
I would be loth to leave you in that other which you hold, namely,
that a material Sphere doth not touch a plain in one ſole point:
and I could wiſh ſome few hours converſation with ſome perſons
converſant in Geometry, might make you a little more intelligent
1amongſt thoſe who know nothing thereof. Now to ſhew you how
great their errour is who ſay, that a Sphere v.g. of braſſe, doth not
touch a plain v.g. of ſteel in one ſole point, Tell me what
ceipt you would entertain of one that ſhould conſtantly aver, that
the Sphere is not truly a Sphere.
The truth
ſometimes gaines
ſtrength by
tradiction.
SIMP. I would eſteem him wholly devoid of reaſon.
SALV. He is in the ſame caſe who ſaith that the material Sphere

doth not touch a plain, alſo material, in one onely point; for to
ſay this is the ſame, as to affirm that the Sphere is not a Sphere.
And that this is true, tell me in what it is that you conſtitute the
Sphere to conſiſt, that is, what it is that maketh the Sphere differ
from all other ſolid bodies.
The sphere
though material,
toucheth the
rial plane but in
one point onely.
SIMP. I believe that the eſſence of a Sphere conſiſteth in

ving all the right lines produced from its centre to the
rence, equal.
The definition of
the ſphere.
SALV. So that, if thoſe lines ſhould not be equal, there ſame
ſolidity would be no longer a ſphere?
SIMP. True.
SALV. Go to; tell me whether you believe that amongſt the
many lines that may be drawn between two points, that may be
more than one right line onely.
SIMP. There can be but one.
SALV. But yet you underſtand that this onely right line ſhall
again of neceſſity be the ſhorteſt of them all?
SIMP. I know it, and alſo have a demonſtration thereof,
duced by a great Peripatetick Philoſopher, and as I take it, if my
memory do not deceive me, he alledgeth it by way of reprehending
Archimedes, that ſuppoſeth it as known, when it may be
ſtrated.
SALV. This muſt needs be a great Mathematician, that knew
how to demonſtrate that which Archimedes neither did, nor could
demonſtrate. And if you remember his demonſtration, I would
gladly hear it: for I remember very well, that Archimedes in his
Books, de Sphærà & Cylindro, placeth this Propoſition amongſt the
Poſtulata; and I verily believe that he thought it demonſtrated.
SIMP. I think I ſhall remember it, for it is very eaſie and
ſhort.
SALV. The diſgrace of Archimedes, and the honour of this
loſopher ſhall be ſo much the greater.
SIMP. I will deſcribe the Figure of it. Between the points

A and B, [in Fig. 5.] draw the right line A B, and the curve line
A C B, of which we will prove the right to be the ſhorter: and
the proof is this; take a point in the curve-line, which let be C,
and draw two other lines, A C and C B, which two lines together;
are longer than the ſole line A B, for ſo demonſtrateth Euelid.
1But the curve-line A C B, is greater than the two right-lines A C,
and C B; therefore, à fortiori, the curve-line A C B, is much
greater than the right line A B, which was to be
The
tion of a
tick, to prove the
right line to be the
ſhorteſt of all lines.
The Paralogiſm
of the ſame
tetick, which
veth ignotum per
ignotius.
SALV. I do not think that if one ſhould ranſack all the
logiſms of the world, there could be found one more commodious
than this, to give an example of the moſt ſolemn fallacy of all
fallacies, namely, than that which proveth ignotum per ignotius.
SIMP. How ſo?
SALV. Do you ask me how ſo? The unknown concluſion
which you deſire to prove, is it not, that the curved line A C B, is
longer than the right line A B; the middle term which is taken
for known, is that the curve-line A C B, is greater than the two
lines A C and C B, the which are known to be greater than A B;
And if it be unknown whether the curve-line be greater than the
ſingle right-line A B, ſhall it not be much more unknown whether
it be greater than the two right lines A C & C B, which are known
to be greater than the ſole line A B, & yet you aſſume it as known?
SIMP. I do not yet very well perceive wherein lyeth the
lacy.
SALV. As the two right lines are greater than A B, (as may be
known by Euclid) and in as much as the curve line is longer than
the two right lines A C and B C, ſhall it not not be much greater
than the ſole right line A B?
SIMP. It ſhall ſo.
SALV. That the curve-line A C B, is greater than the right
line A B, is the concluſion more known than the middle term,
which is, that the ſame curve-line is greater than the two
lines A C and C B. Now when the middle term is leſs known
than the concluſion, it is called a proving ignotum per ignotius.
But to return to our purpoſe, it is ſufficient that you know the
right line to be the ſhorteſt of all the lines that can be drawn
tween two points. And as to the principal concluſion, you ſay,
that the material ſphere doth not touch the ſphere in one ſole
point. What then is its contact?
SIMP. It ſhall be a part of its ſuperficies.
SALV. And the contact likewiſe of another ſphere equal to the
firſt, ſhall be alſo a like particle of its ſuperficies?
SIMP. There is no reaſon vvhy it ſhould be othervviſe.
SALV. Then the tvvo ſpheres vvhich touch each other, ſhall
touch vvith the tvvo ſame particles of a ſuperficies, for each of them
agreeing to one and the ſame plane, they muſt of neceſſity agree
in like manner to each other. Imagine now that the two ſpheres

[in Fig. 6.] whoſe centres are A and B, do touch one another:
and let their centres be conjoyned by the right line A B, which
paſſeth through the contact. It paſſeth thorow the point C, and
1another point in the contact being taken as D, conjoyn the two
right lines A D and B D, ſo as that they make the triangle A D B;
of which the two ſides A D and D B ſhall be equal to the other one
A C B, both thoſe and this containing two ſemidiameters, which
by the definition of the ſphere are all equal: and thus the right
line A B, drawn between the two centres A and B, ſhall not be the
ſhorteſt of all, the two lines A D and D B being equal to it: which
by your own conceſſion is abſurd.
A demon ſtration
that the ſphere
cheth the plane but
in one point.
SIMP. This demonſtration holdeth in the abſtracted, but not in
the material ſpheres.
SALV. Inſtance then wherein the fallacy of my argument
ſiſteth, if as you ſay it is not concluding in the material ſpheres, but
holdeth good in the immaterial and
Why the ſphere in
abſtract, toucheth
the plane onely in
one point, and not
the material in
conerete.
SIMP. The material ſpheres are ſubject to many accidents,
which the immaterial are free from. And becauſe it cannot be,
that a ſphere of metal paſſing along a plane, its own weight ſhould
not ſo depreſs it, as that the plain ſhould yield ſomewhat, or that
the ſphere it ſelf ſhould not in the contact admit of ſome
on. Moreover, it is very hard for that plane to be perfect, if for
nothing elſe, yet at leaſt for that its matter is porous: and
haps it will be no leſs difficult to find a ſphere ſo perfect, as that
it hath all the lines from the centre to the ſuperficies, exactly
equal.
SALV. I very readily grant you all this that you have ſaid; but
it is very much beſide our purpoſe: for whilſt you go about to
ſhew me that a material ſphere toucheth not a material plane in
one point alone, you make uſe of a ſphere that is not a ſphere, and
of a plane that is not a plane; for that, according to what you
ſay, either theſe things cannot be found in the world, or if they
may be found, they are ſpoiled in applying them to work the effect.
It had been therefore a leſs evil, for you to have granted the
cluſion, but conditionally, to wit, that if there could be made of
matter a ſphere and a plane that were and could continue perfect,
they would touch in one ſole point, and then to have denied that
any ſuch could be made.
SIMP. I believe that the propoſition of Philoſophers is to be
underſtood in this ſenſe; for it is not to be doubted, but that the
imperfection of the matter, maketh the matters taken in
crete, to diſagree with thoſe taken in abſtract.
SALV. What, do they not agree? Why, that which you your
ſelf ſay at this inſtant, proveth that they punctually agree.
SIMP. How can that be?
SALV. Do you not ſay, that through the imperfection of the
matter, that body which ought to be perfectly ſpherical, and that
plane which ought to be perfectly level, do not prove to be the
1ſame in concrete, as they are imagined to be in abſtract?
SIMP. This I do affirm.
SALV. Then when ever in concrete you do apply a material Sphere

to a material plane, youapply an imperfect Sphere to an imperfect
plane, & theſe you ſay do not touch only in one point. But I muſt
tell you, that even in abſtract an immaterial Sphere, that is, not a
perfect Sphere, may touch an immaterial plane, that is, not a
fect plane, not in one point, but with part of its ſuperficies, ſo that
hitherto that which falleth out in concrete, doth in like manner
hold true in abſtract. And it would be a new thing that the
putations and rates made in abſtract numbers, ſhould not
wards anſwer to the Coines of Gold and Silver, and to the
chandizes in concrete. But do you know Simplicius, how this
commeth to paſſe? Like as to make that the computations agree
with the Sugars, the Silks, the Wools, it is neceſſary that the
accomptant reckon his tares of cheſts, bags, and ſuch other things:
So when the Geometricall Philoſopher would obſerve in concrete
the effects demonſtrated in abſtract, he muſt defalke the
ments of the matter, and if he know how to do that, I do aſſure
you, the things ſhall jump no leſſe exactly, than Arithmstical
computations. The errours therefore lyeth neither in abſtract, nor
in concrete, nor in Geometry, nor in Phyſicks, but in the
tor, that knoweth not how to adjuſt his accompts. Therefore if
you had a perfect Sphere and plane, though they were material,
you need not doubt but that they would touch onely in one point.
And if ſuch a Sphere was and is impoſſible to be procured, it was
much beſides the purpoſe to ſay, Quod Sphæra ænea non tangit in
puncto. Furthermore, if I grant you Simplicius, that in matter a
figure cannot be procured that is perfectly ſpherical, or perfectly
level: Do you think there may be had two materiall bodies,
whoſe ſuperficies in ſome part, and in ſome ſort are incurvated as
irregularly as can be deſired?
Things are
actly the ſame in
abſtract as in
crete.
SIMP. Of theſe I believe that there is no want.
SALV. If ſuch there be, then they alſo will touch in one ſole

point; for this contact in but one point alone is not the ſole and
peculiar priviledge of the perfect Sphere and perfect plane. Nay, he
that ſhould proſecute this point with more ſubtil contemplations
would finde that it is much harder to procure two bodies that

touch with part of their ſnperſicies, than with one point onely.
For if two ſuperficies be required to combine well together, it is
neceſſary either, that they be both exactly plane, or that if one be
convex, the other be concave; but in ſuch a manner concave,
that the concavity do exactly anſwer to the convexity of the other:
the which conditions are much harder to be found, in regard of
their too narrow determination, than thoſe others, which in their
caſuall latitude are infinite.
1
Contact in a
gle point is not
culiar to the
fect Spheres onely?
but belongeth to all
curved figures.
It is more
cult to find Figures
that touch with a
part of their
face, than in one
ſole point.
SIMP. You believe then, that two ſtones, or two pieces of
ron taken at chance, and put together, do for the moſt part touch
in one ſole point?
SALV. In caſual encounters, I do not think they do; as well
becauſe for the moſt part there will be ſome ſmall yielding filth
upon them, as becauſe that no diligence is uſed in applying them
without ſtriking one another; and every ſmall matter ſufficeth to
make the one ſuperficies yield ſomewhat to the other; ſo that
they interchangeably, at leaſt in ſome ſmall particle, receive ſigure
from the impreſſion of each other. But in caſe their ſuperficies
were very terſe and polite, and that they were both laid upon a
table, that ſo one might not preſſe upon the other, and gently put
towards one another, I queſtion not, but that they might be
brought to the ſimple contact in one onely point.
SAGR. It is requiſite, with your permiſſion, that I propound a
certain ſcruple of mine, which came into my minde, whil'ſt I heard
propoſed by Simplicius, the impoſſibility of finding a materiall
and ſolid body, that is, perfectly of a Spherical figure, and whil'ſt
J law Salviatus in a certain manner, not gainſaying, to give his
conſent thereto; therefore I would know, whether there would
be the ſame difficulty in forming a ſolid of ſome other figure, that
is, to expreſſe my ſelf better, whether there is more difficulty in
reducing a piece of Marble into the figure of a perfect Sphere, than
into a perfect Pyramid, or into a perfect Horſe, or into a perfect
Graſſe-hopper?
SALV. To this I will make you the firſt anſwer: and in the
firſt place, I will acquit my ſelf of the aſſent which you think I
gave to Simplicius, which was only for a time; for I had it alſo in
my thoughts, betore I intended to enter upon any other matter, to
ſpeak that, which, it may be, is the ſame, or very like to that which
you are about to ſay, And anſwering to your firſt queſtion, I ſay,

that if any figure can be given to a Solid, the Spherical is the
eſt of all others, as it is likewiſe the moſt ſimple, and holdeth the
ſame place amongſt ſolid figures, as the Circle holdeth amongſt

the ſuperficial. The deſcription of which Circle, as being more
ſie than all the reſt, hath alone been judged by Mathematicians
worthy to be put amongſt the ^{*} poſtulata belonging to the

ption of all other figures. And the formation of the Sphere is
ſo very eaſie, that if in a plain plate of hard metal you take an
empty or hollow circle, within which any Solid goeth caſually
volving that was before but groſly rounded, it ſhall, without any
other artifice be reduced to a Spherical figure, as perfect as is
ſible for it to be; provided, that that ſame Solid be not leſſe than
the Sphere that would paſſe thorow that Circle. And that which is
yet more worthy of our conſideration is, that within the ſelf-ſame
1incavity one may form Spheres of ſeveral magnitudes. But what

is required to the making of an Horſe, or (as you ſay) of a
hopper, I leave to you to judge, who know that there are but few
ſtatuaries in the world able to undertake ſuch a piece of work.
And I think that herein Simplicius will not diſſent from me.
The Sphericall
Figure is eaſier to
be made than any
other.
The circular
gure only is placed
amongst the
lata of
ticians.
* Demands or
Petitions.
Sphericall
gures of ſundry
magnitudes may
be made with one
onely inſtrument.
SIMP. I know not whether I do at all diffent from you; my
opinion is this, that none of the afore-named figures can be
fectly obteined; but for the approaching as neer as is poſſible to
the moſt perfect degree, I believe that it is incomparably more
ſie to reduce the Solid into a Spherical figure, than into the ſhape
of an Horſe, or Graſſe-hopper?
SAGR. And this greater difficulty, wherein think you doth it
depend?
SIMP. Like as the great facility in forming the Sphere ariſeth

from its abſolute ſimplicity and uniformity ſo the great
larity rendereth the conſtruction of all other figures difficult.
Irregular forms
difficult to be
troduced.
SAGR. Therefore the irregularity being the cauſe of the
culty, than the figure of a ſtone broken with an hammer by
chance, ſhall be one of the figures that are difficult to be
ced, it being perhaps more irregular than that of the horſe?
SIMP. So it ſhould be.
SAGR. But tell me; that figure what ever it is which the ſtone
hath, hath it the ſame in perfection, or no?
SIMP. What it hath, it hath ſo perfectly, that nothing can be
more exact.
SAGR. Then, if of figures that are irregular, and
ly hard to be procured, there are yet infinite which are moſt
fectly obteined, with what reaſon can it be ſaid, that the moſt
ſimple, and conſequently the moſt eaſie of all, is impoſſible to be
procured?
SALV. Gentlemen, with your favour, I may ſay that we have
ſallied out into a diſpute not much more worth than the wool of a
goat; and whereas our argumentations ſhould continually be
verſant about ſerious and weighty points, we conſume our time in

frivolous and impertinent wranglings. Let us call to minde, I pray
you, that the ſearch of the worlds conſtitution, is one of the
teſt and nobleſt Problems that are in nature; and ſo much the
greater, inaſmuch as it is directed to the reſolving of that other;
to wit, of the cauſe of the Seas ebbing and flowing, enquired
to by all the famous men, that have hitherto been in the world,
and poſſibly found out by none of them. Therefore if we have
nothing more remaining for the full confutation of the argument
taken from the Earths vertigo, which was the laſt, alledged to
prove its immobility upon its own centre, let us paſſe to the
amination of thoſe things that are alledged for, and againſt the
Annual Motion.
1
The conſtitution
of the Univerſe is
one of the moſt
ble Problems.
SAGR. I would not have you, Salviatus, meaſure our wits by
the ſcale of yours: you, who uſe to be continually buſied about
the ſublimeſt contemplations, eſteem thoſe notions frivolous and
below you, which we think matters worthy of our profoundeſt
thoughts: yet ſometimes for our ſatisfaction do not diſdain to
ſtoop ſo low as to give way a little to our curioſity. As to the
refutation of the laſt argument, taken from the extruſions of the
diurnal vertigo, far leſs than what hath been ſaid, would have
given me ſatisfaction: and yet the things ſuperfluouſly ſpoken,
ſeemed to me ſo ingenious, that they have been ſo far from
rying my fancy, as that they have, by reaſon of their novelty,
tertained me all along with ſo great delight, that I know not how
to deſire greater: Therefore, if you have any other ſpeculation
to add, produce it, for I, as to my own particular, ſhall gladly
hearken to it.
SALV. I have always taken great delight in thoſe things which
I have had the fortune to diſcover, and next to that, which is my
chief content, I find great pleaſure in imparting them to ſome
friends, that apprehendeth and ſeemeth to like them: Now, in
gard you are one of theſe, ſlacking a little the reins of my
tion, which is much pleaſed when I ſhew my ſelf more
cacious, than ſome other that hath the reputation of a ſharp
ſight, I will for a full and true meaſure of the paſt diſpute,
duce another fallacy of the Sectators of Ptolomey and Ariſtotle,
which I take from the argument alledged.
SAGR. See how greedily I wait to hear it.
SALV. We have hitherto over-paſſed, and granted to Ptolomey,
as an effect indubitable, that the extruſion of the ſtone
ing from the velocity of the wheel turn'd round upon its centre,
the cauſe of the ſaid extruſion encreaſeth in proportion, as the
locity of the vertigo (or whirling) is augmented: from whence
it was inferred, that the velocity of the Earth's vertigo being
very much greater than that of any machin whatſoever, that we
can make to turn round artificially; the extruſion of ſtones, of
animals, &c. would conſequently be far more violent. Now, I
obſerve that there is a great fallacy in this diſcourſe, in that we do
compare theſe velocities indifferently and abſolutely to one
ther. It's true, that if I compare the velocities of the ſame wheel,
or of two wheels equal to each other, that which ſhall be more
ſwiftly turn'd round, ſhall extrude the ſtone with greater
lence; and the velocity encreaſing, the cauſe of the projection
ſhall likewiſe encreaſe: but when the velocity is augmented, not
by encreaſing the velocity in the ſame wheel, which would be by
cauſing it to make a greater number of revolutions in equal times;
but by encreaſing the diameter, and making the wheel greater, ſo
as that the converſion taking up the ſame time in the leſſer wheel,
1as in the greater, the velocity is greater onely in the bigger wheel,

for that its circumference is bigger; there is no man that thinketh
that the cauſe of the extruſion in the great wheel will encreaſe
cording to the proportion of the velocity of its circumference, to
the velocity of the circumference of the other leſſer wheel; for that
this is moſt falſe, as by a moſt expeditious experiment I ſhall thus
groſly declare: We may ſling a ſtone with a ſtick of a yard long,
farther than we can do with a ſtick ſix yards long, though
the motion of the end of the long ſtick, that is of the ſtone placed
in the ſlit thereof, were more than double as ſwift as the
tion of the end of the other ſhorter ſtick, as it would be if
the velocities were ſuch that the leſſer ſtick ſhould turn thrice
round in the time whilſt the greater is making one onely
verſion.
The cauſe of the
projection
eth not according
to the proportion of
the velocity,
creaſed by making
the wheel bigger.
SAGR. This which you tell me, Salviatus, muſt, I ſee, needs
ſucceed in this very manner; but I do not ſo readily apprehend
the cauſe why equal velocities ſhould not operate equally in
extruding projects, but that of the leſſer wheel much more than
the other of the greater wheel; therefore I intreat you to tell me
how this cometh to paſs.
SIMP. Herein, Sagredus, you ſeem to differ much from your
ſelf, for that you were wont to penetrate all things in an inſtant,
and now you have overlook'd a fallacy couched in the experiment
of the ſtick, which I my ſelf have been able to diſcover: and this
is the different manner of operating, in making the projection one
while with the ſhort ſling and another while with the long one,
for if you will have the ſtone fly out of the ſlit, you need not
tinue its motion uniformly, but at ſuch time as it is at the ſwifteſt,
you are to ſtay your arm, and ſtop the velocity of the ſtick;
upon the ſtone which was in its ſwifteſt motion, flyeth out, and
moveth with impetuoſity: but now that ſtop cannot be made in
the great ſtick, which by reaſon of its length and flexibility, doth
not entirely obey the check of the arm, but continueth to
pany the ſtone for ſome ſpace, and holdeth it in with ſo much leſs
force, and not as if you had with a ſtiff ſling ſent it going with a
jerk: for if both the ſticks or ſlings ſhould be check'd by one and
the ſame obſtacle, I do believe they would fly aſwell out of the
one, as out of the other, howbeit their motions were equally
ſwift.
SAGR. With the permiſſion of Salviatus, I will anſwer
thing to Simplicius, in regard he hath addreſſed himſelf to me;
and I ſay, that in his diſcourſe there is ſomewhat good
and ſomewhat bad: good, becauſe it is almoſt all true;
bad, becauſe it doth not agree with our caſe: Truth is, that when
that which carrieth the ſtones with velocity, ſhall meet with a
1check that is immoveable, they ſhall fly out with great
ſity: the ſame effect following in that caſe, which we ſee dayly
to fall out in a boat that running a ſwift courſe, runs a-ground, or
meets with ſome ſudden ſtop, for all thoſe in the boat, being

prized, ſtumble forwards, and fall towards the part whither the
boat ſteered. And in caſe the Earth ſhould meet with ſuch a
check, as ſhould be able to reſiſt and arreſt its vertigo, then indeed
I do believe that not onely beaſts, buildings and cities, but
tains, lakes and ſeas would overturn, and the globe it ſelf would
go near to ſhake in pieces; but nothing of all this concerns our
preſent purpoſe, for we ſpeak of what may follow to the motion
of the Earth, it being turn'd round uniformly, and quietly about
its own centre, howbeit with a great velocity. That likewiſe
which you ſay of the ſlings, is true in part; but was not alledged
by Salviatus, as a thing that punctually agreed with the matter
whereof we treat, but onely, as an example, for ſo in groſs it may
prompt us in the more accurate conſideration of that point,
ther, the velocity increaſing at any rate, the cauſe of the
ction doth increaſe at the ſame rate: ſo that v. g. if a wheel of
ten yards diameter, moving in ſuch a manner that a point of its
circumference will paſs an hundred yards in a minute of an hour,
and ſo hath an impetus able to extrude a ſtone, that ſame impetus
ſhall be increaſed an hundred thouſand times in a wheel of a million
of yards diameter; the which Salviatus denieth, and I incline to his
opinion; but not knowing the reaſon thereof, I have requeſted it
of him, and ſtand impatiently expecting it.
Graming the
urnal vertigo of
the Earth, & that
by ſome ſudden ſtop
or obſtacle it were
arreſted, houſes,
mountains
ſelves, and perhaps
the whole Globe
would be ſhaken n
pieces.
SALV. I am ready to give you the beſt ſatisfaction, that my
abilities will give leave: And though in my firſt diſcourſe you
thought that I had enquired into things eſtranged from our
poſe, yet nevertheleſſe I believe that in the ſequel of the diſpute,
you will find that they do not prove ſo. Therefore let Sagredus
tell me wherein he hath obſerved that the reſiſtance of any
able to motion doth conſiſt.
SAGR. I ſee not for the preſent that the moveable hath any
internal reſiſtance to motion, unleſſe it be its natural inclination
and propenſion to the contrary motion, as in grave bodies, that
have a propenſion to the motion downwards, the reſiſtance is to
the motion upwards; and I ſaid an internal reſiſtance, becauſe
of this, I think, it is you intend to ſpeak, and not of the external
reſiſtances, which are many and accidental.
SALV. It is that indeed I mean, and your nimbleneſſe of wit
hath been too hard for my craftineſſe, but if I have been too
ſhort in asking the queſtion, I doubt whether Sagredus hath been
full enough in his anſwer to ſatisſie the demand; and whether
there be not in the moveable, beſides the natural inclination to the
1contrary term, another intrinſick and natural quality, which

keth it averſe to motion. Therefore tell me again; do you not
think that the inclination v. g. of grave bodies to move
wards, is equal to the reſiſtance of the ſame to the motion of
jection upwards?
The inclination of
grave bodies to the
motion downwards,
is equal to their
reſiſtance to the
motion upwards.
SAGR. I believe that it is exactly the ſame. And for this reaſon
I ſee that two equal weights being put into a ballance, they do
ſtand ſtill in equilibrium, the gravity of the one reſiſting its
ing raiſed by the gravity wherewith the other preſſing
wards would raiſe it.
SALV. Very well; ſo that if you would have one raiſe up the
other, you muſt encreaſe the weight of that which depreſſeth,
or leſſen the weight of the other. But if the reſiſtance to
ing motion cunſiſt onely in gravity, how cometh it to paſſe, that

in ballances of unequal arms, to wit in the ^{*} Stiliard, a weight
ſometimes of an hundred pounds, with its preſſion downwards,
doth not ſuffice to raiſe up on of four pounds; that ſhall
poiſe with it, nay this of four, deſcending ſhall raiſe up that
of an hundred; for ſuch is the effect of the pendant weight upon
the weight which we would weigh? If the reſiſtance to motion
reſideth onely in the gravity, how can the arm with its weight of
four pounds onely, reſiſt the weight of a ſack of wool, or bale of
ſilk, which ſhall be eight hundred, or a thouſand weight; yea
more, how can it overcome the ſack with its moment, and raiſe
it up? It muſt therefore be confeſt Sagredus, that here it maketh
uſe of ſome other reſiſtance, and other force, beſides that of
ſimple gravity.
* A portable
lance wherewith
market-people
weigh their
modities, giving it
gravity by
ving the weight
farther from the
cock: call'd by the
Latines, Campana
trutina.
SAGR. It muſt needs be ſo; therefore tell me what this
cond virtue ſhould be.
SALV. It is that which was not in the ballance of equal
arms; you ſee then what variety there is in the Stiliard; and
on this doubtleſſe dependeth the cauſe of the new effect.
SAGR. I think that your putting me to it a ſecond time, hath
made me remember ſomething that may be to the purpoſe. In
both theſe beams the buſineſs is done by the weight, and by the
motion; in the ballance, the motions are equal, and therefore the
one weight muſt exceed it in gravity before it can move it; in the
ſtiliard, the leſſer weight will not move the greater, unleſs when
this latter moveth little, as being ſlung at a leſſer diſtance, and the
other much, as hanging at a greater diſtance from the lacquet or
cock. It is neceſſary therefore to conclude, that the leſſer weight
overcometh the reſiſtance of the greater, by moving much, whilſt
the other is moved but little.
SALV. Which is as much as to ſay, that the velocity of the
moveable leſs grave, compenſateth the gravity of the moveable
more grave and leſs
1
The greater
city exactly
penſates thegreater
gravity.
SAGR. But do you think that the velocity doth fully make
good the gravity? that is, that the moment and force of a
able of v. g. four pounds weight, is as great as that of one of an
hundred weight, whenſoever that the firſt hath an hundred degrees
of velocity, and the later but four onely?
SALV. Yes doubtleſs, as I am able by many experiments to
demonſtrate: but for the preſent, let this onely of the ſtiliard
ſuffice: in which you ſee that the light end of the beam is then
able to ſuſtain and equilibrate the great Wool ſack, when its
ſtance from the centre, upon which the ſtiliard reſteth and
eth, ſhall ſo much exceed the leſſer diſtance, by how much the
ſolute gravity of the Wool-ſack exceedeth that of the pendent
weight. And we ſee nothing that can cauſe this inſufficiencie in
the great ſack of Wool, to raiſe with its weight the pendent
weight ſo much leſs grave, ſave the diſparity of the motions which
the one and the other ſhould make, whilſt that the Wool ſack by
deſcending but one inch onely, will raiſe the pendent weight an
hundred inclies: (ſuppoſing that the ſack did weigh an hundred
times as much, and that the diſtance of the ſmall weight from the
centre of the beam were an hundred times greater, than the
ſtance between the ſaid centre and the point of the ſacks
on.) And again, the pendent weight its moving the ſpace of an
hundred inches, in the time that the ſack moveth but one inch
onely, is the ſame as to ſay, that the velocity of the motion of the
little pendent weight, is an hundred times greater than the
city of the motion of the ſack. Now fix it in your belief, as a
true and manifeſt axiom, that the reſiſtance which proceedeth from
the velocity of motion, compenſateth that which dependeth on
the gravity of another moveable: So that conſequently, a
able of one pound, that moveth with an hundred degrees of
locity, doth as much reſiſt all obſtruction, as another moveable
of an hundred weight, whoſe velocity is but one degree onely.
And two equal moveables will equally reſiſt their being moved,
if that they ſhall be moved with equal velocity: but if one be
to be moved more ſwiftly than the other, it ſhall make greater
ſiſtance, according to the greater velocity that ſhall be conferred
on it. Theſe things being premiſed, let us proceed to the
nation of our Problem; and for the better underſtanding of
things, let us make a ſhort Scheme thereof. Let two unequal
wheels be deſcribed about this centre A, [in Fig. 7.] and let the
circumference of the leſſer be B G, and of the greater C E H, and
let the ſemidiameter A B C, be perpendicular to the Horizon; and
by the points B and C, let us draw the right lined Tangents B F
and C D; and in the arches B G and C E, take two equal parts
B G and C E: and let the two wheels be ſuppoſed to be turn'd
1round upon their centres with equal velocities, ſo as that two
veables, which ſuppoſe for example to be two ſtones placed in the
points B and C, come to be carried along the circumferences B G
and C E, with equal velocities; ſo that in the ſame time that the
ſtone B ſhall have run the arch B G, the ſtone C will have paſt the
arch C E. I ſay now, that the whirl or vertigo of the leſſer wheel
is much more potent to make the projection of the ſtone B, than
the vertigo of the bigger wheel to make that of the ſtone C.
Therefore the projection, as we have already declared, being to be
made along the tangent, when the ſtones B and C are to ſeparate
from their wheels, and to begin the motion of projection from the
points B and C, then ſhall they be extruded by the impetus
ceived from the vertigo by (or along) the tangents B F and C D.
The two ſtones therefore have equal impetuoſities of running
long the tangents B F and C D, and would run along the ſame, if
they were not turn'd aſide by ſome other force: is it not ſo
gredus?
SAGR. In my opinion the buſineſſe is as you ſay.
SALV. But what force, think you, ſhould that be which averts
the ſtones from moving by the tangents, along which they are
tainly driven by the impetus of the vertigo.
SAGR. It is either their own gravity, or elſe ſome glutinous
matter that holdeth them faſt and cloſe to the wheels.
SALV. But for the diverting of a moveable from the motion
to which nature inciteth it, is there not required greater or leſſer
force, according as the deviation is intended to be greater or
ſer? that is, according as the ſaid moveable in its deviation hath a
greater or leſſer ſpace to move in the ſame time?
SAGR. Yes certainly: for it was concluded even now, that to
make a moveable to move; the movent vertue muſt be increaſed
in proportion to the velocity wherewith it is to move.
SALV. Now conſider, that for the deviating the ſtone upon
the leſſe wheel from the motion of projection, which it would
make by the tangent B F, and for the holding of it faſt to the
wheel, it is required, that its own gravity draw it back the whole
length of the ſecant F G, or of the perpendicular raiſed from the
point G, to the line B F, whereas in the greater wheel the
on needs to be no more than the ſecant D E, or the
lar let fall from the tangent D G to the point E, leſſe by much
than F G, and alwayes leſſer and leſſer according as the wheel is
made bigger. And foraſmuch as theſe retractions (as I may call
them) are required to be made in equal times, that is, whil'ſt the
wheels paſſe the two equal arches B G and C E, that of the ſtone
B, that is, the retraction F G ought to be more ſwift than the
ther D E; and therefore much greater force will be required for
1holding faſt the ſtone B to its little wheel, than for the holding
the ſtone C to its great one, which is as much as to ſay, that ſuch
a ſmall thing will impede the extruſion in the great wheel, as will
not at all hinder it in the little one. It is manifeſt therefore that
the more the wheel augmenteth, the more the cauſe of the
jection diminiſheth.
SAGR. From this which I now underſtand, by help of your
nute diſſertation, I am induced to think, that I am able to ſatisfie
my judgment in a very few words. For equal impetus being
preſſed on both the ſtones that move along the tangents, by the
equal velocity of the two wheels, we ſee the great circumference,
by means of its ſmall deviation from the tangent, to go ſeconding,
as it were, and in a fair way refraining in the ſtone the appetite, if
I may ſo ſay, of ſeparating from the circumference; ſo that any
ſmall retention, either of its own inclination, or of ſome
tion ſufficeth to hold it faſt to the wheel. Which, again, is not
ble to work the like effect in the little wheel, which but little
ſecuting the direction of the tangent, ſeeketh with too much
gerneſſe to hold faſt the ſtone; and the reſtriction and glutination
not being ſtronger than that which holdeth the other ſtone faſt to

the greater wheel, it ^{*} breaks looſe, and runneth along the
gent. Therefore I do not only finde that all thoſe have erred,
who have believed the cauſe of the projection to increaſe
ding to the augmentation of the vertigo's velocity; but I am
further thinking, that the projection diminiſhing in the inlarging of
the wheel, ſo long as the ſame velocity is reteined in thoſe wheels;
it may poſſibly be true, that he that would make the great wheel
extrude things like the little one, would be forced to increaſe
them as much in velocity, as they increaſe in diameter, which he
might do, by making them to finiſh their converſions in equal
times; and thus we may conclude, that the Earths revolution or
vertigo would be no more able to extrude ſtones, than any little
wheel that goeth ſo ſlowly, as that it maketh but one turn in
ty four hours.
* Strappar la
vezza, is to break
the bridle.
SALV. We will enquire no further into this point for the
ſent: let it ſuffice that we have abundantly (if I deceive not my
ſelf) demonſtrated the invalidity of the argument, which at firſt
ſight ſeemed very concluding, and was ſo held by very famous
men: and I ſhall think my time and words well beſtowed, if I
have but gained ſome belief in the opinion of Simplicius, I will
not ſay or the Earths mobility, but only that the opinion of thoſe
that believe it, is not ſo ridiculous and fond, as the rout of vulgar
Philoſophers eſteem it.
SIMP. The anſwers hitherto produced againſt the arguments
brought againſt this Diurnal Revolution of the Earth taken from
1grave bodies falling from the top of a Tower, and from
ctions made perpendicularly upwards, or according to any
tion ſidewayes towards the Eaſt, Weſt, North, South, &c. have
ſomewhat abated in me the antiquated incredulity I had conceived
againſt that opinion: but other greater doubts run in my mind
at this very inſtant, which I know not in the leaſt how to free my
ſelf of, and haply you your ſelf will not be able to reſolve them;
nay, its poſſible you may not have heard them, for they are very
modern. And theſe are the objections of two Authours, that ex
profeſſo write againſt Copernicus. Some of which are read in a

little Tract of natural concluſions; The reſt are by a great both
Philoſopher and Mathematician, inſerted in a Treatiſe which he
hath written in favour of Aristotle, and his opinion touching the
inalterability of the Heavens, where he proveth, that not onely
the Comets, but alſo the new ſtars, namely, that anno 1572. in
Caſſiopeia, and that anno 1604. in Sagittarius were not above the
Spheres of the Planets, but abſolutely beneath the concave of
the Moon in the Elementary Sphere, and this he demonſtrateth
gainſt Tycho, Kepler, and many other Aftronomical Obſervators,
and beateth them at their own weapon; to wit, the Doctrine of
Parallaxes. If you like thereof, I will give you the reaſons of
both theſe Authours, for I have read them more than once,
with attention; and you may examine their ſtrength, and give
your opinion thereon.
Other objections
of two modern
thors against
pernicus.
SALV. In regard that our principal end is to bring upon the
ſtage, and to conſider what ever hath been ſaid for, or againſt the
two Syſtemes, Ptolomaick, and Copernican, it is not good to omit
any thing that hath been written on this ſubject.
SIMP. I will begin therefore with the objections which I finde
in the Treatiſe of Concluſions, and afterwards proceed to the

reſt. In the firſt place then, he beſtoweth much paines in
lating exactly how many miles an hour a point of the terreſtrial
Globe ſituate under the Equinoctial, goeth, and how many miles
are paſt by other points ſituate in other parallels: and not being
content with finding out ſuch motions in horary times, he findeth
them alſo in a minute of an hour; and not contenting himſelf
with a minute, he findes them alſo in a ſecond minute; yea more,
he goeth on to ſhew plainly, how many miles a Cannon bullet
would go in the ſame time, being placed in the concave of the

nar Orb, ſuppoſing it alſo as big as Copernicus himſelf repreſenteth
it, to take away all ſubterfuges from his adverſary. And having
made this moſt ingenious and exquiſite ſupputation, he ſheweth,
that a grave body falling from thence above would conſume more
than ſix dayes in attaining to the centre of the Earth, to which all
grave bodies naturally move. Now if by the abſolute Divine
1Power, or by ſome Angel, a very great Cannon bullet were
ed up thither, and placed in our Zenith or vertical point, and from
thence let go at liberty, it is in his, and alſo in my opinion, a moſt
incredible thing that it, in deſcending downwards, ſhould all the
way maintain it ſelf in our vertical line, continuing to turn round
with the Earth, about its centre, for ſo many dayes, deſcribing
under the Equinoctial a Spiral line in the plain of the great circle
it ſelf: and under other Parallels, Spiral lines about Cones, and
under the Poles falling by a ſimple right line. He, in the next
place, ſtabliſheth and confirmeth this great improbability by
ving, in the way of interrogations, many difficulties impoſſible to
be removed by the followers of Copernicus; and they are, if I do
well remember-----.
The firſt
ction of the
dern Author of
the little tract of
Concluſions.
A Cannon
let would ſpend
more than ſix days
in falling from the
Concave of the
Moon to the
tre of the Earth,
according to the
pinion of that
dern Author of the
Concluſions.
SALV. Take up a little, good Simplicius, and do not load me
with ſo many novelties at once: I have but a bad memory, and
therefore I muſt not go too faſt. And in regard it cometh into
my minde, that I once undertook to calculate how long time ſuch a
grave body falling from the concave of the Moon, would be in
paſſing to the centre of the Earth, and that I think I remember
that the time would not be ſo long; it would be fit that you ſhew
us by what rule this Author made his calculation.
SIMP. He hath done it by proving his intent à fortiori, a
cient advantage for his adverſaries, ſuppoſing that the velocity of
the body falling along the vertical line, towards the centre of the
Earth, were equal to the velocity of its circular motion, which it
made in the grand circle of the concave of the Lunar Orb.
Which by equation would come to paſſe in an hour, twelve
ſand ſix hundred German miles, a thing which indeed ſavours of
impoſſibility: Yet nevertheleſſe, to ſhew his abundant caution,
and to give all advantages to his adverſaries, he ſuppoſeth it for
true, and concludeth, that the time oſ the fall ought however to
be more than ſix dayes.
SALV. And is this the ſum of his method? And doth he by
this demonſtration prove the time of the fall to be above ſix
dayes?
SAGR. Me thinks that he hath behaved himſelf too modeſtly,
for that having it in the power of his will to give what velocity he
pleaſed to ſuch a deſcending body, and might aſwell have made it
ſix moneths, nay, ſix years in falling to the Earth, he is content
with ſix dayes. But, good Salviatus, ſharpen my appetite a
tle, by telling me in what manner you made your computation, in
regard you ſay, that you have heretofore caſt it up: for I am
fident that if the queſtion had not required ſome ingenuity in
working it, you would never have applied your minde unto
it.
1
SALV. It is not enough, Sagredus, that the ſubjects be noble
and great, but the buſineſſe conſiſts in handling it nobly. And
who knoweth not, that in the diſſection of the members of
a beaſt, there may be diſcovered infinite wonders of provident
and prudent Nature; and yet for one, that the Anatomiſt
ſects, the butcher cuts up a thouſand. Thus I, who am now
ſeeking how to ſatisfie your demand, cannot tell with which of the
two ſhapes I had beſt to appear on the Stage; but yet, taking
heart from the example of Simplicius, his Authour, I will,
out more delays, give you an account (if I have not forgot) how
I proceeded. But before I go any further, I muſt not omit to tell
you, that I much fear that Simplicius hath not faithfully related
the manner how this his Authour found, that the Cannon
let in coming from the concave of the Moon to the centre of the
Earth, would ſpend more than fix dayes: for if he had
ſed that its velocity in deſcending was equal to that of the
concave (as Simplicius ſaith he doth ſuppoſe) he would have
ſhewn himſelf ignorant of the firſt, and more ſimple principles
of Geometry; yea, I admire that Simplicius, in admitting the
ſuppoſition which he ſpeaketh of, doth not ſee the monſtrous
ſurdity that is couched in it.
SIMP. Its poſſible that I may have erred in relating it; but
that I ſee any fallacy in it, I am ſure is not true.
SALV. Perhaps I did not rightly apprehend that which you
ſaid, Do you not ſay, that this Authour maketh the velocity
of the bullet in deſcending equall to that which it had in
ning round, being in the concave of the Moon, and that
ming down with the ſame velocity, it would reach to the centre
in ſix dayes?
SIMP. So, as I think, he writeth.
SALV. And do not you perceive a ſhamefull errour therein?
But queſtionleſſe you diſſemble it: For it cannot be, but that
you ſhould know that the ſemidiameter of the Circle is leſſe than

the ſixth part of the circumference; and that conſequently, the
time in which the moveable ſhall paſſe the ſemidiameter, ſhall be
leſſe than the ſixth part of the time; in which, being moved
with the ſame velocity, it would paſſe the circumference; and
that therefore the bullet deſcending with the velocity,
with it moved in the concave, will arrive in leſſe than four hours
at the centre, ſuppoſing that in the concave one revolution
ſhould be conſummate in twenty four hours, as he muſt of
ceſſity have ſuppoſed it, for to keep it all the way in the ſame
vertical line.
A ſhamefull
errour in the
gument taken from
the bullets falling
out of the Moons
concave.
SIMP. Now I thorowly perceive the miſtake: but yet I
would not lay it upon him undeſervedly, for it's poſſible that I
1may have erred in rehearſing his Argument, and to avoid running
into the ſame miſtakes for the future, I could wiſh I had his
Book; and if you had any body to ſend for it, I would take it
for a great favour.
SAGR. You ſhall not want a Lacquey that will runne for it
with all ſpeed: and he ſhall do it preſently, without loſing any
time; in the mean time Salviatus may pleaſe to oblige us with his
computation.
SIMP. If he go, he ſhall finde it lie open upon my Desk,
together with that of the other Author, who alſo argueth
gainſt Copernicus.
SAGR. We will make him bring that alſo for the more
tainty: and in the interim Salviatus ſhall make his calculation: I
have diſpatch't away a meſſenger.
SALV. Above all things it muſt be conſidered, that the motion
of deſcending grave bodies is not uniform, but departing from

reſt they go continually accelerating: An effect known and
ſerved by all men, unleſſe it be by the forementioned modern
thour, who not ſpeaking of acceleration, maketh it even and
niforme. But this general notion is of no avail, if it be not known
according to what proportion this increaſe of velocity is made; a
concluſion that hath been until our times unknown to all
phers; and was firſt found out & demonſtrated by the ^{*} Academick,

our common friend, who in ſome of his ^{*} writings not yet

ed, but in familiarity ſhewn to me, and ſome others of his
quaintance he proveth, how that the acceleration of the right
tion of grave bodies, is made according to the numbers uneven
beginning ab unitate, that is, any number of equal times being
ſigned, if in the firſt time the moveable departing from reſt ſhall

have paſſed ſuch a certain ſpace, as for example, an ell, in the
cond time it ſhall have paſſed three ells, in the third five, in the
fourth ſeven, and ſo progreſſively, according to the following odd
numbers; which in ſhort is the ſame, as if I ſhould ſay, that the
ſpaces paſſed by the moveable departing from its reſt, are unto

each other in proportion double to the proportion of the times,
in which thoſe ſpaces are meaſured; or we will ſay, that the
ſpaces paſſed are to each other, as the ſquares of their times.
An exact
pute of the time of
the fall of the
non bullet from the
Moons concave to
the Earths centre.
* The Author.
* By theſe
tings, he every
where meanes his
Dialogues, De
tu, which I promiſe
to give you in my
ſecond Volume.
Acceleration of
the natural motion
of grave bodies is
made according to
the odde numbers
beginning at unity.
The ſpaces paſt
by the falling
grave body are as
the ſquares of their
times.
SAGR. This is truly admirable: and do you ſay that there is
a Mathematical demonſtration for it?
SALV. Yes, purely Mathematical; and not onely for this, but
for many other very admirable paſſions, pertaining to natural
tions, and to projects alſo, all invented, and demonſtrated by Our

Friend, and I have ſeen and conſidered them all to my very great
content and admiration, ſeeing a new compleat Doctrine to ſpring
up touching a ſubject, upon which have been written hundreds of
1Volumes; and yet not ſo much as one of the infinite admirable
concluſions that thoſe his writings contain, hath ever been
ſerved, or underſtood by any one, before Our Friend made
them out.
An intire and
new Science of the
Academick
ning local motion.
SAGR. You make me loſe the deſire I had to underſtand
more in our diſputes in hand, onely that I may hear ſome of
thoſe demonſtrations which you ſpeak of; therefore either give
them me preſently, or at leaſt promiſe me upon your word, to
appoint a particular conference concerning them, at which
plicius alſo may be preſent, if he ſhall have a mind to hear the
paſſions and accidents of the primary effect in Nature.
SIMP. I ſhall undoubtedly be much pleaſed therewith, though
indeed, as to what concerneth Natural Philoſophy, I do not think
that it is neceſſary to deſcend unto minute particularities, a
ral knowledg of the definition of motion, and of the
ction of natural and violent, even and accelerate, and the like,
ſufficing: For if this were not ſufficient, I do not think that
ſtotle would have omitted to have taught us what ever more was
neceſſary.
SALV. It may be ſo. But let us not loſe more time about
this, which I promiſe to ſpend half a day apart in, for your
faction; nay, now I remember, I did promiſe you once before to
ſatisfie you herein. Returning therefore to our begun
tion of the time, wherein the grave cadent body would paſs from
the concave of the Moon to the centre of the Earth, that we may
not proceed arbitrarily and at randon, but with a Logical method,
we will firſt attempt to aſcertain our ſelves by experiments often
repeated, in how long time a ball v. g. of Iron deſcendeth to the
Earth from an altitude of an hundred yards.
SAGR. Let us therefore take a ball of ſuch a determinate
weight, and let it be the ſame wherewith we intend to make the
computation of the time of deſcent from the Moon.
SALV. This is not material, for that a ball of one, of ten, of an
hundred, of a thouſand pounds, will all meaſure the ſame hundred
yards in the ſame time.
SIMP. But this I cannot believe, nor much leſs doth Ariſtotle
think ſo, who writeth, that the velocities of deſcending grave
bodies, are in the ſame proportion to one another, as their
vities.
SALV. If you will admit this for true, Simplicius, you muſt

lieve alſo, that two balls of the ſame matter, being let fall in the
ſame moment, one of an hundred pounds, and another of one,
from an altitude of an hundred yards, the great one arriveth at the
ground, before the other is deſcended but one yard onely: Now
bring your fancy, if you can, to imagine, that you ſee the great
1ball got to the ground, when the little one is ſtill within leſs than
a yard of the top of the Tower.
The error of
ſtotle in affirming,
falling grave
dies to move
ding to the
tion of their
ties.
SAGR. That this propoſition is moſt falſe, I make no doubt in
the world; but yet that yours is abſolutely true, I cannot well
aſſure my ſelf: nevertheleſs, I believe it, ſeeing that you ſo
ſolutely affirm it; which I am ſure you would not do, if you had
not certain experience, or ſome clear demonſtration thereof.
SALV. I have both: and when we ſhall handle the buſineſs
of motions apart, I will communicate them: in the interim, that
we may have no more occaſions of interrupting our diſcourſe, we
will ſuppoſe, that we are to make our computation upon a ball of

Iron of an hundred (a) pounds, the which by reiterated
ments deſcendeth from the altitude of an hundred (b) yards, in
five ſecond-minutes of an hour. And becauſe, as we have ſaid,
the ſpaces that are meaſured by the cadent moveable, increaſe in
double proportion; that is, according to the ſquares of the times,
being that the time of one firſt-minute is duodecuple to the time
of five ſeconds, if we multiply the hundred yards by the ſquare of
12, that is by 144, we ſhall have 14400, which ſhall be the
ber of yards that the ſame moveable ſhall paſs in one firſt-minute
of an hour: and following the ſame rule becauſe one hour is 60
minutes, multiplying 14400, the number of yards paſt in one
nute, by the ſquare of 60, that is, by 3600, there ſhall come forth
51840000, the number of yards to be paſſed in an hour, which
make 17280 miles. And deſiring to know the ſpace that the ſaid
ball would paſs in 4 hours, let us multiply 17280 by 16, (which
is the ſquare of 4) and the product will be 276480 miles: which
number is much greater than the diſtance from the Lunar concave
to the centre of the Earth, which is but 196000 miles, making the
diſtance of the concave 56 ſemidiameters of the Earth, as that
dern Author doth; and the ſemidiameter of the Earth 3500 miles,

of 3000 ^{*}Braces to a †mile, which are our Italian miles.
(a) (b) Note that
theſe Calculations
are made in
an weights and
meaſures. And 100
pounds
poiſe make 131 l.
Florentine. And
100 Engliſh yards
makes 150 2/5 Braces
Florent. ſo that the
brace or yard of
our Author is 3/4
of cur yard.
* The Italian
ſure which I
monly tranſl te
yards.
Therefore, Simplicius, that ſpace from the concave of the Moon
to the centre of the Earth, which your Accomptant ſaid could

not be paſſed under more than ſix days, you ſee that (computing
by experience, and not upon the fingers ends) that it ſhall be
ſed in much leſs than four hours; and making the computation
exact, it ſhall be paſſed by the moveable in 3 hours, 22 min. prim.
and 4 ſeconds.
† The Italian mile
is 1000/1056 of our mile.
SAGR. I beſeech you, dear Sir, do not defraud me of this
act calculation, for it muſt needs be very excellent.
SALV. So indeed it is: therefore having (as I have ſaid) by
diligent tryal obſerved, that ſuch a moveable paſſeth in its deſcent,
the height of 100 yards in 5 ſeconds of an hour, we will ſay, if
100 yards are paſſed in 5 ſeconds; in how many ſeconds ſhall
1588000000 yards (for ſo many are in 56 diameters of the Earth)
be paſſed? The rule for this work is, that the third number muſt
be multiplied by the ſquare of the ſecond, of which doth come
14700000000, which ought to be divided by the firſt, that is, by
100, and the root ſquare of the quotient, that is, 12124 is the
number ſought, namely 12124 min. ſecun. of an hour, which are
3 hours, 22 min. prim. and 4 ſeconds.
SAGR. I have ſeen the working, but I know nothing of the
reaſon for ſo working, nor do I now think it a time to ask it.
SALV. Yet I will give it, though you do not ask it, becauſe it
is very eaſie. Let us mark theſe three numbers with the Letters
A firſt, B ſecond, C
8[Figure 8]
third. A and C are the
numbers of the ſpaces,
B is the number of the
time; the fourth number
is ſought, of the time
alſo. And becauſe we
know, that look what
proportion the ſpace A,
hath to the ſpuace C, the
ſame proportion ſhall the
ſquare of the time B
have to the ſqare of the
time, which is ſought.
Therefore by the Golden Rule, let the number C be
plied by the ſquare of the number B, and let the product be
vided by the number A, and the quotient ſhall be the ſquare of
the number ſought, and its ſquare root ſhall be the number it ſelf
that is ſought. Now you ſee how eaſie it is to be underſtood.
SAGR. So are all truths, when once they are found out, but the
difficulty lyeth in finding them. I very well apprehend it, and kindly
thank you. And if there remain any other curioſity touching this
point, I pray you let us hear it; for if I may ſpeak my mind, I
will with the favour of Simplicius, that from your diſcourſes I
wayes learn ſome new motion, but from thoſe of his
phers, I do not remember that I have learn't any thing of
ment.
SALV. There might be much more ſaid touching theſe local
motions; but according to agreement, we will reſerve it to a
ticular conference, and for the preſent I will ſpeak ſomething
touching the Author named by Simplicius, who thinketh he hath
given a great advantage to the adverſe party in granting that, that
Canon bullet in falling from the concave of the Moon may
ſcend with a velocity equal to the velocity wherewith it would
1turn round, ſtaying there above, and moving along with the
urnal converſion. Now I tell him, that that ſame ball falling from
the concave unto the centre, will acquire a degree of velocity
much more than double the velocity of the diurnal motion of the
Lunar concave; and this I will make out by ſolid and not

tinent ſuppoſitions. You muſt know therefore that the grave
body falling and acquiring all the way new velocity according
to the proportion already mentioned, hath in any whatſoever
place of the line of its motion ſuch a degree of velocity, that if it
ſhould continue to move therewith, uniformly without farther
encreaſing it; in another time like to that of its deſcent, it would
paſſe a ſpace double to that paſſed in the line of the precedent
motion of deſcent. And thus for example, if that ball in coming
from the concave of the Moon to its centre hath ſpent three hours,
22 min. prim. and 4 ſeconds, I ſay, that being arrived at the
tre, it ſhall find it ſelf conſtituted in ſuch a degree of velocity, that
if with that, without farther encreaſing it, it ſhould continue to
move uniformly, it would in other 3 hours, 22 min. prim. and
4 ſeconds, paſſe double that ſpace, namely as much as the whole
diameter of the Lunar Orb; and becauſe from the Moons
cave to the centre are 196000 miles, which the ball paſſeth in 3
hours 22 prim. min. and 4 ſeconds, therefore (according to what
hath been ſaid) the ball continuing to move with the velocity
which it is found to have in its arrival at the centre, it would
paſſe in other 3 hours 22 min. prim. and 4 ſeconds, a ſpace
ble to that, namely 392000 miles; but the ſame continuing in
the concave of the Moon, which is in circuit 1232000 miles, and
moving therewith in a diurnal motion, it would make in the ſame
time, that is in 3 hours 22 min. prim. and 4 ſeconds, 172880
miles, which are fewer by many than the half of the 392000
miles. You ſee then that the motion in the concave is not as the
modern Author ſaith, that is, of a velocity impoſſible for the
ing ball to partake of, &c.
The falling
able if it move with
a degree of
ty acquired in a
like time with an
uniform motion, it
ſhall paß a ſpace
double to that
ſed with the
leratedmotion.
SAGR. The diſcourſe would paſs for current, and would give
me full ſatisfaction, if that particular was but ſalved, of the
ving of the moveable by a double ſpace to that paſſed in falling
in another time equal to that of the deſcent, in caſe it doth continue
to move uniformly with the greateſt degree of velocity acquired
in deſcending. A propoſition which you alſo once before
ſed as true, but never demonſtrated.
SALV. This is one of the demonſtrations of Our Friend, and
you ſhall ſee it in due time; but for the preſent, I will with ſome
conjectures (not teach you any thing that is new, but) remember you
of a certain contrary opinion, and ſhew you, that it may haply ſo be.
A bullet of lead hanging in a long and fine thread faſtened to the
1roof, if we remove it far from perpendicularity, and then let it go,
have you not obſerved that, it declining, will paſs freely, and well
near as far to the other ſide of the perpendicular?
SAGR. I have obſerved it very well, and find (eſpecially if the
plummet be of any conſiderable weight) that it riſeth ſo little leſs
than it deſcended, ſo that I have ſometimes thought, that the
ſcending arch is equal to that deſcending, and thereupon made it
a queſtion whether the vibrations might not perpetuate themſelves;
and I believe that they might, if that it were poſſible to remove

the impediment of the Air, which reſiſting penetration, doth ſome
ſmall matter retard and impede the motion of the pendulum,
though indeed that impediment is but ſmall: in favour of which
opinion the great number of vibrations that are made before the
moveable wholly ceaſeth to move, ſeems to plead.
The motion of
grave penduli
might be
ted, impediments
being removed.
SALV. The motion would not be perpetual, Sagredus,
though the impediment of the Air were totally removed, becauſe
there is another much more abſtruſe.
SAGR. And what is that? as for my part I can think of no
other?
SALV. You will be pleaſed when you hear it, but I ſhall not
tell it you till anon: in the mean time, let us proceed. I have
propoſed the obſervation of this Pendulum, to the intent, that you
ſhould underſtand, that the impetus acquired in the deſcending
arch, where the motion is natural, is of it ſelf able to drive the
ſaid ball with a violent motion, as far on the other ſide in the like
aſcending arch; if ſo, I ſay, of it ſelf, all external impediments
being removed: I believe alſo that every one takes it for granted,
that as in the deſcending arch the velocity all the way increaſeth,
till it come to the loweſt point, or its perpendicularity; ſo from
this point, by the other aſcending arch, it all the wav diminiſheth,
untill it come to its extreme and higheſt point: and diminiſhing
with the ſame proportions, where with it did before increaſe, ſo that
the dgrees of the velocities in the points equidiſtant from the point
of perpendicularity, are equal to each other. Hence it ſeemeth
to me (arguing with all due modeſty) that I might eaſily be induced
to believe, that if the Terreſtrial Globe were bored thorow the

centre, a Canon bullet deſcending through that Well, would
quire by that time it came to the centre, ſuch an impulſe of
city, that, it having paſſed beyond the centre, would ſpring it
wards the other way, as great a ſpace, as that was wherewith it had
deſcended, all the way beyond the centre diminiſhing the velocity
with decreaſements like to the increaſements acquired in the
ſcent: and the time ſpent in this ſecond motion of aſcent, I
lieve, would be equal to the time of deſcent. Now if the
able by diminiſhing that its greateſt degree of velocity which it
1had in the centre, ſucceſſively until it come to total extinction,
do carry the moveable in ſuch a time ſuch a certain ſpace, as it had
gone in ſuch a like quantity of time, by the acquiſt of velocity
from the total privation of it until it came to that its greateſt degree;
it ſeemeth very reaſonable, that if it ſhould move always with the
ſaid greateſt degree of velocity it would paſs, in ſuch another
quantity of time, both thoſe ſpaces: For if we do but in our
mind ſucceſſively divide thoſe velocities into riſing and falling
degrees, as v. g. theſe numbers in the margine; ſo that the
firſt ſort unto 10 be ſuppoſed the increaſing velocities, and the
others unto 1, be the decreaſing; and let thoſe of the time
of the deſcent, and the others of the time of the aſcent being
added all together, make as many, as if one of the two ſums of
them had been all of the greateſt degrees, and therefore the
whole ſpace paſſed by all the degrees of the increaſing
ties, and decreaſing, (which put together is the whole
ter) ought to be equal to the ſpace paſſed by the greateſt
cities, that are in number half the aggregate of the increaſing
and decreaſing velocities. I know that I have but obſcurely
expreſſed my ſelf, and I wiſh I may be underſtood.
If the Terreſtrial
Globe were
rated, a grave
dy deſcending by
that bore, would
paß and aſcend as
far beyond the
tre, as it did
ſcend.
SAGR. I think I underſtand you very well; and alſo that I
can in a few words ſhew, that I do underſtand you. You had
a mind to ſay, that the motion begining from reſt, and all the
way increaſing the velocity with equal augmentations, ſuch as
are thoſe of continuate numbers begining at 1, rather at 0,
which repreſenteth the ſtate of reſt, diſpoſed as in the margine:
and continued at pleaſure, ſo as that the leaſt degree may be 0,
and the greateſt v. g. 5, all theſe degrees of velocity wherewith
the moveable is moved, make the ſum of 15; but if the
moveable ſhould move with as many degrees in number as
theſe are, and each of them equal to the biggeſt, which is 5, the
aggregate of all theſe laſt velocities would be double to the
others, namely 30. And therefore the moveable moving with
a like time, but with uniform velocity, which is that of the
higheſt degree 5, ought to paſs a ſpace double to that which it
paſſeth in the accelerate time, which beginneth at the ſtate of reſt.
SALV. According to your quick and piercing way of
hending things, you have explained the whole buſineſs with more
plainneſs than I my ſelf; and put me alſo in mind of adding
thing more: for in the accelerate motion, the augmentation
ing continual, you cannot divide the degrees of velocity, which
continually increaſe, into any determinate number, becauſe
ging every moment, they are evermore infinite. Therefore we
ſhall be the better able to exemplifie our intentions by deſcribing
a Triangle, which let be this A B C, [in Fig. 8.] taking in the
1ſide A C, as many equal parts as we pleaſe, A D, D E, E F, F G,
and drawing by the points D, E, F, G, right lines parallel to the baſe
B C. Now let us imagine the parts marked in the line A C, to be
equal times, and let the parallels drawn by the points D, E, F, G,
repreſent unto us the degrees of velocity accelerated, and
ing equally in equal times; and let the point A be the ſtate of reſt,
from which the moveable departing, hath v. g. in the time A D,
acquired the degree of velocity D H, in the ſecond time we will
ſuppoſe, that it hath increaſed the velocity from D H, as far as to
E I, and ſo ſuppoſing it to have grown greater in the ſucceeding
times, according to the increaſe of the lines F K, G L, &c. but

becauſe the acceleration is made continually from moment to
ment, and not disjunctly from one certain part of time to another;
the point A being put for the loweſt moment of velocity, that is,
for the ſtate of reſt, and A D for the firſt inſtant of time
ing; it is manifeſt, that before the acquiſt of the degree of velocity
D H, made in the time A D, the moveable muſt have paſt by
infinite other leſſer and leſſer degrees gained in the infinite inſtants
that are in the time D A, anſwering the infinite points that are in
the line D A; therefore to repreſent unto us the infinite degrees
of velocity that precede the degree D H, it is neceſſary to imagine
infinite lines ſucceſſively leſſer and leſſer, which are ſuppoſed to
be drawn by the infinite points of the line D A, and parallels to
D H, the which infinite lines repreſent unto us the ſuperficies of
the Triangle A H D, and thus we may imagine any ſpace paſſed
by the moveable, with a motion which begining at reſt, goeth
formly accelerating, to have ſpent and made uſe of infinite degrees
of velocity, increaſing according to the infinite lines that
ing from the point A, are ſuppoſed to be drawn parallel to the
line H D, and to the reſt I E, K F, L G, the motion continuing as
far as one will.
The acceleration
of grave bodies
turally deſcendent,
increaſeth from
moment to moment.
Now let us compleat the whole Parallelogram A M B C, and let
us prolong as far as to the ſide thereof B M, not onely the Parallels
marked in the Triangle, but thoſe infinite others imagined to be
drawn from all the points of the ſide A C; and like as B C, was
the greateſt of thoſe infinite parallels of the Triangle,
ing unto us the greateſt degree of velocity acquired by the
able in the accelerate motion, and the whole ſuperficies of the ſaid
Triangle, was the maſs and ſum of the whole velocity, wherewith
in the time A C it paſſed ſuch a certain ſpace, ſo the parallelogram
is now a maſs and aggregate of a like number of degrees of
locity, but each equal to the greateſt B C, the which maſs of
locities will be double to the maſs of the increaſing velocities in
the Triangle, like as the ſaid Parallelogram is double to the
angle: and therefore if the moveable, that falling did make uſe
1of the accelerated degrees of velocity, anſwering to the triangle
A B C, hath paſſed in ſuch a time ſuch a ſpace, it is very reaſonable
and probable, that making uſe of the uniform velocities anſwering
to the parallelogram, it ſhall paſſe with an even motion in the
ſame time a ſpace double to that paſſed by the accelerate
tion.
SAGR. I am entirely ſatisfied. And if you call this a probable
Diſcourſe, what ſhall the neceſſary demonſtrations be? I wiſh
that in the whole body of common Philoſophy, I could find one
that was but thus
In natural
ences it is not
ceſſary to ſeek
thematicall
dence.
SIMP. It is not neceſſary in natural Philoſophy to ſeek
ſite Mathematical evidence.
SAGR. But this point of motion, is it not a natural queſtion?
and yet I cannot find that Ariſtotle hath demonſtrated any the
leaſt accident of it. But let us no longer divert our intended
Theme, nor do you fail, I pray you Salviatus, to tell me that
which you hinted to me to be the cauſe of the Pendulum's
eſcence, beſides the reſiſtance of the Medium ro penetration.
SALV. Tell me; of two penduli hanging at unequal
ces, doth not that which is faſtned to the longer threed make its
vibrations more ſeldome?
The pendulum
hanging at a
er threed, maketh
its vibrations more
ſeldome than the
pendulum hanging
at a ſhorter threed.
SAGR. Yes, if they be moved to equall diſtances from their
perpendicularity.
SALV. This greater or leſſe elongation importeth nothing at
all, for the ſame pendulum alwayes maketh its reciprocations in
quall times, be they longer or ſhorter, that is, though the pendulum

be little or much removed from its perpendicularity, and if they
are not abſolutely equal, they are inſenſibly different, as
rience may ſhew you: and though they were very unequal, yet
would they not diſcountenance, but favour our cauſe.
fore let us draw the perpendicular A B [in Fig. 9.] and hang from
the point A, upon the threed A C, a plummet C, and another
on the ſame threed alſo, which let be E, and the threed A C, being
removed from its perpendicularity, and then letting go the
mets C and E, they ſhall move by the arches C B D, E G F, and
the plummet E, as hanging at a leſſer diſtance, and withall, as
(by what you ſaid) leſſe removed, will return back again faſter,
and make its vibrations more frequent than the plummet C, and
therefore ſhall hinder the ſaid plummet C, from running ſo much
farther towards the term D, as it would do, if it were free: and
thus the plummet E bringing unto it in every vibration continuall

impediment, it ſhall finally reduce it to quieſcence. Now the
ſame threed, (taking away the middle plummet) is a compoſition
of many grave penduli, that is, each of its parts is ſuch a
lum faſtned neerer and neerer to the point A, and therefore
1ſed to make its vibrations ſucceſſively more and more frequent;
and conſequently is able to bring a continual impediment to the
plummet C; and for a proof that this is ſo, if we do but obſerve
the thread A C, we ſhall ſee it diſtended not directly, but in an
arch; and if inſtead of the thread we take a chain, we ſhall
cern the effect more perſectly; and eſpecially removing the

vity C, to a conſiderable diſtance from the perpendicular A B, for
that the chain being compoſed of many looſe particles, and each of
them of ſome weight, the arches A E C, and A F D, will appear
notably incurvated. By reaſon therefore, that the parts of the
chain, according as they are neerer to the point A, deſire to make
their vibrations more frequent, they permit not the lower parts of
the ſaid chain to ſwing ſo far as naturally they would: and by
continual detracting from the vibrations of the plummet C, they
finally make it ceaſe to move, although the impediment of the air
might be removed.
The vibrations
of the ſame
dulum are made
with the ſame
quency, whether
they be ſmall or
great.
The cauſe which
impedeth the
dulum, and
ceth it to reſt.
The thread or
chain to which a
pendulum is
ned, maketh an
arch, and doth not
ſtretch it ſelfe
ſtreight out in its
vibrations.
SAGR. The books are now come; here take them Simplicius,
and find the place you are in doubt of.
SIMP. See, here it is where he beginneth to argue againſt the
diurnal motion of the Earth, he having firſt confuted the annual.
Motus terræ annuus aſſerrere Copernicanos cogit converſionem
juſdem quotidianam; alias idem terræ Hemiſphærium continenter
ad Solem eſſet converſum obumbrato ſemper averſo. [In Engliſh
thus:] The annual motion of the Earth doth compell the
pernicans to aſſert the daily converſion thereof; otherwiſe the
ſame Hemiſphere of the Earth would be continually turned
wards the Sun, the ſhady ſide being always averſe. And ſo one
half of the Earth would never come to ſee the Sun.
SALV. I find at the very ſirſt ſight, that this man hath not rightly
apprehended the Copernican Hypotheſis, for if he had but taken
notice how he alwayes makes the Axis of the terreſtrial Globe
perpetually parallel to it ſelf, he would not have ſaid, that one
half of the Earth would never ſee the Sun, but that the year
would be one entire natural day, that is, that thorow all parts of
the Earth there would be ſix moneths day, and ſix moneths night,
as it now befalleth to the inhabitants under the Pole, but let
this miſtake be forgiven him, and let us come to what
neth.
SIMP. It followeth, Hanc autem gyrationem Terræ
poſſibilem eſſe ſic demonſtramus. Which ſpeaks in Engliſh thus:
That this gyration of the Earth is impoſſible we thus demonſtrate.
That which enſueth is the declaration of the following figure,
wherein is delineated many deſcending grave bodies, and
ing light bodies, and birds that fly too and again in the air, &c.
SAGR. Let us ſee them, I pray you. Oh! what fine figures,
1what birds, what balls, and what other pretty things are here?
SIMP. Theſe are balls which come from the concave of the
Moon.
SAGR. And what is this?
SIMP. This is a kind of Shell-fiſh, which here at Venice they
call buovoli; and this alſo came from the Moons concave.
SAGR. Indeed, it ſeems then, that the Moon hath a great

er over theſe Oyſter-fiſhes, which we call ^{*} armed ſiſbes.
* Peſci armai, or
armati.
SIMP. And this is that calculation, which I mentioned, of this
Journey in a natural day, in an hour, in a firſt minute, and in a
ſecond, which a point of the Earth would make placed under the
Equinoctial, and alſo in the parallel of 48 gr. And then followeth
this, which I doubted I had committed ſome miſtake in reciting,
therefore let us read it. His poſitis, neceſſe est, terra circulariter
mota, omnia ex aëre eidem, &c. Quod ſi haſce pilas æquales
nemus pondere, magnitudine, gravitate, & in concavo Sphæræ
naris poſitas libero deſcenſui permittamus, ſi motum deorſum
mus celeritate motui circum, (quod tamen ſecus eſt, cum pila A,
&c.) elabentur minimum (ut multum cedamus adverſariis) dies
ſex: quo tempore ſexies circa terram, &c. [In Engliſb thus.]
Theſe things being ſuppoſed, it is neceſſary, the Earth being
cularly moved, that all things from the air to the ſame, &c. So
that if we ſuppoſe theſe balls to be equal in magnitude and
vity, and being placed in the concave of the Lunar Sphere, we
permit them a free deſcent, and if we make the motion
wards equal in velocity to the motion about, (which nevertheleſs
is otherwiſe, if the ball A, &c.) they ſhall be falling at leaſt (that
we may grant much to our adverſaries) ſix dayes; in which time
they ſhall be turned ſix times about the Earth, &c.
SALV. You have but too faithfully cited the argument of this
perſon. From hence you may collect Simplicius, with what
tion they ought to proceed, who would give themſelves up to
lieve others in thoſe things, which perhaps they do not believe
themſelves. For me thinks it a thing impoſſible, but that this
thor was adviſed, that he did deſign to himſelf a circle, whoſe
meter (which amongſt Mathematicians, is leſſe than one third part
of the circumference) is above 72 times bigger than it ſelf: an
errour that affirmeth that to be conſiderably more than 200,
which is leſſe than one.
SAGR. It may be, that theſe Mathematical proportions, which
are true in abſtract, being once applied in concrete to Phyſical and
Elementary circles, do not ſo exactly agree: And yet, I think,
that the Cooper, to find the ſemidiameter of the bottom, which he
is to fit to the Cask, doth make uſe of the rule of Mathematicians
in abſtract, although ſuch bottomes be things meerly material,
1and concrete: therefore let Simplicius plead in excuſe of this
Author; and whether he chinks that the Phyſicks can differ ſo
very much from the Mathematicks.
SIMP. The ſubſtractions are in my opinion inſufficient to ſalve
this difference, which is ſo extreamly too great to be reconciled:
and in this caſe I have no more to ſay but that, Quandoque bonus
dormitet Homerus. But ſuppoſing the calculation of ^{*} Salviatus

to be more exact, and that the time of the deſcent of the ball
were no more than three hours; yet me thinks, that coming from
the concave of the Moon, which is ſo great a diſtance off, it would
be an admirable thing, that it ſhould have an inſtinct of
ing it ſelf all the way over the ſelf-ſame point of the Earth, over
which it did hang in its departure thence and not rather be left a
very great way behind.
* Not
dus, as the Latine
ha hit.
SALV. The effect may be admirable, and not admirable, but
natural and ordinary, according as the things precedent may fall
out. For if the ball (according to the Authors ſuppoſitions)
whilſt it ſtaid in the concave of the Moon, had the circular motion
of twenty four hours together with the Earth, and with the reſt of
the things contained within the ſaid Concave; that very vertue
which made it turn round before its deſcent, will continue it in
the ſame motion in its deſcending. And ſo far it is from not
ing pace with the motion of the Earth, and from ſtaying behind,
that it is more likely to out-go it; being that in its approaches to
the Earth, the motion of gyration is to be made with circles
tinually leſſer and leſſer; ſo that the ball retaining in it ſelf that
ſelf-ſame velocity which it had in the concave, it ought to
pate, as I have ſaid, the vertigo or converſion of the Earth. But
if the ball in the concave did want that circulation, it is not
ged in deſcending to maintain it ſelf perpendicularly over that
point of the Earth, which was juſt under it when the deſcent
gan. Nor will Copernicus, or any of his followers affirm the
ſame.
SIMP. But the Author maketh an objection, as you ſee,
manding on what principle this circular motion of grave and light
bodies, doth depend: that is, whether upon an internal or an
ternal principle.
SALV. Keeping to the Probleme of which we ſpeak, I ſay,
that that very principle which made the ball turn round, whil'ſt it
was in the Lunar concave, is the ſame that maintaineth alſo the
circulation in the deſcent: yet I leave the Author at liberty to
make it internal or external at his pleaſure.
SIMP. The Author proveth, that it can neither be inward nor
outward.
SALV. And I will ſay then, that the ball in the concave did
1not move, and ſo he ſhall not be bound to ſhew how that in
cending it continueth all the way vertically over one point, for
that it will not do any ſuch thing.
SIMP. Very well; But if grave bodies, and light can have no
principle, either internal or external of moving circularly, than
neither can the terreſtrial Globe move with a circular motion: and
thus you have the intent of the Author.
SALV. I did not ſay, that the Earth had no principle, either
interne, or externe to the motion of gyration, but I ſay, that I do
not know which of the two it hath; and yet my not knowing it
hath not a power to deprive it of the ſame; but if this Author
can tell by what principle other mundane bodies are moved round,
of whoſe motion there is no doubt; I ſay, that that which
keth the Earth to move, is a vertue, like to that, by which Mars
and Jupiter are moved, and wherewith he believes that the ſtarry
Sphere it ſelf alſo doth move; and if he will but aſſure me, who is
the mover of one of theſe moveables, I will undertake to be able
to tell him who maketh the Earth to move. Nay more; I will
undertake to do the ſame, if he can but tell me, who moveth the
parts of the Earth downwards.
SIMP. The cauſe of this is moſt manifeſt, and every one knows
that it is gravity.
SALV. You are out, Simplicius, you ſhould ſay, that every
one knowes, that it is called Gravity: but I do not queſtion you
about the name, but the eſſence of the thing, of which eſſence
you know not a tittle more than you know the eſſence of the
mover of the ſtars in gyration; unleſſe it be the name that hath
been put to this, and made familiar, and domeſtical, by the many

experiences which we ſee thereof every hour in the day,: but not
as if we really underſtand any more, what principle or vertue that
is which moveth a ſtone downwards, than we know who moveth
it upwards, when it is ſeparated from the projicient, or who
veth the Moon round, except (as I have ſaid) onely the name,
which more particularly and properly we have aſſigned to the
tion of deſcent, namely, Gravity; whereas for the cauſe of
cular motion, in more general termes, we aſſign the Vertue
ſed, and call the ſame an Intelligence, either aſſiſting, or informing;
and to infinite other motions we aſcribe Nature for their cauſe.
We know no more
who moveth grave
bodies downwards;
than who moveth
the Stars round,
nor know we any
thing of theſe
ſes, more than the
names impoſed on
them by us.
SIMP. It is my opinion, that this Author asketh far leſſe than
that, to which you deny to make anſwer; for he doth not ask
what is nominally and particularly the principle that moveth
grave and light bodies circularly, but whatſoever it be, he
reth to know, whether you think it intrinſecal, or extrinſecal:
For howbeit, v. gr. I do not know, what kind of thing that gravity
is, by which the Earth deſcendeth; yet I know that it is an intern
1principle, ſeeing that if it be not hindered, it moveth
ouſly: and on the contrary, I know that the principle which
veth it upwards, is external, although that I do not know, what
thing that vertue is, impreſſed on it by the projicient.
SALV. Into how many queſtions muſt we excurre, if we would
decide all the difficulties, which ſucceſſively have dependance one
upon another! You call that an external (and you alſo call it a
preternatural and violent) principle, which moveth the grave
ject upwards; but its poſſible that it may be no leſſe interne and
natural, than that which moveth it downwards; it may

ture be called external and violent, ſo long as the moveable is
ned to the projicient; but being ſeparated, what external thing
remaineth for a mover of the arrow, or ball? In ſumme, it muſt
neceſſarliy be granted, that that vertue which carrieth ſuch a
able upwards, is no leſſe interne, than that which moveth it
wards; and I think the motion of grave bodies aſcending by the
impetus conceived, to be altogether as natural, as the motion of
deſcent depending on gravity.
The vertue which
carrieth grave
jects upwards, is
no leſſe natural to
them, than the
gravity which
veth them
wards.
SIMP. I will never grant this; for the motion of deſcent hath
its principle internal, natural, and perpetual, and the motion of
aſcent hath its principle externe, violent, and finite.
SALV. If you refuſe to grant me, that the principles of the
motions of grave bodies downwards and upwards, are equally

ternal and natural; what would you do, if I ſhould ſay, that they
may alſo be the ſame in number?
Contrary
ciples cannot
rally reſide in the
ſame ſubject.
SIMP. I leave it to you to judge.
SALV. But I deſire you your ſelf to be the Judge: Therefore
tell me, Do you believe that in the ſame natural body, there may
reſide interne principles, that are contrary to one another?
SIMP. I do verily believe there cannot.
SALV. What do you think to be the natural inclination of
Earth, of Lead, of Gold, and in ſum, of the moſt ponderous
ters; that is, to what motion do you believe that their interne
principle draweth them?
SIMP. To that towards the centre of things grave, that is, to
the centre of the Univerſe, and of the Earth, whither, if they be
not hindered, it will carry them.
SALV. So that, if the Terreſtrial Globe were bored thorow,
and a Well made that ſhould paſſe through the centre of it, a
Cannon bullet being let fall into the ſame, as being moved by a
natural and intrinſick principle, would paſſe to the centre; and it
would make all this motion ſpontaneouſly, and by intrinſick
ciple, is it not ſo?
SIMP. So I verily believe.
SALV. But when it is arrived at the centre, do you think that
1it will paſſe any further, or elſe that there it would immediately
ſtand ſtill, and move no further?
SIMP. I believe that it would continue to move a great way
further.
SALV. But this motion beyond the centre, would it not be
wards, and according to your aſſertion preternatural, and violent?
And yet on what other principle do you make it to depend, but
only upon the ſelf ſame, which did carry the ball to the centre,
and which you called intrinſecal, and natural? Finde, if you can,
another external projicient, that overtaketh it again to drive it
upwards. And this that hath been ſaid of the motion thorow
the centre, is alſo ſeen by us here above; for the interne impetus

of a grave body falling along a declining ſuperficies, if the ſaid
ſuperficies be reflected the other way, it ſhall carry it, without a
jot interrupting the motion, alſo upwards. A ball of lead that
hangeth by a thread, being removed from its perpendicularity,
ſcendeth ſpontaneouſly, as being drawn by its internal inclination,
and without any interpoſure of reſt, paſſeth beyond the loweſt
point of perpendicularity: and without any additional mover,
moveth upwards. I know that you will not deny, but that the
principle of grave bodies that moveth them downwards, is no leſs
natural, and intrinſecal, than that principle of light bodies, which
moveth them upwards: ſo that I propoſe to your conſideration a
ball of lead, which deſcending through the Air from a great
titude, and ſo moving by an intern principle, and comming to a
depth of water, continueth its deſcent, and without any other
terne mover, ſubmergeth a great way; and yet the motion of
deſcent in the water is preternatural unto it; but yet nevertheleſs
dependeth on a principle that is internal, and not external to the
ball. You ſee it demonſtrated then, that a moveable may be
moved by one and the ſame internal principle, with contrary
tions.
The natural
tion changeth it
ſelfe into that
which is called
ternatural and
olent.
SIMP. I believe there are ſolutions to all theſe objections,
though for the preſent I do not remember them; but however it
be, the Author continueth to demand, on what principle this
cular motion of grave and light bodies dependeth; that is,
ther on a principle internal, or external; and proceeding
wards, ſheweth, that it can be neither on the one, nor on the other,
ſaying; Si ab externo; Deuſne illum excitat per continuum
culum? an verò Angelus, an aër? Et hunc quidem multi
nant. Sed contra----[In Engliſh thus] If from an externe
ciple; Whether God doth not excite it by a continued Miracle?
or an Angel, or the Air? And indeed many do aſſign this. But
on the contrary-----.
SALV. Trouble not your ſelf to read his argument; for I am
1none of thoſe who aſcribe that principle to the ambient air. As
to the Miracle, or an Angel, I ſhould rather incline to this ſide; for
that which taketh beginning from a Divine Miracle, or from an
Angelical operation; as for inſtance, the tranſportation of a
non ball or bullet into the concave of the Moon, doth in all
bability depend on the vertue of the ſame principle for
ing the reſt. But, as to the Air, it ſerveth my turn, that it doth
not hinder the circular motion of the moveables, which we did
ſuppoſe to move thorow it. And to prove that, it ſufficeth (nor is
more required) that it moveth with the ſame motion, and
eth its circulations with the ſame velocity, that the Terreſtrial
Globe doth.
SIMP. And he likewiſe makes his oppoſition to this alſo;
demanding who carrieth the air about, Nature, or Violence?
And proveth, that it cannot be Nature, alledging that that is
trary to truth, experience, and to Copernicus himſelf.
SALV. It is not contrary to Copernicus in the leaſt, who writeth
no ſuch thing; and this Author aſcribes theſe things to him with
two exceſſive courteſie. It's true, he ſaith, and for my part I
think he ſaith well, that the part of the air neer to the Earth,
ing rather a terreſtrial evaporation, may have the ſame nature,
and naturally follow its motion; or, as being contiguous to it,
may follow it in the ſame manner, as the Peripateticks ſay, that
the ſuperiour part of it, and the Element of fire, follow the
tion of the Lunar Concave, ſo that it lyeth upon them to declare,
whether that motion be natural, or violent.
SIMP. The Author will reply, that if Copernicus maketh only
the inferiour part of the Air to move, and ſuppoſeth the upper
part thereof to want the ſaid motion, he cannot give a reaſon, how
that quiet air can be able to carry thoſe grave bodies along with
it, and make them keep pace with the motion of the Earth.
SALV. Copernicus will ſay, that this natural propenſion of the

elementary bodies to ſollow the motion of the Earth, hath a
mited Sphere, out of which ſuch a natural inclination would ceaſe;
beſides that, as I have ſaid, the Air is not that which carrieth the
moveables along with it; which being ſeparated from the Earth,
do follow its motion; ſo that all the objections come to nothing,
which this Author produceth to prove, that the Air cannot cauſe
ſuch effects.
The propenſion
of elementary
dies to follow the
Earth, hath a
mited Sphere of
activity.
SIMP. To ſhew therefore, that that cannot be, it will be
ſary to ſay, that ſuch like effects depend on an interne principle,
againſt which poſition, oboriuntur difficillimæ, immò inextricabiles
quæſtiones ſecundæ, of which ſort are theſe that follow.
pium illud internum vel eſt accidens, vel ſubſtantia. Si primum;
quale nam illud? nam qualitas locomotiva circum, hactenus nulla
1videtur agnita. (In Engliſh thus:) Contrary to which poſition
there do ariſe moſt difficult, yea inextricable ſecond queſtions,
ſuch as theſe; That intern principle is either an accident, or a
ſubſtance. If the firſt; what manner of accident is it? For a
locomotive quality about the centre, ſeemeth to be hitherto
knowledged by none.
SALV. How, is there no ſuch thing acknowledged? Is it not
known to us, that all theſe elementary matters move round,
gether with the Earth? You ſee how this Author ſuppoſeth for
true, that which is in queſtion.
SIMP. He ſaith, that we do not ſee the ſame; and me thinks,
he hath therein reaſon on his ſide.
SALV. We ſee it not, becauſe we turn round together with
them.
SIMP. Hear his other Argument. Quæ etiam ſi eſſet,
modo tamen inveniretur in rebus tam contrariis? in igne, ut in
quâ; in aëre, ut in terra; in viventibus, ut in anima carentibus?
[in Engliſh thus:] Which although it were, yet how could it be
found in things ſo contrary? in the fire, as in the water? in the
air, as in the earth? in living creatures, as in things wanting
life?
SALV. Suppoſing for this time, that water and fire are
ries; as alſo the air and earth; (of which yet much may be ſaid)
the moſt that could follow from thence would be, that thoſe
tions cannot be common to them, that are contrary to one
ther: ſo that v. g. the motion upwards, which naturally agreeth
to fire, cannot agree to water; but that, like as it is by nature
trary to fire: ſo to it that motion ſuiteth, which is contrary to the
motion of fire, which ſhall be the motion deorſùm; but the
cular motion, which is not contrary either to the motion ſurſùm,
or to the motion deorſùm, but may mix with both, as Aristotle
himſelf affirmeth, why may it not equally ſuit with grave bodies
and with light? The motions in the next place, which cannot be
common to things alive, and dead, are thoſe which depend on the
ſoul: but thoſe which belong to the body, in as much as it is
mentary, and conſequently participateth of the qualities of the
lements, why may not they be common as well to the dead corps,
as to the living body? And therefore, if the circular motion be
proper to the elements, it ought to be common to the mixt bodies
alſo.
SAGR. It muſt needs be, that this Author holdeth, that a dead
cat, falling from a window, it is not poſſible that a live cat alſo
could fall; it not being a thing convenient, that a carcaſe ſhould
partake of the qualities which ſuit with things alive.
SALV. Therefore the diſcourſe of this Author concludeth
1nothing againſt one that ſhould affirm, that the principle of the
cular motions of grave and light bodies is an intern accident: I
know not how he may prove, that it cannot be a ſubſtance.
SIMP. He brings many Arguments againſt this. The firſt of
which is in theſe words: Si ſecundum (nempè, ſi dieas tale
pium eſſe ſubſtantiam) illud eſt aut materia, aut forma, aut
ſitum. Sed repugnant iterum tot diverſæ rerum naturæ, quales
ſunt aves, limaces, ſaxa, ſagittæ, nives, fumi, grandines, piſces,
&c. quæ tamen omnia ſpecie & genere differentia, moverentur à
naturâ ſuâ circulariter, ipſa naturis diverſiſſima, &c. [In Engliſh
thus] If the ſecond, (that is, if you ſhall ſay that this principle is
a ſubſtance) it is either matter, or form, or a compound of both.
But ſuch diverſe natures of things are again repugnant, ſuch as are
birds, ſnails, ſtones, darts, ſnows, ſmoaks, hails, fiſhes, &c. all
which notwithſtanding their differences in ſpecies and kind, are
moved of their own nature circularly, they being of their natures
moſt different, &c.
SALV. If theſe things before named are of diverſe natures, and
things of diverſe natures cannot have a motion in common, it muſt
follow, if you would give ſatisfaction to all, that you are to think
of, more than two motions onely of upwards and downwards: and
if there muſt be one for the arrows, another for the ſnails, another
for the ſtones, and another for fiſhes; then are you to bethink your
ſelf of worms, topazes and muſhrums, which are not leſs different
in nature from one another, than ſnow and hail.
SIMP. It ſeems that you make a jeſt of theſe Arguments.
SALV. No indeed, Simplicius, but it hath been already
ſwered above, to wit, that if one motion, whether downwards or
upwards, can agree with all thoſe things afore named, a circular
motion may no leſs agree with them: and as you are a
tick, do not you put a greater difference between an elementary
comet and a celeftial ſtar, than between a fiſh and a bird? and
yet both thoſe move circularly. Now propoſe your ſecond
gument.
SIMP. Si terra ſtaret per voluntatem Dei, rotaréntne cætera, an
non? ſi hoc, falſum eſt à naturâ gyrare; ſi illud, redeunt priores
quæſtiones. Et ſanè mirum eſſet, quòd Gavia piſciculo, Alauda
nidulo ſuo, & corvus limaci, petraque, etiam volans, imminere
non poſſet. [Which I thus render:] If the Earth be ſuppoſed to
ſtand ſtill by the will of God, ſhould the reſt of bodies turn round
or no? If not, then it's falſe that they are revolved by nature; if
the other, the former queſtions will return upon us. And
truly it would be ſtrange that the Sea-pie ſhould not be able to
hover over the ſmall fiſh, the Lark over her neſt, and the Crow
ver the ſnail and rock, though flying.
1
SALV. I would anſwer for my ſelf in general terms, that if
it were appointed by the will of God, that the Earth ſhould ceaſe
from its diurnal revolution, thoſe birds would do what ever ſhould
pleaſe the ſame Divine will. But if this Author deſire a more
particular anſwer, I ſhould tell him, that they would do quite
trary to what they do now, if whilſt they, being ſeparated from
the Earth, do bear themſelves up in the air, the Terreſtrial Globe
by the will of God, ſhould all on a ſudden be put upon a
tate motion; it concerneth this Author now to aſcertain us what
would in this caſe ſucceed.
SAGR. I pray you, Salviatus, at my requeſt to grant to this
Author, that the Earth ſtanding ſtill by the will of God, the other
things, ſeparated from it, would continue to turn round of their
own natural motion, and let us hear what impoſſibilities or
veniences would follow: for I, as to my own particular, do not
ſee how there can be greater diſorders, than theſe produced by the
Author himſelf, that is, that Larks, though they ſhould flie, could
not be able to hover over their neſts, nor Crows over ſnails, or
rocks: from whence would follow, that Crows muſt ſuffer for
want of ſnails, and young Larks muſt die of hunger, and cold, not
being able to be fed or ſheltered by the wings of the old ones.
This is all the ruine that I can conceive would follow, ſuppoſing
the Authors ſpeech to be true. Do you ſee, Simplicius, if
ter inconveniences would happen?
SIMP. I know not how to diſcover greater; but it is very
dible, that the Author beſides theſe, diſcovered other diſorders in
Nature, which perhaps in reverend reſpect of her, he was not
ing to inſtance in. Therefore let us proceed to the third
ction. Inſuper quî fit, ut istæ res tam variæ tantùm moveantur
ab Occaſu in Ortum, parallelæ ad Æquatorem? ut ſemper
tur, nunquam quieſcant? [which ſpeaks to this ſenſe:] Moreover,
how comes it to paſs that theſe things, ſo diverſe, are onely moved
from the Weſt towards the Eaſt, parallel to the Æquinoctial?
that they always move, and never reſt?
SALV. They move from Weſt to Eaſt parallel to the
noctial without ceaſing, in the ſame manner as you believe the
fixed ſtars to move from Eaſt to Weſt, parallel to the
al, without ever reſting.
SIMP. Quarè, quò ſunt altiores, celeriùs; quò humiliores,
diùs? (i. e.) Why are the higher the ſwifter, and the lower the
ſlower?
SALV. Becauſe that in a Sphere or circle, that turns about
on its own centre, the remoter parts deſcribe greater circuits, and
the parts nearer at hand deſcribe leſſer in the ſame time.
SIMP. Quare, quæ Æquinoctiali propriores, in majori; quæ
1remotiores, in minori circulo feruntur? [ſcilicet:] Why are
thoſe near the Æquinoctial carried about in a greater circle, and
thoſe which are remote in a leſſer?
SALV. To imitate the ſtarry Sphere, in which thoſe neareſt
to the Æquinoctial, move in greater circles, than the more
mote.
SIMP. Quarè Pila eadem ſub Æquinoctiali tota circa centrum
terr æ, ambitu maximo, celeritate incredibili; ſub Polo verò circa
centrum proprium, gyro nullo, tarditate ſupremâ volveretur?
[That is:] Why is the ſame ball under the Æquinoctial wholly
turned round the centre of the Earth in the greateſt
rence, with an incredible celerity; but under the Pole about its
own centre, in no circuite, but with the ultimate degree of
dity?
SALV. To imitate the ſtars of the Firmament, that would do
the like if they had the diurnal motion.
SIMP. Quare eadem res, pila v. g. plumbea, ſi ſemel terram
circuivit, deſcripto circulo maximo, eandem ubique non
migret ſecundùm circulum maximum, ſed tranſlata extra
ctialem in circulis minoribus agetur? [Which ſpeaketh thus:]
Why doth not the ſame thing, as for example, a ball of lead
turn round every where according to the ſame great circle, if once
deſcribing a great circle, it hath incompaſſed the Earth, but being
removed from the Æquinoctial, doth move in leſſer circles?
SALV. Becauſe ſo would, nay, according to the doctrine of
Ptolomey, ſo have ſome fixed ſtars done, which once were very
near the Æquinoctial, and deſcribed very vaſt circles, and now that
they are farther off, deſcribe leſſer.
SAGR. If I could now but keep in mind all theſe fine
tions, I ſhould think that I had made a great purchaſe; I muſt
needs intreat you, Simplicius, to lend me this Book, for there
not chuſe but be a ſea of rare and ingenious matters contained in
it.
SIMP. I will preſent you with it.
SAGR. Not ſo, Sir; I would not deprive you of it: but are
the Queries yet at an end?
SIMP. No Sir; hearken therefore. Si latio circularis
vibus & levibus eſt naturalis, qualis eſt ea quæ fit ſecundùm
am rectam? Nam ſi naturalis, quomodo & is motus qui circum est,
naturalis eſt, cùm ſpecie differat à recto? Si violentus, quî fit, ut
miſſile ignitum ſurſùm evolans ſcintilloſum caput ſurſùm à terrâ,
non autem circum volvatur, &c. [Which take in our idiom:] If
a circular lation is natural to heavy and light things, what is that
which is made according to a right line? For if it be natural, how
then is that motion which is about the centre natural, ſeeing it
1differs in ſpecies from a right motion? If it be violent, how is it
that a fiery dart flying upwards, ſparkling over our heads at a
ſtance from the Earth, but not turning about, &c.
Of the mixt
tion we ſee not the
part that is
lar, becauſe we
partake thereof.
SALV. It hath been ſaid already very often, that the circular
motion is natural to the whole, and to its parts, whilſt they are in
perfect diſpoſure, and the right is to reduce to order the parts
diſordered; though indeed it is better to ſay, that neither the
parts ordered or diſordered ever move with a right motion, but
with one mixed, which might as well be averred meerly circular:
but to us but one part onely of this motion is viſible and
vable, that is, the part of the right, the other part of the circular
being imperceptible to us, becauſe we partake thereof. And this
anſwers to the rays which move upwards, and round about, but we
cannot diſtinguiſh their circular motion, for that, with that we our
ſelves move alſo. But I believe that this Author never thought
of this mixture; for you may ſee that he reſolutely ſaith, that the
rays go directly upwards, and not at all in gyration.
SIMP. Quare centrum ſphære delapſæ ſub Æquatore ſpiram
ſcribit in ejus plano: ſub aliis parallelis ſpiram deſcribit in cono?
ſub Polo deſcendit in axe lineam gyralem, decurrens in ſuperficie
cylindricâ conſignatam? (In Engliſh to this purpoſe:) Why doth
the centre of a falling Globe under the Æquinoctial deſcribe a
ſpiral line in the plane of the Æquator; and in other parallels
a ſpiral about a Cone; and under the Pole deſcend in the
axis deſcribing a gyral line, running in a Cylindrical
cies?
SALV. Becauſe of the lines drawn from the Centre to the
cumference of the ſphere, which are thoſe by which graves
fcend, that which terminates in the Æquinoctial deſigneth a
cle, and thoſe that terminate in other parallels deſcribe conical
ſuperficies; now the axis deſcribeth nothing at all, but continueth
in its own being. And if I may give you my judgment freely, I
will ſay, that I cannot draw from all theſe Queries, any ſenſe that
interfereth with the motion of the Earth; for if I demand of this
Author, (granting him that the Earth doth not move) what would
follow in all theſe particulars, ſuppoſing that it do move, as
pernicus will have it; I am very confident, that he would ſay that
all theſe effects would happen, that he hath objected, as
niences to diſprove its mobility: ſo that in this mans opinion
ceſſary conſequences are accounted abſurdities: but I beſeech
you, if there be any more, diſpatch them, and free us ſpeedily
from this weariſom task.
SIMP. In this which follows he oppoſes Copernicus & his Sectators,
who affirm, that the motion of the parts ſeparated from their whole,
is onely to unite themſelves to their whole; but that the moving
1circularly along with the vertigenous diurnal revolution is
lutely natural: againſt which he objecteth, ſaying, that according
to theſe mens opinion; Si tota terra, unà cum aquâ in nihilum
redigeretur, nulla grando aut pluvia è nube decideret, ſed
raliter tantùm circumferetur, neque ignis ullus, aut igneum
deret, cùm illorum non improbabili ſententià ignis nullus ſit ſuprà.
[Which I tranſlate to this ſenſe:] If the whole Earth, together
with the Water were reduced into nothing, no hail or rain would
fall from the clouds, but would be onely naturally carried round;
neither any fire or fiery thing would aſcend, ſeeing to theſe that men
it is no improbable opinion that there is no fire above.
SALV. The providence of this Philoſopher is admirable, and
worthy of great applauſe, for he is not content to provide for
things that might happen, the courſe of Nature continuing, but
will ſhew hic care in what may follow from thoſe things that he
very well knows ſhall never come to paſs. I will grant him
fore, (that I may get ſom pretty paſſages out of him) that if the
Earth and Water ſhould be reduced to nothing, there would be no
more hails or rains, nor would igneal matters aſcend any longer
upwards, but would continually turn round: what will follow?
what will the Philoſopher ſay then?
SIMP. The objection is in the words which immediately
low; here they are: Quibus tamen experientia & ratio
ſatur. Which nevertheleſs (ſaith he) is contrary to experience and
reaſon.
SALV. Now I muſt yield, ſeeing he hath ſo great an
tage of me as experience, of which I am unprovided. For as yet
I never had the fortune to ſee the Terreſtrial Globe and the
ment of Water turn'd to nothing, ſo as to have been able to
ſerve what the hail and water did in that little Chaos. But he
perhaps tells us for our inſtruction what they did.
SIMP. No, he doth not.
SALV. I would give any thing to change a word or two with
this perſon, to ask him, whether when this Globe vaniſhed, it
ried away with it the common centre of gravity, as I believe it did;
in which caſe, I think that the hail and water would remain
ſate and ſtupid amongſt the clouds, without knowing what to do
with themſelves. It might be alſo, that attracted by that great
void Vacuum, left by the Earths abſenting, all the ambients would
be rarified, and particularly, the air, which is extreme eaſily drawn,
and would run thither with very great haſte to fill it up. And
perhaps the more ſolid and material bodies, as birds, (for there
would in all probability be many of them ſcattered up and down
in the air) would retire more towards the centre of the great
cant ſphere; (for it ſeemeth very reaſonable, that ſubſtances that
1under ſmall bulk contain much matter, ſhould have narrower
ces aſſigned them, leaving the more ſpacious to the more rarified)
and there being dead of hunger, and reſolved into Earth, would
form a new little Globe, with that little water, which at that time
was among the clouds. It might be alſo, that thoſe matters as
not beholding the light, would not perceive the Earths departure,
but like blind things, would deſcend according to their uſual cuſtom
to the centre, whither they would now go, if that globe did not
hinder them. And laſtly, that I may give this Philoſopher a leſs
irreſolute anſwer, I do tell him, that I know as much of what
would follow upon the annihilation of the Terreſtrial Globe, as
he would have done that was to have followed in and about the
ſame, before it was created. And becauſe I am certain he will
ſay, that he would never have been able to have known any of
all thoſe things which experience alone hath made him knowing
in, he ought not to deny me pardon, and to excuſe me if I know
not that which he knows, touching what would enſue upon the
annihilation of the ſaid Globe: for that I want that experience
which he hath. Let us hear if he have any thing elſe to ſay.
SIMP. There remains this figure, which repreſents the
ſtrial Globe with a great cavity about its centre, full of air; and
to ſhew that Graves move not downwards to unite with the
reſtrial Globe, as Copernicus ſaith, he conſtituteth this ſtone in
the centre; and demandeth, it being left at liberty, what it would
do; and he placeth another in the ſpace of this great vacuum, and
asketh the ſame queſtion. Saying, as to the firſt: Lapis in centro
conſtitutus, aut aſcendet ad terram in punctum aliquod, aut non. Si
ſecundum; falſum est, partes ob ſolam ſejunctionem à toto, ad
lud moveri. Si primum; omnis ratio & experientia renititur,
neque gravia in ſuœ gravitatis centro conquieſcent. Item ſi
ſpenſus lapis, liberatus decidat in centrum, ſeparabit ſe à toto,
tra Copernicum: ſi pendeat, refragatur omnis experientia, cùm
videamus integros fornices corruere. (Wherein he ſaith:) The
ſtone placed in the centre, either aſcendeth to the Earth in ſome
point, or no. If the ſecond, it is falſe that the parts ſeparated
from the whole, move unto it. If the firſt; it contradicteth all
reaſon and experience, nor doth the grave body reſt in the centre
of its gravity. And if the ſtone being ſuſpended in the air, be let
go, do deſcend to the centre, it will ſeparate from its whole,
trary to Copernicus: if it do hang in the air, it contradicteth all
experience: ſince we ſee whole Vaults to fall down.
SALV. I will anſwer, though with great diſadvantage to my
ſelf, ſeeing I have to do with one who hath ſeen by experience,
what theſe ſtones do in this great Cave: a thing, which for my
part I have not ſeen; and will ſay, that things grave have an
1ſtence before the common centre of gravity: ſo that it is not one

centre alone, which is no other than indiviſible point, and therefore
of no efficacie, that can attract unto it grave matters; but that thoſe
matters conſpiring naturally to unite, form to themſelves a
mon centre, which is that about which parts of equal moment
conſiſt: ſo that I hold, that if the great aggregate of grave

dies were gathered all into any one place, the ſmall parts that were
ſeparated from their whole, would follow the ſame, and if they
were not hindered, would penetrate wherever they ſhould find
parts leſs grave than themſelves: but coming where they ſhould
meet with matters more grave, they would deſcend no farther.
And therefore I hold, that in the Cave full of air, the whole Vault
would preſs, and violently reſt it ſelf onely upon that air, in caſe
its hardneſs could not be overcome and broken by its gravity; but
looſe ſtones, I believe, would deſcend to the centre, and not ſwim
above in the air: nor may it be ſaid, that they move not to their
whole, though they move whither all the parts of the whole
would transfer themſelves, if all impediments were removed.
Things grave are
before the centre of
gravity.
The great maſs
of grave bodies
ing transferred out
of their place, the
ſeparated parts
would follow that
maß.
SIMP. That which remaineth, is a certain Errour which he
ſerveth in a Diſciple of Copernicus, who making the Earth to
move with an annual motion, and a diurnal, in the ſame manner
as the Cart-wheel moveth upon the circle of the Earth, and in it
ſelf, did conſtitute the Terreſtrial Globe too great, or the great
Orb too little; for that 365 revolutions of the Æquinoctial, are
leſs by far than the circumference of the great Orb.
SALV. Take notice that you miſtake, and tell us the direct
contrary to what muſt needs be written in that Book; for you
ſhould ſay, that that ſame Copernican Author did conſtitute the
Terreſtrial Globe too little, and the great Orb too big; and not
the Terreſtrial Globe too big, and the annual too little.
SIMP. The miſtake is not mine; ſee here the words of the
Book. Non videt, quòd vel circulum annuum æquo minorem, vel
orbem terreum juſto multò fabricet majorem. (In Engliſh thus:)
He ſeeth not, that he either maketh the annual circle equal to the
leſs, or the Terreſtrial Orb much too big.
SALV. I cannot tell whether the firſt Author erred or no, ſince
the Author of this Tractate doth not name him; but the error of
this Book is certain and unpardonable, whether that follower of
Copernicus erred or not erred; for that your Author paſſeth by ſo
material an error, without either detecting or correcting it. But
let him be forgiven this fault, as an error rather of inadvertencie,
than of any thing elſe: Farthermore, were it not, that I am
ready wearied and tired with talking and ſpending ſo mnch time
with very little profit, in theſe frivolous janglings and
tions, I could ſhew, that it is not impoſſible for a circle, though
1
no bigger than a Cart-wheel, with making not 365, but leſſe than
20 revolutions, to deſcribe and meaſure the circumference, not
onely of the grand Orb, but of one a thouſand times greater;
and this I ſ y to ſhew, that there do not want far greater
ties, than this wherewith your Author goeth about to detect the
errour of Copernicus: but I pray you, let us breath a little, that
ſo we may proceed to the other Philoſopher, that oppoſeth of the
ſame Copernicus.
It is not
ble with the
cumference of a
ſmall circle few
times revolved to
meaſure and
ſcribe a line bigger
than any great
cle what ſoever.
SAGR. To confeſſe the truth, I ſtand as much in need of
ſpite as either of you; though I have onely wearied my eares:
and were it not that I hope to hear more ingenious things from
this other Author, I queſtion whether I ſhould not go my ways, to

take the air in my ^{*} Pleaſure-boat.
Gondola.
SIMP. I believe that you will hear things of greater moment;
for this is a moſt accompliſhed Philoſopher, and a great
tician, and hath confuted Tycho in the buſineſſe of the Comets,
and new
* The name of
the Author is
pie Claramontius.
SALV. Perhaps he is the ſame with the Author of the Book,
called Anti-Tycho?
SIMP. He is the very ſame: but the confutation of the new
Stars is not in his Anti-Tycho, onely ſo far as he proveth, that they
were not prejudicial to the inalterability and ingenerability of the
Heavens, as I told you before; but after he had publiſhed his
Anti-Tycho, having found out, by help of the Parallaxes, a way to
demonſtrate, that they alſo are things elementary, and contained
within the concave of the Moon, he hath writ this other Book,
de tribus uovis Stellis, &c. and therein alſo inſerted the
ments againſt Copernicus: I have already ſhewn you what he
harh written touching theſe new Stars in his Anti-Tycho, where he
denied not, but that they were in the Heavens; but he proved, that
their production altered not the inalterability of the Heavens, and
that he did, with a Diſcourſe purely philoſophical, in the ſame man
ner as you have already heard. And I then forgot to tell you, how
that he afterwards did finde out a way to remove them out of the
Heavens; for he proceeding in this confutation, by way of
putations and parallaxes, matters little or nothing at all
ſtood by me, I did not mention them to you, but have bent all my
ſtudies upon theſe arguments againſt the motion of the Earth,
which are purely natural.
SALV. I underſtand you very well: and it will be convenient
after we have heard what he hath to ſay againſt Copernicus, that
we hear, or ſee at leaſt the manner wherewith he, by way of
rallaxes, proveth thoſe new ſtars to be elementary, which ſo many
famous Aſtronomers conſtitute to be all very high, and amongſt
the ſtars of the Firmament; and as this Author accompliſheth ſuch
1an enterprize of pulling the new ſtars out of heaven, and placing
them in the elementary Sphere, he ſhall be worthy to be highly
exalted, and transferred himſelf amongſt the ſtars, or at leaſt,
that his name be by fame eternized amongſt them. Yet before we
enter upon this, let us hear what he alledgeth againſt the opinion
of Copernicus, and do you begin to recite his Arguments.
SIMP. It will not be neceſſary that we read them ad verbum,
becauſe they are very prolix; but I, as you may ſee, in reading
them ſeveral times attentively, have marked in the margine thoſe
words, wherein the ſtrength of his arguments lie, and it will
ſuffice to read them. The ſirſt Argument beginneth here. Et

primo, ſi opinio Copernici recipiatur, Criterium naturalis
ſophiæ, ni prorſus tollatur, vehementer ſaltem labefactari
videtur. [In our Idiom thus] And firſt, if Copernicus his opinion
be imbraced, the Criterium of natural Philoſophy will be, if not
wholly ſubverted, yet at leaſt extreamly ſhaken.
The opinion of
Copernicus
throws the
rium of Philoſophy
Which, according to the opinion of all the ſects of Philoſophers
requireth, that Senſe and Experience be our guides in
ting: But in the Copernican poſition the Senſes are greatly
ded, whil'ſt that they viſibly diſcover neer at hand in a pure
um, the graveſt bodies to deſcend perpendicularly downwards,
ver deviating a ſingle hairs breadth from rectitude; and yet
ding to the opinion of Copernicus, the ſight in ſo manifeſt a thing
is deceived, and that motion is not reall ſtraight, but mixt of
right and circular.
SALV. This is the firſt argument, that Ariſtotle, Ptolomy, and
all their followers do produce; to which we have
ly anſwered, and ſhewn the Paralogiſme, and with ſufficient
plainneſſe proved, that the motion in common to us and other
veables, is, as if there were no ſuch thing; but becauſe true
cluſions meet with a thouſand accidents, that confirme them, I

will, with the favour of this Philoſopher, adde ſomething more;
and you Simplicius perſonating him, anſwer me to what I ſhall
ask you: And firſt tell me, what effect hath that ſtone upon you,

which falling from the top of the Tower, is the cauſe that you
ceive that motion; for if its fall doth operate upon you neither
more nor leſſe, than its ſtanding ſtill on the Towers top, you
doubtleſſe could not diſcern its deſcent, or diſtinguiſh its moving
from its lying ſtill.
Common motion
is, as if it never
were.
The argument
taken from things
falling
larly, another way
confuted.
SIMP. I comprehend its moving, in relation to the Tower,
for that I ſee it one while juſt againſt ſuch a mark in the ſaid
Tower, and another while againſt another lower, and ſo
ſively, till that at laſt I perceive it arrived at the ground.
SALV. Then if that ſtone were let fall from the tallons of an
Eagle flying, and ſhould deſcend thorow the ſimple inviſible Air,
1and you had no other object viſible and ſtable, wherewith to make
compariſons to that, you could not perceive its motion?
SIMP. No, nor the ſtone it ſelf; for if I would ſee it, when

it is at the higheſt, I muſt raiſe up my head, and as it deſcendeth
I muſt hold it lower and lower, and in a word, muſt continually
move either that, or my eyes, following the motion of the ſaid
ſtone.
Whence the
tion of a cadent
dy is collected.
SALV. You have now rightly anſwered: you know then that

the ſtone lyeth ſtill, when without moving your eye, you alwayes
ſee it before you; and you know that it moveth, when for the
keeping it in ſight, you muſt move the organ of ſight, the eye. So
then when ever without moving your eye, you continually
hold an object in the ſelf ſame aſpect, you do always judge it
immoveable.
The motion of
the eye argueth
the motion of the
object looked on.
SIMP. I think it muſt needs be ſo.
SALV. Now fancy your ſelf to be in a ſhip, and to have fixed
your eye on the point of the Sail-yard: Do you think, that
cauſe the ſhip moveth very faſt, you muſt move your eye, to keep
your ſight alwayes upon the point of the Sail-yard, and to
low its motion?
SIMP. I am certain, that I ſhould need to make no change at
all; and that not only in the ſight; but if I had aimed a Musket
at it, I ſhould never have need, let the ſhip move how it will,
to ſtir it an hairs breadth to keep it full upon the ſame.
SALV. And this happens becauſe the motion, which the Ship
conferreth on the Sail-yard, it conferreth alſo upon you, and upon
your eye; ſo that you need not ſtir it a jot to behold the top of
the Sail-yard: and conſequently, it will ſeem to you
able. Now this Diſcourſe being applied to the revolution of the
Earth, and to the ſtone placed in the top of the Tower, in which
you cannot diſcern any motion, becauſe that you have that
tion which is neceſſary for the following of it, in common with it
from the Earth; ſo that you need not move your eye. When
gain there is conferred upon it the motion of deſcent, which is its
particular motion, and not yours, and that it is intermixed with the
circular, that part of the circular which is common to the ſtone,
and to the eye, continueth to be imperceptible, and the right
ly is perceived, for that to the perception of it, you muſt follow it
with your eye, looking lower and lower. I wiſh for the
ving of this Philoſopher, that I could adviſe him, that ſome time

or other going by water, he would carry along with him a Veſſel
of reaſonable depth full of water, and prepare a ball of wax, or
other matter that would deſcend very ſlowly to the bottome, ſo
that in a minute of an hour, it would ſcarce ſink a yard; and that
rowing the boat as faſt as could be, ſo that in a minute of an hour
1it ſhould run above an hundred yards, he would let the ball
merge into the water, & freely deſcend, & diligently obſerve its
tion. If he would but do thus, he ſhould ſee, firſt, that it would go in a
direct line towards that point of the bottom of the veſſel, whither it
would tend, if the boat ſhould ſtand ſtill; & to his eye, and in
tion to the veſſel, that motion would appear moſt ſtraight and
pendicular, and yet he could not ſay, but that it would be compoſed
of the right motion downwards, and of the circular about the
ment of water. And if theſe things befall in matters not natural,
and in things that we may experiment in their ſtate of reſt; & then
again in the contrary ſtate of motion, and yet as to appearance no
diverſity at all is diſcovered, & that they ſeem to deceive our ſenſe
what can we diſtinguiſh touching the Earth, which hath been
petually in the ſame conſtitution, as to motion and reſt? And in
what time can we experiment whether any difference is diſcernable
amongſt theſe accidents of local motion, in its diverſe ſtates of
tion and reſt, if it eternally indureth in but one onely of them?
An experiment
that ſheweth how
the common motion
is imperceptible.
SAGR. Theſe Diſcourſes have ſomewhat whetted my ſtomack,
which thoſe fiſhes, and ſnails had in part nauſeated; and the former
made me call to minde the correction of an errour, that hath ſo
much appearance of truth, that I know not whether one of a
thouſand would refuſe to admit it as unqueſtionable. And it was
this, that ſailing into Syria, and carrying with me a very good
Teleſcope, that had been beſtowed on me by our Common Friend,
who not many dayes before had invented, I propoſed to the
riners, that it would be of great benefit in Navigation to make uſe
of it upon the round top of a ſhip, to diſcover and kenne Veſſels
afar off. The benefit was approved, but there was objected the

difficulty of uſing it, by reaſon of the Ships continual fluctuation;
and eſpecially on the round top, where the agitation is ſo much
greater, and that it would be better for any one that would make
uſe thereof to ſtand at the Partners upon the upper Deck, where
the toſſing is leſſe than in any other place of the Ship. I (for I
will not conceal my errour) concurred in the ſame opinion, and
for that time ſaid no more: nor can I tell you by what hints I was
moved to return to ruminate with my ſelf upon this buſineſſe, and
in the end came to diſcover my ſimplicity (although excuſable) in
admitting that for true, which is moſt falſe; falſe I ſay, that the
great agitation of the basket or round top, in compariſon of the
ſmall one below, at the partners of the Maſt, ſhould render the
uſe of the Teleſcope more difficult in finding out the object.
An ingenuous
conſideration
bout the poſſibility
of uſing the
cope with as much
facility on the
round top of the
Maſt of a ſhip,
as on the Deck.
SALV. I ſhould have accompanied the Mariners, and your ſelf
at the beginning.
SIMP. And ſo ſhould I have done, and ſtill do: nor can I
lieve, if I ſhould think of it an hundred years, that I could
ſtand it otherwiſe.
1
SAGR. I may then, it ſeems, for once prove a Maſter to you both.
And becauſe the proceeding by interrogatories doth in my opinion
much dilucidate things, beſides the pleaſure which it affords of
founding our companion, forcing from him that which he thought he
knew not, I will make uſe of that artifice. And firſt, I ſuppoſe that the
Ship, Gally, or other Veſſel, which we would diſcover, is a great way
off, that is, four, ſix, ten, or twenty ^{*} miles, for that to kenne thoſe

neer at hand there is no need of theſe Glaſſes: & conſequently, the
Teleſcope may at ſuch a diſtance of four or ſix miles conveniently
diſcover the whole Veſſel, & a muchgreater bulk. Now I demand
what for ſpecies, & how many for number are the motions that are
made upon the round top, depending on the fluctuation of the Ship.
* I deviate here
from the ſtrict Sea
Diallect, which
denominatesall
ſtances by Leagues.
SALV. We will ſuppoſe that the Ship goeth towards the Eaſt.
Firſt, in a calme Sea, it would have no other motion than

this of progreſſion, but adding the undulation of the Waves,
there ſhall reſult thence one, which alternately hoyſting and
ering the poop and prow, maketh the round top, to lean forwards
and backwards; other waves driving the veſſel ſidewayes, bow the
Maſt to the Starboard and Larboard; others, may bring the ſhip
ſomewhat abovt, and bear her away by the Miſne from Eaſt, one

while towards the ^{*} Northeaſt; another while toward the
eaſt; others bearing her up by the Carine may make her onely to
riſe, and fall; and in ſum, theſe motions are for ſpecies two, one
that changeth the direction of the Teleſcope angularly, the other
lineally, without changing angle, that is, alwayes keeping the
tube of the Inſtrument parallel to its ſelf.
Different
ons depending on
the fluctuation of
the Ship.
* Greco, which
the Latine
ſlator according to
his uſual
neſſe (to call it no
worſe) tranſlates
Corum Ventum,
the Northweſt
Wind, for Ventum
Libanotum.
SAGR. Tell me, in the next place, if we, having firſt directed

the Teleſcope yonder away towards the Tower of ^{*} Burano, ſix
miles from hence, do turn it angularly to the right hand, or to the
left, or elſe upwards or downwards, but a ^{*}ſtraws breadth, what

fect ſhall it have upon us touching the finding out of the ſaid tower?
Two mutations
made in the
ſcope, depending on
the agitation of the
Ship.
* This is a Caſtle
ſix Italian miles
from Venice
Northwards.
SALV. It would make us immediately loſe ſight of it, for ſuch
a declination, though ſmall here, may import there hundreds and

thouſands of yards.
* Vnnerod'
na, the black or
paring of a nail.
SAGR. But if without changing the angle, keeping the tube
alwayes parallel to it ſelf, we ſhould transfer it ten or twelve
yards farther off to the right or left hand, upwards or downwards,
what alteration would it make as to the Tower?
SALV. The change would be abſolutely undiſcernable; for
that the ſpaces here and there being contained between parallel
rayes, the mutations made here and there, ought to be equal, and
becauſe the ſpace which the Inſtrument diſcovers yonder, is
ble of many of thoſe Towers; therefore we ſhall not loſe ſight of it.
SAGR. Returning now to the Ship, we may undoubtedly
firm, that the Teleſcope moving to the right or left, upwards, or
1downwards, and alſo forwards or backwards ten or fifteen fathom,
keeping it all the while parallel to its ſelf, the viſive ray cannot
ſtray from the point obſerved in the object, more than thoſe
teen fathom; and becauſe in a diſtance of eight or ten miles, the
Inſtrument takes in a much greater ſpace than the Gally or other
Veſſel kenn'd; therefore that ſmall mutation ſhall not make me
loſe ſight of her. The impediment therefore, and the cauſe of
loſing the object cannot befall us, unleſſe upon the mutation made
angularly; ſince that Teleſcopes tranſportation higher or lower, to
the right, or to the left, by the agitation of the ſhip, cannot import
any great number of fathomes. Now ſuppoſe that you had two
Teleſcopes fixed, one at the Partners cloſe by the Deck, and the
ther at the round top, nay at the main top, or main top-gallant
top, where you hang forth the Pennon or ſtreamer, and that they
be both directed to the Veſſel that is ten miles off, tell me,
ther you believe that any agitation of the ſhip, & inclination of the
Maſt, can make greater changes, as to the angle, in the higher tube,
than in the lower? One wave ariſing, the prow will make the main
top give back fifteen or twenty fathom more than the foot of the
Maſt, and it ſhall carry the upper tube along with it ſo greata ſpace,
& the lower it may be not a palm; but the angle ſhall change in one
Inſtrument aſwell as in the other; and likewiſe a ſide-billow ſhall
bear the higher tube an hundred times as far to the Larboard or
Starboard, as it will the other below; but the angles change not at
all, or elſe alter both alike. But the mutation to the right hand or
left, forwards or backwards, upwards or downwards, bringeth no
ſenſible impediment in the kenning of objects remote, though the
alteration of the angle maketh great change therein; Therefore it
muſt of neceſſity be confeſſed, that the uſe of the Teleſcope on the
round top is no more difficult than upon the Deck at the Partners;
ſeeing that the angular mutations are alike in both places.
SALV. How much circumſpection is there to be uſed in affirming
or denying a propoſition? I ſay again, thar hearing it reſolutely
med, that there is a greater motion made on the Maſts top, than at
its partners, every one will perſwade himſelf, that the uſe of the
leſcope is much more difficult above than below. And thus alſo I w
ill excuſe thoſe Philoſophers, who grow impatient and fly out into
paſſion againſt ſuch as will not grant them, that that Cannon bullet
which they cleerly ſee to fall in a right line perpendicularly, doth
abſolutely move in that manner; but will have its motion to be by
an arch, and alſo very much inclined and tranſverſal: but let us
leave them in theſe labyrinths, and let us hear the other objections,
that our Author in hand brings againſt Copernicus.
SIMP. The Author goeth on to demonſtrate that in the
ctrine of Copernicus, it is requiſite to deny the Senſes, and the
1greateſt Senſations, as for inſtance it would be, if we that feel the

reſpirations of a gentle gale, ſhould not feel the impulſe of a
petual winde that beateth upon us with a velocity that runs more
than 2529 miles an hour, for ſo much is the ſpace that the centre
of the Earth in its annual motion paſſeth in an hour upon the
cumference of the grand Orb, as he diligently calculates; and
becauſe, as he ſaith, by the judgment of Copernicus, Cum terra
movetur circumpoſitus aër, motus tamen ejus, velocior licet ac
pidior celerrimo quocunque vento, à nohis non ſentiretur, ſed
ma tum tranquilitas reputaretur, niſi alius motus accederet. Quid
eſt verò decipi ſenſum, niſi hæc eſſet deceptio? [Which I make to
ſpeak to this ſenſe.] The circumpoſed air is moved with the Earth,
yet its motion, although more ſpeedy and rapid than the ſwifteſt
wind whatſoever, would not be perceived by us, but then would
be thought a great tranquillity, unleſſe ſome other motion ſhould
happen; what then is the deception of the ſenſe, if this be
not?
The annual
tion of the Earth
muſt cauſe a
petual and ſtrong
winde.
SALV. It muſt needs be that this Philoſopher thinketh, that
that Earth which Copernicus maketh to turn round, together with
the ambient air along the circumference of the great Orb, is not that
whereon we inhabit, but ſome other ſeparated from this; for that this
of ours carrieth us alſo along with it with the ſame velocity, as

ſo the circumjacent air: And what beating of the air can we feel,
when we fly with equal ſpeed from that which ſhould accoſt us?
This Gentleman forgot, that we no leſs than the Earth and air are
carried about, and that conſequently we are always touch'd by
one and the ſame part of the air, which yet doth not make us feel
it.
The air alwayes
touching us with
the ſame part of it
cannot make us
feel it.
SIMP. But I rather think that he did not ſo think; hear the
words which immediately follow. Præterea nos quoque rotamur
ex circumductione terræ &c.
SALV. Now I can no longer help nor excuſe him; do you
plead for him and bring him off, Simplicius.
SIMP. I cannot thus upon the ſudden think of an excuſe that
pleaſeth me.
SALV. Go to; take this whole night to think on it, and
fend him to morrow; in the mean time let us hear ſome other of
his objections.
SIMP. He proſecuteth the ſame Objection, ſhewing, that in the

way of Copernicus, a man muſt deny his own ſenſes. For that
this principle whereby we turn round with the Earth, either is
intrinſick to us, or external; that is, a rapture of that Earth; and
if it be this ſecond, we not feeling any ſuch rapture, it muſt be
confeſſed that the ſenſe of feeling, doth not feel its own object
touching it, nor its impreſſion on the ſenſible part: but if the
1ciple be intrinſecal, we ſhall not perceive a local motion that is
rived from our ſelves, and we ſhall never diſcover a propenſion
petually annexed to our ſelves.
He that will
low Copernicus,
must deny his
ſes.
SALV. So that the inſtance of this Philoſopher lays its ſtreſs
on this, that whether the principle by which we move round with
the Earth be either extern, or intern, yet however we muſt
ceive it, and not perceiving it, it is neither the one nor the other,
and therefore we move not, nor conſequently the Earth. Now I

ſay, that it may be both ways, and yet we not perceive the ſame.
And that it may be external, the experiment of the boat
bundantly ſatisſieth me; I ſay, ſuperabundantly, becauſe it being
in our power at all times to make it move, and alſo to make it
ſtand ſtill, and with great exactneſs to make obſervation, whether
by ſome diverſity that may be comprehended by the ſenſe of
ing, we can come to know whether it moveth or no, ſeeing that
as yet no ſuch ſcience is obtained: Will it then be any matter of
wonder, if the ſame accident is unknown to us on the Earth, the
which may have carried us about perpetually, and we, without our

being ever able to experiment its reſt? You, Simplicius, as I
lieve, have gone by boat many times to Padoua, and if you will
confeſs the truth, you never felt in your ſelf the participation of
that motion, unleſs when the boat running a-ground, or
tring ſome obſtacle, did ſtop, and that you with the other
gers being taken on a ſudden, were with danger over-ſet. It
would be neceſſary that the Terreſtrial Globe ſhould meet with
ſome rub that might arreſt it, for I aſſure you, that then you
would diſcern the impulſe reſiding in you, when it ſhould toſs you
up towards the Stars. It's true, that by the other ſenſes, but yet

aſſiſted by Reaſon, you may perceive the motion of the boat, that
is, with the ſight, in that you ſee the trees and buildings placed on
the ſhoar, which being ſeparated from the boat, ſeem to move the

contrary way. But if you would by ſuch an experiment receive
intire ſatisfaction in this buſineſs of the Terreſtrial motion, look
on the ſtars, which upon this reaſon ſeem to move the contrary
way. As to the wondering that we ſhould not feel ſuch a
ciple, ſuppoſing it to be internal, is a leſs reaſonable conceit; for
if we do not feel ſuch a one, that cometh to us from without,
and that frequently goeth away, with what reaſon can we expect
to feel it, if it immutably and continually reſides in us? Now let
us ſee what you have farther to allege on this argument.
Our motion may
be either interne or
externe, and yet
we never perceive
or feel it.
The motion of a
Boat inſenſible to
thoſe that are with
in it, as to the ſenſe
of feeling.
The boats
on is perceptible to
the ſight joyn'd
with reaſon.
The terreſtrial
motion collected
from the ſtars.
SIMP. Take this ſhort exclamation. Ex hac itaque opinione
neceſſe est diffidere noſtris ſenſibus, ut penitùs fall acibus vel ſtupidis
in ſenſilibus, etiam conjunctiſſimis, dijudicandis. Quam ergò
ritatem ſperare poſſumus à facultate adeò fallaci ortum trabentem?
[Which I render thus:] From this opinion likewiſe, we muſt of
1neceſſity ſuſpect our own ſenſes, as wholly fallible, or ſtupid in
judging of ſenſible things even very near at hand. What truth
therefore can we hope for, to be derived from ſo deceiveable a
culty?
SALV. But I deſire not to deduce precepts more profitable, or
more certain, learning to be more circumſpect and leſs confident
about that which at firſt bluſh is repreſented to us by the ſenſes,
which may eaſily deceive us. And I would not have this Author
trouble himſelf in attemptiug to make us comprehend by ſenſe,
that this motion of deſcending Graves is ſimply right, and of
no other kind; nor let him exclaim that a thing ſo clear, manifeſt,
and obvious ſhould be brought in queſtion; for in ſo doing, he
maketh others believe, that he thinketh thoſe that deny that
tion to be abſolutely ſtreight, but rather circular, the ſtone did
ſenſibly ſee it to move in an arch, ſeeing that he inviteth their ſenſes
more than their Reaſon, to judg of that effect: which is not true,
Simplicius, for like as I, that am indifferent in all theſe
ons, and onely in the manner of a Comedian, perſonate
cus in theſe our repreſentations, have never ſeen, nor thought
that I have ſeen that ſtone fall otherwiſe than perpendicularly,
ſo I believe, that to the eyes of all others it ſeemed to do the
ſame. Better it is therefore, that depoſing that appearance in
which all agree, we make uſe of our Reaſon, either to confirm the
reality of that, or to diſcover its fallacy.
SAGR. If I could any time meet with this Philoſopher, who
yet me thinks is more ſublime than the reſt of the followers of
the ſame doctrines, I would in token of my affection put him in
mind of an accident which he hath doubtleſs very often beheld;
from which, with great conformity to that which we now diſcourſe
of, it may be collected how eaſily one may be deceived by the bare
appearance, or, if you will, repreſentation of the ſenſe. And the
accident is, the Moons ſeeming to follow thoſe that walk the ſtreets
in the night, with a pace equal to theirs, whilſt they ſee it go
ding along the Roofs of houſes, upon which it ſheweth juſt like a
cat, that really running along the ridges of houſes, leaveth them
behind. An appearance that, did not reaſon interpoſe, would but
too manifeſtly delude the ſight.
SIMP. Indeed there want not experiments that render us

tain of the fallacy of the meer ſenſes; therefore ſuſpending ſuch
ſenſations for the preſent, let us hear the Arguments that follow
which are taken, as he ſaith, ex rerum naturâ. The firſt of which
is, that the Earth cannot of its own nature move with three
ons very different; or otherwiſe we muſt deny many manifeſt

Axioms. The firſt whereof is, that Omnïs effectus dependeat ab
aliquâ cauſâ; [i. e.] that every effect dependeth on ſome cauſe.
1The ſecond, that Nulla res ſeipſam producat; [i. e.] that nothing
produceth it ſelf: from whence it follows, that it is not
ble that the mover and moved ſhould be totally the ſame thing:
And this is manifeſt, not onely in things that are moved by an
trinſick mover; but it is gathered alſo from the principles
pounded, that the ſame holdeth true in the natural motion
dent on an intrinſick principle; otherwiſe, being that the mover,
as a mover, is the cauſe, and the thing moved, as moved, is the
effect, the ſame thing would totally be both the cauſe and effect.
Therefore a body doth not move its whole ſelf, that is, ſo as
that all moveth, and all is moved; but its neceſſary in the thing
moved to diſtinguiſh in ſome manner the efficient principle of the
motion, and that which with that motion is moved. The third
Axiom is, that in rebus quæ ſenſui ſubjiciuntur, unum, quatenus
unum, unam ſolam rem producat; i. e. That in things ſubject to
the ſenſes, one, as it is one, produceth but onely one thing: That
is, the ſoul in animals produceth its true divers operations, as the
ſight, the hearing, the ſmell, generation, &c. but all theſe with
ſeveral inſtruments. And in ſhort, in things ſenſible, the
ty of operations, is obſerved to derive it ſelf from the diverſity
that is in the cauſe. Now if we put all theſe Axioms together, it

will be a thing very manifeſt, that one ſimple body, as is the
Earth, cannot of its own nature move at the ſame time with
three motions, very divers: For by the foregoing ſuppoſitions,
all moveth not its ſelf all; it is neceſfary therefore to diſtinguiſh
in it three principles of its three motions; otherwiſe one and the
ſame principle would produce many motions; but if it contein in
it three principles of natural motions, beſides the part moved, it
ſhall not be a ſimple body, but compounded of three principle
movers, and of the part moved. If therefore the Earth be a

ple body, it ſhall not move with three motions; nay more, it will
not move with any of thoſe which Copernicus aſcribeth to it, it
being to move but with one alone, for that it is manifeſt, by the
reaſons of Ariſtotle, that it moveth to its centre, as its parts do
ſhew, which deſcend at right angles to the Earths Spherical
Surface.
Arguments
gainſt the Earths
motion taken, ex
rerum natura.
Three Axioms
that are ſuppoſed
manifeſt.
A ſimple body
as the Earth,
not move with
three ſeveral
ons.
The Earth
not move with any
of the motions
gned it by
cus.
SALV. Many things might be ſaid, and conſidered touching
the connection of this argument; but in regard that we can

ſolve it in few words, I will not at this time without need inlarge
upon it; and ſo much the rather, becauſe the ſame Author hath
furniſhed me with an anſwer, when he ſaith that from one ſole
ple in animals, there are produced divers operations; ſo that for
the preſent my anſwer ſhall be, that in the ſame manner the Earth
from one onely principle deriveth ſeveral operations.
Anſwers to the
arguments
ry to the Earths
motion, taken ex
rerum natura.
SIMP. But this anſwer will not at all ſatisfie the Author who
1makes the objection, yea, it is totally overthrown by that which
immediately after he addeth for a greater confirmation of his
ment, as you ſhall hear. He re-inforceth his argument, I ſay, with

another Axiome, which is this; That natura in rebus neceſſari is
nec deficiat, nec abundat: i.e. That nature in things neceſſary is
neither defective, nor ſuperfluous. This is obvious to the

vers of natural things, and chiefly of animals, in which, becauſe
they are to move with many motions, Nature hath made many
flexures, and hath thereunto commodiouſly knitted the parts for
motion, as to the knees, to the hips, for the inabling of living
creatures to go, and run at their pleaſure. Moreover in man he
hath framed many flexions, and joynts, in the elbow, and hand, to
enable them to perform many motions. From theſe things the

gument is taken againſt the threefold motion of the Earth. [
ther the Body, that is one, and continuate, without any manner of
knittings or flexions, can exerciſe divers motions, or cannot: If it
can without them, then in vain hath nature framed the flexures in
animals; which is contrary to the Axiome: but if it cannot
out them, then the Earth, one body, and continuate, and deprived of
flexures, and joynts, cannot of its own nature move with
ty of motions.] You ſee now how craftily he falls upon your an­
ſwer, as if he had foreſeen it.
A fourth
iome againſt the
motion of the Earth
Flexures
ſary in animals for
the diverſity of
their motions.
Another
ment againſt the
three fold motion of
the Earth.
SALV. Are you ſerious, or do you jeſt?
SIMP. I ſpeak it with the beſt judgment I have.
SALV. You muſt therefore ſee that you have as fortunate an
hand in defending the reply of this Philoſopher, againſt ſome
ther rejoynders made to him; therefore anſwer for him, I pray
you, ſeeing we cannot have him here. You firſt admit it for true,
that Nature hath made the joynts, flexures, and knuckles of
ving creatures, to the intent that they might move with ſnndry
and divers motions; and I deny this propoſition; and ſay, that
theſe flexions are made, that the animal may move one, or more

of its parts, the reſt remaining immoved: and I ſay, that as to the
ſpecies and differences of motions thoſe are of one kind alone, to
wit, all circular, and for this cauſe you ſee all the ends of the

veable bones to be convex or concave, and of theſe ſome are
rical, as are thoſe that are to move every way, as in the

joynt, the arme of the Enſigne doth, in diſplaying the Colours,
and that of the Falconer in bringing his Hawk to the lure; and
ſuch is the flexure of the elbow, upon which the hand turns round,
in boring with an augure: others are circular onely one way, and
as it were cylindrical, which ſerve for the members that bend

ly in one faſhion, as the joynts of the fingers one above another,
&c. But without more particular inductions, one only general
courſe may make this truth underſtood; and this is, that of a ſolid
1body that moveth, one of its extreams ſtanding ſtill without
ching place, the motion muſt needs be circular, and no other: and

becauſe in the living creatures moving, one of its members doth
not ſeparate from the other its conterminal, therefore that motion
is of neceſſity circular.
The Flexures in
animals are not
made for the
verſity of motions.
The motions of
animals are of one
ſort.
The ends of the
bones are all
tund.
It is
ted, that the ends
of the bones are of
neceſſity to be
tund.
The motions of
animals are all
circular.
SIMP. How can this be? For I ſee the animal move with an
hundred motions that are not circular, and very different from one
another, as to run, to skip, to climbe, to deſcend, to ſwim, and
many
Secondary
ons of animals
pendent on the firſt
SALV. Tis well: but theſe are ſecondary motions, depending
on the preceding motions of the joynts and flexures. Upon the
plying of the legs to the knees, and the thighs to the hips, which
are circular motions of the parts, is produced, as conſequents, the
skip, or running, which are motions of the whole body, and theſe
may poſſibly not be circular. Now becauſe one part of the ter­

reſtrial Globe is not required to move upon another part
able, but that the motion is to be of the whole body, there is no
need in it of flexures.
The Terreſtriall
Globe hath noe
need of flexures.
SIMP. This (will the aduerſary rejoyn) might be, if the
on were but one alone, but they being three, and thoſe very
ferent from each other, it is not poſſible that they ſhould concur in

an ^{*} articulate body.
* Without joynts
SALV. I verily believe that this would be the anſwer of the
Philoſopher. Againſt which I make oppoſition another way; and
ask you, whether you think that by way of joynts and flexures one
may adapt the terreſtrial Globe to the participation of three
rent circular motions? Do you not anſwer me? Seeing you are
ſpeechleſſe, I will undertake to anſwer for the Philoſopher, who
would abſolutely reply that they might; for that otherwiſe it
would have been ſuperfluous, and beſides the purpoſe to have
poſed to conſideration, that nature maketh the flexions, to the
end, the moveable may move with different motions; and that
therefore the terreſtrial Globe having no flexures, it cannot have
thoſe three motions which are aſcribed to it. For if he had
thought, that neither by help of flexures, it could be rendered apt
for ſuch motions, he would have freely affirmed, that the Globe
could not move with three motions. Now granting this, I intreat

you, and by you, if it were poſſible, that Philoſopher,
thor of the Argument, to be ſo courteous as to teach me in what
manner thoſe flexures ſhould be accommodated, ſo that thoſe
three motions might commodiouſly be excerciſed; and I grant you
four or ſix moneths time to think of an anſwer. As to me, it
eth that one principle onely may cauſe a plurality of motions in

the Terreſtrial Globe, juſt in the ſame manner that, as I told you
before, one onely principle with the help of various inſtruments
1produceth ſundry and divers motions in living creatures. And as
to the flexures there is no need of them, the motions being of the
whole, and not of ſome particular parts; and becauſe they are
to be circular, the meer ſpherical figure is the moſt perfect
lation or flection that can be deſired.
It is deſired to
know, by means of
what flexures and
joynts the
ſtrial Globe might
move with three
diverſe motions.
One only
ple may cauſe a
plurality of
ons in the Earth.
SIMP. The moſt that ought to be granted upon this, would be,
that it may hold true in one ſingle motion, but in three different
motions, in my opinion, and that of the Author, it is
ble; as he going on, proſecuting the objection, writes in the
lowing words. Let us ſuppoſe, with Copernicus, that the Earth
moveth of its own faculty, and upon an intrinſick principle from
Weſt to Eaſt in the plane of the Ecliptick; and again, that it alſo
by an intrinſick principle revolveth about its centre, from Eaſt to
Weſt; and for a third motion, that it of its own inclination
cteth from North to South, and ſo back again. It being a
nuate body, and not knit together with joints and flections, our
fancy and our judgment will never be able to comprehend, that
one and the ſame natural and indiſtinct principle, that is, that
one and the ſame propenſion, ſhould actuate it at the ſame inſtant
with different, and as it were of contrary motions. I cannot
lieve that any one would ſay ſuch a thing, unleſſe he had
took to maintain this poſition right or wrong.
SALV. Stay a little; and find me out this place in the Book.
Fingamus modo cum Copernico terram aliqua ſuâ vi, & ab indito
principio impelli ab Occaſu ad Ortum in Eclipticæ plano; tum
ſus revolvi ab indito etiam principio, circa ſuimet centrum, ab

Ortu in Occaſum; tertio deſlecti rurſus ſu opte nutu à
ne in Auſtrum, & viciſſim. I had thought, Simplicius, that
that you might have erred in reciting the words of the
thor, but now I ſee that he, and that very groſſely,
veth himſelf; and to my grief, I find that he hath ſet himſelf to
oppoſe a poſition, which he hath not well underſtood; for theſe
are not the motions which Copernicus aſſignes to the Earth.
Where doth he find that Copernicus maketh the annual motion
by the Ecliptick contrary to the motion about its own centre? It
muſt needs be that he never read his Book, which in an hundred
places, and in the very firſt Chapters affirmeth thoſe motions to
be both towards the ſame parts, that is from Weſt to Eaſt.
But without others telling him, ought he not of himſelf to
prehend, that attributing to the Earth the motions that are ta
ken, one of them from the Sun, and the other from the
mum wobile, they muſt of neceſſity both move one and the ſame

A groſſe error
of the oppoſer of
Copernicus.
A ſubtil and
withal ſimple
gument againſt
Copernicus.
SIMP. Take heed that you do not erre your ſelf, and
cus alſo. The Diurnal motion of the primum mobile, is it not from
1Eaſt to Weſt? And the annual motion of the Sun through the
Ecliptick, is it not on the contrary from Weſt to Eaſt? How
then can you make theſe motions being conferred on the Earth, of
contraries to become conſiſtents?
SAGR. Certainly, Simplicius hath diſcovered to us the original
cauſe of error of this Philoſopher; and in all probability he
would have ſaid the very ſame.
SALV. Now if it be in our power, let us at leaſt recover
Simplicius from this errour, who ſeeing the Stars in their riſing
to appear above the Oriental Horizon, will make it no difficult
thing to underſtand, that in caſe that motion ſhould not belong

to the Stars, it would be neceſſary to confeſſe, that the Horizon,
with a contrary motion would go down; and that conſequently
the Earth would reoolve in it ſelf a contrary way to that
with the Stars ſeem to move, that is from Weſt to Eaſt, which
is according to the order of the Signes of the Zodiack. As, in the
next place, to the other motion, the Sun being fixed in the
tre of the Zodiack, and the Earth moveable about its
rence, to make the Sun ſeem unto us to move about the ſaid
diack, according to the order of the Signes, it is neceſſary, that
the E arth move according to the ſame order, to the end that the
Sun may ſeem to us to poſſeſſe alwayes that degree in the Zodiack,
that is oppoſite to the degree in which we find the Earth; and thus
the Earth running, verbi gratia, through Aries, the Sun will
appear to run thorow Libra; and the Earth paſſing thorow the
ſigne Taurus, the Sun will paſſe thorow Scorpio, and ſo the
Earth going thorow Gemini, the Sun ſeemeth to go thorow
gittarius; but this is moving both the ſame way, that is
ing to the order of the ſignes; as alſo was the revolution of the
Earth about its own centre.
The error of the
Antagoniſt is
nifeſt, by
ring that the
nual and diurnal
motions belonging
to the Earth are
both one way, and
not contrary.
SIMP. I underſtand you very well, and know not what to
ledge in excuſe of ſo groſſe an error.
SALV. And yet, Simplicius, there is one yet worſe then this; and
it is, that he makes the Earth move by the diurnal motion about
its own centre from Eaſt to Weſt; and perceives not that if this
were ſo, the motion of twenty four hours appropriated by him
to the Univerſe, would, in our ſeeming, proceed from Weſt to
Eaſt; the quite contrary to that which we behold.
SIMP. Oh ſtrange! Why I, that have ſcarce ſeen the firſt
elements of the Sphere, would not, I am confident, have erred
ſo horribly.
SALV. Judg now what pains this Antagoniſt may be thought
to have taken in the Books of Copernicus, if he abſolutely invert

the ſenſe of this grand and principal Hypotheſis, upon which is
founded the whole ſumme of thoſe things wherein Copernicus
1diſſenteth from the doctrine of Ariſtotle and Ptolomy. As again,

to this third motion, which the Author aſſignes to the Terreſtrial
Globe, as the judgment of Copernicus, I know not which he would
mean thereby: it is not that queſtionleſſe, which Copernicus
cribes unto it conjunctly with the other two, annual and diurnal,
which hath nothing to do with declining towards the South and
North; but onely ſerveth to keep the axis of the diurnal
on continually parallel to it ſelf; ſo that it muſt be confeſt, that
either the Authour did not underſtand this, or that elſe he
bled it. But although this great miſtake ſufficeth to free us from
any obligation of a farther enquiry into his objections; yet
vertheleſſe I ſhall have them in eſteem; as indeed they deſerve to
be valued much before the many others of impertinent
niſts. Returning therefore to his objection, I ſay, that the two
motions, annual and diurnal, are not in the leaſt contrary, nay are
towards the ſame way, and therefore may depend on one and the
ſame principle. The third is of it ſelf, and voluntarily ſo
tial to the annual, that we need not trouble our ſelves (as I ſhall
ſhew in its place) to ſtudy for principles either internal or external,
from which, as from its cauſe, to make it produced.
By another
error it is ſeen that
the Antagoniſt had
but little ſtudied
Copernicus.
It is queſtioned,
whether the
nent underſtood
the third motion
aſſigned to the
Earth by
cus.
SAGR. I ſhall alſo, as being induced thereto by natural reaſon,
ſay ſomething to this Antagoniſt. He will condemn Copernicus,
unleſſe I be able to anſwer him to all objections, and to ſatisfie
him in all queſtions he ſhall ask; as if my ignorance were a
ſary argument of the falſhood of his Doctrine. But if this way of
condemning Writers be in his judgment legal, he ought not to
think it unreaſonable, if I ſhould not approve of Arîſtotle and
lomy, when he cannot reſolve, better than my ſelf, thoſe doubts
which I propound to him, touching their Doctrine. He asketh me,
what are the principles by which the Terreſtrial Globe is moved

with the Annual motion through the Zodiack, and with the
nal through the Equinoctial about its own axis. I anſwer, that
they are like to thoſe by which Saturn is moved about the
ack in thirty years, and about its own centre in a much ſhorter
time along the Equinoctial, as the collateral apparition and
cultation of its Globes doth evince. They are principles like to
thoſe, whereby he ſcrupleth not to grant, that the Sun runneth
row the Ecliptick in a year, and revolveth about its own centre
parallel to the Equinoctial in leſſe than a moneth, as its ſpots doth
ſenſibly demonſtrate. They are things like to thoſe whereby the
Medicean Stars run through the Zodiack in twelve years, and
all the while revolve in ſmall circles, and ſhort periods of time
bout Jupiter.
The ſame
ment anſwered by
examples of the
like motions in
ther cœleſtial
dies.
SIMP. This Author will deny all theſe things, as deluſions of
the fight, cauſed by the cryſtals of the Teleſcope.
1
SAGR. But this would be to draw a further inconvenience
on himſelf, in that he holdeth, that the bare eye cannot be
ved in judging of the right motion of deſcending graves, and yet
holds that it is deceived in beholding theſe other motions at ſuch
time as its viſive vertue is perfected, and augmented to thirty times
as much as it was before. We tell him therefore, that the Earth in
like manner partaketh of the plurality of motions: and it is
haps the ſame, whereby the Loadſtone hath its motion
wards, as grave, and two circular motions, one Horizontal, and the
other Vertical under the Meridian. But what more; tell me,
plicius, between which do you think this Author would put a
greater difference, 'twixt right and circular motion, or 'twixt
on and reſt?
SIMP. 'Twixt motion and reſt, certainly. And this is

feſt, for that circular motion is not contrary to the right, according
to Aristotle; nay, he granteth that they may mix with each
ther; which it is impoſſible for motion and reſt to do.
Motion and reſt
are more different
than right motion
and circular.
SAGR. Therefore its a propoſition leſſe improbable to place
in one natural body two internal principles, one to right motion,
and the other to circular, than two ſuch interne principles one to
motion, and the other to reſt. Now both theſe poſitions agree to

the natural inclination that reſideth in the parts of the Earth to
turn to their whole, when by violence they are divided from it;
and they onely diſſent in the operation of the whole: for the
ter of them will have it by an interne principle to ſtand ſtill, and
the former aſcribeth to it the circular motion. But by your
ceſſion, and the confeſſion of this Philoſopher, two principles, one
to motion, and the other to reſt, are incompatible together, like as
their effects are incompatible: but now this evenes not in the two
motions, right, and circular, which have no repugnance to each
other.
One may more
rationally aſcribe
to the Earth two
internal principles
to the right, and
circular motion,
than two to motion
and reſt.
SALV. Adde this more, that in all probability it may be that

the motion, that the part of the Earth ſeparated doth make whilſt
it returneth towards its whole, is alſo circular, as hath been
dy declared; ſo that in all reſpects, as far as concernes the preſent
caſe, Mobility ſeemeth more likely than Reſt. Now proceed,
Simplicius, to what remains.
The motion of
the parts of the
Earth returning to
their whole may be
circular.
SIMP. The Authour backs his Argument with producing
ther abſurdity, that is, that the ſame motions agree to Natures
treamly different; but experience ſheweth, that the operations

and motions of different natures, are different; and Reaſon
firmeth the ſame: for otherwiſe we ſhould have no way left to
know and diſtinguiſh of natures, if they ſhould not have their
particular motions and operations, that might guide us to the
knowledge of their ſubſtances.
1
The diverſity of
motions helpeth us
in knowing the
verſity of natures.
SAGR. I have twice or thrice obſerved in the diſcourſes of this
Authour, that to prove that a thing is ſo, or ſo, he ſtill alledgeth,
that in that manner it is conformable with our underſtanding; or
that otherwiſe we ſhould never be able to conceive of it; or that
the Criterium of Philoſophy would be overthrown. As if that

ture had firſt made mens brains, and then diſpoſed all things in
conformity to the capacity of their intellects. But I incline rather
to think that Nature firſt made the things themſelves, as ſhe beſt
liked, and afterwards framed the reaſon of men capable of
ceiving (though not without great pains) ſome part of her
crets.
Nature firſt
made things as ſhe
pleaſed, and
wards capacitated
mens
ings for conceiving
of them.
SALV. I am of the ſame opinion. But tell me, Simplicius,
which are theſe different natures, to which, contrary to
rience and reaſon, Copernicus aſſignes the ſame motions and
rations.
SIMP. They are theſe. The Water, the Air, (which
leſſe are Natures different from the Earth) and all things that
are in thoſe elements compriſed, ſhall each of them have thoſe
three motions, which Copernicus pretends to be in the Terreſtriall
Globe; and my Authour proceedeth to demonſtrate

cally, that, according to the Copernican Doctrine, a cloud that is
ſuſpended in the Air, and that hangeth a long time over our
heads without changing place, muſt of neceſſity have all thoſe three
motions that belong to the Terreſtrial Globe. The
tion is this, which you may read your ſelf, for I cannot repeat it
without book.
Copernicus
roneouſly aſſigneth
the ſame operations
to different natures
SALV. I ſhall not ſtand reading of it, nay I think it an
tinency in him to have inſerted it, for I am certain, that no
Copernican will deny the ſame. Therefore admitting him what he
would demonſtrate, let us ſpeak to the objection, which in my
judgment hath no great ſtrength to conclude any thing contrary
to the Copernican Hypotheſis, ſeeing that it derogates nothing from
thoſe motions, and thoſe operations, whereby we come to the
knowledge of the natures, &c. Anſwer me, I pray you,
us: Thoſe accidents wherein ſome things exactly concur, can
they ſerve to inform us of the different natures of thoſe
From commune
accidents one
not know different
natures.
SIMP. No Sir: nay rather the contrary, for from the idendity
of operations and of accidents nothing can be inferred, but an
idendity of natures.
SALV. So that the different natures of the Water, Earth, Air,
and other things conteined in theſe Elements, is not by you
ed from thoſe operations, wherein all theſe Elements and their
fixes agree, but from other operations; is it ſo?
SIMP. The very ſame.
SALV. So that he who ſhould leave in the Elements all thoſe
1motions, operations, and other accidents, by which their natures
are diſtinguiſhed, would not deprive us of the power of coming
to the knowledge of them; although he ſhould remove thoſe
perations, in which they unitedly concur, and which for that reaſon
are of no uſe for the diſtinguiſhing of thoſe natures.
SIMP. I think your diſſertation to be very good.
SALV. But that the Earth, Water, Air, are of a nature equally
conſtituted immoveable about the centre, is it not the opinion of
your ſelf, Ariſtotle, Prolomy, and all their ſectators?
SIMP. Its on all hands granted as an undeniable truth.
SALV. Then from this common natural condition of
cence about the centre, there is no argument drawn of the different
natures of theſe Elements, and things elementary, but that
knowledge muſt be collected from other qualities not common;
and therefore whoſo ſhould deprive the Elements of this common
reſt only, and ſhould leave unto them all their other operations,
would not in the leaſt block up the way that leadeth to the
ledge of their eſſences. But Copernicus depriveth them onely of
this common reſt, and changeth the ſame into a common motion,
leaving them gravity, levity, the motions upwards, downwards,

ſlower, faſter, rarity, denſity, the qualities of hot, cold, dry, moiſt,
and in a word, all things beſides. Therefore ſuch an abſurdity, as
this Authour imagineth to himſelf, is no Copernican poſition; nor
doth the concurrence in an identity of motion import any more or
leſs, than the concurrence in an identity of reſt about the
fying, or not diverſifying of natures. Now tell us, if there be any
argument to the contrary.
The concurrence
of the Elements in
a common motion
importeth no more
or leſſe, than their
concurrence in a
common reſt.
SIMP. There followeth a fourth objection, taken from a

ral obſervation, which is, That bodies of the ſame kind, have
tions that agree in kinde, or elſe they agree in reſt. But by the
pernican Hypotheſis, bodies that agree in kinde, and are moſt ſem-

blable to one another, would be very diſcrepant, yea diametrically
repugnant as to motion; for that Stars ſo like to one another, would
be nevertheleſſe ſo unlike in motion, as that ſix Planets would
tually turn round; but the Sun and all the fixeed Stars would ſtand
perpetually immoveable.
A fourth
ment againſt
pernicus.
Bodies of the
ſame kinde have
motions that agree
in kinde.
SALV. The forme of the argument appeareth good; but yet
I believe that the application or matter is defective: and if the
Authour will but perſiſt in his aſſumption, the conſequence ſhall
make directly againſt him. The Argument runs thus; Amongſt
mundane bodies, ſix there are that do perpetually move, and they

are the ſix Planets; of the reſt, that is, of the Earth, Sun, and
fixed Stars, it is diſputable which of them moveth, and which
ſtands ſtill, it being neceſſary, that if the Earth ſtand ſtill, the Sun
and ſixed Stars do move; and it being alſo poſſible, that the Sun
1and fixed Stars may ſtand immoveable, in caſe the Earth ſhould
move: the matter of fact in diſpute is, to which of them we may
with moſt convenience aſcribe motion, and to which reſt. Natural
reaſon dictates, that motion ought to be aſſigned to the bodies,
which in kind and eſſence moſt agree with thoſe bodies which do
undoubtedly move, and reſt to thoſe which moſt diſſent from them;
and in regard that an eternal reſt and perpetual motion are moſt
different, it is manifeſt, that the nature of the body always
able ought to be moſt different from the body alwayes ſtable.
Therefore, in regard that we are dubious of motion and reſt,
let us enquire, whether by the help of ſome other eminent
on, we may diſcover, which moſt agreeth with the bodies
ly moveable, either the Earth, or the Sun and fixed Stars. But ſee
how Nature, in favour of our neceſſity and deſire, preſents us
with two eminent qualities, and no leſs different than motion and
reſt, and they are light and darkneſs, to wit, the being by nature
moſt bright, and the being obſcure, and wholly deprived of light:
the bodies therefore adorned with an internal and eternal
dour, are moſt different in eſſence from thoſe deprived of light:
The Earth is deprived of light, the Sun is moſt ſplendid in it ſelf,
and ſo are the fixed Stars. The ſix Planets do abſolutely
want light, as the Earth; therefore their eſſence agreeth with
the Earth, and differeth from the Sun and fixed Stars.
fore is the Earth moveable, immoveable the Sunne and Starry
Sphere.
From the Earths
obſcurity, and the
ſplendour of the
Sun, and fixed
Stars, is argued,
that it is
ble, and they
moveable.
SIMP. But the Authour will not grant, that the ſix Planets are
tenebroſe, and by that negative will he abide. Or he will argue
the great conformity of nature between the ſix Planets, and the
Sun, and Fixed Stars; and the diſparity between them and the
Earth from other conditions than from tenebroſity and light; yea,
now I remember in the fifth objection, which followeth, he layeth
down the vaſt difference between the Earth and the Cœleſtial

Bodies, in which he writeth, That the Copernican Hypotheſis
would make great confuſion and perturbation in the Syſteme of the
Vniverſe, and amongst its parts: As for inſtance, amongſt

bodies that are immutable and incorruptible, according to
tle, Tycho, and others; amongſt bodies, I ſay, of ſuch nobility, by
the confeſſion of every one, and Copernicus himſelf, who affirmeth
them to be ordinate, and diſpoſed in a perfect conſtitution, and
removeth from them all inconſtancy of vertue amongſt, theſe
dies, I ſay once more, ſo pure, that is to ſay, amongſt Venus, Mars,
&c. to place the very ſink of all corruptible matters, to wit, the
Earth, Water, Air, and all mixt bodies.
A fifih
ment againſt
pernicus.
Another
rence between the
Earth and the
leſtial bodies,
ken from purity &
impurity.
But how much properer a diſtribution, and more with nature,
yea with God himſelf, the Architect, is it, to ſequeſter the pure
1from the impure, the mortal from the immortal, as other Schools
teach; which tell us that theſe impure and frail matters are
teined within the anguſt concave of the Lunar Orb, above which
with uninterrupted Series the things Celeſtial diſtend themſelves.
SALV. It's true that the Copernican Syſteme introduceth

ſtraction in the univerſe of Aristotle; but we ſpeak of our own
Univerſe, that is true and real. Again if this Author will infer
the diſparity of eſſence between the Earth and Celeſtial bodies
from the incorruptibility of them, and the corruptibility of it in
the method of Ariſtotle, from which diſparity he concludeth
tion to belong to the Sun and fixed Stars, and the immobility of
the Earth, he will flatter himſelf with a Paralogiſme, ſuppoſing

that which is in queſtion; for Ariſtotle inferreth the
lity of Celeſtial bodies from motion, which is in diſpute,
ther it belongeth to them or to the Earth. Of the vanity of theſe
Rhetorical Illations enough hath been ſpoken. And what can be

more fond, than to ſay, that the Earth and Elements are
ſhed and ſequeſtred from the Celeſtial Spheres, and confined
within the Lunar Orb? Is, not then the Moons Orb one of the
Celeſtial Spheres, and according to conſent compriſed in the
middle of all the reſt? Its a new way to ſeparate the pure from
the impure, and the ſick from the ſound, to aſſigne the infected
quarters in the heart of the City: I had thought that the ^{*}

houſe ought to have been removed as far off as was poſſible.
Copernicus admireth the diſpoſition of the parts of the Univerſe,
for that God hath conſtituted the grand Lamp, which is to give
light all over his Temple in the centre of it, and not on one
ſide. And as to the Earths being betwixt Venus and Mars,
we will but hint the ſame; and do you, in favour of this Author,
trie to remove it thence. But let us not ^{*} mix theſe Rhetorical

Flowers with ſolid Demonſtrations, rather let us leave them to
the Orators, or if you will to the Poets, who know how in their
drolling way to exalt by their prayſes things moſt ſordid, yea and
ſometimes moſt pernicious. And if any thing elſe remain, let us
diſpatch it, as we have done the reſt.
Copernicus in
troduceth confuſion
in the Univerſe of
Ariſtotle.
The Paralogiſme
of the Author of
Anti-Tycho.
It ſeemeth a
folly to affirm the
Earth to be
out the Heavens.
* Lazeretto
* Intrecciare, to
twine flowers in a
garland.
SIMP. There is the ſixth and laſt argument, wherein he

keth it a very improbale thing. [That a corruptible and diſſipable
body ſhould move with a perpetual and regular motion; and this
he confirmeth with the example of living creatures, which moving
with a motion natural to them, yet grow weary, and have need of
repoſe to reſtore their ſtrength.] But what hath this motion to do
with that of the Earth, that in compariſon to theirs is immenſe?
Beſides, to make it move with three motions that run and draw
ſeveral wayes: Who would ever aſſert ſuch Paradoxes, unleſſe
he had ſworn to be their defender? Nor doth that avail in this
1caſe, which Copernicus alledgeth, that by reaſon this motion is
natural to the Earth and not violent, it worketh contrary effects
to violent motions; and that thoſe things diſſolve and cannot
long ſubſiſt, to which impulſe is conferred, but thoſe ſo made
by nature do continue in their perfect diſpoſure; this anſwer
ficeth not, I ſay, for it is overthrown by that of ours. For the
nimal is a natural body, and not made by art, and its motion is
natural, deriving it ſelf from the ſoul, that is, from an intrinſick
principle; and that motion is violent, whoſe beginning is
out, and on which the thing moved conferreth nothing;
ever, if the animal continueth its motion any long time, it grows
weary, and alſo dyeth, if it obſtinately ſtrive to perſiſt therein.
You ſee then that in nature we meet on all ſides with notions
trary to the Copernican Hypotheſis, and none in favour of it. And
for that I have nothing more wherein to take the part of this
ponent, hear what he produceth againſt Keplerus (with whom
he diſputeth) upon that argument, which the ſaid Kepler bringeth
againſt thoſe who think it an inconvenient, nay impoſſible thing,
to augment the Starry Sphere immenſely, as the Copernican
potheſis requireth. Kepler therefore inſtanceth, ſaying:
us ect, accidens præter modulum ſubjecti intendere, quàm ſub-

jectum ſine accidente augere. Copernicus ergo veriſimilius facit,
qui auget Orbem Stellarum fixarum abſque motu, quam Ptolomæus,
qui auget motum fixarum immenſà velocitate. [Which makes this
Engliſh.] Its harder to ſtretch the accident beyond the model of the
ſubject than to augment the ſubject without the accident. Coperni-
hath more probability on his ſide, who encreaſeth the Orb of the
fixed Stars without motion, than Ptolomy who augmenteth the
motion of the fixed Stars to an immenſe degree of velocity.

Which objection the Author anſwereth, wondering how much
Kepler deceived himſelf, in ſaying, that in the Ptolomaick
ſis the motion encreaſeth beyond the model of the ſubject, for in
his judgment it doth not encreaſe, ſave onely in conformity to the
model, and that according to its encreaſement, the velocity of

the motion is augmented. Which he proveth by ſuppoſing a
chine to be framed, that maketh one revolution in twenty four
hours, which motion ſhall be called moſt ſlow; afterwards
poſing its ſemidiameter to be prolonged, as far as to the diſtance
of the Sun, its extreme will equal the velocity of the Sun; and
it being cantinued out unto the Starry Sphere, it will equal the
velocity of the fixed Stars, though in the circumferrnce of the
machine it be very ſlow. Now applying this conſideration of the
machine to the Starry Sphere, let us imagine any point in its
midiameter, as neer to the centre as is the ſemidiameter of the
chine; the ſame motion that in the Starry Sphere is exceeding
1ſwift, ſhall in that point be exceeding ſlow; But the great
nitude of the body is that which maketh it of exceeding ſlow, to
become exceeding ſwift, although it continueth ſtill the ſame, and
thus the velocity encreaſeth, not beyond the model of the
ject, but rather according to it, and to its magnitude; very
ferently from the imagination of Kepler.
A ſixth
ment againſt
pernicus, taken
from animals, who
have need of
though their
on be natural.
An argument
from Kepler in
vour of
cus.
The Author of
the Anti Tycho
poſeth Kepler.
The velocity of
the circular
on increaſeth,
cording to the
creaſe of the
meter of the circle.
SALV. I do not believe that this Author hath entertained ſo
mean and poor a conceit of Kepler, as to perſwade himſelf that
he did not underſtand, that the higheſt term of a line drawn from
the centre unro the Starry Sphere, moveth more ſwiftly than a
point of the ſame line taken within a yard or two of the centre. And
therefore of neceſſity he muſt have conceived and

ed that the mind and intention of Kepler was to have ſaid, that
it is leſſe inconvenient to encreaſe an immoveable body to an
traordinary magnitude, than to aſcribe an extraordinary velocity
to a body, though very bigge, having regard to the model,
that is to the gauge, and to the example of other natural bodies;
in which we ſee, that the diſtance from the centre encreaſing, the
velocity diminiſheth; that is, that the periods of their
ons take up longer times. But in reſt which is not capable of

mentation or diminution, the grandure or ſmalneſſe of the body
maketh no differeuce. So that if the anſwer of the Author would
be directed againſt the argument of Kepler, it is neceſſary, that
that Author doth hold, that to the movent principle its one and the
ſame to move in the ſame time a body very ſmall, or very
menſe, in regard that the augmentation of velocity inſeparably
attends the augmentation of the maſſe. But this again is contrary

to the Architectonical rule of nature, which doth in the leſſer
Spheres, as we ſee in the Planets, and moſt ſenſibly in the
cean Stars, obſerve to make the leſſer Orbs to circulate in ſhorter
times: Whence the time of Saturns revolution is longer than all
the times of the other leſſer Spheres, it being thirty years; now
the paſſing from this to a Sphere very much bigger, and to make
it move in 24. hours, may very well be ſaid to exceed the rules of
the model. So that if we would but attentively conſider it, the
Authors anſwer oppoſeth not the intent and ſenſe of the argument,
but the expreſſing and manner of delivering of it; where again
the Author is injurious, and cannot deny but that he artificially
diſſembled his underſtanding of the words, that he might charge
Kepler with groſſe ignorance; but the impoſture was ſo very dull
and obvions, that he could not with all his craft alter the
on which Kepler hath begot of his Doctrine in the minds of all
the Learned. As in the next place, to the inſtance againſt the
perpetual motion of the Earth, taken from the impoſſibility of
its moving long without wearineſſe, in regard that living
1tures themſelves, which yet move naturally, and from an intern
principle, do grow weary, and have need of reſt to relax and
freſh their members --------
An explanation
of the true ſenſe of
Kepler and his
fence.
The greatneſſe
and ſmalneſſe of
the body make a
difference in
on and not in reſt.
The order of
ture is to make the
leſſer Orbs to
culate in ſhorter
times, and the
ger in longer times.
SAGR. Methinks I hear Kepler anſwer him to that, that
there are ſome kinde of animals which refreſh themſelves after
wearineſſe, by rowling on the Earth; and that therefore there

is no need to fear that the Terreſtrial Globe ſhould tire, nay it
may be reaſonably affirmed, that it enjoyeth a perpetual & moſt
tranquil repoſe, keeping it ſelf in an eternal rowling.
The feigned
ſwer of Kepler
vered with an
tificial Irony.
SALV. You are too tart and Satyrical, Sagredus: but let us
lay aſide jeſts, whilſt we are treating of ſerious things.
SAGR. Excuſe me, Salviatus, this that I ſay is not ſo
lutely beſides the buſineſs, as you perhaps make it; for a motion
that ſerveth inſtead of reſt, and removeth wearineſs from a body
tired with travail, may much more eaſily ſerve to prevent the

ming of that wearineſs, like as preventive remedies are more eaſie
than curative. And I hold for certain, that if the motion of
mals ſhould proceed in the ſame manner as this that is aſcribed to
the Earth, they would never grow weary; Seeing that the
neſs of the living creature, deriveth it ſelf, in my opinion, from

the imployment of but one part alone in the moving of its ſelf,
and all the reſt of the body; as v. g. in walking, the thighs and
the legs onely are imployed for carrying themſelves and all the
reſt: on the contrary, you ſee the motion of the heart to be as it
were indefatigable, becauſe it moveth it ſelf alone. Beſides, I

know not how true it may be, that the motion of the animal is
tural, and not rather violent: nay, I believe that one may truly
ſay, that the ſoul naturally moveth the members of an animal with
a motion preternatural, for if the motion upwards is
ral to grave bodies, the lifting up of the legs, and the thighs,
which are grave bodies, in walking, cannot be done without
lence, and therefore not without labour to the mover. The
climbing upwards by a ladder carrieth the grave body contrary to
its natural inclination upwards, from whence followeth wearineſs,
by reaſon of the bodies natural averſneſs to that motion: but in
moving a moveable with a motion, to which it hath no averſion,

what laſſitude, what diminution of vertue and ſtrength need we
fear in the mover? and how ſhould the forces waſte, where they
are not at all imployed?
Animals would
not grow weary of
their motion,
ceeding as that
which is aſſigned
to the terreſtrial
Globe.
The cauſe of the
wearineſſe of
mals.
The motion of
an animal is rather
to be called violent
than natural.
The ſtrength
miniſheth not,
where it is not
ployed.
SIMP. They are the contrary motions wherewith the Earth is
pretended to move, againſt which the Authour produceth his
gument.
SAGR. It hath been ſaid already, that they are no wiſe
traries, and that herein the Authour is extteamly deceived, ſo
that the whole ſtrength of the argument recoileth upon the
1ponent himſelf, whilſt he will make the Firſt Mover to hurry

along with it all the inferiour Spheres, contrary to the motion
which they themſelves at the ſame time exerciſe. It belongs
fore to the Primum Mobile to grow weary, which beſides the
moving of its ſelf is made to carry ſo many other Spheres, and
which alſo ſtrive againſt it with a contrary motion. So that
the ultimate concluſion that the Authour inferred, ſaying, that
diſcourſing of the effects of Nature, a man alwayes meets with
things that favour the opinion of Ariſtoile and Ptolomy, and
ver any one that doth not interfer with Copernicus, ſtands in need
of great conſideration; and it is better to ſay, that one of theſe
two Hypotheſes being true, and the other neceſſarily falſe, it is
impoſſible that a man ſhould ever be able to finde any
ment, experience, or right reaſon, in favour of that which is

falſe, like as to the truth none of theſe things can be repugnant.
Vaſt difference, therefore, muſt needs be found between the
ſons and arguments produced by the one and other party, for and
againſt theſe two opinions, the force of which I leave you your
ſelf to judge of, Simplicius.
The argument
of Claramontius
recoileth upon
ſelf.
True
ons meet with
ny concluſive
guments, ſo do not
the falſe.
SALV. But you, Sagredus, being tranſported by the velocity
of your wit, have taken my words out of my mouth, whilſt I was
about to ſay ſomething, touching this laſt argument of the Author;
and although you have more then ſufficiently refuted him, yet
nevertheleſſe I will adde ſomewhat, which then ran in my minde.
He propoſeth it as a thing very unlikely, that a body diſſipable
and corruptible, as the Earth, ſhould perpetually move with a
gular motion, cſpecially for that we ſee living creatures in the end
to grow weary, and to ſtand in need of reſt: and the improbability
is increaſed, in that the ſaid motion is required to be of velocity
incomparable and immenſe, in reſpect to that of animals. Now, I
cannot ſee why the velocity of the Earth ſhould, at preſent,
ble it; ſo long as that of the ſtarry Sphere ſo very much bigger
doth not occaſion in it any diſturbance more conſiderable, than that
which the velocity of a machine, that in 24 hours maketh but one
ſole revolution, produceth in the ſame. If the being of the
city of the Earths converſion, according to the model of that
chine, inferreth things of no greater moment than that, let the
thor ceaſe to fear the Earths growing weary; for that not one of
the moſt feeble and ſlow-pac't animals, no not a Chamæleon would

tire in moving no more than ^{*} four or five yards in 24 hours; but
if he pleaſe to conſider the velocity to be no longer, in relation to

the model of the machine, but abſolutely, and inaſmuch as the
moveable in 24 hours is to paſs a very great ſpace, he ought to ſhew
himſelf ſo much more reſerved in granting it to the ſtarry Sphere,
which with a velocity incomparably greater than that of the
1Earth is to carry along with it a thouſand bodies, each much
ger than the Terreſtrial Globe.
* Cinque ò ſei
braccia Fiorentini.
Wearineß more
to be feared in the
ſtarry Sphere than
in the terreſtriall
Globe.
Here it remains for us to ſee the proofs, whereby the Authour
concludes the new ſtars Anno 1572. and Anno 1604. to be
nary, and not cœleſtial, as the Astronomers of thoſe times were
generally perſwaded; an enterprize very great certainly; but I
have conſidered, that it will be better, in regard the Book is new
and long, by reaſon of its many calculations, that between this
vening and to morrow morning I make them as plain as I can, and
ſo meeting you again to morrow to continue our wonted
rences, give you a brief of what I ſhall obſerve therein; and if we
have time left, we will ſay ſomething of the Annual motion
bed to the Earth. In the mean time, if either of you, and
cius in particular, hath any thing to ſay more, touching what relates
to the Diurnal motion, at large examined by me, we have a little
time ſtill left to treat thereof.
SIMP. I have no more to ſay, unleſſe it be this, that the
ſes that this day have falne under our debate, have appeared to me
fraught with very acute and ingenious notions, alledged on
nicus his ſide, in confirmation of the motion of the Earth, but yet
I find not my ſelf perſwaded to believe it; for in ſhort, the things
that have been ſaid conclude no more but this, that the reaſons
for the ſtability of the Earth are not neceſſary; but all the while
no demonſtration hath been produced on the other ſide, that doth
neceſſarily convince and prove its mobility.
SALV. I never undertook, Simplicius, to remove you from that
your opinion; much leſs dare I preſume to determine definitively
in this controverſie: it onely was, and ſtill ſhall be in the enſuing
diſputations my intent, to make it appear to you, that thoſe who
have thought that moſt ſwift motion of 24 hours doth belong to
the Earth alone, and not to the Univerſe, the Earth onely
ded, were not induced to believe, that ſo it might and ought to do
out of any blind perſwaſion; but that they did very well ſee, try,
and examine the reaſons on the contrary ſide, and alſo not
ly anſwer them. With the ſame intention, if it ſtand with your
liking, and that of Sagredus, we may paſſe to the conſideration of
that other motion; firſt, by Aristarchus Samius, and afterwards
by Nicholaus Copernicus aſcribed to the ſaid Terreſtrial Globe,
which is, as, I believe, you have heretofore heard, made under the
Zodiack within the ſpace of a year about the Sun, immoveably
placed in the centre of the ſaid Zodiack.
SIMP. The diſquiſition is ſo great, and ſo noble, that I ſhall
gladly hearken to the diſcuſſion thereof, perſwading my ſelf that I
ſhall hear what ever can be ſaid of that matter. And I will
1wards by my ſelf, according to my uſual cuſtome, make more
liberate reflexions upon what hath been, and is to be ſpoken; and
if I ſhould gain no more but this, it will be no ſmall benefit
that I ſhall be able to diſcourſe more Logically.
SAGR. Therefore, that we may no further weary Salviatus,
we will put a period to the diſputations of this day, and
aſſume our conference to morrow in the uſual manner, with hope
to hear very pleaſing novelties.
SIMP. I will leave with you the Book De ſtellis novis, and
ry back this of the Concluſions, to ſee what is written therein
gainſt the Annual motion, which are to be the arguments of our
diſcourſe to morrow.
1
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19[Figure 9]10[Figure 10]11[Figure 11]12[Figure 12]13[Figure 13]14[Figure 14]15[Figure 15]16[Figure 16]17[Figure 17]
Place this Plate
at the end of
the Second
Dialogue.
1
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1
GALILÆUS
Galilæus Lyncæus,
HIS
SYSTEME
OF THE
WORLD.
The Third Dialogue.
INTERLOCVTORS.
SALVIATUS, SAGREDUS, and SIMPLICIUS.
SAGR. The great deſire wherewith I have expected
your coming, that I might hear the novel
conceits touching the annual
on of this our Globe, hath made me
think the houres of the laſt night, and
thoſe of this morning very tedious,
though I ſpent them not idly, but lying
awake I imployed a good part thereof in
ruminating upon our yeſterdayes
ſes, weighing the reaſons alledged by both parties, in favour of
the two contrary Hypotheſes, that of Ariſtotle and Ptolomy, and
this of Ariſtarchus, and Copernicus. And really methinks, that
which ever of theſe parties have been deceived, they are worthy of
excuſe, ſo ſpecious and valid in appearance are the reaſons that
may have perſwaded them either way; though nevertheleſſe we
1do for the moſt part cloſe with thoſe produced by the grave
thours firſt above mentioned. But albeit that the Peripatetick
potheſis, by reaſon of its antiquity, hath had many followers and
fautors, and the other very few; firſt, for its obſcurity, and next,
for its novelty, yet methinks I diſcover amongſt thoſe many,
and particularly amongſt the modernes ſome, who for the
port of the opinion by them eſteemed true, have introduced
other reaſons ſufficiently childiſh, I could ſay ridiculous.
SALV. I have met with the like, and ſo much worſe than

yours, that I bluſh to rehearſe them, not ſo much to ſpare the fame
of their Authours, the names of whom might be perpetually
cealed, as becauſe I am aſhamed ſo much to ſtain the honour of
mankinde. In obſerving of theſe men, I have found that ſome
there are who prepoſterouſly reaſoning, firſt ſtabliſh the
ſion in their fancy, and (either becauſe it is their own, or elſe
longs to a perſon whom they much confide in) ſo firmly imprint
it in their opinions, that it is altogether impoſſible ever wholly to
efface it: and thoſe reaſons which they themſelves ſtumble upon,
or which they hear others to alledge in confirmation of the
ceit entertained, though never ſo ſimple and inſipid, inſtantly find
credit and applauſe with them: but on the contrary, thoſe which
are brought againſt their opinion, though ingenuous and
ding, they receive not only with nauſeating, but with diſdain and
bitter indignation, yea, you ſhall have one of theſe ſo inraged, as
that he will not be backward to try all wayes to ſuppreſs and ſilence
their adverſaries: and of this I my ſelf have had ſome experience.
Some in arguing
firſt fix in their
minds the
ſion beleeved by
them, and then
dapt their reaſons
to that.
SAGR. Indeed theſe men deduce not the concluſion from the
premiſes, nor confirme them with reaſons, but accomodate, or to
ſay better, diſcommodate and diſtort the premiſes and arguments
to make them ſpeak in favour of their pre-aſſumed and
ous concluſions. It is not good therefore to contract familiarity
with theſe men; and the rather, for that their converſation is not
only unpleaſant, but alſo dangerous. Yet let us continue our
ference with Simplicius however, whom I have known this long
while for a man of great ingenuity, and altogether void of malice:
beſides he is well verſt in the Peripatetick Doctrine; ſo that I may
aſſure my ſelf, that what ſhall not fall within the reach of his
ſon for the ſupport of the Ariſtotelian Hypotheſis, will not eaſily
be found out by others. But ſee yonder he comes, quite out of
winde, whoſe company we have ſo long deſired: we were juſt now
ſpeaking againſt the ſmall haſt you made to come to us.
SIMP. You muſt not blame me, but Neptune, for this my long
ſtay; which in the ebbe of this mornings tide hath in a manner
drain'd away the waters, for the Gondola that brought me, being
entered not far from hence into a certain Channel, wanting depth,
1where I was ſtranded, and forced to ſtay there more than a full
hour, in expecting the return of the tide: and there waiting in
this manner, without being able to get out of the boat, which on a
ſudden ran a ground, I obſerved a certain accident, which to me

ſeemed very ſtrange; and it was this, that in the waters ebbing
I ſaw it retreat very faſt by ſeveral ſmall rivolets, the ouze being
in many places diſcovered, and whilſt I ſtood looking upon this
fect, I ſaw this motion in an inſtant to ceaſe, and without a
nutes interval the ſame water to begin to return back again, and
the tide from ebbing to become young flood, without ſtanding
ſtill a moment: an effect that as long as I have dwelt in Venice,
I never took notice of before.
The motion of
the water in ebbing
and flowing not
terrupted by reſt.
SAGR. It is very much, that you ſhould be left thus on ground,
amongſt ſmall Channels; in which rivolets, as having very little
declivity, the riſing or falling of the main ſea, the thickneſs onely
of a paper is ſufficient to make the water to ebbe and flow for good
long ſpaces of time: like as in ſome creeks of the Sea, its flowing
four or ſix ^{*} yards onely, maketh the water to overflow the
cent Marſhes for ſome hundreds and thouſands of ^{*}
* Pertiche
tiani.
SIMP. This I know very well, but I ſhould have thought, that
between the ultimate terme of ebbing, and the firſt beginnng to
flow, there ſhould have interpoſed ſome conſiderable interval of
reſt.
SAGR. This will appear unto you, if you caſt your eye upon
the bank or piles, where theſe mutations are made
ly, but not that there is any real time of ceſſation.
SIMP. I did think, that becauſe theſe two motions were
trary, there ought to be in the midſt between them ſome kind of
reſt; conformable to the Doctrine of Ariſtotle, which demonſtrates.
that in puncto regreſſus mediat quies.
SAGR. I very well remember this place: but I bear in minde
alſo, that when I read Philoſophy, I was not thorowly ſatisfied
with Ariſtotles demonſtration; but that I had many experiments
on the contrary, which I could ſtill rehearſe unto you, but I am
unwilling to ſally out into any other digreſſions, we being met
here to diſcourſe of the propoſed mattes, if it be poſſible, without
theſe excurſions wherewith we have interrupted our diſputes in
thoſe dayes that are paſt.
SIMP. And yet we may with convenience, if not interrupt
them, at leaſt prolong them very much, for returning
day home, I ſet my ſelſ to read the Tractate of Concluſions, where
I find Demonſtrations againſt this annual motion aſcribed to the
Earth, very ſolid; and becauſe I would not truſt my memory with
the punctual relation of them, I have brought back the Book
long with me.
1
SAGR. You have done very well; but if we would re-aſſume
our Diſputations according to yeſterdayes appointment, it is
quiſite that we firſt hear what account Salviatus hath to give us
of the Book, De ſtellis novis, and then without interruption we
may proceed to the Annual motion. Now what ſay you,
tus touching thoſe ſtars? Are they really pull'd down from
ven to theſe lower regions, by vertue of that Authours
ons, whom Simplicius mentioneth?
SALV. I ſet my ſelf laſt night to peruſe his proceedings, and I
have this morning had another view of him, to ſee whether that
which he ſeemed over night to affirm, were really his ſenſe, or my
dreams and phantaſtical nocturnal imaginations; and in the cloſe
found to my great grief that thoſe things were really written and
printed, which for the reputation-ſake of this Philoſopher I was
unwilling to believe. It is in my judgment impoſſible, but that he
ſhould perceive the vanity of his undertaking, aſwell becauſe it is
too apert, as becauſe I remember, that I have heard him
ned with applauſe by the Academick our Friend: it ſeemeth to
me alſo to be a thing very unlikely, that in complacency to others,
he ſhould be induced to ſet ſo low a value upon his reputation, as
to give conſent to the publication of a work, for which he could
expect no other than the cenſure of the Learned.
SAGR. Yea, but you know, that thoſe will be much fewer
than one for an hundred, compared to thoſe that ſhall celebrate
and extoll him above the greateſt wits that are, or ever have been
in the world: He is one that hath mentioned the
tick inalterability of Heaven againſt a troop of Aſtronomers, and
that to their greater diſgrace hath foiled them at their own
pons; and what do you think four or five in a Countrey that
cern his triflings, can do againſt the innumerable multitude, that,
not being able to diſcover or comprehend them, ſuffer themſelves
to be taken with words, and ſo much more applaud him, by how
much the leſſe they underſtand him? You may adde alſo, that
thoſe few who underſtand, ſcorn to give an anſwer to papers ſo
trivial and unconcludent; and that upon very good reaſons,
cauſe to the intelligent there is no need thereof, and to thoſe that
do not underſtand, it is but labour loſt.
SALV. The moſt deſerved puniſhment of their demerits would
certainly be ſilence, if there were not other reaſons, for which it
is haply no leſſe than neceſſary to reſent their timerity: one of
which is, that we Italians thereby incur the cenſure of Illiterates,
and attract the laughter of Forreigners; and eſpecially to ſuch
who are ſeparated from our Religion; and I could ſhew you
ny of thoſe of no ſmall eminency, who ſcoff at our Academick,
and the many Mathematicians that are in Italie, for ſuffering the
1follies of ſuch a ^{*} Fabler againſt Aſtronomers to come into the

light, and to be openly maintained without contradiction; but
this alſo might be diſpenſed with, in reſpect of the other greater
occaſions of laughter, wherewith we may confront them
ing on the diſſimulation of the intelligent, touching the follies of
theſe opponents of the Doctrines that they well enough
ſtand.
* Lorenzini.
SAGR. I deſire not a greater proof of thoſe mens petulancy,
and the infelicity of a Copernican, ſubject to be oppoſed by ſuch
as underſtand not ſo much as the very firſt poſitions, upon which
he undertakes the quarrel.
SALV. You will be no leſſe aſtoniſhed at their method in
futing the Astronomers, who affirm the new Stars to be ſuperiour
to the Orbs of the Planets; and peradventure in the ^{†} Firmament

it ſelf.
† He taketh the
Firmament for the
Starry Sphere, and
as we vulgarly
ceive the word.
SAGR. But how could you in ſo ſhort a time examine all this
Book, which is ſo great a Volume, and muſt needs contain very
many demonſtrations.?
SALV. I have confined my ſelf to theſe his firſt confutations, in
which with twelve demonſtrations founded upon the obſervations
of twelve Aſtronomers, (who all held, that the Star, Anno 1572.
which appeared in Caſſiopeia, was in the Firmament) he proveth it
on the contrary, to be beneath the Moon, conferring, two by two,
the meridian altitudes, proceeding in the method that you ſhall
underſtand by and by. And becauſe, I think, that in the
nation of this his firſt progreſſion, I have diſcovered in this
thour a great unlikelihood of his ability to conclude any thing
gainſt the Aſtronomers, in favour of the Peripatetick Philoſophers,
and that their opinion is more and more concludently confirmed,
I could not apply my ſelf with the like patience in examining his
other methods, but have given a very ſlight glance upon them,
and am certain, that the defect that is in theſe firſt impugnations,
is likewiſe in the reſt. And as you ſhall ſee, by experience, very
few words will ſuffice to confute this whole Book, though
led with ſo great a number of laborious calculations, as here you

ſee. Therefore obſerve my proceedings. This Authour
taketh, as I ſay, to wound his adverſaries with their own weapons,
i.e. a great number of obſervations made by themſelves, to wit, by
twelve or thirteen Authours in number, and upon part of them he
makes his ſupputations, and concludeth thoſe ſtars to have been
below the Moon. Now becauſe the proceeding by
ries very much pleaſeth me, in regard the Authour himſelf is not
here, let Simplicius anſwer me to the queſtions that I ſhall ask
him, as he thinks he himſelf would, if he were preſent. And
ſuppoſing that we ſpeak of the foreſaid Star, of Anno 1572.
1pearing in Caſſiopeia, tell me, Simplicius, whether you believe that
it might be in the ſame time placed in divers places, that is,
mongſt the Elements, aud alſo amongſt the planetary Orbs, and
alſo above theſe amongſt the fixed Stars, and yet again infinitely
more high.
The method
ſerved by Clar. in
confuting the
ſtronomers, and by
Salviatus in
ting him.
SIMP. There is no doubt, but that it ought to be confeſſed
that it is but in one only place, and at one ſole and determinate
diſtance from the Earth.
SALV. Therefore if the obſervations made by the
mers were exact, and the calculations made by this Author were
not erroneous, it were eaſie from all thoſe and all theſe to
collect the ſame diſtances alwayes to an hair, is not this true?
SIMP. My reaſon hitherto tells me that ſo it muſt needs be;
nor do I believe that the Author would contradict it
SALV. But when of many and many computations that have
been made, there ſhould not be ſo much as two onely that prove
true, what would you think of them?
SIMP. I would think that they were all falſe, either through
the fault of the computiſt, or through the defect of the
vators, and at the moſt that could be ſaid, I would ſay, that but
onely one of them and no more was true; but as yet I know not
which to chooſe.
SALV. Would you then from falſe fundamentals deduce and
eſtabliſh a doubtful concluſion for ttue? Certainly no. Now the
calculations of this Author are ſuch, that no one of them agrees
with another, you may ſee then what credit is to be given to
them.
SIMP. Indeed, if it be ſo, this is a notable failing.
SAGR. But by the way I have a mind to help Simplicius, and
the Author by telling Salviatus, that his arguments would hold
good if the Author had undertook to go about to find out
ly the diſtance of the Star from the Earth, which I do not think
to be his intention; but onely to demonſtrate that from thoſe
obſervations he collected that the Star was ſublunary. So
that if from thoſe obſervations, and from all the computations
made thereon, the height of the Star be alwayes collected to be
leſſe than that of the Moon, it ſerves the Authors turn to
vince all thoſe Aſtronomers of moſt impardonable ignorance,
that through the defect either of Geometry or Arithmetick, have
not known how to draw true concluſions from their own
tions themſelves.
SALV. It will be convenient therefore that I turn my ſelf to
you, Sagredus, who ſo cunningly aphold the Doctrine of this
Author. And to ſee whether I can make Simplicius, though not
very expert in calcnlations, and demonſtrations to apprehend the
1inconcluſiveneſſe at leaſt of the demonſtrations of this Author,
firſt propoſed to conſideration, and how both he, and all the
Aſtronomers with whom he contendeth, do agree that the new
Star had not any motion of its own, and onely went round with
the diurnal motion of the primum mobile; but diſſent about the
placing of it, the one party putting it in the Celeſtial Region,
that is above the Moon, and haply above the fixed Stars, and
the other judging it to be neer to the Earth, that is, under the
concave of the Lunar Orb. And becauſe the ſituation of the new
ſtar, of which we ſpeak, was towards the North, and at no very
great diſtance from the Pole, ſo that to us Septentrionals, it did
never ſet, it was an eaſie matter with Aſtronomical inſtruments
to have taken its ſeveral meridian altitudes, as well its ſmalleſt
under the Pole, as its greateſt above the ſame; from the
ring of which altitudes, made in ſeveral places of the Earth,
ſituate at different diſtances from the North, that is, different
from one another in relation to polar altitudes, the ſtars diſtance
might be inferred: For if it was in the Firmament amongſt the

other fixed ſtars, its meridian altitudes taken in divers elevations
of the pole, ought neceſſarily to differ from each other with the
ſame variations that are found amongſt thoſe elevations
ſelves; that is, for example, if the elevation of the ſtar above
the horizon was 30 degrees, taken in the place where the polar
altitude was v. gr. 45 degrees, the elevation of the ſame ſtar
ought to have been encreaſed 4 or 5 degrees in thoſe more
thernly places where the pole was higher by the ſaid 4 or 5
grees. But if the ſtars diſtance from the Earth was but very little,
in compariſon of that of the Firmament; its meridian altitudes
ought approaching to the North to encreaſe conſiderably more
than the polar altitudes; and by that greater encreaſe, that is,
by the exceſſe of the encreaſe of the ſtars elevation, above the
encreaſe of the polar elevation (which is called the difference of
Parallaxes) is readily calculated with a cleer and ſure method,
the ſtars diſtance from the centre of the Earth. Now this Author
taketh the obſervations made by thirteen Aſtronomers in ſundry
elevations of the pole, and conferring a part of them at his
ſure, he computeth by twelve collations the new ſtars height to
have been alwayes beneath the Moon; but this he adventures to
do in hopes to find ſo groſſe ignorance in all thoſe, into whoſe
hands his book might come, that to ſpeak the truth, it hath turn'd
my ſtomack; and I wait to ſee how thoſe other Aſtronomers, and
particularly Kepler, againſt whom this Author principally
veigheth, can contein themſelves in ſilence, for he doth not uſe
to hold his tongue on ſuch occaſions; unleſſe he did poſſibly
think the enterprize too much below him. Now to give you to
1underſtand the ſame, I have upon this paper tranſcribed the
cluſions that he inferreth from his twelve indagations; the firſt of
which is upon the two
The greateſt and
leaſt elevations of
the new ſtar differ
not from each
ther more than the
polar allitudes, the
ſaid ſtar being in
the Firmnment.
Of Maurolicus and Hainzelius, from which the Star is collected to have been diſtant from the centre leſſe than 3 ſemidiameters of the Earth, the difference of Parallaxes being 4 gr. 42 m.30 ſec.3 ſemid.2. And is calculated on the obſervations of Hain-zelius, with Parall. of 8. m. 30 ſec. and its di-ſtance from the centre is computed to be more than25 ſemid.3. And upon the obſervations of Tycho and Hain-zelius, with Parall. of 10 m. and the diſtance of the centre is collected to be little leſſe than19 ſemid.4. And upon the obſervations of Tycho and the Landgrave, with Parall. of 14 m. the diſtance from the centre is made to be about10 ſemid.5. And upon the obſervations of Hainzelius and Gemma, with Parall. of 42 m. 30 ſec. whereby the diſtance is gathered to be about4 ſemid.6. And upon the obſervations of the Landgraveand Camerarius, with Parall. of 8 m. the di-ſtance is concluded to be about4 ſemid.7. And upon the obſervations of Tycho and Hage-cius, with Parall. of 6 m. and the diſtance is made31 ſemid.8. And upon the obſervations of Hagecius and Vr-ſinus with Parall. of 43 m. and the ſtars diſtance from the ſuperficies of the Earth is rendred1/2 ſemid.9. And upon the obſervations of Landgravius and Buſchius, with Parall. of 15 m. and the di-ſtance from the ſuperficies of the Earth is by ſupputation1/48 ſemid.10. And upon the obſervations of Maurolice and Munocius, with Parall. of 4 m. 30 ſec. and the compnted diſtance from the Earths ſurface is1/5 ſemid.11. And upon the obſervations of Munocius and Gemma, with Parall. of 55 m. and the diſtance from the centre is rendred13 ſemid.
112. And upon the obſervations of Munoſius and Vrſinus with Parall. of 1 gr. 36 m. and the di-ſtance from the centre cometh forth leſſe than7 ſemid.
Theſe are twelve indagations made by the Author at his
on, amongſt many which, as he ſaith, might be made by
ning the obſervations of theſe thirteen obſervators. The which
twelve we may believe to be the moſt favourable to prove his
intention.
SAGR. I would know whether amongſt the ſo many other
dagations pretermitted by the Author, there were not ſome that
made againſt him, that is, from which calculating one might find
the new ſtar to have been above the Moon, as at the very firſt
ſight I think we may reaſonably queſtion; in regard I ſee theſe
already produced to be ſo different from one another, that ſome
of them give me the diſtance of the ſaid ſtar from the Earth, 4, 6,
10, 100, a thouſand, and an hundred thouſand times bigger one
than another; ſo that I may well ſuſpect that amongſt thoſe that
he did not calculate, there was ſome one in fauour of the adverſe
party. And I gueſſe this to be the more probable, for that I
not conceive that thoſe Aſtronomers the obſervators could want
the knowledg and practice of theſe computations, which I think
do not depend upon the abſtruceſt things in the World. And
deed it will ſeem to me a thing more than miraculous, if whilſt in
theſe twelve inveſtigations onely, there are ſome that make the
ſtar to be diſtant from the Earth but a few miles, and others that
make it to be but a very fmall matter below the Moon, there are
none to be found that in favour of the contrary part do make it
ſo much as twenty yards above the Lunar Orb. And that which
ſhall be yet again more extravagant, that all thoſe Aſtronomers
ſhould have been ſo blind as not to have diſcovered that their ſo
apparent miſtake.
SALV. Begin now to prepare your ears to hear with infinite
admiration to what exceſſes of confidence of ones own authority
and others folly, the deſire of contradicting and ſhewing ones
ſelf wiſer than others, tranſports a man. Amongſt the
tions omitted by the Author, there are ſuch to be found as make
the new ſtar not onely above the Moon, but above the fixed
ſtars alſo. And theſe are not a few, but the greater part, as you
ſhall ſee in this other paper, where I have ſet them down.
SAGR. But what ſaith the Author to theſe? It may be he did
not think of them?
SALV. He hath thought of them but too much: but ſaith, that
the obſervations upon which the calculations make the ſtar to be
infinitely remote, are erroneous, and that they cannot be
bined to one another.
1
SIMP. But this ſeemeth to me a very lame evaſion; for the
verſe party may with as much reaſon reply, that thoſe are
ous wherewith he collecteth the ſtar to have been in the
tary Region.
SALV. Oh Simplicius, if I could but make you comprehend
the craft, though no great craftineſſe of this Author, I ſhould
make you to wonder, and alſo to be angry to ſee how that he
palliating his ſagacity with the vail of the ſimplicity of your ſelf;
and the reſt of meer Philoſophers, would inſinuate himſelf into
your good opinion, by tickling your cars, and ſwelling your
bition, pretending to have convinced and ſilenced theſe petty
Aſtronomers, who went about to aſſault the impregnable
rability of the Peripatetick Heaven, and which is more, to have
foild and conquered them with their own arms. I will try with all
my ability to do the ſame; and in the mean time let Sagredus
take it in good part, if Simplicius and I try his patience, perhaps
a little too much, whilſt that with a ſuperfluous circumlocution
(ſuperfluous I ſay to his moſt nimble apprehenſion) I go about to
make out a thing, which it is not convenient ſhould be hid and
unknown unto him.
SAGR. I ſhall not onely without wearineſſe, but alſo with
much delight hearken to your diſcourſes; and ſo ought all
tetick Philoſophers, to the end they may know how much they
are oblieged to this their Protector.
SALV. Tell me, Simplicius, whether you do well comprehend,
how, the new ſtar being placed in the meridian circle yonder
wards the North, the ſame to one that from the South ſhould
go towards the North, would ſeem to riſe higher and higher
bove the Horizon, as much as the Pole, although it ſhould have
been ſcituate amongſt the fixed ſtars; but, that in caſe it were
conſiderably lower, that is nearer to the Earth, it would appear
to aſcend more than the ſaid pole, and ſtill more by how much
its vicinity was greater?
SIMP. I think that I do very well conceive the ſame; in
ken whereof I will try if I can make a mathematical Scheme of
it, and in this great circle [in Fig. 1. of this Dialogue.] I will
marke the pole P; and in theſe two lower circles I will note two
ſtars beheld from one place on the Earth, which let be A; and
let the two ſtars be theſe B and C, beheld in the ſame line A B C,
which line I prolong till it meet with a fixed ſtar in D. And then
walking along the Earth, till I come to the term E, the two
ſtars will appear to me ſeparated from the fixed ſtar D, and
vanced neerer to the pole P, and the lower ſtar B more, which
will appear to me in G, and the ſtar C leſſe, which will ap
pear to me in F, but the fixed ſtar D will have kept the ſame
diſtance from the Pole.
1
SALV. I ſee that you underſtand the buſineſſe very well. I
lieve that you do likewiſe comprehend, that, in regard the ſtar B
is lower than C, the angle which is made by the rayes of the
ſight, which departing from the two places A and E, meet in C,
to wit, this angle A C E, is more narrow, or if we will ſay more
acute than the angle conſtituted in B, by the rayes A B and
E B.
SIMP. This I likewiſe underſtand very well.
SALV. And alſo, the Earth beine very little and almoſt
ſible, in reſpect of the Firmament (or Starry Sphere;) and
ſequently the ſpace A E, paced on the Earth, being very ſmall in
compariſon of the immenſe length of the lines E G and E F,
ſing from the Earth unto the Firmament, you thereby collect that
the ſtar C might riſe and aſcend ſo much and ſo much above the
Earth, that the angle therein made by the rayes which depart
from the ſaid ſtationary points A and E, might become moſt
cute, and as it were abſolutely null and inſenſible.
SIMP. And this alſo is moſt manifeſt to ſenſe.
SALV. Now you know Simplicius that Aſtronomers and
thematicians have found infallible rules by way of Geometry and
Arithmetick, to be able by help of the quantity of theſe angles
B and C, and of their differences, with the additional knowledg
of the diſtance of the two places A and E, to find to a foot the
remoteneſſe of ſublime bodies; provided alwayes that the
ſaid diſtance, and angles be exactly taken.
SIMP. So that if the Rules dependent on Geometry and
nomy be true, all the fallacies and errours that might be met with
in attempting to inveſtigate thoſe altitudes of new Stars or
mets, or other things muſt of neceſſity depend on the diſtance A E,
and on the angles B and C, not well meaſured. And thus all thoſe
differences which are found in theſe twelve workings depend, not
on the deſects of the rules of the Calculations, but on the errours
committed in finding out thoſe angles, and thoſe diſtances, by means
of the Inſtrumental Obſervations.
SALV. True; and of this there is no doubt to be made. Now
it is neceſſary that you obſerve intenſely, how in removing the Star
from B to C, whereupon the angle alwayes grows more acute, the
ray E B G goeth farther and farther off from the ray A B D in
the part beneath the angle, as you may ſee in the line E C F,
whoſe inferiour part E C is more remote from the part A C, than
is the part E B, but it can never happen, that by any whatſoever
immenſe receſſion, the lines A D and E F ſhould totally ſever from
each other, they being finally to go and conjoyn in the Star: and
onely this may be ſaid, that they would ſeparate, and reduce
ſelves to parallels, if ſo be the receſſion ſhould be infinite, which
1caſe is not to be ſuppoſed. But becauſe (obſerve well) the diſtance
of the Firmament, in relation to the ſmallneſſe of the Earth, as
hath been ſaid, is to be accounted, as if it were infinite; therefore
the angle conteined betwixt the two rayes, that being drawn from
the points A and E, go to determine in a fixed Star, is eſteemed
nothing, and thoſe rayes held to be two parallel lines; and
fore it is concluded, that then only may the New Star be affirmed
to have been in the Firmament, when from the collating of the
Obſervations made in divers places, the ſaid angle is, by
tion, gathered to be inſenſible, and the lines, as it were, parallels.
But if the angle be of a conſiderable quantity, the New Star muſt
of neceſſity be lower than thoſe fixed; and alſo than the Moon, in
caſe the angle A B E ſhould be greater than that which would be
made in the Moons centre.
SIMP. Then the remoteneſſe of the Moon is not ſo great, that
a like angle ſhould be ^{*}inſenſible in
* Imperceptible.
SALV. No Sir; nay it is ſenſible, not onely in the Moon, but
in the Sun alſo.
SIMP. But if this be ſo, it's poſſible that the ſaid angle may
be obſerved in the New Star, without neceſſitating it to be
our to the Sun, aſwell as to the Moon.
SALV. This may very well be, yea, and is in the preſent caſe,
as you ſhall ſee in due place; that is, when I ſhall have made plain
the way, in ſuch manner that you alſo, though not very perfect in
Aſtronomical calculations, may clearly ſee, and, as it were, with
your hands feel how that this Authour had it more in his eye to
write in complacency of the Peripateticks, by palliating and
ſembling ſundry things, than to eſtabliſh the truth, by producing
them with naked ſincerity: therefore let us proceed forwards. By
the things hitherto ſpoken, I ſuppoſe that you comprehend very
well how that the diſtance of the new Star can never be
made ſo immenſe, that the angle ſo often named ſhall wholly
appear, and that the two rayes of the Obſervators at the places
A and E, ſhall become altogether parallels: and you may
quently comprehend to the full, that if the calculations ſhould
collect from the obſervations, that that angle was totally null, or
that the lines were truly parallels, we ſhould be certain that the
obſervations were at leaſt in ſome ſmall particular erroneous:
But, if the calculations ſhould give us the ſaid lines to be
ted not only to equidiſtance, that is, ſo as to be parallel, but to
have paſt beyond that terme, and to be dilated more above than
below, then muſt it be reſolutely concluded, that the obſervations
were made with leſſe accurateneſſe, and in a word, to be
ous; as leading us to a manifeſt impoſſibility. In the next place,
you muſt believe me, and ſuppoſe it for true, that two right lines
1which depart from two points marked upon another right line, are
then wider above than below, when the angles included between
them upon that right line are greater than two right angles; and
if theſe angles ſhould be equal to two right angles, the lines would
be parallels; but if they were leſs than two right angles, the lines
would be concurrent, and being continued out would
ly interſect the triangle.
SIMP. Without taking it upon truſt from you, I know the
ſame; and am not ſo very naked of Geometry, as not to know a
Propoſition, which I have had occaſion of reading very often in
Ariſtotle, that is, that the three angles of all triangles are equall to
two right angles: ſo that if I take in my Figure the triangle ABE,
it being ſuppoſed that the line E A is right; I very well conceive,
that its three angles A, E, B, are equal to two right angles; and
that conſequently the two angles E and A are leſſe than two right
angles, ſo much as is the angle B. Whereupon widening the lines
A B and E B (ſtill keeping them from moving out of the points A
and E) untill that the angle conteined by them towards the parts
B, diſappear, the two angles beneath ſhall be equal to two right
angles, and thoſe lines ſhall be reduced to parallels: and if one
ſhould proceed to enlarge them yet more, the angles at the points
E and A would become greater than two right angles.
SALV. You are an Archimedes, and have freed me from the
expence of more words in declaring to you, that whenſoever the
calculations make the two angles A and E to be greater than two
right angles, the obſervations without more adoe will prove
neous. This is that which I had a deſire that you ſhould
ly underſtand, and which I doubted that I was not able ſo to make
out, as that a meer Peripatetick Philoſopher might attain to the
certain knowledg thereof. Now let us go on to what remains.
And re-aſſuming that which even now you granted me, namely,
that the new ſtar could not poſſibly be in many places, but in one
alone, when ever the ſupputations made upon the obſervations of
theſe Aſtronomers do not aſſign it the ſame place, its neceſſary
that it be an errour in the obſervations, that is, either in taking the
altitudes of the pole, or in taking the elevations of the ſtar, or in
the one or other working. Now for that in the many workings
made with the combinations two by two, there are very few of
the obſervations that do agree to place the ſtar in the ſame
tion; therefore theſe few onely may happily be the
ous, but the others are all abſolutely falſe.
SAGR. It will be neceſſary then to give more credit to theſe
few alone, than to all the reſt together, and becauſe you ſay,
that theſe which accord are very few, and I amongſt theſe 12,
do find two that ſo accord, which both make the diſtance of the
1ſtar from the centre of the Earth 4 ſemidiameters, which are theſe,
the fifth and ſixth, therefore it is more probable that the new ſtar
was elementary, than celeſtial.
SALV. You miſtake the point; for if you note well it was not
written, that the diſtance was exactly 4 ſemidiameters, but about
4 ſemidiameters; and yet you ſhall ſee that thoſe two diſtances
differed from each other many hundreds of miles. Here they are;
you ſee that this fifth, which is 13389 Italian miles, exceeds the
ſixth, which is 13100 miles, by almoſt 300 miles.
SAGR. Which then are thoſe few that agree in placing the ſtar
in the ſame ſituation?
SALV. They are, to the diſgrace of this Author five workings,
which all place it in the firmament, as you ſhall ſee in this note,
where I have ſet down many other combinations. But I will grant
the Author more than peradventure he would demand of me, which
is in ſum, that in each combination of the obſervations there is
ſome error; which I believe to be abſolutely neceſſary; for the
obſervations being four in number that ſerve for one working,
that is, two different altitudes of the Pole, and two different
tions of the ſtar, made by different obſervers, in different
ces, with different inſtruments, who ever hath any ſmall know­

ledg of this art, will ſay, that amongſt all the four, it is impoſſible
but there will be ſome error; and eſpecially ſince we ſee that in
taking but one onely altitude of the Pole, with the ſame
ment, in the ſame place, by the ſame obſerver, that hath
peated the obſervation a thouſand times, there will ſtill be a
bation of one, or ſometimes of many minutes, as in this ſame
book you may ſee in ſeveral places. Theſe things preſuppoſed,
I ask you Simplicius whether you believe that this Authour held
theſe thirteen obſervators for wiſe, underſtanding and expert men
in uſing thoſe inſtruments, or elſe for inexpert, and bunglers?
Aſtronomical
struments are very
ſubject to errour.
SIMP. It muſt needs be that he eſteemed them very acute and
intelligent; for if he had thought them unskilful in the buſineſſe,
he might have omitted his ſixth book as inconcluſive, as being
founded upon ſuppoſitions very erroneous; and might take us for
exceſſively ſimple, if he ſhould think he could with their
pertneſſe perſwade us to believe a falſe poſition of his for truth.
SALV. Therefore theſe obſervators being ſuch, and that yet
notwithſtanding they did erre, and ſo conſequently needed
rection, that ſo one might from their obſervations infer the
beſt hints that may be; it is convenient that we apply unto them
the leaſt and neereſt emendations and corrections that may be;
ſo that they do but ſuffice to reduce the obſervations from
ſibility to poſſibility; ſo as v. gr. if one may but correct a
feſt errour, and an apparent impoſſibility of one of their
1vations by the addition or ſubſtraction of two or three minutes, and
with that amendment to reduce it to poſſibility, a man ought
not to eſſay to adjuſt it by the addition or ſubſtraction of fifteen,
twenty, or fifty.
SIMP. I think the Authour would not deny this: for granting
that they are expert and judicious men, it ought to be thought that
they did rather erre little than much.
SALV. Obſerve again; The places where the new Star is
ced, are ſome of them manifeſtly impoſſible, and others poſſible.
Abſolutely impoſſible it is, that it ſhould be an infinite ſpace
riour to the fixed Stars, for there is no ſuch place in the world;
and if there were, the Star there ſcituate would have been
ceptible to us: it is alſo impoſſible that it ſhould go creeping along
the ſuperficies of the Earth; and much leſſe that it ſhould be
within the ſaid Terreſtrial Globe. Places poſſible are theſe that
be in controverſie, it not interferring with our underſtanding, that
a viſible object in the likeneſſe of a Star might be aſwell above the
Moon, as below it. Now whilſt one goeth about to compute by
the way of Obſervations and Calculations made with the utmoſt
certainty that humane diligence can attain unto what its place was,
it is found that the greateſt part of thoſe Calculations make it
more than infinitely ſuperiour to the Firmament, others make it
very neer to the ſurface of the Earth, and ſome alſo under the
ſame; and of the reſt, which place it in ſituations not impoſſible,
none of them agree with each other; inſomuch that it muſt be
confeſſed, that all thoſe obſervations are neceſſarily falſe; ſo that
if we would nevertheleſs collect ſome fruit from ſo many laborious
calculations, we muſt have recourſe to the corrections, amending
all the obſervations.
SIMP. But the Authour will ſay, that of the obſervations that
aſſign to the Star impoſſible places, there ought no account to be
made, as being extreamly erroneous and falſe; and thoſe onely
ought to be accepted, that conſtitute it in places not impoſſible:
and amongſt theſe a man ought to ſeek, by help of the moſt
bable, and moſt numerous concurrences, not if the particular and
exact ſituation, that is, its true diſtance from the centre of the
Earth, at leaſt, whether it was amongſt the Elements, or elſe
mongſt the Cœleſtial bodies.
SALV. The diſcourſe which you now make, is the ſelf ſame
that the Author made, in favour of his cauſe, but with too
ſonable a diſadvantage to his adverſaries; and this is that
pal point that hath made me exceſſively to wonder at the too great
confidence that he expreſſed to have, no leſs of his own authority,
than of the blindneſs and inadvertency of the Aſtronomers; in
favour of whom I will ſpeak, and you ſhall anſwer for the Author.
1And firſt, I ask you, whether the Aſtronomers, in obſerving with
their Inſtruments, and ſeeking v. gr. how great the elevation of a
Star is above the Horizon, may deviate from the truth, aſwell in
making it too great, as too little; that is, may erroneouſly
pute, that it is ſometime higher than the truth, and ſometimes
er; or elſe whether the errour muſt needs be alwayes of one
kinde, to wit, that erring they alwayes make it too much, and
ver too little, or alwayes too little, and never too much?
SIMP. I doubt not, but that it is as eaſie to commit an errour
the one way, as the other.
SALV. I believe the Author would anſwer the ſame. Now of
theſe two kinds of errours, which are contraries, and into which the
obſervators of the new ſtar may equally have fallen, applied to
calculations, one ſort will make the ſtar higher, and the other lower
than really it is. And becauſe we have already agreed, that all
the obſervations are falſe; upon what ground would this
thor have us to accept thoſe for moſt congruous with the truth,
that ſhew the ſtar to have been near at hand, than the others that
ſhew it exceſſively remote?
SIMP. By what I have, as yet, collected of the Authors mind,
I ſee not that he doth refuſe thoſe obſervations, and indagations
that might make the ſtar more remote than the Moon, and alſo
than the Sun, but only thoſe that make it remote (as you your ſelf
have ſaid) more than an infinite diſtance; the which diſtance,
cauſe you alſo do refuſe it as impoſſible, he alſo paſſeth over, as
being convicted of infinite falſhood; as alſo thoſe obſervations
are of impoſſibility. Methinks, therefore, that if you would
vince the Author, you ought to produce ſupputations, more exact,
or more in number, or of more diligent obſervers, which conſtitute
the ſtar in ſuch and ſuch a diſtance above the Moon, or above the
Sun, and to be brief, in a place poſſible for it to be in, like as he
produceth theſe twelve, which all place the ſtar beneath the Moon
in places that have a being in the world, and where it is poſſible for
it to be.
SALV. But Simplicius yours and the Authors Equivocation
lyeth in this, yours in one reſpect, and the Authors in another; I
diſcover by your ſpeech that you have formed a conceit to your
ſelf, that the exorbitancies that are commited in the eſtabliſhing
the diſtance of the Star do encreaſe ſucceſſively, according to the
proportion of the errors that are made by the Inſtrument, in
ing the obſervations, and that by converſion, from the greatneſs
of the exorbitancies, may be argued the greatneſſe of the error;
and that thereforefore hearing it to be infered from ſuch an
vation, that the diſtance of the ſtar is infinite, it is neceſſary, that
the errour in obſerving was infinite, and therefore not to be
1ed, and as ſuch to be refuſed; but the buſineſſe doth not ſucceed
in that manner, my Simplicius, and I excuſe you for not having
comprehended the matter as it is, in regard of your ſmall
ence in ſuch affairs; but yet cannot I under that cloak palliate the
error of the Author, who diſſembling the knowledge of this which
he did perſwade himſelf that we in good earneſt did not
ſtand, hath hoped to make uſe of our ignorance, to gain the
ter credit to his Doctrine, among the multitude of illiterate men.
Therefore for an advertiſement to thoſe who are more credulous
then intelligent, and to recover you from error, know that its
ſible (and that for the moſt part it will come to paſſe) that an
obſervation, that giveth you the ſtar v. gr. at the diſtance of
turn, by the adition or ſubſtraction of but one ſole minute from
the elevation taken with the inſtrument, ſhall make it to become
infinitely diſtant; and therefore of poſſible, impoſſible, and by
converſion, thoſe calculations which being grounded upon thoſe
obſervations, make the ſtar infinitely remote, may poſſibly
times with the addition or ſubduction of one ſole minute, reduce it
to a poſſible ſcituation: and this which I ſay of a minute, may
ſo happen in the correction of half a minute, a ſixth part, and leſs.
Now fix it well in your mind, that in the higheſt diſtances, that is
v. g. the height of Saturn, or that of the fixed Stars, very ſmall
errors made by the Obſervator, with the inſtrument, render the
ſcituation determinate and poſſible, infinite & impoſſible. This doth
not ſo evene in the ſublunary diſtances, and near the earth, where
it may happen that the obſervation by which the Star is collected to
be remote v. g. 4. Semidiameters terreſtrial, may encreaſe or
niſh, not onely one minute but ten, and an hundred, and many
more, without being rendred by the calculation either infinitely
remote, or ſo much as ſuperior to the Moon. You may hence
comprehend that the greatneſſe of the error (to ſo ſpeak)
mental, are not to be valued by the event of the calculation, but
by the quantity it ſelf of degrees and minutes numbred upon the
inſtrument, and theſe obſervations are to be called more juſt or
leſs erroneous, which with the addition or ſubſtraction of fewer
minutes, reſtore the ſtar to a poſſible ſituation; and amongſt the
poſſible places, the true one may be believed to have been that,
bout which a greater number of diſtances concurre upon
ting the more exact obſervations.
SIMP. I do not very well apprehend this which you ſay: nor
can I of my ſelf conceive how it can be, that in greater diſtances,
greater exorbitancies can ariſe from the errour of one minute only,
than in the ſmaller from ten or an hundred; and therefore would
gladly underſtand the ſame.
SALV. You ſhall ſee it, if not Theorically, yet at leaſt
1cally, by this ſhort aſſumption, that I have made of all the
nations, and of part of the workings pretermitted by the Author,
which I have calculated upon this ſame paper.
SAGR. You muſt then from yeſterday, till now, which yet is
not above eighteen hours, have done nothing but compute,
out taking either food or ſleep.
SALV. I have refreſhed my ſelf both thoſe wayes; but truth is,
make theſe ſupputations with great brevity; and, if I may ſpeak
the truth, I have much admired, that this Author goeth ſo farre
bout, and introduceth ſo many computations no wiſe neceſsary to
the queſtion in diſpute. And for a full knowledge of this, and
ſo to the end it may ſoon be ſeen, how that from the obſervations
of the Aſtronomers, whereof this Author makes uſe, it is more
bably gathered, that the new ſtar might have been above the
Moon, and alſo above all the Planets, yea amongſt the fixed ſtars,
and yet higher ſtill than they, I have tranſcribed upon this paper
all the obſervations ſet down by the ſaid Authour, which were
made by thirteen Aſtronomers, wherein are noted the Polar
tude, and the altitudes of the ſtar in the meridian, aſwell the
leſſer under the Pole, as the greater and higher, and they are


1


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1Tycho.gr.m.Altitude of the Pole5558Altitude of the Star8400the greateſt.2757the leaſt.And theſe are, according to the firſt paper: but accor-ding to the ſecond, the greateſt is ------------2745Hainzelius.gr.m.ſec.Altitude of the Pole4822Altitude of the Star76347633457635200940200930200920Peucerus and Sculerus.Landgravius.gr.m.gr.m.Altitude of the pole5154Altitude of the pole5118Altitude of the Star7956Altitude of the Star79302333Camerarius.gr.m.Altitude of the pole5224Altitude of the Star803080278026242824202417HageciusMaurolycus.gr.m.gr.m.Altitude of the pole4822Altitude of the pole3830Altitude of the Star2015Altitude of the Star6200Munocius.Vrſinus.gr.m.gr.m.Altitude of the pole3930Altitude of the pole4924Altitude of the ſtar6730Altitude of the ſtar790011302200Reinholdus.Buchius.gr.m.gr.m.Altitude of the pole5118Altitude of the pole5110Altitude of the ſtar7930Altitude of the ſtar792023022240Gemma.gr.m.Altitude of the pole5050Altitude of the ſtar7945
Now to ſee my whole proceeding, we may begin from theſe
calculations, which are four, omitted by the Author, perhaps
cauſe they make againſt him, in regard they place the ſtar above
the moon by many ſemidiameters of the Earth. The firſt of
which is this, computed upon the obſervations of the Landgrave of
Haſſia, and Tycho; which are, even by the Authors conceſſion,
two of the moſt exact obſervers: and in this firſt, I will declare
the order that I hold in the working; which ſhall ſerve for all the
reſt, in that they are all made by the ſame rule, not varying in any
thing, ſave in the quantity of the given ſummes, that is, in the
number of the degrees of the Poles altitude, and of the new Stars
elevation above the Horizon, the diſtance of which from the
tre of the Earth, in proportion to the ſemidiameter of the terre­
ſtrial Globe is ſought, touching which it nothing imports in this
caſe, to know how many miles that ſemidiameter conteineth;
whereupon the reſolving that, and the diſtance of places where
the obſervations were made, as this Author doth, is but time and
labour loſt; nor do I know why he hath made the ſame, and
cially why at the laſt he goeth about to reduce the miles found,
to ſemidiameters of the Terreſtrial Globe.
SIMP. Perhaps he doth this to finde with ſuch ſmall meaſures,
and with their fractions the diſtance of the Star terminated to three
or four inches; for we that do not underſtand your rules of
metick, are ſtupified in hearing your concluſions; as for inſtance,
whilſt we read; Therefore the new Star or Comet was diſtant
from the Earths centre three hundred ſeventy and three thouſand
eight hundred and ſeven miles; and moreover, two hundred and
eleven, four chouſand ninety ſevenths 373807 211/4097, and upon theſe
preciſe punctualities, wherein you take notice of ſuch ſmall
ters, we do conceive it to be impoſſible, that you, who in our
culations keep an account of an inch, can at the cloſe deceive us ſo
much as an hundred miles.
SALV. This your reaſon and excuſe would paſſe for currant,
if in a diſtance of thouſands of miles, a yard over or under were
of any great moment, and if the ſuppoſitions that we take for
true, were ſo certain, as that they could aſſure us of producing an
indubitable truth in the concluſion; but here you ſee in the twelve
workings of the Author, the diſtances of the Star, which from
them one may conclude to have been different from each other,
(and therefore wide of the truth) for many hundreds and
ſands of miles: now whilſt that I am more than certain, that that
which I ſeek muſt needs differ from the truth by hundreds of miles,
to what purppſe is it to be ſo curious in our calculations, for fear
of miſſing the quantity of an inch? But let us proceed, at laſt,
to the working, which I reſolve in this manner. Tycho, as may be
1ſeen in that ſame note obſerved the ſtar in the polar altitude of 55
degrees and 58 mi. pri. And the polar altitude of the Landgrave
was 51 degrees and 18 mi. pri. The altitude of the ſtar in the
ridian taken by Tycho was 27 degrees 45 mi. pri. The
grave found its altitude 23 degrees 3 mi. pri. The which altitudes
are theſe noted here, as you
gr.m.gr.m.Tycho Pole5558* 2745Landgr. Pole5118* 233
This done, ſubſtract the leſſe from the greater, and there remains
theſe differences here
gr.m.440442Parall.2
Where the difference of the poles altitudes 4 gr. 4 mi. pr.
is leſſe than the difference of the altitudes of the Star 4 gr. 42 mi.
pr. and therefore we have the difference of parallaxes, 0 gr. 2 mi.
pri. Theſe things being found, take the Authours own figure
[Fig. 2.] in which the point B is the ſtation of the Landgrave,
D the ſtation of Tycho, C the place of the ſtar, A the centre
of the Earth, A B E the vertical line of the Landgrave, A D F



of Tycho, and the angle B C D the difference of Parallaxes. And
1becauſe the angle B A D, conteined between the vertical lines, is
equal to the difference of the Polar altitudes, it ſhall be 4gr. 40m.
which I note here apart; and I finde the chord of it by the Table
of Arches and Chords, and ſet it down neer unto it, which is 8142
parts, of which the ſemidiameter A B is 100000. Next, I finde
the angle B D C with eaſe, for the half of the angle B A D, which
is 2 gr. 20 m. added to a right angle, giveth the angle B D F 92 gr.
20 m. to which adding the angle C D F, which is the diſtance from
the vertical point of the greateſt altitude of the Star, which here is
62 gr. 15 m. it giveth us the quantity of the angle B D C,
154 grad. 45 min. the which I ſet down together with its Sine,
taken out of the Table, which is 42657, and under this I note
the angle of the Parallax B C D 0 gr. 2 m. with its Sine 58.
And becauſe in the Triangle B C D, the ſide D B is to the ſide
B C; as the ſine of the oppoſite angle B C D, to the ſine of the
oppoſite angle B D C: therefore, if the line B D were 58. B C
would be 42657. And becauſe the Chord D B is 8142. of thoſe
parts whereof the ſemidiameter B A is 100000. and we ſeek to
know how many of thoſe parts is B C; therefore we will ſay, by
the Golden Rule, if when B D is 58. B G is 42657. in caſe the
ſaid D B were 8142. how much would B C be? I multiply the
ſecond term by the third, and the product is 347313294. which
ought to be divided by the firſt, namely, by 58. and the quotient
ſhall be the number of the parts of the line B C, whereof the
midiameter A B is 100000. And to know how many
ters B A, the ſaid line B C doth contein, it will be neceſſary anew
to divide the ſaid quotient ſo found by 100000. and we ſhall have
the number oſ ſemidiameters conteined in B G. Now the
ber 347313294. divided by 58. giveth 5988160 1/4. as here you
may
gr.m.Its chord 8142 of thoſeAng. B A D440parts, whereof the ſemid.B D F9220A B is an 100000.B D C15445Sines42657B C D02585842657814281428531417062842657341256595834731329457155988160 1/4583473132945717941543
And this divided by 100000. the product is 59
1 |00000| 59 |88160.
But we may much abbreviate the operation, dividing the firſt
quotient found, that is, 347313294. by the product of the
plication of the two numbers 58. and 100000. that
1
5958 000003473132945715
And this way alſo there will come forth 59 5113294/5800000
And ſo many ſemidiameters are contained in the line B C, to
which one being added for the line A B, we ſhall have little leſſe
than 61. ſemidiameters for the two lines A B C; and therefore
the right diſtance from the centre A, to the Star C, ſhall be more
than 60. ſemidiameters, and therefore it is ſuperiour to the Moon,
according to Ptolomy, more than 27. ſemidiameters, and according
to Copernicus, more than 8. ſuppoſing that the diſtance of the
Moon from the centre of the Earth by Copernicus his account is
what the Author maketh it, 52 ſemidiameters. With this ſame
working, I find by the obſervations of Camerarius, and of
ſius, that the Star was ſituate in that ſame diſtance, to wit,
what more than 60. ſemidiameters. Theſe are the obſervations,
and theſe following next after them the

gr.m.gr.m.Altitude of Camerar.5224Altitude of2428the Pole Munoſ.3930the Star1130Differences of the1254Differences1258Polar Altitudesof the alt. of *1254Difference of Parallaxes0004. ang. BCD.gr.m.B A D1254and its chord or ſubtenſe 22466.AnglesB D C16159Sines30930B C D0004116
The Golden Rule.

12246611630930224666739802021946739859_______Diſtance B C 59. and116694873380almoſt 60. ſemidiameters.114410
The next working is made upon two obſervations of Tycho, and
of Munoſius, from which the Star is calculated to be diſtant from
the Centre of the Earth 478 Semidiameters and


gr.m.gr.m.AltitudesTycho.5558Altitude8400of the Pole.Munoſ.3930of the Star.6730Differences of the1628Differ. of the16 30Polar Altitudes.Alt. of the *16 28Difference of Parallax.0 2 and ang. BCDgr.m.B A D.1628its chord28640AnglesB D C.10414Sines96930B C D.0258
The Golden Rule.
589693028640286403877200581587754419386478582776075200450653
Theſe workings following make the Star remote from the
tre, more than 358

1gr.m.gr.m.AltitudesPeucerus5154Altitude7956of the Pole.Munoſius3930of the *473012241226122402gr.m.B A D.1224its chord21600AnglesB D C.10616Sines95996B C D.0258
The Golden
58----95996----21600216005759760095996191992357582073513600333942
From this other working the ſtar is found to be diſtant from the
centre more than 716.

gr.m.gr.m.ſec.AltitudesLandgr.5118Altitude793000of the PoleHainzel.4822of the Star7633452562561525600015gr.m.ſec.B A D25600its Chord5120AnglesB D C1015800Sines97845B C D000157
The Golden
7----97845----5120512019569005784548922571575009664004
Theſe as you ſee are five workings which place the ſtar very
much above the Moon. And here I deſire you to conſider upon
that particular, which even now I told you, namely, that in great
1diſtances, the mutations, or if you pleaſe corrections, of a
ry few minutes, removeth the ſtar a very great way farther off.
As for example, in the firſt of theſe workings, where the
lation made the ſtar 60. ſemidiameters remote from the centre,
with the Parallax of 2. minutes; he that would maintain that it
was in the Firmament, is to correct in the obſervations but onely
two minutes, nay leſſe, for then the Parallax ceaſeth, or
commeth ſo ſmall, that it removeth the ſtar to an immenſe
ſtance, which by all is received to be the Firmament. In the
cond indagation, or working, the correction of leſſe than 4 m.
prim. doth the ſame. In the third, and fourth, like as in the firſt,
two minutes onely mount the ſtar even above the Firmament.
In the laſt preceding, a quarter of a minute, that is 15. ſeconds,
gives us the ſame. But it doth not ſo occur in the ſublunary
tudes; for if you fancy to your ſelf what diſtance you moſt
like, and go about to correct the workings made by the
thour, and adjuſt them ſo as that they all anſwer in the ſame
determinate diſtance, you will find how much greater
ons they do require.
SAGR. It cannot but help us in our fuller underſtanding of
things, to ſee ſome examples of this which you ſpeak of.
SALV. Do you aſſign any whatſoever determinate ſublunary
diſtance at pleaſure in which to conſtitute the ſtar, for with ſmall
ado we may aſſertain our ſelves whether corrections like to theſe,
which we ſee do ſuffice to reduce it amongſt the fixed ſtars, will
reduce it to the place by you aſſigned.
SAGR. To take a diſtance that may favour the Authour, we
will ſuppoſe it to be that which is the greateſt of all thoſe found
by him in his 12 workings; for whilſt it is in controverſie
tween him and Aſtronomers, and that they affirm the ſtar to
have been ſuperiour to the Moon, and he that it was inferiour,
very ſmall ſpace that he proveth it to have been lower, giveth
him the victory.
SALV. Let us therefore take the ſeventh working wrought
upon the obſervations of Tycho and Thaddæus Hagecius, by
which the Authour found the ſtar to have been diſtant from the
centre 32. ſemidiameters, which ſituation is moſt favourable to
his purpoſe; and to give him all advantages, let us moreover
place it in the diſtance moſt disfavouring the Aſtronomers, which
is to ſituate it above the Firmament. That therefore being
poſed, let us ſeek in the next place what corrections it would be
ceſſary to apply to his other 11 workings. And let us begin at the
firſt calculated upon the obſervations of Hainzelius and Mauroice;
in which the Authour findeth the diſtance from the centre about
3. ſemidiameters with the Parallax of 4 gr. 42 m. 30. ſec. Let
1us ſee whether by withdrawing it 20. minutes onely, it will riſe
to the height of 32. ſemidiameters: See the ſhort and true
tion. Multiply the ſine of the angle B D C, by the ſine of the



chord B D, and divide the product, the five laſt figures being cut
off by the ſine of the Parallax, and the quotient will be 28.
midiameters, and an half, ſo that though you make a correction
of 4 gr. 22 min. 30 ſec. taken from 4 gr. 42 min. 30 ſec. it ſhall
not elevate the ſtar to the altitude of 32. ſemidiameters, which
correction for Simplicius his underſtanding it, is of 262. minutes,
and an half.
gr.m.gr.m.ſec.HainzeliusPole4832----*763430MaurolicusPole3830----*62000095214343095200Parallax44230gr.m.ſec.B A D95200Chord17200AnglesB D C1082130Sine94910B C D02000Sine58294910172001898200066437949128582163245200046882
In the ſecond operation made upon the obſervations of
zelius, and Sculerus, with the Parallax of 0 gr. 8 min. 30 ſec.
the ſtar is found in the height of 25. ſemidiameters or
bouts, as may be ſeen in the ſubſequent
1
B DChord6166B D CSines97987B C D2479798761665879225879229798758792224247604187842110311
And bringing back the Parallax 0 gr. 8 m. 30 ſec. to 7 gr.
7 m. whoſe ſine is 204, the ſtar elevateth to 30 ſemidiameters or
thereabouts; therefore the correction of 0 gr. 1 mi. 30 ſec. doth
not
20204604187342196512
Now let us ſee what correction is requiſite for the third
ing made upon the obſervations of Hainzelius and Tycho, which
rendereth the ſtar about 19 ſemidiameters high, with the
rallax of 10 m. pri. The uſual angles and their ſines, and chord
found by the Authour, are theſe next following; and they
move the ſtar (as alſo in the Authours working) 19
meters from the centre of the Earth. It is neceſſary therefore for
the raiſing of it, to diminiſh the Parallax according to the Rule
which he likewiſe obſerveth in the ninth working. Let us
fore ſuppoſe the Parallax to be 6 m. prim. whoſe ſine is 175, and
the diviſion being made, there is found likewiſe leſſe than 31
ſemidiameters for the ſtars diſtance. And therefore the
on of 4 min. prim. is too little to ſerve the Authours
1
B A D736Chord13254AnglesB D C15552Sine40886B C D010Sine291132544088679524106032106032530161830291541903044175541925016181
Let us come to the fourth working, and the reſt with the ſame
rule, and with the chords and ſines found out by the Authour
himſelf; in this the Parallax is 14 m. prim. and the height found
leſſe than 10 ſemidiameters, and diminiſhing the Parallax from
14 min. to 4 min. yet nevertheleſſe you ſee that the ſtar doth not
elevate full 31 ſemidiameters. Therefore 10 min. in 14 min. doth
not

B A DChord8142AnglesB D CSine43235B C DSine4074323581428647017294043235345880301163520193704
In the fifth operation of the Authour we have the ſines and the
chord as you ſee, and the Parallax is 0 gr. 42 m. 30 ſec. which
rendereth the height of the ſtar about 4 ſemidiameters, and
recting the Parallax, with reducing it from 0 gr. 42 m. 30 ſec.
to 0 gr. 5 m. onely, doth not ſuffice to raiſe it to ſo much as 28
midiameters, the correction therefore of 0 gr. 37 m. 30 ſec. is
too
1
B A DChord4034AnglesB D CSine97998B C D12369799840343919922939943919922714539532393210583
In the ſixth operation the chord, the ſines and Parallax are as
followeth, and the ſtar is found to be about 4 ſemidiameters; let
us ſee whether it will be reduced, abating the Parallax from 8 m.
to 1 m. onely; Here is the operation, and the ſtar raiſed but to
27. ſemidiameters or thereabout; therefore the correction of 7 m.
in 8 m. doth not

B DChord1920B D CSine40248B C D 8 gr.Sine233402481920804960362232402482629772761601981
In the eighth operation the chord, the ſines, and the Parallax,
as you ſee, are theſe enſuing, and hence the Authour calculates
the height of the ſtar to be 1. ſemidiameter and an half, with the
Parallax of 43. min. which reduced to 1 min. yet
ing giveth the ſtar leſſe remote than 24. ſemidiameters, the
ction therefore of 42. min. is not
1
B DChord1804B D CSine36643B C DSine2936643180414657229314436643222966103972832
Let us now ſee the ninth. Here is the chord, the ſines and
the Parallax which is 15 m. From whence the Authour
lates the diſtance of the ſtar from the ſuperficies of the Earth
to be leſſe than a ^{*} ſeven and fortieth part of a ſemidiameter,

but this is an errour in the calcultaion, for it cometh forth truly,
as we ſhall ſee here below, more than a ſifth: See here the
tienr is 90/436, which is more than one

* Here the
tine verſion is
neous, making it
a fortieth part of,
&c.
B DChord232B D CSine39046B C DSine4363904623278092117138780924369058672
That which the Authour preſently after ſubjoyns in way of
amending the obſervations, that is, that it ſuſſiceth not to
duce the difference of Parallax, neither to a minute, nor yet
to the eighth part of a minute is true. But I ſay, that neither
will the tenth part of a minute reduce the height of the ſtar to
32. ſemidiameters; for the ſine of the tenth part of a minute,
that is of ſix ſeconds, is 3; by which if we according to our Rule
ſhould divide 90. or we may ſay, if we ſhould divide 9058672.
by 300000. the quotient will be 30 58672/100000, that is little more
than 30. ſemidiameters and an half.
The tenth giveth the altitude of the ſtar one fifth of a
diameter, with theſe angles, ſines, and Parallax, that is, 4 gr.
130 m. which I ſee that being reduced from 4 gr. 30 min. to 2 min.
yet nevertheleſſe it elevates not the ſtar to 29.

B DChord1746B D CSine92050B C D4 gr. 30 m.Sine784692050174605523003682064435920527581607193004414
The eleventh rendereth the ſtar to the Authour remote about
13. ſemidiameters, with the Parallax of 55. min. let us ſee,
ducing it to 20 min. whether it will exalt the ſtar: See here the
calculation elevates it to little leſſe than 33. ſemidiameters, the
correction therefore is little leſſe than 35. min. in 55. min.

B DChord19748B D CSine96166B C Do gr. 55 m.Sine1600961661974863932838466467316286549496166325821899056168153656
The twelfth with the Parallax of 1. gr. 36. min. maketh the
ſtar leſſe high than 6. ſemidiameters, reducing the Parallax to
20 min. it carrieth the ſtar to leſſe than 30. ſemidiameters
ſtance, therefore the correction of 1 gr. 16. min. ſufficeth
1
B DChord17258B D CSine96150B C D1 gr. 36 m.Sine2792172589615086290017258103548155322285821659356700495729
Theſe are the Corrections of the Parallaxes
of the ten workings of the Author, to
reduce the Star to the altitude of
32 Semidiameters.

gr.m.ſec.gr.m.ſec.042230in044230000400in001000001000in001400003700in004230000700in001800004200in004300001450in001500042800in043000003500in005500011600in013600216296.60540240.9765836.540
From hence we ſee, that to reduce the Star to 32.
ters in altitude, it is requiſite from the ſum of the Parallaxes 836.
to ſubtract 756. and to reduce them to 80. nor yet doth that
correction ſuffice.
1
Here we ſee alſo, (as I have noted even now) that ſhould the
Authour conſent to aſſign the diſtance of 32. Semidiameters for
the true height of the Star, the correction of thoſe his 10. workings,
(I ſay 10. becauſe the ſecond being very high, is reduced to the
height of 32. Semidiameters, with 2. minutes correction) to make
them all to reſtore the ſaid Star to that diſtance, would require ſuch
a reduction of Parallaxes, that amongſt the whole number of ſub
ſtractions they ſhould make more than 756 m. pr. whereas in the
5. calculated by me, which do place the Star above the Moon, to
correct them in ſuch ſort, as to conſtitute it in the Firmament,
the correction onely of 10. minutes, and one fourth ſufficeth.
Now adde to theſe, other 5. workings, that place the Star
ciſely in the Firmament, without need of any correction at all,
and we ſhall have ten workings or indagations that agree to place
it in the Firmament, with the correction onely of 5. of them (as
hath been ſeen) but 10. m. and 15 ſec. Whereas for the
on of thoſe 10. of the Authour, to reduce them to the altitude of
32. ſemidiameters, there will need the emendations of 756
nutes in 836. that is, there muſt from the ſumme 836 be
cted 756. if you would have the Star elevated to the altitude of
32. ſemidiameters, and yet that correction doth not fully ſerve.
The workings that immediately without any correction free the
Star from Parallaxes, and therefore place it in the Firmament,
and that alſo in the remoteſt parts of it, and in a word, as high
as the Pole it ſelf, are theſe 5. noted
gr.m.gr.m.Camerar.Polar altit.5224Altit. of the Star8026Peucerus51547956030030gr.m.gr.m.Landgrav.Polar altit.5118Altit. of the Star7930Hainzel.48227634256256gr.m.gr.m.TychoPolar altit.5558Altit. of the Star8400Peucerus515479564444
1gr.m.gr.m.Reinhold.Polar altit.5118Altit. of the Star7930Hainzel.48223634256256gr.m.gr.m.Camerar.Polar altit.5224Altit. of the Star2417Hagecius482220154242
Of the remaining combinations that might be made of the
ſervations of all theſe Aſtronomers, thoſe that make the Stars
lime to an infinite diſtance, are many in number, namely, about
30. more than thoſe who give the Star, by calculation, to be
low the Moon; and becauſe (as it was agreed npon between us) it
is to be believed that the Obſervators have erred rather little than
much, it is a manifeſt thing that the corrections to be applied to
the Obſervaations, which make the ſtar of an infinite altitude, to
reduce it lower, do ſooner, and with leſſer amendment place it in
the Firmament, than beneath the Moon; ſo that all theſe applaud
the opinion of thoſe who put it amongſt the fixed Stars. You may
adde, that the corrections required for thoſe emendations, are
much leſſer than thoſe, by which the Star from an unlikely
mity may be removed to the height more favourable for this
thour, as by the foregoing examples hath been ſeen; amongſt
which impoſſible proximities, there are three that ſeem to remove
the Star from the Earths centre, a leſſe diſtance than one
ameter, making it, as it were, to turn round under ground, and
theſe are thoſe combinations, wherein the Polar altitude of one
of the Obſervators being greater than the Polar altitude of the
other, the elevation of the Star taken by the firſt, is leſſer than the
elation of the Star taken by the latter.
The firſt of theſe is this of the Landgrave with Gemma,
where the Polar altitude of the Landgrave 51 gr. 18 min. is
greater than the Polar altitude of Gemma, which is 50 gr. 50 m.
But the altitude of the Star of the Landgrave 79 gr. 30 min.
is leſſer than that of the Star, of Gemma 79 gr. 45 min.
1gr.m.gr.m.LandgravePolar altit.5118Altit. of the Star7930Gemma50507945
The other two are theſe
gr.m.gr.m.Buſchius.Polar Altitude5110Altit. of the Star7920Gemma.50507945Reinholdus.Polar Altitude5118Altit. of the Star7930Gemma.50507945
From what I have hitherto demonſtrated, you may gueſſe how
much this firſt way of finding out the diſtance of the Star, and
proving it ſublunary introduced by the Authour, maketh againſt
himſelf, and how much more probably and clearly the diſtance
thereof is collected to have been amongſt the more remote fixed
Stars.
SIMP. As to this particular, I think that the inefficacy of the
Authors demonftrations is very plainly diſcovered; But I ſee that all
this was compriſed in but a few leaves of his Book, and it may be,
that ſome other of his Arguments are more concluſive then theſe
firſt.
SALV. Rather they muſt needs be leſſe valid, if we will take
thoſe that lead the way for a proof of the reſt: For (as it is clear)
the uncertainty and inconcluſiveneſſe of thoſe, is manifeſtly
ſerved to derive it ſelf from the errours committed in the
mental obſervations, upon which the Polar Altitude, and height
of the Star was thought to have been juſtly taken, all in effect
having eaſily erred; And yet to find the Altitude of the Pole,
ſtronomers have had Ages of time to apply themſelves to it, at their
leaſure: and the Meridian Altitudes of the Star are eaſier to be
obſerved, as being moſt terminate, and yielding the Obſervator
ſome time to continue the ſame, in regard they change not ſenſibly,
in a ſhort time, as thoſe do that are remote from the Meridian. And
if this be ſo, as it is moſt certain, what credit ſhall we give to
lations founded upon Obſervations more numerous, more difficult
to be wrought, more momentary in variation, and we may add,
with Inſtruments more incommodious and erroneous? Upon a
ſlight peruſal of the enſuing demonſtrations, I ſee that the
putations are made upon Altitudes of the Star taken in different
Vertical Circles, which are called by the Arabick name, Azimuths; in
which obſervations moveable inſtruments are made uſe of, not
ly in the Vertical Circles, but in the Horizon alſo, at the ſame time;
inſomuch that it is requiſite in the ſame moment that the altitude
is taken, to have obſerved, in the Horizon, the diſtance of the
1tical point in which the Star is, from the Meridian; Moreover,
after a conſiderable interval of time, the operation muſt be
peated, and exact account kept of the time that paſſed, truſting
either to Dials, or to other obſervations of the Stars. Such an Olio
of Obſervations doth he ſet before you, comparing them with
ſuch another made by another obſerver in another place with
nother different inſtrument, and at another time; and from this
the Authour ſeeks to collect what would have been, the Elevations
of the Star, and Horizontal Latitudes happened in the time and
hour of the other firſt obſervations, and upon ſuch a coæquation he
in the end grounds his account. Now I refer it to you, what credit
is to be given to that which is deduced from ſuch like workings.
Moreover, I doubt not in the leaſt, but that if any one would
ture himſelf with ſuch tedious computations, he would find, as in
thoſe aforegoing, that there were more that would favour the
verſe party, than the Authour: But I think it not worth the while
to take ſo much pains in a thing, which is not, amongſt thoſe
ry ones, by us underſtood.
SAGR. I am of your Opinion in this particular: But this
neſſe being environed with ſo many intricacies, uncertainties, and
errours, upon what confidence have ſo many Aſtronomers
ly pronounced the new Star to have been ſo high?
SALV. Upon two ſorts of obſervations moſt plain, moſt eaſie,
and moſt certain; one only of which is more than ſufficient to aſſure
us, that it was ſcituate in the Firmament, or at leaſt by a great
diſtance ſuperiour to the Moon. One of which is taken from the
equality, or little differing inequality of its diſtances from the
Pole, aſwell whilſt it was in the loweſt part of the Meridian, as
when it was in the uppermoſt: The other is its having
ly kept the ſame diſtances from certain of the fixed Stars, adjacent
to it, and particularly from the eleventh of Caſſiopea, no more
remote from it than one degree and an half; from which two
ticulars is undoubtedly inferred, either the abſolute want of
lax, or ſuch a ſmalneſſe thereof, that it doth aſſure us with very
expeditious Calculations of its great diſtance from the Earth.
SAGR. But theſe things, were they not known to this Author?
and if he ſaw them, what doth he ſay unto them?
SALV. We are wont to ſay, of one that having no reply that
is able to cover his fault, produceth frivolous excuſes, cerca di
taccarſi alle funi del cielo, [He ſtrives to take hold of the Cords of
Heaven;] but this Authour runs, not to the Cords, but to the Spi­
ders Web of Heaven; as you ſhall plainly ſee in our examination
of theſe two particulars even now hinted. And firſt, that which
ſheweth us the Polar diſtances of the Obſervators one by one, I
have noted down in theſe brief Calculations; For a full
1ſtanding of which, I ought firſt to advertiſe you, that when ever
the new Star, or other Phænomenon is near to the earth, turning
with a Diurnal motion about the Pole, it will ſeem to be farther
off from the ſaid Pole, whilſt it is in the lower part of the
an, then whilſt it is above, as in this Figure [being fig. third of
this Dial.] may be ſeen. In which the point T. denotes the
tre of the Earth; O the place of the Obſervator; the Arch VPC
the Firmament; P. the Pole. The Phænomenon, [or appearance]
moving along the Circle F S. is ſeen one while under the Pole by
the Ray O F C. and another while above, according to the Ray
O S D. ſo that the places ſeen in the Firmament are D. and C. but
the true places in reſpect of the Centre T, are B, and A,
ſtant from the Pole. Where it is manifeſt that the apparent place
of the Phænomenon S, that is the point D, is nearer to the Pole than
the other apparent place C, ſeen along the Line or Ray O F C,
which is the firſt thing to be noted. In the ſecond place you muſt
note that the exces of the apparent inferiour diſtance from the Pole,
over and above the apparent ſuperiour diſtance from the ſaid Pole,
is greater than the Inferiour Parallax of the Phænomenon, that is, I
ſay, that the exceſſe of the Arch C P, (the apparent inferior
ſtance) over and above the Arch P D, (the apparent ſuperior
ſtance) is greater then the Arch C A, (that is the inferiour
lax.) Which is eaſily proved; for the Arch C P. more exceedeth
P D, then P B; P B, being bigger than P D, but P B. is equal to
P A, and the exceſſe of C P, above P A, is the arch, C A,
fore the exceſſe of the arch C P above the arch P D, is
er than the arch C A, which is the parallax of the Phænomenon
placed in F, which was to be demonſtrated. And to give all
vantages to the Author, let us ſuppoſe that the parallax of the ſtar
in F, is the whole exceſſe of the arch C P (that is of the inferiour
diſtance from the pole) above the arch P D (the inferiour
ſtance.) I proceed in the next place to examine that which the
obſervations of all Aſtronomers cited by the Authour giveth us,
amongſt which, there is not one that maketh not againſt himſelf
and his purpoſe. And let us begin with theſe of Buſchius, who
findeth the ſtars diſtance from the pole, when it was ſuperiour, to be
28 gr. 10 m. and the inferiour to be 28 gr. 30 m. ſo that the
ceſſe is 0 gr. 20 m. which let us take (in favour of the Author) as
if it all were the parallax of the ſtar in F, that is the angle T F O.
Then the diſtance from the Vertex [or Zenith] that is the arch
C V, is 67 gr. 20 m. Theſe two things being found, prolong the
line C O, and from it let fall the perpendicular T I, and let us
conſider the triangle T O I, of which the angle I is right angle,
and the angle I O T known, as being vertical to the angle V O C,
the diſtance of the ſtar from the Vertex, Moreover in the triangle
1T I F, which is alſo rectangular, there is known the angle F,
ken by the parallax. Then note in ſome place apart the two
gles I O T and I F T, and of them take the ſines, which are
here ſet down to them, as you ſeen. And becauſe in the triangle
I O T, the ſine T I is 92276. of thoſe parts, whereof the whole
ſine TO is 100000; and moreover in the triangle I F T, the ſine T I
is 582. of thoſe parts, whereof the whole ſine T F is 100000, to
find how many T F is of thoſe parts, whereof T O is 100000;
we will ſay by the Rule of three: If T I be 582. T F is an
100000. but if T I were 92276. how much would T F be.
Let us multiply 92276. by 100000. and the product will be
9227600000. and this muſt be divided by 582. and the quotient
will be 15854982. and ſo many ſhall there be in T F of thoſe
parts, of which there are in T O an 100000. So that if it were
required to know how many lines T O, are in T F, we would
divide 15854982 by 100000. and there will come forth 158. and
very near an half; and ſo many diameters ſhall be the diſtance
of the ſtar F, from the centre T, and to abreviate the
tion, we ſeeing, that the product of the multiplication of 92276.
by 100000, ought to be divided firſt by 582, and then the
tient of that diviſion by 100000. we may without multiplying
92276. by 100000. and with one onely diviſion of the ſine
92276. by the ſine 582. ſoon obtain the ſame ſolution, as may
be ſeen there below; where 92276. divided by 582. giveth us the
ſaid 158 1/2, or thereabouts. Let us bear in mind therefore, that
the onely diviſion of the ſine T I, as the ſine of the angle T O I
by the ſine T I, as the ſine of the angle I F T, giveth us the
ſtance ſought T F, in ſo many diameters T


1gr.m.AnglesI O T6720Sines92276I F T020582T IT FT IT F582100009227601585498258292276000003407002746492978673254141000001585498215858292276340704923
See next that which the obſervations of Peucerus giveth us, in
which the inferiour diſtance from the Pole is 28 gr. 21 m. and the
ſuperiour 28 gr. 2 m. the difference 0 gr. 19 m. and the diſtance
from the vertical point 66 gr. 27 m. from which particulars is
thered the ſtars diſtance from the centre almoſt 166


gr.m.AnglesI A C6627Sines91672I E C019553165 427/55355391672363973124
Here take what Tycho his obſervation holdeth forth to us,
terpreted with greateſt favour to the adverſary; to wit, the
our diſtance from the pole is 28 gr. 13 m. and the ſuperiour 28 gr.
2 m. omitting the difference which is 0 gr. 11 m. as if all were one
Parallax; the diſtance from the vertical point 62 gr. 15 m. Behold
here below the operation, and the diſtance of the ſtar from the
centre found to be 976 9/16

gr.m.AnglesI A C6215Sines88500I E C011320276 9/163208850024181
The obſervation of Reinholdus, which is the next enſuing,
eth us the diſtance of the Star from the Centre 793.


1gr.m.AnglesI A C6658Sines92026I E C04116793 38/116116920261088833
From the following obſervation of the Landgrave, the diſtance
of the Star from the Centre is made to be 1057,

gr.m.AnglesI A C6657Sines92012I E C03871057 53/87879201256635
Two of the moſt favourable obſervations for the Authour
ing taken from Camerarius, the diſtance of the Star from the
tre is found to be 3143

gr.m.AnglesI A C6543Sines91152I E C0129314329911524295
The Obſervation of Munoſius giveth no Parallax, and
fore rendreth the new Star amongſt the higheſt of the fixed. That
of Hainzelius makes it infinitely remote, but with the correction
of an half min. prim. placeth it amongſt the fixed Stars. And the
ſame is collected from Vrſinus, with the correction of 12. min. prim.
The other Aſtronomers have not given us the diſtance above and
below the Pole, ſo that nothing can be concluded from them. By
this time you ſee, that all the obſervations of all theſe men conſpire
againſt the Author, in placing the Star in the Heavenly and
eſt Regions.
SAGR. But what defence hath he for himſelf againſt ſo manifeſt
contradictions?
SALV. He betakes himſelf to one of thoſe weak threads which
I ſpeak of; ſaying that the Parallaxes come to be leſſened by means
of the refractions, which opperating contrarily ſublimate the
nomenon, whereas the Parallaxes abaſe it. Now of what little
ſtead this lamentable refuge is, judge by this, that in caſe that effectof
the refractions were of ſuch an efficacy, as that which not long time
ſince ſome Aſtronomers have introduced, the moſt that they could
work touching the elevating a Phæuomenon above the Horizon
1more than truth, when it is before hand 23. or 24. Degrees high,
would be the leſſening its Parallax about 3. minutes, the which
abatement is too ſmall to pull down the Star below the Moon, and
in ſome caſes is leſſe than the advantage given him by us in
ting that the exceſſe of the inferiour diſtance from the Pole above
the Superiour, is all Parallax, the which advantage is far more clear
and palpable than the effect of Refracton, of the greatneſſe of
which I ſtand in doubt, and not without reaſon. But beſides, I
demand of the Author, whether he thinks that thoſe Aſtronomers,
of whoſe obſervations he maketh uſe, had knowledge of theſe
fects of Refractions, and conſidered the ſame, or no; if they did
know and conſider them, it is reaſonable to think that the, kept
count of them in aſſigning the true Elevation of the Star, making
in thoſe degrees of Altitude diſcovered with the Inſtruments, ſuch
abatements as were convenient on the account of the alterations
made by the Refractions; inſomuch that the diſtances by them
livered, were in the end thoſe corrected and exact, and not the
parent and falſe ones. But if he think that thoſe Authors made
no reflection upon the ſaid Refractions, it muſt be confeſſed, that
they had in like manner erred in determining all thoſe things which
cannot be perfectly adjuſted without allowance for the
ons; amongſt which things one is the preciſe inveſtigation of the
Polar Altitudes, which are commonly taken from the two
an Altitudes of ſome of the fixed Stars that are conſtantly viſible,
which Altitudes will come to be altered by Refraction in the ſame
manner, juſt as thoſe of the new Star; ſo that the Polar Altitude
that is deduced from them, will prove to be defective, and to
take of the ſelf ſame want which this Author aſſigns to the
tudes aſcribed to the new Star, to wit, both that and theſe will
be with equal falſhood placed higher than really they are. But any
ſuch errour, as far as concerns our preſent buſineſſe, doth no
judce at all: For we not needing to know any more, but onely
the difference between the two diſtances of the new Star from the
Pole at ſuch time as it was inferiour and ſuperiour, it is evident that
ſuch diſtances would be the ſame, taking the alteration of
ction commonly for the Star and for the Pole, or for them when
commonly amended. The Authors Argument would indeed have
had ſome ſtrength, though very ſmall, if he had aſſured us that
the Altitude of the Pole had been once preciſely aſſigned, and
rected from the errour depending on refraction, from which
gain the Aſtronomers had not kept themſelves in aſſigning the
titudes of the new Star; but he hath not aſcertained us of that,
nor perhaps could he have done, nor haply, (and this is more
bable) was that caution wanting in the Obſervators.
SAGR. This argument is in my judgment ſufficiently
1ed; therefore tell me how he diſ-ingageth himſelf in the next place
from that particular of the Stars having conſtantly kept the ſame
diſtance from the fixed Stars circumjacent to it.
SALV. He betakes himſelf, in like manner, to two threads, yet
more unable to uphold him than the former: one of which is
wiſe faſtened to refraction, but ſo much leſs firmly, in that he
ſaith, that refraction operating upon the new Star, and ſublimating
it higher than its true ſituation, maketh the ſeeming diſtances
tain to be diſtinguiſhed from the true, when compared to the
cumpoſed fixed Stars that environ it. Nor can I ſufficiently
mire how he can diſſemble his knowing how that the ſame
ction will work alike upon the new Star, as upon the antient one
its neighbour, elevating both equally, ſo as that ſuch a like
dent altereth not the ſpace betwixt them. His other ſubterfuge is
yet more unhappy, and carryeth with it much of ridiculous, it
ing founded upon the errour that may ariſe in the inſtrumen
peration it ſelf; whilſt that the Obſervator not being able to
conſtitute the centre of the eyes pupil in the centre of the
tant (an Inſtrument imployed in obſerving the diſtance between
two Stars) but holding it elevated above that centre, as much as
the ſaid pupil is diſtant from I know not what bone of the cheek,
againſt which the end of the Inſtrument reſteth, there is formed
in the eye an angle more acute than that which is made by the ſides
of the Inſtrument; which angle of rayes differeth alſo from it
ſelf, at ſuch time as a man looketh upon Stars, not much elevated
above the Horizon, and the ſame being afterwards placed at a
great height; that angle, ſaith he, is made different, while the
ſtrument goeth aſcending, the head ſtanding ſtill: but if in
ting the Inſtrument, the neck ſhould bend backwards, and the
head go riſing, together with the Inſtrument, the angle would then
continue the ſame. So that the Authours anſwer ſuppoſeth that
the Obſervators in uſing the Inſtrument have not raiſed the head,
as they ought to have done; a thing which hath nothing of
hood in it. But granting that ſo it had been, I leave you to judge
what difference can be between two acute angles of two
ral triangles, the ſides of one of which triangles are each four
[Italian] Braces [i.e. about three Engliſh yards] and thoſe of the
other, four braces within the quantity of the diameter of a Pea;
for the differences cannot be abſolutely greater between the length
of the two viſive rayes, whilſt the line is drawn perpendicularly
from the centre of the pupil, upon the plain of the Rule of the
Sextant (which line is no bigger than the breath of the thumb)
and the length of the ſame rayes, whilſt elevating the Sextant,
without raiſing the head together with it, that ſame line no longer
falleth perpendicularly upon the ſaid plane, but inclineth, making
1the angle towards the circumference ſomething acute. But wholly
to free this Authour from theſe unhappy lies, let him know, (in
gard it appears that he is not very skilful in the uſe of
call Inſtruments) that in the ſides of the Sextant or Quadrant

there are placed two ^{*} Sights, one in the centre, and the other at
the other at the oppoſite end, which are raiſed an inch or more
bove the plane of the Rule; and through the tops of thoſe ſights
the ray of the eye is made to paſſe, which eye likewiſe is held an
hands breadth or two, or it may be more, from the Inſtrument; ſo
that neither the pupil, nor any bone of the cheek, nor of the whole
body toucheth or ſtayeth it ſelf upon the Inſtrument, nor much
leſſe is the Inſtrument upheld or mounted in the armes, eſpecially
if it be one of thoſe great ones, as is uſual, which weighing tens,
hundreds, and alſo thouſands of pounds, are placed upon very
ſtrong feet or frames: ſo that the whole objection vaniſheth.
Theſe are the ſubterfuges of this Authour, which, though they were
all of ſteel, would not ſecure him the hundredth part of a minute;
and with theſe he conceits to make us believe, that he hath
penſated that difference, which importeth more than an hundred
minutes; I mean, that of the not obſerving a notable difference
in the diſtances between one of the fixed ſtars, and the new ſtar in
in any of their circulations; which, had it been neer to the Moon,
it ought to have been very conſpicuous to the meer ſight, without
any Inſtrument, eſpecially comparing it with the eleventh of
ſiopeia, its neighbour, within 1 gr. 30 m. which ought to have
ried from it more than two diameters of the moon, as the more
intelligent Aſtronomers of t' oſe times do well note.
* Traguardi.
SAGR. Methinks I ſee that unfortunate Husbandman, who
ter all his expected crops, have been beaten down and deſtroyed by
a ſtorm, goeth up and down with a languiſhing and down-caſt
look, gleaning up every ſmall ear that would not ſuffice to keep a
chicken alive one ſole day.
SALV. Truly, this Authour came out too ſlenderly provided
with armes againſt the aſſailants of the Heavens inalterability, and
with too brittle a chain attempted to pull down the new ſtar of
Caſſiopeia from the higheſt Regions, to theſe ſo low and
ry. And for that I think that we have ſufficiently demonſtrated
the vaſt difference that is between the arguments of thoſe
nomers, and of this their Antagoniſt, it will be convenient that we
leave this particular, and return to our principal matter; in which
there preſents it ſelf to our conſideration the annual motion
monly aſcribed to the Sun, but by Aristarchus Samius firſt of all,
and after by Copernicus taken from the Sun, and transferred upon
the Earth; againſt which Hypotheſis, methinks I ſee Simplicius to
come ſtrongly provided, and particularly with the ſword and
1buckler of the little Treatiſe of Concluſions, or Diſquiſitions
thematical, the oppugnations of which it would be good to
gin to produce.
SIMP. I will, if you ſo pleaſe, reſerve them to the laſt, as thoſe
that are of lateſt invention.
SALV. It will therefore be neceſſary, that in conformity to the
method hitherto obſerved, you do orderly, one by one, propound
the arguments, on the contrary, aſwell of Ariſtotle, as of the
ther ancients, which ſhall be my task alſo, that ſo nothing may
ſcape our ſtrict conſideration and examination; and likewiſe
gredus, with the vivacity of his wit, ſhall interpoſe his thoughts, as
he ſhall finde himſelf inclined.
SAGR. I will do it with my wonted freedome; and your
mands ſhall oblige you to excuſe me in ſo doing.
SALV. The favour will challenge thanks, and not an excuſe.
But now let Simplicius begin to propoſe thoſe doubts which
ſwade him from believing that the Earth, in like manner, as the
other pianets, may move round about a fixed centre.
SIMP. The firſt and greateſt difficulty is the repugnance and
incompatibility that is between being in the centre, and being far
from it; for if the Terreſtrial Globe were to move in a year by
the circumference of a circle, that is, under the Zodiack, it is
poſſible that it ſhould, at the ſame time, be in the centre of the
diack; but that the Earth is in the ſaid centre Aristotle, Ptolomy,
and others have many wayes proved.
SALV. You very well argue, aud there is no queſtion but that
one that would make the Earth to move in the circumference of a
circle, muſt firſt of neceſſity prove, that it is not in the centre of
that ſame circle; it now followeth, that we enquire, whether the
Earth be, or be not in that centre, about which, I ſay, that it
neth, and you ſay that it is fixed; and before we ſpeak of this, it
is likewiſe neceſſary that we declare our ſelves, whether you and I
have both the ſame conceit of this centre, or no. Therefore tell
me, what and where is this your intended centre?
SIMP. When I ſpeak of the centre, I mean that of the
verſe, that of the World, that of the Starry Sphere.
SALV. Although I might very rationally put it in diſpute,
ther there be any ſuch centre in nature, or no; being that neither

you nor any one elſe hath ever proved, whether the World be
nite and figurate, or elſe infinite and interminate; yet nevertheleſs
granting you, for the preſent, that it is finite, and of a terminate
Spherical Figure, and that thereupon it hath its centre; it will be
requiſite to ſee how credible it is that the Earth, and not rather
ſome other body, doth poſſeſſe the ſaid centre.
It hath not been
hitherto proved by
any, whether the
World be finite or
infinite.
SIMP. That the world is finite, terminato, and ſpherical, Ari-
1ſtotle proveth with an hundred
The
tions of Ariſtotle
to Prove that the
Vniverſe is finite,
are all nullified by
denying it to be
moveable.
SALV. All which in the end are reduced to one alone, and that
one to none at all; for if I deny his aſſumption, to wit, that the
Univerſe is moveable, all his demonſtrations come to nothing, for
he onely proveth the Univerſe to be finite and terminate, for that
it is moveable. But that we may not multiply diſputes, let it be
granted for once, that the World is finite, ſpherical, and hath
its centre. And ſeeing that that centre and figure is argued from
its mobility, it will, without doubt, be very reaſonable, if from the
circular motions of mundane bodies we proceed to the particular
inveſtigation of that centres proper place: Nay Ariſtotle himſelf

hath argued and determined in the ſame manner, making that
ſame to be the centre of the Univerſe about which all the
leſtial Spheres revolve, and in which he beleived the Terreſtrial
Globe to have been placed. Now tell me Simplicius, if Ariſtotle

ſhould be conſtrained by evident experience to alter in part this
his diſpoſure and order of the Univerſe, and confeſſe himſelf to
have been deceived in one of theſe two propoſitions, namely,
ther in placing the Earth in the centre, or in ſaying, that the
Cœleſtial Spheres do move about that centre, which of the two
confeſſions think you would he chooſe?
Ariſtotle makes
that point to be the
centre of the
verſe about which
all the Celeſtial
Spheres do revolve.
A queſtion is
put, in caſe that
if Ariſtotle were
forced to receive
one of two
tions that make
gainſt his doctrine,
which he would
admit.
SIMP. I believe, that if it ſhould ſo fall out, the
ticks.
SALV. I do not ask the Peripateticks, I demand of Ariſtotle,
for as to thoſe, I know very well what they would reply; they, as
obſervant and humble vaſſals of Ariſtotle, would deny all the
periments and all the obſervations in the World, nay, would alſo
refuſe to ſee them, that they might not be forced to acknowledg
them, and would ſay that the World ſtands as Ariſtotle writeth,
and not as nature will have it, for depriving them of the ſhield
of his Authority, with what do you think they would appear in the
field? Tell me therefore what you are perſwaded Ariſtotle
ſelf would do in the caſe.
SIMP. To tell you the truth, I know not how to reſolve
which of the two inconveniences is to be eſteemed the leſſer.
SALV. Apply not I pray you this term of inconvenience to a
thing which poſſibly may of neceſſity be ſo. It was an
ence to place the Earth in the centre of the Cœleſtial revolutions;
but ſeeing you know not to which part he would incline, I
ſteeming him to be a man of great judgment, let us examine
which of the two choices is the more rational, and that we will
hold that Ariſtotle would have received. Reaſſuming therefore our
diſcourſe from the beginning, we ſuppoſe with the good liking of
Ariſtotle, that the World (of the magnitude of which we have
no ſenſible notice beyond the fixed ſtars) as being of a ſpherical
1figure; and moveth circularly, hath neceſſarily, and in reſpect of
its figure a centre; and we being moreover certain, that within
the ſtarry Sphere there are many Orbs, the one within another,
with their ſtars, which likewiſe do move circulary, it is in diſpute
whether it is moſt reaſonable to believe and to ſay that theſe
teined Orbs do move round the ſaid centre of the World, or elſe
about ſome other centre far remote from that? Tell me now
plicius what you think concerning this particular.
SIMP. If we could ſtay upon this onely ſuppoſition, and that

we were ſure that we might encounter nothing elſe that might
ſturb us, I would ſay that it were much more reaſonable to
firm that the Orb containing, and the parts contained, do all
move about one common centre, than about divers.
Its more
nal that the Orb
conteining, and the
parts conteined, do
move all about one
centre, than uoon
divers.
SALV. Now if it were true that the centre of the World is the

ſame about which the Orbs of mundane bodies, that is to ſay, of
the Planets, move, it is moſt certain that it is not the Earth, but
the Sun rather that is fixed in the centre of the World. So that as
to this firſt ſimple and general apprehenſion, the middle place
belongeth to the Sun, and the Earth is as far remote from the
centre, as it is from that ſame Sun.
If the centre of
the World be the
ſame with that
bout which the
nees move the Sun
and not the Earth
is placed in it.
SIMP. But from whence do you argue that not the Earth, but
the Sun is in the centre of the Planetary revolutions?
SALV. I infer the ſame from moſt evident, and therefore
ceſſarily concludent obſervations, of which the moſt palpable to

exclude the Earth from the ſaid centre, and to place the Sun
therein, are, the ſeeing all the Planets one while neerer and
ther while farther off from the Earth with ſo great differences, that
for example, Venus when it is at the fartheſt, is ſix times more
remote from us, than when it is neereſt, and Mars riſeth almoſt
eight times as high at one time as at another. See therefore
ther Ariſtotle was not ſomewhat miſtaken in thinking that it was
at all times couidiſtant from us.
Obſervations from
whence it is
lected that the Sun
and not the Earth
is in the centre of
the Celeſtial
lutions.
SIMP. What in the next place are the tokens that their
ons are about the Sun?
SALV. It is argued in the three ſuperiour planets Mars,
ter, and Saturn, in that we find them alwayes neereſt to the
Earth when they are in oppoſition to the Sun, and fartheſt off
when they are towards the conjunction, and this approximatian
and receſſion importeth thus much that Mars neer at hand,
peareth very neer 60 times greater than when it is remote. As to

Venus in the next place, and to Mercury, we are certain that
they revolve about the Sun, in that they never move far from
him, and in that we ſee them one while above and another while

below it, as the mutations of figure in Venus neceſſarily argueth.
Tonchiug the Moon it is certain, that ſhe cannot in any way
1ſeperate from the Earth, for the reaſons that ſhall be more
ly alledged hereafter.
The mutation
of figure in Venus
argueth its motion
to be about the Sun.
The Moon
not ſeperate from
the Earth.
SAGR. I expect that I ſhall hear more admirable things that
depend upon this annual motion of the Earth, than were thoſe
dependant upon the diurnal
The annual
tion of the Earth
mixing with the
motions of the
ther Planets
duce extravagant
appearances.
SALV. You do not therein erre: For as to the operation of
the diurnal motion upon the Celeſtial bodies, it neither was, nor
can be other, than to make the Univerſe ſeem to run precipitately
the contrary way; but this annual motion intermixing with the
particular motions of all the planets, produceth very many
travagancies, which have diſarmed and non-pluſt all the greateſt
Scholars in the World. But returning to our firſt general
henſions, I reply that the centre of the Celeſtial converſions of
the five planets Saturn, Jupiter, Mars, Venus and Mercury, is
the Sun; and ſhall be likewiſe the centre of the motion of the
Earth, if we do but ſucceed in our attempt of placing it in
ven. And as for the Moon, this hath a circular motion about the
Earth, from which (as I ſaid before) it can by no means alienate
it ſelf, but yet doth it not ceaſe to go about the Sun together with
the Earth in an annual motion.
SIMP. I do not as yet very well apprehend this ſtructure, but
it may be, that with making a few draughts thereof, one may
ter and more eaſily diſcourſe concerning the ſame.
SALV. Tis very true: yea for your greater ſatisfaction and
miration together, I deſire you, that you would take the pains
to draw the ſame; and to ſee that although you think you do not
apprehend it, yet you very perfectly underſtand it; And onely
by anſwering to my interrogations you ſhall deſigne it punctually.

Take therefore a ſheet of paper and Compaſles; And let this
white paper be the immenſe expanſion of the Univerſe; in which
you are to diſtribute and diſpoſe its parts in order, according as
reaſon ſhall direct you. And firſt, in regard that without my
ſtruction you verily believe that the Earth is placed in this
verſe, therefore note a point at pleaſure, about which you
tend it to to be placed, and mark it with ſome characters.
The Syſteme of
the Univerſe
ſigned from the
pearances.
SIMP. Let this mark A be the place of the Terreſtrial Globe.
SALV. Very well. I know ſecondly, that you underſtand
fectly that the ſaid Earth is not within the body of the Sun, nor
ſo much as contiguous to it, but diſtant for ſome ſpace from the
ſame, and therefore aſſign to the Sun what other place you beſt
like, as remote from the Earth as you pleaſe, and mark this in
like manner.
SIMP. Here it is done: Let the place of the Solar body
be O.
SALV. Theſe two being conſtituted, I deſire that we may
1think of accomodating the body of Venus in ſuch a manner that
its ſtate and motion may agree with what ſenſible experiments do
ſhew us; and therefore recall to mind that. which either by the
paſt diſcourſes, or your own obſervations you have learnt to
fal that ſtar, and afterwards aſſign unto it that ſtate which you
think agreeth with the ſame.
SIMP. Suppoſing thoſe Phænomena expreſſed by you, and
which I have likewiſe read in the little treatiſe of Concluſions, to
18[Figure 18]
be true, namely, that that ſtar never recedes from the Sun beyond
ſuch a determinate ſpace of 40 degrees or thereabouts, ſo as that
it never cometh either to appoſition with the Sun, or ſo much as
to quadrature, or yet to the ſextile aſpect; and more than that,

ſuppoſing that it ſheweth at one time almoſt 40 times greater than
at another; namely, very great, when being retrograde, it goeth to
the veſpertine conjnnction of the Sun, and very ſmall when with a
1motion ſtraight forwards, it goeth to the matutine conjunction;
and moreover it being true, that when it appeareth bigge it ſhews
with a corniculate figure, and when it appeareth little, it ſeems
perfectly round, theſe appearances, I ſay, being true, I do not ſee
how one can chooſe but affirm the ſaid ſtar to revolve in a circle

bout the Sun, for that the ſaid circle cannot in any wiſe be ſaid
to encompaſſe or to contain the Earth within it, nor to be
our to the Sun, that is between it and the Earth, nor yet
riour to the Sun. That circle cannot incompaſſe the Earth,
cauſe Venus would then ſometimes come to oppofition with the
Sun; it cannot be inferiour, for then Venus in both its
ons with the Sun would ſeem horned; nor can it be ſuperiour,
for then it would alwayes appear round, and never cornicular;
and therefore for receit of it I will draw the circle CH, about
the Sun, without encompaſſing the Earth.
Venus very greas
towards the
ctive conjunction
and very ſmall
wards the
tine.
Venus
rily proved to move
about the Sun.
SALV. Having placed Venus, it is requiſite that you think of
Mercury, which, as you know, alwayes keeping about the Sun,
doth recede leſſe diſtance from it than Venus; therefore conſider
with your ſelf, what place is moſt convenient to aſſign
The revolution of
Mercury concluded
to be about the Sun,
within the Orb of
Venus.
SIMP. It is not to be queſtioned, but that this Planet
ing Venus, the moſt commodious place for it will be, a leſſer
cle within this of Venus, in like manner about the Sun, being
that of its greateſt vicinity to the Sun, an argument, an evidence
ſufficiently proving the vigour of its illumination, above that of
Venus, and of the other Planets, we may therefore upon theſe
conſiderations draw its Circle, marking it with the Characters
BG.
Mars neceſſarily
includeth within its
Orb the Earth, and
alſo the Sun.
SALV. But Mars, Where ſhall we place it?
SIMP. Mars, Becauſe it comes to an oppoſition with the Sun,
its Circle muſt of neceſſity encompaſs the Earth; But I ſee that it
muſt neceſſarily encompaſs the Sun alſo, for coming to
on with the Sun, if it did not move over it, but were below it, it
would appear horned, as Venus and the Moon; but it ſhews
wayes round, and therefore it is neceſſary, that it no leſs includ­

eth the Sun within its circle than the Earth. And becauſe I
member that you did ſay, that when it is in oppoſition with the
Sun, it ſeems 60 times bigger than when it is in the conjunction,
me thinks that a Circle about the Centre of the Sun, and that
eth in the earth, will very well agree with theſe Phænomena,
which I do note and mark D I, where Mars in the point D, is near
to the earth, and oppoſite to the Sun; but when it is in the point
I, it is at Conjuction with the Sun, but very far from the Earth.

And becauſe the ſame appearances are obſerved in Jupiter and
Saturn, although with much leſſer difference in Jupiter than in
Mars, and with yet leſſe in Saturn than in Jupiter; me thinks I
1underſtand that we ſhould very commodiouſly ſalve all the
nomena of theſe two Planets, with two Circles, in like manner,
drawn about the Sun, and this firſt for Jupiter, marking it E L, and
another above that for Saturn marked F
Mars at its
ſition to the Sun
ſhews to be ſixty
times bigger than
towards the
junction.
Jupiter and
turn do likewiſe
compaſſe the Earth,
and the Sun.
The
tion and receſſion of
the three ſuperiour
Planets, importeth
double the Suns
ſtance.
SALV. You have behaved your ſelf bravely hitherto. And
becauſe (as you ſee) the approach and receſſion of the three
periour Planets is meaſured with double the diſtance between the
Earth and Sun, this maketh greater difference in Mars than in Ju-

piter, the Circle D I, of Mars, being leſſer than the Circle E L,
of Jupiter, and likewiſe becauſe this E L, is leſſe than this Circle
F M, of Saturn, the ſaid difference is alſo yet leſſer in Saturn than
in Jupiter, and that punctually anſwereth the Phænomena.
It remains now that you aſſign a place to the Moon.
The difference of
the apparent
nitude leſſe in
turn, than in
ter, an dn Jupiter
than in Mars, and
why.
SIMP. Following the ſame Method (which ſeems to me very

concluſive) in regard we ſee that the Moon cometh to conjunction
and oppoſition with the Sun, it is neceſſary to ſay, that its circle
encompaſſeth the Earth, but yet doth it not follow, that it muſt
environ the Sun, for then at that time towards its conjunction, it
would not ſeem horned, but alwayes round and full of Light.
Moreover it could never make, as it often doth, the Eclipſe of the
Sun, by interpoſing betwixt it and us; It is neceſſary therefore
to aſſign it a circle about the Earth, which ſhould be this N P, ſo
that being conſtituted in P, it will appear from the Earth A, to be
in conjunction with the Sun, and placed in N, it appeareth oppoſite
to the Sun, and in that poſition it may fall under the Earths
dow, and be obſcured.
The Moons Orb
invironeth the
Earth, but not the
Sun.
SALV. Now, Simplicius, what ſhall we do with the fixed
ſtars? Shall we ſuppoſe them ſcattered through the immenſe
ſes of the Univerſe, at different diſtances, from any one
nate point; or elſe placed in a ſuperficies ſpherically diſtended
bout a centre of its own, ſo that each of them may be
diſtant from the ſaid
The probable
ſituation of the
fixed ſtars.
SIMP. I would rather take a middle way; and would aſſign
them an Orb deſcribed about a determinate centre and comprized
within two ſpherical ſuperficies, to wit, one very high, and
cave, and the other lower, and convex, betwixt which I would

conſtitute the innumerable multitude of ſtars, but yet at divers
titudes, and this might be called the Sphere of the Univerſe,
ing within it the Orbs of the planets already by us deſcribed.
Which ought to
be accounted the
ſphere of the
verſe.
SALV. But now we have all this while, Simplicius, diſpoſed the
mundane bodies exactly, according to the order of Copernicus,
and we have done it with your hand; and moreover to each of
them you have aſſigned peculiar motions of their own, except to
the Sun, the Earth, and ſtarry Sphere; and to Mercury with
Venus, you have aſcribed the circular motion about the Sun,
1without encompaſſing the Earth; about the ſame Sun you make
the three ſuperiour Planets Mars, Jupiter, and Saturn, to move,
comprehending the Earth within their circles. The Moon in the
next place can move in no other manner than about the Earth,
without taking in the Sun, and in all theſe motions you agree alſo
with the ſame Copernicus. There remains now three things to be
decided between the Sun, the Earth, and fixed ſtars, namely,

Reſt, which ſeemeth to belong to the Earth; the annual motion
under the Zodiack, which appeareth to pertain to the Sun; and the
diurnal motion, which ſeems to belong to the Starry Sphere, and
to be by that imparted to all the reſt of the Univerſe, the Earth
excepted, And it being true that all the Orbs of the Planets, I

mean of Mercury, Venus, Mars, Jupiter, and Saturn, do move
about the Sun as their centre; reſt ſeemeth with ſo much more
reaſon to belong to the ſaid Sun, than to the Earth, in as much
as in a moveable Sphere, it is more reaſonable that the centre
ſtand ſtill, than any other place remote from the ſaid centre; to
the Earth therefore, which is conſtituted in the midſt of
able parts of the Univerſe, I mean between Venus and Mars, one
of which maketh its revolution in nine moneths, and the other in
two years, may the motion of a year very commodiouſly be

ſigned, leaving reſt to the Sun. And if that be ſo, it followeth
of neceſſary conſequence, that likewiſe the diurnal motion
longeth to the Earth; for, if the Sun ſtanding ſtill, the Earth
ſhould not revolve about its ſelf, but have onely the annual
tion about the Sun, our year would be no other than one day and
one night, that is ſix moneths of day, and ſix moneths of night,
as hath already been ſaid. You may conſider withal how
diouſly the precipitate motion of 24 hours is taken away from
the Univerſe, and the fixed ſtars that are ſo many Suns, are made
in conformity to our Sun to enjoy a perpetual reſt. You ſee
over what facility one meets with in this rough draught to render
the reaſon of ſo great appearances in the Celeſtial bodies.
Reſt, the annual
motion and the
urnal ought to be
diſtributed
twixt the Sun,
Earth, and
mament.
In a moveable
ſphere, it ſeemeth
more veaſonable
that its centre be
ſtable, than any
ther of its parts.
Granting to the
Earth the annual,
it muſt of neceſſity
alſo have the
nal motion
ed to it.
SAGR. I very well perceive that facility, but as you from this
ſimplicity collect great probabilities for the truth of that Syſtem,
others haply could make thence contrary deductions; doubting,
not without reaſon, why that ſame being the ancient Syſteme of
Pythagoreans, and ſo well accommodated to the Phænomena,
hath in the ſucceſſion of ſo many thouſand years had ſo few
lowers, and hath been even by Ariſtotle himſelf refuted, and
ſince that Copernicus himſelf hath had no better fortune.
SALV. If you had at any time been aſſaulted, as I have been,
many and many a time, with the relation of ſuch kind of frivolous
reaſons, as ſerve to make the vulgar contumacious, and difficult to
be perſwaded to hearken, (I will not ſay to conſent) to this
1ty, I believe that you wonder at the paucity of thoſe who are
lowers of that opinion would be much diminiſhed. But ſmall

gard in my judgement, ought to be had of ſuch thick ſculs, as think
it a moſt convincing proof to confirm, and ſteadfaſtly ſettle them
in the belief of the earths immobility, to ſee that if this day they
cannot Dine at Conſtantinople, nor Sup in Jappan, that then the
Earth as being a moſt grave body cannot clamber above the Sun,
and then ſlide headlong down again; Of ſuch as theſe I ſay,
whoſe number is infinite, we need not make any reckoning, nor
need we to record their foolieries, or to ſtrive to gain to our ſide
as our partakers in ſubtil and ſublime opinions, men in whoſe
finition the kind onely is concerned, and the difference is wanting.
Moreover, what ground do you think you could be able to gain,
with all the demonſtrations of the World upon brains ſo ſtupid,
as are not able of themſelves to know their down right follies? But
my admiration, Sagredus, is very different from yours, you
der that ſo few are followers of the Pythagorean Opinion; and I
am amazed how there could be any yet left till now that do
brace and follow it: Nor can I ſufficiently admire the eminencie of

thoſe mens wits that have received and held it to be true, and with
the ſprightlineſſe of their judgements offered ſuch violence to their
own ſences, as that they have been able to prefer that which their
reaſon dictated to them, to that which ſenſible experiments
preſented moſt manifeſtly on the contrary. That the reaſons againſt
the Diurnal virtiginous revolution of the Earth by you already
amined, do carry great probability with them, we have already
ſeen; as alſo that the Ptolomaicks, and Ariſtotelicks, with all their
Sectators did receive them for true, is indeed a very great argument
of their efficacie; but thoſe experiments which apertly contradict
the annual motion, are of yet ſo much more manifeſtly repugnant,

that (I ſay it again) I cannot find any bounds for my admiration,
how that reaſon was able in Ariſtarchus and Copernicus, to
mìt ſuch a rape upon their Sences, as in deſpight thereof, to make
her ſelf miſtreſs of their credulity.
Diſcourſes more
than childiſh, ſerve
to keep fools in the
opinion of the
Earths ſtability.
A declaration
of the
lity of Copernicus
his opinion.
Reaſons and
courſe in
cus and
cus prevailed over
manifeſt ſence.
SAGR. Are we then to have ſtill more of theſe ſtrong
ons againſt this annual motion?
SALV. We are, and they be ſo evident and ſenſible, that if a
ſence more ſublime and excellent than thoſe common and vulgar,
did not take part with reaſon, I much fear, that I alſo ſhould have
been much more averſe to the Copernican Syſteem than I have been
ſince the time that a clearer lamp than ordinary hath enlightned
me.
SAGR. Now therefore Salviatus, let us come to joyn battail
for every word that is ſpent on any thing elſe, I take to be caſt
way.
1
SALV. I am ready to ſerve you. You have already ſeen me
draw the form of the Copernican Syſteme; againſt the truth of

which Mars himſelf, in the firſt place, makes an hot charge; who, in
caſe it were true, that its diſtances from the earth ſhould ſo much
vary, as that from the leaſt diſtance to the greateſt, there were
twice as much difference, as from the earth to the Sun; it would be
neceſſary, that when it is neareſt unto us, its diſcus would ſhew
more than 60. times bigger than it ſeems, when it is fartheſt from
us; nevertheleſs that diverſity of apparent magnitude is not to be
ſeen, nay in its oppoſition with the Sun, when its neareſt to the
Earth, it doth not ſhew ſo much as quadruple and quintuple in
bigneſs, to what it is, when towards the conjunction it cometh to
be occulted under the Suns rayes. Another and greater difficulty
doth Venus exhibit; For if revolving about the Sun, as Copernicus

affirmeth, it were one while above, & another while below the ſame,
receding and approaching to us ſo much as the Diameter of the
cle deſcribed would be, at ſuch time as it ſhould be below the Sun,
and neareſt to us, its diſcus would ſhew little leſs than 40 times
ger than when it is above the Sun, near to its other conjunction; yet
nevertheleſſe, the difference is almoſt imperceptible Let us add

other difficulty, that in caſe the body of Venus be of it ſelf dark, and
onely ſhineth as the Moon, by the illumination of the Sun, which
ſeemeth moſt reaſonable; it would ſhew forked or horned at ſuch
time as it is under the Sun, as the Moon doth when ſhe is in like
manner near the Sun; an accident that is not to be diſcovered in
her. Whereupon Copernicus affirmeth, that either ſhe is light of

her ſelf, or elſe that her ſubſtance is of ſuch a nature, that it can
imbue the Solar light, and tranſmit the ſame through all its whole
depth, ſo as to be able to appear to us alwayes ſhining; and in this
manner Copernicus excuſeth the not changing figure in Venus: but
of her ſmall variation of Magnitude, he maketh no mention at all;

and much leſs of Mars than was needful; I believe as being
ble ſo well as he deſired to ſalve a Phænomenon ſo contrary to his
Hypotheſis, and yet being convinced by ſo many other occurrences
and reaſons he maintained, and held the ſame Hypotheſis to be true.
Beſides theſe things, to make the Planets, together with the Earth,
to move above the Sun as the Centre of their converſions, and the

Moon onely to break that order, and to have a motion by it ſelf
about the earth; and to make both her, the Earth, and the whole
Elementary Sphere, to move all together about the Sun in a year,
this ſeemeth to pervert the order of this Syſteme, which rendreth
it unlikely and falſe. Theſe are thoſe difficulties that make me
wonder how Aristarchus and Copernicus, who muſt needs have
ſerved them, not having been able for all that to ſalve them, have
yet notwithſtanding by other admirable occurrences been induced
1to conſide ſo much in that which reaſon dictated to them, as that
they have conſidently affirmed that the ſtructure of the Univerſe
could have no other figure than that which they deſigned to
ſelves. There are alſo ſeveral other very ſerious and curious doubts,
not ſo eaſie to be reſolved by the middle ſort of wits, but yet
netrated and declared by Coperninus, which we ſhall defer till by
and by, after we have anſwered to other objections that ſeem to
make againſt this opinion. Now coming to the declarations and
anſwers to thoſe three before named grand Objections, I ſay, that
the two firſt not onely contradict not the Copernican Syſteme, but

greatly and abſolutely favour it; For both Mars and Venus ſeems
unequal to themſelves, according to the proportions aſſigned; and
Venus under the Sun ſeemeth horned, and goeth changing figures
in it ſelf exactly like the Moon.
Mars makes an
hot aſſault upon the
Copernican
ſteme.
The
na of Venus appear
contrary to the
ſteme of
cus.
Another
culty raiſed by
nus againſt
nicus.
Venus, according
to Copernicus,
ther lucid in it
ſelf, or elſe of a
tranſparent
ſtance.
Copernicus
eth nothing of the
ſmall variation of
bigneſs in Venus
and in Mars.
The moon much
diſturbeth the
der of the other
Planets.
Anſwers to the
three first
ons againſt the
pernican Syſteme.
SAGR. But how came this to be concealed from Copernicus,
and revealed to you?
SALV. Theſe things cannot be comprehended, ſave onely by
the ſenſe of ſeeing, the which by nature was not granted to man
ſo perfect, as that it was able to attain to the diſcovery of ſuch
ferences; nay even the very inſtrument of ſight is an impediment
to it ſelf: But ſince that it hath pleaſed God in our age to
ſafe to humane ingenuity, ſo admirable an invention of perfecting
our ſight, by multiplying it four, ſix, ten, twenty, thirty, and
ty times, infinite objects, that either by reaſon of their diſtance, or
for their extream ſmallneſſe were inviſible unto us, have by help
of the Teleſcope been rendered viſible.
SAGR. But Venus and Mars are none of the objects inviſible
for their diſtance or ſmallneſſe, yea, we do diſcern them with our
bare natural ſight; why then do we not diſtinguiſh the differences
of their magnitudes and figures?
SALV. In this, the impediment of our very eye it ſelf hath a

great ſhare, as but even now I hinted, by which the reſplendent and
remote objects are not repreſented to us ſimple and pure; but gives
them us fringed with ſtrange and adventitious rayes, ſo long and
denſe, that their naked body ſheweth to us agrandized ten,
ty, an hundred, yea a thouſand times more than it would appear, if
the capillitious rayes were taken away.
Thereaſon whence
it happens that
nus and Mars do
not appear to vary
magnitude ſo much
as is requiſite.
SAGR. Now I remember that I have read ſomething on this
ſubject, I know not whether in the Solar Letters, or in the
giatore of our common Friend, but it would be very good, aſwell
for recalling it into my memory, as for the information of
cius, who it may be never ſaw thoſe writings, that you would
clare unto us more diſtinctly how this buſineſſe ſtands, the
ledge whereof I think to be very neceſſary for the aſſiſting of us to
underſtand that of which we now ſpeak.
1
SIMP. I muſt confeſſe that all that which Salviatus hath
ken is new unto me, for truth is, I never have had the curioſity to
read thoſe Books, nor have I hitherto given any great credit to
the Teleſcope newly introduced; rather treading in the ſteps of

ther Peripatetick Philoſophers my companions, I have thought
thoſe things to be fallacies and deluſions of the Chryſtals, which
others have ſo much admired for ſtupendious operations: and
therefore if I have hitherto been in an errour, I ſhall be glad to be
freed from it, and allured by theſe novelties already heard from
you, I ſhall the more attentively hearken to the reſt.
The operations of
the Teleſcope
counted fallacies by
the Peripateticks.
SALV. The confidence that theſe men have in their own
prehenſiveneſſe, is no leſs unreaſonable than the ſmall eſteem they
have of the judgment of others: yet its much that they ſhould
ſteem themſelves able to judge better of ſuch an inſtrument,
out ever having made trial of it, than thoſe who have made, and
daily do make a thouſand experiments of the ſame: But I pray
you, let us leave this kind of pertinacious men, whom we
not ſo much as tax without doing them too great honour. And

turning to our purpoſe, I ſay, that reſplendent objects, whether
it is that their light doth refract on the humidity that is upon the
pupils, or that it doth reflect on the edges of the eye-browes,
fuſing its reflex rayes upon the ſaid pupils, or whether it is for ſome
other reaſon, they do appear to our eye, as if they were environ'd
with new rayes, and therefore much bigger than their bodies
would repreſent themſelves to us, were they diveſted of thoſe

radiations. And this aggrandizement is made with a greater and
greater proportion, by how much thoſe lucid objects are leſſer and
leſſer; in the ſame manner for all the world, as if we ſhould
poſe that the augmentation of ſhining locks were v.g. four inches,
which addition being made about a circle that hath four inches
ameter would increaſe its appearance to nine times its former
neſſe: but---------
Shining objects
ſeem environed
with adventitious
rayes.
The reaſon why
luminous bodies
pear enlarged
much the more, by
how much they are
leſſer.
SIMP. I believe you would have ſaid three times; for adding
four inches to this ſide, and four inches to that ſide of the
ter of a circle, which is like wiſe four inches, its quantity is
by tripled, and not made nine times bigger.
SALV. A little more Geometry would do well, Simplicius.

True it is, that the diameter is tripled, but the ſuperficies, which is
that of which we ſpeak, increaſeth nine times: for you muſt know,
Simplicius, that the ſuperficies of circles are to one another, as
the ſquares of their diameters; and a circle that hath four inches
diameter is to another that hath twelve, as the ſquare of four to
the ſquare of twelve; that is, as 16. is to 144 and therefore it ſhall
be increaſed nine times, and not three; this, by way of
ment to Simplicius. And proceeding forwards, if we ſhould add
1the ſaid irradiation of four inches to a circle that hath but two
ches of diameter onely, the diameter of the irradiation or
land would be ten inches, and the ſuperficial content of the circle
would be to the area of the naked body, as 100. to 4. for thoſe
are the ſquares of 10. and of 2. the agrandizement would
fore be 25. times ſo much; and laſtly, the four inches of hair or
fringe, added to a ſmall circle of an inch in diameter, the ſame
would be increaſed 81. times; and ſo continually the
tions are made with a proportion greater and greater, according
as the real objects that increaſe, are leſſer and leſſer.
Superficial
gures encreaſing
proportion double to
their lines.
SAGR. The doubt which puzzled Simplicius never troubled
me, but certain other things indeed there are, of which I deſire
a more diſtinct underſtanding; and in particular, I would know
on what ground you affirm that the ſaid agrandizement is alwayes
equal in all viſible
Objects the more
vigorous they are
in light, the more
they do ſeem to
creaſe.
SALV. I have already declared the ſame in part, when I ſaid,
that onely lucid objects ſo increaſed, and not the obſcure; now I
adde what remaines, that of the reſplendent objects thoſe that are
of a more bright light, make the reflection greater and more
ſplendent upon our pupil; whereupon they ſeem to augment
much more than the leſſe lucid: and that I may no more inlarge
my ſelf upon this particular, come we to that which the true
ſtris of Astronomy, Experience, teacheth us. Let us this evening,
when the air is very obſcure, obſerve the ſtar of Jupiter; we
ſhall ſee it very glittering, and very great; let us afterwards look

through a tube, or elſe through a ſmall trunk, which clutching the
hand cloſe, and accoſting it to the eye, we lean between the palm
of the hands and the fingers, or elſe by an hole made with a ſmall
needle in a paper; and we ſhall ſee the ſaid ſtar diveſted of its
beams, but ſo ſmall, that we ſhall judge it leſſe, even than a
eth part of its great glittering light ſeen with the eye at liberty:
we may afterwards behold the Dog-ſtars beautiful and bigger than

any of the other fixed ſtars, which ſeemeth to the bare eye no
great matter leſſe than Jupiter; but taking from it, as before, the
irradiation, its Diſcus will ſhew ſo little, that it will not be
thought the twentieth part of that of Jupiter, nay, he that hath not
very good eyes, will very hardly diſcern it; from whence it may
be rationally inferred, that the ſaid ſtar, as having a much more
lively light than Jupiter, maketh its irradiation greater than
ter doth his. In the next place, as to the irradiation of the Sun
and Moon, it is as nothing, by means of their magnitude, which

poſſeſſeth of it ſelf alone ſo great a ſpace in our eye, that it
veth no place for the adventitious rayes; ſo that their faces ſeem
cloſe clipt, and terminate. We may aſſure our ſelves of the ſame
truth by another experiment which I have often made triall of;
1
we may aſſure our ſelves, I ſay, that bodies ſhining with moſt|
ly light do irradiate, or beam forth rayes more by far than thoſe
that are of a more languiſhing light. I have many times ſeen
piter and Venus together twenty or thirty degrees diſtant from the
Sun, and the air being very dark, Venus appeared eight or ten
times bigger than Jupiter, being both beheld by the eye at
ty; but being beheld afterwards with the Teleſcope, the Diſcus
of Jupiter diſcovered it ſelf to be four or more times greater than
that of Venus, but the vivacity of the ſplendour of Venus was
comparably bigger than the languiſhing light of Jupiter; which
was only becauſe of Jupiters being far from the Sun, and from us;
and Venus neer to us, and to the Sun. Theſe things premiſed, it
will not be difficult to comprehend, how Mars, when it is in
ſition to the Sun, and therefore neerer to the Earth by ſeven times,
and more, than it is towards the conjunction, cometh to appear
ſcarce four or five times bigger in that ſtate than in this, when as it
ſhould appear more than fifty times ſo much; of which the only
irradiation is the cauſe; for if we diveſt it of the adventitious
rayes, we ſhall find it exactly augmented with the due proportion:
but to take away the capillitious border, the Teleſcope is the beſt

and only means, which inlarging its Diſcus nine hundred or a
thouſand times, makes it to be ſeen naked and terminate, as that
of the Moon, and different from it ſelf in the two poſitions,

cording to its due proportions to an hair. Again, as to Venus,
that in its veſpertine conjunction, when it is below the Sun, ought
to ſhew almoſt fourty times bigger than in the other matutine
junction, and yet doth not appear ſo much as doubled; it
eth, beſides the effect of the irradiation, that it is horned; and its
creſcents, beſides that they are ſharp, they do receive the Suns light
obliquely, and therefore emit but a faint ſplendour; ſo that as
being little and weak, its irradiation becometh the leſſe ample
and vivacious, than when it appeareth to us with its Hemiſphere all
ſhining: but now the Teleſcope manifeſtly ſhews its hornes to
have been as terminate and diſtinct as thoſe of the Moon, and
appear, as it were, with a great circle, and in a proportion thoſe
well neer fourty times greater than its ſame Diſcus, at ſuch time
as it is ſuperiour to the Sun in its ultimate matutine apparition.
An eaſie
riment that
eth the increaſe in
the ſtars, by means
of the adventitious
rays.
Jupiter augments
leſſe than the
ſtar.
The Sun and
Moon increaſe
tle.
It is ſeen by
nifeſt experience,
that the more
ſplendid bodies do
much more
ate than the leſſe
lucid.
The Teleſcope
is the beſt means to
take away the
radiations of the
Stars.
Another ſecond
reaſon of the ſmall
apparent increaſe
of Venus.
SAGR. Oh, Nicholas Copernicus, how great would have been
thy joy to have ſeen this part of thy Syſteme, confirmed with ſo
manifeſt
Copernicus
ſwaded by reaſons
contrary to ſenſible
experiments.
SALV. Tis true. But how much leſſe the fame of his ſublime
wit amongſt the intelligent? when as it is ſeen, as I alſo ſaid before,
that he did conſtantly continue to affirm (being perſwaded thereto
by reaſon) that which ſenſible experiments ſeemed to contradict;
for I cannot ceaſe to wonder that he ſhould conſtantly perſiſt in
ſaying, that Venus revolveth about the Sun, and is more than ſix
1times farther from us at one time, than at another; and alſo
eth to be alwayes of an equal bigneſs, although it ought to ſhew
forty times bigger when neareſt to us, than when fartheſt off.
SAGR. But in Jupiter, Saturn and Mercury, I believe that
the differences of their apparent magnitudes, ſhould ſeem
ally to anſwer to their different diſtances.
SALV. In the two Superiour ones, I have made preciſe
ſervations yearly for this twenty two years laſt paſt: In Mercury

there can be no obſervation of moment made, by reaſon it
fers not it ſelf to be ſeen, ſave onely in its greateſt digrſſieons
from the Sun, in which its diſtances from the earth are inſenſibly
unequal, and thoſe differences conſequently not to be obſerved;
as alſo its mutations of figures which muſt abſolutely happen in
it, as in Venus. And if we do ſee it, it muſt of neceſſity appear
in form of a Semicircle, as Venus likewiſe doth in her greateſt
digreſſions; but its diſcus is ſo very ſmall, and its ſplendor ſo
very great, by reaſon of its vicinity to the Sun, that the virtue
of the Teleſcope doth not ſuffice to clip its treſſes or adventitious
rayes, ſo as to make them appear ſhaved round about. It

mains, that we remove that which ſeemed a great inconvenience
in the motion of the Earth, namely that all the Planets moving
about the Sun, it alone, not ſolitary as the reſt, but in company
with the Moon, and the whole Elementary Sphear, ſhould move
round about the Sun in a year; and that the ſaid Moon withal
ſhould move every moneth about the earth. Here it is neceſſary
once again to exclaim and extol the admirable perſpicacity of
pernicus, and withal to condole his misfortune, in that he is not
now alive in our dayes, when for removing of the ſeeming
ſurdity of the Earth and Moons motion in conſort we ſee
ter, as if it were another Earth, not in conſort with the Moon,
but accompanied by four Moons to rovolve about the Sun in 12.
years together, with what ever things the Orbs of the four
cæan Stars can contain within them.
Mercury
teth not of clear
obſervations.
The difficulties
removed that ariſe
from the Earths
moving about the
Sun, not ſolitarily,
but in conſort with
the Moon.
SALV. Why do you call the four jovial Planets, Moons?
SAGR. Such they would ſeem to be to one that ſtanding in

Jupiter ſhould behold them; for they are of themſelves dark, and
receive their light from the Sun, which is manifeſt from their
ing eclipſed, when they enter into the cone of Jupiters ſhadow:
and becauſe onely thoſe their Hemiſpheres, that look towards the
Sun are illuminated, to us that are without their Orbs, and
er to the Sun, they ſeem alwayes lucid, but to one that ſhould be
in Jupiter, they would ſhew all illuminated, at ſuch time as they
were in the upper parts of their circles; but in the parts
our, that is between Jupiter and the Sun, they would from
piter be obſerved to be horned; and in a word they would, to
1the obſervators ſtanding in Jupiter, make the ſelf ſame changes
of Figure, that to us upon the Earth, the Moon doth make. You
ſee now how theſe three things, which at ſirſt ſeémed diſſonant,
do admirably accord with the Copernican Syſteme. Here alſo by
the way may Simplicius ſee, with what probability one may
clude, that the Sun and not the Earth, is in the Centre of the
Planetary converſions. And ſince the Earth is now placed
mongſt mundane Bodies, that undoubtedly move about the Sun,
to wit, above Mercury and Venus, and below Saturn, Jupiter,
and Mars; ſhall it not be in like manner probable, and perhaps
neceſſary to grant, that it alſo moveth round?
The Medicean
Stars areas it were
four Moons about
Jupiter.
SIMP. Theſe accidents are ſo notable and conſpicuous, that
it is not poſſible, but that Ptolomy and others his Sectators, ſhould
have had knowledge of them, and having ſo, it is likewiſe
ſary, that they have found a way to render reaſons of ſuch, and
ſo ſenſible appearances that were ſufficient, and alſo congruous
and probable, ſeeing that they have for ſo long a time been
ceived by ſuch numbers of learned
The Principal
ſcope of
mers, is to give a
reaſon of
ances.
SALV. You argue very well; but you know that the principal
ſcope of Aſtronomers, is to render only reaſon for the appearances
in the Cæleſtial Bodies, and to them, and to the motions of the
Stars, to accomodate ſuch ſtructures and compoſitions of Circles,
that the motions following thoſe calculations, anſwer to the ſaid
appearances, little ſcrupling to admit of ſome exorbitances, that
indeed upon other accounts they would much ſtick at. And Co-

pernic us himſelf writes, that he had in his firſt ſtudies reſtored the
Science of Aſtronomy upon the very ſuppoſitions of Ptolomy, and
in ſuch manner corrected the motions of the Planets, that the
computations did very exactly agree with the Phænomena, and
the Phænomena with the ſupputations, in caſe that he took the
Planets ſeverally one by one. But he addeth, that in going
bout to put together all the ſtructures of the particular Fabricks,
there reſulted thence a Monſter and Chimæra, compoſed of
bers moſt diſproportionate to one another, and altogether
patible; So that although it ſatisfied an Aſtronomer meerly
rithmetical, yet did it not afford ſatisfaction or content to the

Aſtronomer Phyloſophical. And becauſe he very well
ſtood, that if one might ſalve the Cæleſtial appearances with falſe
aſſumptions in nature, it might with much more eaſe be done by
true ſuppoſitions, he ſet himſelf diligently to ſearch whether
ny amongſt the antient men of fame, had aſcribed to the World
any other ſtructure, than that commonly received by Ptolomy;
and finding that ſome Pythagoreans had in particular aſſigned
the Diurnal converſion to the Earth, and others the annual
tion alſo, he began to compare the appearances, and
1ties of the Planets motions, with theſe two new ſuppoſitions, all
which things jumpt exactly with his purpoſe; and ſeeing the whole
correſpond, with admirable facility to its parts, he imbraced this
new Syſteme, and it took up his reſt.
Copernicus
ſtored Aſtronomy
upon the
ous of Ptolomy:
What moved
pernicus to
bliſh his Syſteme.
SIMP. But what great exorbitancies are there in the
maick Syſteme, for which there are not greater to be found in this
of Copernicus?
SALV. In the Ptolomaick Hypotheſis there are diſeaſes, and in

the Copernican their cures. And firſt will not all the Sects of
Phyloſophers, account it a great inconvenience, that a body
turally moveable in circumgyration, ſhould move irregularly upon
its own Centre, and regularly upon another point? And yet
there are ſuch deformed motions as theſe in the Ptolomæan
theſis, but in the Copernican all move evenly about their own
Centres. In the Ptolomaick, it is neceſſary to aſſign to the
leſtial bodies, contrary motions, and to make them all to move,
from Eaſt to Weſt, and at the ſame time, from Weſt to Eaſt;
But in the Copernican, all the Cæleſtial revolutions are towards
one onely way, from Weſt to Eaſt. But what ſhall we ſay of
the apparent motion of the Planets, ſo irregular, that they not
ly go one while ſwift, and another while ſlow, but ſometimes
wholly ſeace to move; and then after a long time return back
gain? To ſalve which appearances Ptolomie introduceth very great
Epicicles, accommodating them one by one to each Planet, with
ſome rules of incongruous motions, which are all with one
gle motion of the Earth taken away. And would not you,
plicius, call it a great abſurditie, if in the Ptolomaick
ſis, in which the particular Planets, have their peculiar Orbs
ſigned them one above another, one muſt be frequently forced
to ſay, that Mars, conſtituted above the Sphære of the Sun, doth
ſo deſcend, that breaking the Solar Orb, it goeth under it, and
approacheth neaer to the Earth, than to the Body of the Sun,
and by and by immeaſurably aſcendeth above the ſame? And
yet this, and other exorbitancies are remedied by the Soul and
fingle annual motion of the Earth.
Inconveniencies
that are in the
ſteme of Ptolomy.
SAGR. I would gladly be bettter informed how theſe ſtations,
and retrograde and direct motions, which did ever ſeem to me
great improbalities, do accord in this Copernican
Its a great
gument in favour
of Copernicus, that
he obviates the
tions &
tions of the motions
of the Planets.
SALV. You ſhall ſee them ſo to accord, Sagredus, that
this onely conjecture ought to be ſufficient to make one that
is not more than pertinacious or ſtupid, yield, aſſent to all the
reſt of this Doctrine. I tell you therefore, that nothing being
altered in the motion of Saturn, which is 30 years, in that
of Jupiter, which is 12, in that of Mars, which is 2, in that of
Venus, which is 9. moneths, in that of Mercury, which is 80.
1dayes, or thereabouts, the ſole annual motion of the Earth
tween Mars and Venus, cauſeth the apparent inequalities in all

the five ſtars before named. And for a facile and full
ſtanding of the whole, I will deſcribe this figure of it.
fore ſuppoſe the Sun to be placed in the centre O, about which
we will draw the Orb deſcribed by the Earth, with the
nual motion B G M, and let the circle deſcribed, v. gr. by
Jupiter about the Sun in 12. years, be this BGM, and in the
19[Figure 19]

ſtarry ſphere let us imagine the Zodiack Y V S. Again, in the
annual Orb of the Earth let us take certain equal arches, B C,
C D, E F, F G, G H, H I, I K, K L, L M, and in the Sphere
of Jupiter let us make certain other arches, paſſed in the ſame
times in which the Earth paſſeth hers, which let be B C, C D,
D E, E F, F G, G H, H I, I K, K L, L M, which ſhall each be
proportionally leſſe than theſe marked in the Earths Orb, like
as the motion of Jupiter under the Zodiack is ſlower than the
annual. Suppoſing now, that when the Earth is in B, Jupiter is
in B, it ſhall appear to us in the Zodiack to be in P, deſcribing
1the right line B B P. Next ſuppoſe the Earth to be moved from
B to C, and Jupiter from B to C, in the ſame time; Iupiter
ſhall appear to have paſſed in the Zodiack to Q, and to have
moved ſtraight forwards, according to the order of the ſignes
P que In the next place, the Earth paſſing to D, and Iupiter
to D, it ſhall be ſeen in the Zodiack in R, and from E,
ter being come to E; will appear in the Zodiack in S, having
all this while moved right forwards. But the Earth afterwards
beginning to interpoſe more directly between Iupiter and the
Sun, ſhe being come to F, and Iupiter to F, he will appear in
T, to have already begun to return apparently back again
der the Zodiack, and in that time that the Earth ſhall have
ed the arch E F, Iupiter ſhall have entertained himſelf between
the points S T, and ſhall have appeared to us almoſt
leſſe and ſtationary. The Earth being afterwards come to G,
and Iupiter to G, in oppoſition to the Sun, it ſhall be viſible in
the Zodiack at V, and much returned backwards by all the arch
of the Zodiack T V; howbeit that all the way purſuing its even
courſe it hath really gone forwards not onely in its own circle,
but in the Zodiack alſo in reſpect to the centre of the ſaid
ack, and to the Sun placed in the ſame. The Earth and Iupiter
again continuing their motions, when the Earth is come to H,
and Iupiter to H, it ſhall ſeem very much gone backward in the
Zodiack by all the arch V X. The Earth being come to I, and
Iupiter to I, it ſhall be apparently moved in the Zodiack by the
tle ſpace X Y, and there it will ſeem ſtationary. When
wards the Earth ſhall be come to K, and Iupiter to K; in the
Zodiack he ſhall have paſſed the arch Y N in a direct motion;
and the Earth purſuing its courſe to L, ſhall ſee Iupiter in L, in
the point Z. And laſtly Iupiter in M ſhall be ſeen from the Earth
M, to have paſſed to A, with a motion ſtill right forwards; and
its whole apparent retrogadation in the Zodiack ſhall anſwer to
the arch S Y, made by Iupiter, whilſt that he in his own circle
paſſeth the arch E I, and the Earth in hers the arch E I. And

this which hath been ſaid, is intended of Saturn and of Mars
alſo; and in Saturn thoſe retrogradations are ſomewhat more
frequent than in Jupiter, by reaſon that its motion is a little
ſlower than that of Jupiter, ſo that the Earth overtaketh it
it in a ſhorter ſpace of time; in Mars again they are more
rare, for that its motion is more ſwift than that of Jupiter.
Whereupon the Earth conſumeth more time in recovering it. Next
as to Venus and Mercury, whoſe Circles are comprehended by that

of the Earth, their ſtations and regreſſions appear to be
oned, not by their motions that really are ſuch, but by the anual
motion of the ſaid Earth, as Copernicus exellently demonſtrateth,
1together with Appollonius Pergæus in lib. 5. of his Revolutions,
Chap. 35.
The ſole annual
motion of the
Earth cauſeth
great inequality of
motions in the five
Planets.
A demonſtration of
the inequalities of
the three ſuperiour
Planets dependent
on the annual
tion of the Earth.
Retrogradations
more frequent in
Saturn, leſſe in
piter, and yet leſſe
in Mars, and why.
The
tion of Venus and
Mercury
ſtrated by
nius and
cus.
You ſee, Gentlemen, with what facility and ſimplicity the

al motion, were it appertaining to the Earth, is accommodated
to render a reaſon of the apparent exorbitances, that are obſerved
in the motions of the five Planets, Saturn, Jupiter, Mars,
nus and Mercury, taking them all away, and reducing them to

equal and regular motions. And of this admirable effect,
cholas Copernicus, hath been the firſt that hath made the reaſon
plain unto us. But of another effect, no leſſe admirable than
this, and that with a knot, perhaps more difficult to unknit,
bindeth the wit of man, to admit this annual converſion, and to
leave it to our Terreſtrial Globe; a new and unthought of
jecture ariſeth from the Sun it ſelf, which ſheweth that it is
ling to be ſingular in ſhifting, of this atteſtation of ſo eminent a
concluſion, rather as a teſtimony beyond all exception, it hath
deſired to be heard apart. Hearken then to this great and new

The annual
tion of the Earth
moſt apt to render
a reaſon of the
orbttances of the
five Planets.
The Sun it ſelf
teſtifieth the
al motion to belong
to the Earth.
The Lyncæan
Academick the
firſt diſcoverer of
the Solar ſpots, and
all the other
ſtial novelties.
The firſt diſcoverer and obſerver of the Solar ſpots, as alſo of
all the other Cœleſtial novelties, was our Academick Lincæus; and
he diſcovered them anno 1610. being at that time Reader of the
Mathematicks, in the Colledge of Padua, and there, and in
nice, he diſcourſed thereof with ſeveral perſons, of which ſome

are yet living: And the year following, he ſhewed them in Rome
to many great perſonages, as he relates in the firſt of his Letters
to Marcus Velſerus, ^{*} Sheriffe of Auguſta. He was the
firſt that againſt the opinions of the too timorous and too jealous

aſſertors of the Heavens inalterability, affirmed thoſe ſpots to be
matters, that in ſhort times were produced and diſſolved: for as
to place, they were contiguous to the body of the Sun, and
volved about the ſame; or elſe being carried about by the ſaid
Solar body, which revolveth in it ſelfe about its own Centre, in
the ſpace almoſt of a moneth, do finiſh their courſe in that time;
which motion he judged at firſt to have been made by the Sun
bout an Axis erected upon the plane of the Ecliptick; in regard
that the arches deſcribed by the ſaid ſpots upon the Diſcus of the
Sun appear unto our eye right lines, and parallels to the plane of
the Ecliptick: which therefore come to be altered, in part, with
ſome accidental, wandring, and irregular motions, to which they
are ſubject, and whereby tumultuarily, and without any order
they ſucceſſively change ſituations amongſt themſelves, one
while crouding cloſe together, another while diſſevering, and
ſome dividing themſelves into many and very much changing
gures, which, for the moſt part, are very unuſual. And albeit
thoſe ſo inconſtant mutations did ſomewhat alter the primary
1riodick courſe of the ſaid ſpots, yet did they not alter the
on of our friend, ſo as to make him believe, that they were any
eſſential and fixed cauſe of thoſe deviations, but he continued to
hold, that all the apparent alterations derived themſelves from
thoſe accidental mutations: in like manner, juſt as it would
pen to one that ſhould from far diſtant Regions obſerve the
tion of our Clouds; which would be diſcovered to move with a
moſt ſwift, great, and conſtant motion, carried round by the
urnal Vertigo of the Earth (if haply that motion belong to the
ſame) in twenty four hours, by circles parallel to the
al, but yet altered, in part, by the accidental motions cauſed by
the winds, which drive them, at all adventures, towards different
quarters of the World. While this was in agitation, it came to
paſs that Velſerus ſent him two Letters, written by a certain

ſon, under the feigned name of ^{*} Apelles, upon the ſubject of
theſe Spots, requeſting him, with importunity, to declare his
thoughts freely upon thoſe Letters, and withall to let him know
what his opinion was touching the eſſence of thoſe ſpots; which his
requeſt he ſatisfied in 3 Letters, ſhewing firſt of all howvain the
conjectures of Apelles were; & diſcovering, ſecondly, his own
nions; withal foretelling to him, that Apelles would undoubtedly
be better adviſed in time, and turn to his opinion, as it afterwards
came to paſs. And becauſe that our Academian (as it was alſo
the judgment of many others that were intelligent in Natures
crets) thought he had in thoſe three Letters inveſtigated and
monſtrated, if not all that could be deſired, or required by
mane curioſity, at leaſt all that could be attained by humane
reaſon in ſuch a matter, he, for ſome time (being buſied in other
ſtudies) intermitted his continual obſervations, and onely in
placency to ſome friend, joyned with him, in making now and
then an abrupt obſervation: till that he, and after ſome years,

we, being then at my ^{*} Country-ſeat, met with one of the
ry Solar ſpots very big, and thick, invited withal by a clear and
conſtant ſerenity of the Heavens, he, at my requeſt, made
vations of the whole progreſſe of the ſaid ſpot, carefully marking
upon a ſheet of paper the places that it was in every day at the
time of the Suns coming into the Meridian; and we having found
that its courſe was not in a right line, but ſomewhat incurvated,
we came to reſolve, at laſt, to make other obſervations from time
to time; to which undertaking we were ſtrongly induced by a
conceit, that accidentally came into the minde of my Gueſt,
which he imparted to me in theſe or the like words.
The hiſtory of
the proceedings of
the Academian
for a long time
bout the
on of the Solar
ſpots.
* Duumviro.
* This Authors
true name is
ſtopher Scheiner us
a Jeſuit, and his
Book here meant
is intituled,
les poſt tabulam.
* La mia villa
delle Selue.
In my opinion, Philip, there is a way opened to a buſineſs of
very great conſequence. For if the Axis about which the Sun
turneth be not erect perpendicularly to the plane of the
1
tick, but is inclined upon the ſame, as its crooked courſe, but
ven now obſerved, makes me believe, we ſhall be able to make
ſuch conjectures of the ſtates of the Sun and Earth, as neither ſo
ſolid or ſo rational have been hitherto deduced from any other
cident whatſoever. I being awakened at ſo great a promiſe,
portun'd him to make a free diſcovery of his conceit unto me.
And he continued his diſcourſe to this purpoſe. If the Earths

motion were along the Ecliptique about the Sun; and the Sun
were conſtituted in the centre of the ſaid Ecliptick, and therein
revolved in its ſelf, not about the Axis of the ſaid Ecliptique
(which would be the Axis of the Earths annual motion) but
on one inclined, it muſt needs follow, that ſtrange changes will
repreſent themſelves to us in the apparent motions of the Solar
ſpots, although the ſaid Axis of the Sun ſhould be ſuppoſed to
perſiſt perpetually and immutably in the ſame inclination, and in
one and the ſame direction towards the ſelf-ſame point of the
Univerſe. Therefore the Terreſtrial Globe in the annual motion
moving round it, it will firſt follow, that to us, carried about by
the ſame, the courſes of the ſpots ſhall ſometimes ſeem to be
made in right lines, but this only twice a year, and at all other
times ſhall appear to be made by arches inſenſibly incurvated.
Secondly, the curvity of thoſe arches for one half of the year,
will ſhew inclined the contrary way to what they will appear in
the other half; that is, for ſix moneths the convexity of the
ches ſhall be towards the upper part of the Solar Diſcus, and for
the other ſix moneths towards the inferiour. Thirdly, the ſpots
ginning to appear, and (if I may ſo ſpeak) to riſe to our eye from
the left ſide of the Solar Diſcus, and going to hide themſelves
and to ſet in the right ſide, the Oriental termes, that is, of their
firſt appearings for ſix moneths, ſhall be lower than the oppoſite
termes of their occultations; and for other ſix moneths it ſhall
happen contrarily, to wit, that the ſaid ſpots riſing from more
levated points, and from them deſcending, they ſhall, in their
courſes, go and hide themſelves in lower points; and onely for
two dayes in all the year ſhall thoſe termes of riſings and
tings be equilibrated: after which freely beginning by ſmall
grees the inclination of the courſes of the ſpots, and day by day
growing bigger, in three moneths, it ſhall arrive at its greateſt
obliquity, and from thence beginning to diminiſh, in ſuch another
time it ſhall reduce it ſelf to the other Æquilibrium. It ſhall
pen, for a fourth wonder, that the courſe of the greateſt
quity ſhall be the ſame with the courſe made by the right line,
and in the day of the Libration the arch of the courſe ſhall ſeem
more than ever incurvated. Again, in the other times,
ing as the pendency ſhall ſucceſſively diminiſh, and make its
1proach towards the Æquilibrium, the incurvation of the arches
of the courſes on the contrary ſhall, by degrees, increaſe.
A concipt that
came ſuddenly
to the minde of
the Academian
Lyncæus
ing the great
ſequence that
lowed upon the
tion of the Solar
ſpots.
Extravagant
tations to be
ved in the motions
of the ſpots,
ſeen by the
demick, in caſe
the Earth had the
annual motion.
SAGR. I confeſſe, Salviatus, that to interrupt you in your
Diſcourſe is ill manners, but I eſteem it no leſſe rudeneſs to
mit you to run on any farther in words, whilſt they are, as the
ſaying is, caſt into the air: for, to ſpeak freely, I know not how
to form any diſtinct conceit of ſo much as one of theſe
ons, that you have pronounced; but becauſe, as I thus
ly and confuſedly apprehend them, they hold forth things of
mirable conſequence, I would gladly, ſome way or other, be
made to underſtand the ſame.
SALV. The ſame that befalls you, befell me alſo, whilſt my
Gueſt tranſported me with bare words; who afterwards aſſiſted
my capacity, by deſcribing the buſineſſe upon a material

ment, which was no other than a ſimple Sphere, making uſe of
ſome of its circles, but to a different purpoſe from that, to which
they are commonly applied. Now I will ſupply the defect of
the Sphere, by drawing the ſame upon a piece of paper, as need
ſhall require. And to repreſent the firſt accident by me
ded, which was, that the courſes or journeys of the ſpots, twice
a year, and no more, might be ſeen to be made in right lines, let
us ſuppoſe this point O [in Fig. 4.] to be the centre of the grand
Orb, or, if you will, of the Ecliptick, and likewiſe alſo of the
Globe of the Sun it ſelf; of which, by reaſon of the great
ſtance that is between it and the Earth, we that live upon the
Earth, may ſuppoſe that we ſee the one half: we will therefore
deſcribe this circle A B C D about the ſaid centre O, which
ſenteth unto us the extream term that divideth and ſeparates the
Hemiſphere of the Sun that is apparent to us, from the other that
is occult. And becauſe that our eye, no leſſe than the centre of
the Earth, is underſtood to be in the plane of the Ecliptick, in
which is likewiſe the centre of the Sun, therefore, if we ſhould
fancy to our ſelves the body of the Sun to be cut thorow by the
ſaid plane, the ſection will appear to our eye a right line, which
let be B O D, and upon that a perpendicular being let fall AOC,
it ſhall be the Axis of the ſaid Ecliptick, and of the annual
tion of the Terreſtrial Globe. Let us next ſuppoſe the Solar body
(without changing centre) to revolve in it ſelf, not about the
Axis A O C (which is the erect Axis upon the plane of the
cliptick) but about one ſomewhat inclined, which let be this
E O I, the which fixed and unchangeable Axis maintaineth it ſelf
perpetually in the ſame inclination and direction towards the
ſame points of the Firmament, and of the Univerſe. And
cauſe, in the revolutions of the Solar Globe, each point of its
perficies (the Poles excepted) deſcribeth the circumference of a
1circle, either bigger or leſſer, according as it is more or leſſe
mote from the ſaid Poles, let us take the point F, equally diſtant
from them, and draw the diameter F O G, which ſhall be
dicular to the Axis E I, and ſhall be the diameter of the grand
circle deſcribed about the Poles E I. Suppoſing not that the
Earth, and we with her be in ſuch a place of the Ecliptick, that
the Hemiſphere of the Sun to us apparent is determin'd or
ed by the circle A B C D, which paſſing (as it alwayes doth) by
the Poles A C, paſſeth alſo by E I. It is manifeſt, that the grand
circle, whoſe diameter is FG, ſhall be erect to the circle A B C D,
to which the ray that from our eye falleth upon the centre O, is
perpendicular; ſo that the ſaid ray falleth upon the plane of
the circle, whoſe diameter is F G, and therefore its circumference
will appear to us a right line, and the ſelf ſame with F G,
upon if there ſhould be in the point F, a ſpot, it comming
wards to be carried about by the Solar converſion, would, upon
the ſurface of the Sun, trace out the circumference of that
cle, which ſeems to us a right line. Its courſe or paſſage will
therefore ſeem ſtraight. And ſtraight alſo will the motion of the
other ſpots appear, which in the ſaid revolution ſhall deſcribe
ſer circles, as being all parallel to the greater, and to our eye
placed at an immenſe diſtance from them. Now, if you do but
conſider, how that after the Earth ſhall in ſix moneths have run
thorow half the grand Orb, and ſhall be ſituate oppoſite to that
Hemiſphere of the Sun, which is now occult unto us, ſo as that
the boundary of the part that then ſhall be ſeen, may be the ſelf
ſame A B C D, which alſo ſhall paſſe by the Poles E I; you
ſhall underſtand that the ſame will evene in the courſes of the
ſpots, as before, to wit, that all will appear to be made by right
lines. But becauſe that that accident takes not place, ſave
ly when the terminator or boundary paſſeth by the Poles E I,
and the ſaid terminator from moment to moment, by meanes of
the Earths annual motion, continually altereth, therefore its
ſage by the fixed Poles E I, ſhall be momentary, and
ly momentary ſhall be the time, in which the motions of thoſe
ſpots ſhall appear ſtraight. From what hath been hitherto ſpoken
one may comprehend alſo how that the apparition and beginning
of the motion of the ſpots from the part F, proceeding towards
G, their paſſages or courſes are from the left hand, aſcending
wards the right; but the Earth being placed in the part
trically oppoſite the appearance of the ſpots about G, ſhall ſtill
be to the left hand of the beholder, but the paſſage ſhall be
cending towards the right hand F. Let us now deſcribe the Earth
te be ſituate one fourth part farther diſtant from its preſent ſtate,
and let us draw, as in the other figure, the terminator A B C D,
1[as in Fig. 5.] and the Axis, as before A C, by which the plane
of our Meridian would paſſe, in which plane ſhould alſo be the
Axis of the Suns revolution, with its Poles, one towards us, that
is, in the apparent Hemiſphere, which Pole we will repreſent by
the point E, and the other ſhall fall in the occult Hemiſphere,
and I mark it I. Inclining therefore the Axis E I, with the
riour part E, towards us, the great circle deſcribed by the Suns
converſion, ſhall be this B F D G, whoſe half by us ſeen,
ly B F D, ſhall no longer ſeem unto us a right line, by reaſon the
Poles E I are not in the circumference A B C D, but ſhall appear
incurvated, and with its convexity towards the inferiour part C.
And it is manifeſt, that the ſame will appear in all the leſſer
cles parallel to the ſame B F D. It is to be underſtood alſo, that
when the Earth ſhall be diametrically oppoſite to this ſtate, ſo
that it ſeeth the other Hemiſphere of the Sun, which now is hid,
it ſhall of the ſaid great circle behold the part D G B incurved,
with its convexity towards the ſuperiour part A; and the
ſes of the ſpots in theſe conſtitutions ſhall be firſt, by the arch
B F D, and afterwards by the other D G B, and the firſt
tions and ultimate occultations made about the points B and D,
ſhall be equilibrated, and not thoſe that are more or leſſe
ted than theſe. But if we conſtitute the Earth in ſuch a place
of the Ecliptick, that neither the boundary A B C D, nor the
Meridian A C, paſſeth by the Poles of the Axis E I, as I will ſhew
you anon, drawing this other Figure [viz. Fig. 6.] wherein the
apparent or viſible Pole E falleth between the arch of the
nator A B, and the ſection of the Meridian A C; the diameter
of the great circle ſhall be F O G, and the apparent ſemicircle
F N G, and the occult ſemicircle G S F, the one incurvated with
its convexity N towards the inferiour part, and the other alſo
bending with its convexity S towards the upper part of the Sun.
The ingreſſions and exitions of the ſpots, that is, the termes F
and G ſhall not be librated, as the two others B and D; but F
ſhall be lower, and G higher: but yet with leſſer difference
than in the firſt Figure. The arch alſo F N G ſhall be
ted, but not ſo much as the precedent B F D; ſo that in this
ſition the paſſages or motions of the ſpots ſhall be aſcendent
from the left ſide F, towards the right G, and ſhall be made by
curved lines. And imagining the Earth to be conſtituted in the
poſition diametrically oppoſite; ſo that the Hemiſphere of the
Sun, which was before the occult, may be the apparent, and
minated by the ſame boundary A B C D, it will be manifeſtly
diſcerned, that the courſe of the ſpots ſhall be by the arch G S F,
beginning from the upper point G, which ſhall then be likewiſe
from the left hand of the beholder, and going to determine,
1ſcending towards the right, in the point F. What I have
therto ſaid, being underſtood, I believe that there remains no
difficulty in conceiving how ſrom the paſſing of the terminator of
the Solar Hemiſpheres by the Poles of the Suns converſion, or
neer or far from the ſame, do ariſe all the differences in the
rent courſes of the ſpots; ſo that by how much the more thoſe Poles
ſhall be remote from the ſaid terminator, by ſo much the more ſhall
thoſe courſes be incurvated, and leſſe oblique; whereupon at
the ſame diſtance, that is, when thoſe Poles are in the ſection of
the Meridian, the incurvation is reduced to the greateſt, but the
obliquity to the leaſt, that is to Æquilibrium, as the ſecond of
theſe three laſt figures [viz. Fig. 5.] demonſtrateth. On the
contrary, when the Poles are in the terminator, as the firſt of
theſe three figures [viz. Fig. 4.] ſheweth the inclination is at
the greateſt, but the incurvation at the leaſt, and reduced to
rectitude. The terminator departing from the Poles, the curvity
begins to grow ſenſible, the obliquity all the way encreaſing,
and the inclination growing leſſer.
The firſt
cident to be
ved in the motion
of the Solar ſpots;
and conſequently
all the reſt
ned.
Theſe are thoſe admirable and extravagant mutations, that my
Gueſt told me would from time to time appear in the progreſſes
of the Solar ſpots, if ſo be it ſhould be true that the annual
tion belonged to the Earth, and that the Sun being conſtituted
in the centre of the Ecliptick, were revolved in it ſelf upon an
Axis, not erect, but inclined to the Plane of the ſaid
tick.
SAGR. I do now very well apprehend theſe conſequences,
and believe that they will be better imprinted in my fancy, when
I ſhall come to reflect upon them, accommodating a Globe to
thoſe inclinations, and then beholding them from ſeveral
ces. It now remains that you tell us what followed afterwards
touching the event of theſe imaginary
The events
ing obſerved, were
anſwerable to the
predictions.
SALV. It came to paſſe thereupon, that continuing many
veral moneths to make moſt accurate obſervations, noting down
with great exactneſſe the courſes or tranſitions of ſundry ſpots at
divers times of the year, we found the events punctually to
reſpond to the predictions.
SAGR. Simplicius, if this which Salviatus ſaith be true; (nor
can we diſtruſt him upon his word) the Ptolomeans and
teleans hadneed of ſolid arguments, ſtrong conjectures, and
well grounded experiments to counterpoiſe an objection of ſo
much weight, and to ſupport their opinion from its final
throw.
SIMP. Fair and ſoftly good Sir, for haply you may not yet
be got ſo far as you perſwade your ſelf you are gone. And
though I am not an abſolute maſter of the ſubject of that
1tion given us by Salviatus; yet do I not find that my Logick,

whilſt I have a regard to form, teacheth me, that that kind of
gumentation affords me any neceſſary reaſon to conclude in
vour of the Copernican Hypotheſis, that is, of the ſtability of
the Sun in the centre of the Zodiack, and of the mobility of
the Earth under its circumference. For although it be true, that
the ſaid converſion of the Sun, and cirnition of the Earth being
granted, there be a neceſſity of diſcerning ſuch and ſuch ſtrange
extravagancies as theſe in the ſpots of the Sun, yet doth it not
follow that arguing per converſum, from finding ſuch like
uſual accidents in the Sun, one muſt of necſſity conclude the
Earth to move by the circumference, and the Sun to be placed
in the centre of the Zodiack. For who ſhall aſſertain me that the
like irregularities may not as well be viſible in the Sun, it being
moveable by the Ecliptick, to the inhabitants of the Earth, it
being alſo immoveable in the centre of the ſame? Unleſſe you
demonſtrate to me, that there can be no reaſon given for that
pearance, when the Sun is made moveable, and the Earth ſtable,
I will not alter my opinion and belief that the Sun moveth, and
the Earth ſtandeth ſtill.
Though the
nual motion
ed to the Earth
ſwerth to the
nomena of the
lar ſpots, yet doth
it not follow by
verſion that from
the Phænomena of
the ſpots one may
infor the annual
motion to belong to
the Earth.
SAGR. Simplicius behaveth himſelf very bravely, and argueth
very ſubtilly in defence of the cauſe of Ariſtotle and Ptolomy;
and if I may ſpeak the truth, mythinks that the converſation of
Salviatus, though it have been but of ſmall continuance, hath
much farthered him in diſcourſing ſilogiſtically. An effect which
I know to be wrought in others as well as him. But as to finding
and judging whether competent reaſon may be rendered of the
apparent exorbitancies and irregularities in the motions of the
ſpots, ſuppoſing the Earth to be immoveable, and the Sun
moveable, I ſhall expect that Salviatus manifeſt his opinion to
us, for it is very probable that he he hath conſidered of the
ſame, and collected together whatever may be ſaid upon the
point.
SALV. I have often thought thereon, and alſo diſcourſed
thereof with my Friend and Gueſt afore-named; and touching
what is to be produced by Philoſophers and Aſtronomers, in
fence of the ancient Syſteme, we are on one hand certain,
tain I ſay, that the true and pure Peripateticks laughing at ſuch

as employ themſelves in ſuch, to their thinking, inſipid
ries, will cenſure all theſe Phænomena to be vain illuſions of the
Chriſtals; and in this manner will with little trouble free
ſelves from the obligation of ſtudying any more upon the ſame.
Again, as to the Aſtronomical Philoſophers, after we have with
ſome diligence weighed that which may be alledged as a mean
between thoſe two others, we have not been able to find out an
1anſwer that ſufficeth to ſatisſie at once the courſe of the ſpots,
and the diſcourſe of the Mind. I will explain unto you ſo much
as I remember thereof, that ſo you may judge thereon as ſeems
beſt unto you.
The Pure
patetick
phers will laugh at
the ſpots and their
Phænomena, as
illuſions of the
Chryſtals in the
Teleſcope.
Suppoſing that the apparent motions of the Solar ſpots are the
ſame with thoſe that have been above declared, and ſuppoſing the
Earth to be immoveable in the centre of the Ecliptick, in whoſe
circumference let the center of the Sun be placed; it is neceſſary
that of all the differences that are ſeen in thoſe motions, the
ſes do reſide in the motions that are in the body of the Sun:
Which in the firſt place muſt neceſſarily revolve in it ſelf (i. e.

about its own axis) carrying the ſpots along therewith; which
ſpots have been ſuppoſed, yea and proved to adhere to the
lar ſuperficies. It muſt ſecondly be confeſt, that the Axis of the
Solar converſion is not parallel to the Axis of the Ecliptick, that
is as much as to ſay, that it is not perpendicularly erected upon
the Plane of the Ecliptick, becauſe if it were ſo, the courſes and
exitions of thoſe ſpots would ſeem to be made by right lines
rallel to the Ecliptick. The ſaid Axis therefore is inclining, in
regard the ſaid courſes are for the moſt part made by curve lines.
It will be neceſſary in the third place to grant that the
on of this Axis is not fixed, and continually extended towards
one and the ſame point of the Univerſe, but rather that it doth
alwayes from moment to moment go changing its direction; for
if the pendency ſhould always look towards the ſelf ſame point,
the courſes of the ſpots would never change appearance; but
appearing at one time either right or curved, bending upwards
or downwards, aſcending or deſcending, they would appear
the ſame at all times. It is therefore neceſſary to ſay, that the
ſaid Axis is convertible; and is ſometimes found to be in the
Plane of the circle that is extreme, terminate, or of the viſible
Hemiſphere, I mean at ſuch time as the courſes of the ſpots
ſeem to be made in right lines, and more than ever pendent,
which happeneth twice a year; and at other times found to be in
the Plane of the Meridian of the Obſervator, in ſuch ſort that
one of its Poles falleth in the viſible Hemiſphere of the Sun, and
the other in the occult; and both of them remote from the
treme points, or we may ſay, from the poles of another Axis of
the Sun, which is parallel to the Axis of the Ecliptick; (which
ſecond Axis muſt neceſſarily be aſſigned to the Solar Globe)
mote, I ſay, as far as the inclination of the Axis of the revolution
of the ſpots doth import; and moreover that the Pole falling in
the apparent Hemiſphere, is one while in the ſuperiour, another
while in the inferiour part thereof; for that it muſt be ſo, the
courſes themſelves do manifeſtly evince at ſuch time as they are
1equilibrated, and in their greateſt curvity, one while with
their convexity towards the upper part, and another while
towards the lower part of the Solar Diſcus. And becauſe
thoſe poſitions are in continuall alteration, making the
clinations and incurvations now greater, now leſſer, and
times reduce themſelves, the firſt ſort to perfect libration, and
the ſecond to perfect perpendicularity, it is neceſſary to aſſert that
the ſelf ſame Axis of the monethly revolution of the ſpots hath
a particular revolution of its own, whereby its Poles deſcribe
two circles about the Poles of another Axis, which for that
ſon ought (as I have ſaid) to be aſſigned to the Sun, the
ameter of which circles anſwereth to the quantity of the
nation of the ſaid Axis. And it is neceſſary, that the time of its
Period be a year; for that ſuch is the time in which all the
pearances and differences in the courſes of the ſpots do return.
And that the revolution of this Axis, is made about the Poles of
the other Axis parallel to that of the Ecliptick, & not about other
points, the greateſt inclinations and greateſt incurvations, which
are always of the ſame bigneſs, do clearly prove. So that finally, to
maintain the Earth fixed in the centre, it will be neceſſary to
ſign to the Sun, two motions about its own centre, upon two
ral Axes, one of which finiſheth its converſion in a year, and the
other in leſſe than a moneth; which aſſumption ſeemeth, to my
underſtanding, very hard, and almoſt impoſſible; and this
pendeth on the neceſſity of aſcribing to the ſaid Solar body two
other motions about the Earth upon different Axes, deſcribing
with one the Ecliptick in a year, and with the other forming
rals, or circles parallel to the Equinoctial one every day:
whereupon that third motion which ought to be aſſigned to the
Solar Clobe about its own centre (I mean not that almoſt
monethly, which carrieth the ſpots about, but I ſpeak of that
ther which ought to paſſe thorow the Axis and Poles of this
monethly one) ought not, for any reaſon that I ſee, to finiſh its
Period rather in a year, as depending on the annual motion by
the Ecliptick, than in twenty four hours, as depending on the
diurnal motion upon the Poles of the Equinoctial. I know, that
what I now ſpeak is very obſcure, but I ſhall make it plain unto
you, when we come to ſpeak of the third motion annual,
ed by Copernicus, to the Earth. Now if theſe four motions, ſo
incongruous with each other, (all which it would be neceſſary to
aſſign to the ſelf ſame body of the Sun) may be reduced to one
ſole and ſimple motion, aſſigned the Sun upon an Axis that never
changeth poſition, and that without innovating any thing in the
motions for ſo many other cauſes aſſigned to the Terreſtrial
Globe, may ſo eaſily ſalve ſo many extravagant appearances in
1the motions of the Solar ſpots, it ſeemeth really that ſuch an
Hypotheſis ought not to be rejected.
If the Earth be
immoveable in the
centre of the
ack, there muſt be
aſcribed to the Sun
four ſeveral
ons, as is declared
at length.
This, Simplicius, is all that came into the minds of our friend,
and my ſelf, that could be alledged in explanation of this
menon by the Copernicans, and by the Ptolomæans, in defence
of their opinions. Do you inferre from thence what your
ment perſwades you.
SIMP. I acknowledge my ſelf unable to interpoſe in ſo
portant a deciſion: And, as to my particular thoughts, I will
ſtand neutral; and yet nevertheleſſe I hope that a time will
come, when our minds being illumin'd by more lofty
tions than theſe our humane reaſonings, we ſhall be awakened
and freed from that miſt which now is ſo great an hinderance to
our ſight.
SAGR. Excellent and pious is the counſel taken by
cius, and worthy to be entertained and followed by all, as that
which being derived from the higheſt wiſdome and ſupreameſt
authority, may onely, with ſecurity be received. But yet ſo far
as humane reaſon is permitted to penetrate, confining my ſelf
within the bounds of conjectures, and probable reaſons, I will
ſay a little more reſolutely than Simplicius doth, that amongſt
all the ingenuous ſubtilties I ever heard, I have never met with
any thing of greater admiration to my intellect, nor that hath
more abſolutely captivated my judgment, (alwayes excepting
pure Geometrical and Arithmetical Demonſtrations) than theſe
two conjectures taken, the one from the ſtations and
tions of the five Planets, and the other from theſe irregularities of
the motions of the Solar ſpots: and becauſe they ſeem to me ſo
eaſily and clearly to aſſign the true reaſon of ſo extravagant
pearances, ſhewing as if they were but one ſole ſimple motion,
mixed with ſo many others, ſimple likewiſe, but different from
each other, without introducing any difficulty, rather with
ating thoſe that accompany the other Hypotheſis; I am
ing that I may rationally conclude, that thoſe who
ouſly withſtand this Doctrine, either never heard, or never
derſtood, theſe ſo convincing arguments.
SALV. I will not aſcribe unto them the title either of
vincing, or non-convincing; in regard my intention is not, as I
have ſeveral times told you, to reſolve any thing upon ſo high a
queſtion, but onely to propoſe thoſe natural and Aſtronomicall
reaſons, which, for the one and other Syſteme, may be produced
by me, leaving the determination to others; which
on cannot at laſt, but be very manifeſt: for one of the two
tions being of neceſſity to be true, and the other of neceſſity to
be falſe, it is a thing impoſſible that (alwayes confining our ſelves
1within the limits of humane doctrine) the reaſons alledged for
the true Hypotheſis ſhould not manifeſt themſelves as concludent
as thoſe for the contrary vain and ineffectual.
SAGR. It will be time therefore, that we hear the objections
of the little Book of^{*} Concluſions, or Diſquiſitions which Simpli-

cius did bring with him.
* I ſhould have
told you, that the
true name of this
concealed
thour is
pher Scheinerus,
and its title
quiſitiones
thematicæ.
SIMP. Here is the Book, and this is the place where the
thor firſt briefly deſcribeth the Syſteme of the world, according
to the Hypotheſis of Copernicus, ſaying, Terram igitur unà cum
Luna, totoque hoc elementari mundo Copernicus, &c.
SALV. Forbear a little, Simplicius, for methinks that this
Authour, in this firſt entrance, ſhews himſelf to be but very ill
verſt in the Hypotheſis which he goeth about to confute, in
gard, he ſaith that Copernicus maketh the Earth, together with
the Moon, to deſcribe the ^{*} grand Orb in a year moving from
Eaſt to Weſt; a thing that as it is falſe and impoſſible, ſo was it

never affirmed by Copernicus, who rather maketh it to move the
contrary way, I mean from Weſt to Eaſt, that is, according to
the order of the Signes; whereupon we come to think the ſame
to be the annual motion of the Sun, conſtituted immoveable in
the centre of the Zodiack. See the too adventurous confidence
of this man; to undertake the confutation of anothers Doctrine,
and yet to be ignorant of the primary fundamentals; upon which
his adverſary layeth the greateſt and moſt important part of all
the Fabrick. This is a bad beginning to gain himſelf credit
with his Reader; but let us go on.
* I.e. the Ecliptick
SIMP. Having explained the Univerſal Syſteme, he beginneth
to propound his objections againſt this annual motion: and
the firſt are theſe, which he citeth Ironically, and in deriſion of

Copernicus, and of his followers, writing that in this phantaſtical
Hypotheſis of the World one muſt neceſſarily maintain very
groſſe abſurdities; namely, that the Sun, Venus, and Mercury
are below the Earth; and that grave matters go naturally
wards, and the light downwards; and that Chriſt, our Lord and
Redeemer, aſcended into Hell, and deſcended into Heaven, when
he approached towards the Sun, and that when Joſhuah
manded the Sun to ſtand ſtill, the Earth ſtood ſtill, or the Sun
moved a contrary way to that of the Earth; and that when the
Sun is in Cancer, the Earth runneth through Capricorn; and that
the Hyemal (or Winter) Signes make the Summer, and the
Æſtival Winter; and that the Stars do not riſe and ſet to
the Earth, but the Earth to the Stars; and that the Eaſt
neth in the Weſt, and the Weſt in the Eaſt; and, in a word,
that almoſt the whole courſe of the World is inverted.
Inſtances of a
certain Book
nically propounded
againſt
cus.
SALV. Every thing pleaſeth me, except it be his having
1mixed places out of the ſacred Scriptures (alwayes venerable, and
to be rever'd) amongſt theſe, but two ſcurrilous fooleries, and
attempting to wound with holy Weapons, thoſe who
phating in jeſt, and for divertiſement, neither affirm nor deny,
but, ſome preſuppoſals and poſitions being aſſumed, do
arly argue.
SIMP. Truth is, he hath diſpleaſed me alſo, and that not a
little; and eſpecially, by adding preſently after that, howbeit,
the Copernichists anſwer, though but very impertinently to theſe
and ſuch like other reaſons, yet can they not reconcile nor anſwer
thoſe things that follow.
SALV. This is worſe than all the reſt; for he pretendeth to
have things more efficacious and concludent than the Authorities
of the ſacred Leaves; But I pray you, let us reverence them,
and paſſe on to natural and humane reaſons: and yet if he give
us amongſt his natural arguments, things of no more ſolidity,
than thoſe hitherto alleadged, we may wholly decline this
taking, for I as to my own parricular, do not think it fit to ſpend
words in anſwering ſuch trifling impertinencies. And as to what
he ſaith, that the Copernicans anſwer to theſe objections, it is
moſt falſe, nor may it be thought, that any man ſhould ſet him
ſelf to waſt his time ſo
Suppoſing the
annual motion to
belong to the Earth,
it followeth, that
one fixed Star, is
bigger than the
whole grand Orb.
SIMP. I concur with you in the ſame judgment; therefore
let us hear the other inſtances that he brings, as much ſtronger.
And obſerve here, how he with very exact computations
eth, that if the grand Orb of the Earth, or the ecliptick, in which
Copernicus maketh it to run in a year round the Sun, ſhould be
as it were, inſenſible, in reſpect of the immenſitie of the Starry
Sphære, according as the ſaid Copernicus, ſaith it is to be
poſed, it would be neceſſary to grant and confirm, that the fixed
Stars were remote from us, an unconceivable diſtance, and that
the leſſer of them, were bigger than the whole grand Orb
ſaid, and ſome other much bigger than the whole Sphære of
turn; Maſſes certainly too exceſſively vaſt, unimaginable, and
incredible.
Tycho his
gument grounded
upon a falſe
theſis.
SALV. I have heretofore ſeen ſuch another objection brought
by Tycho againſt Copernicus, and this is not the firſt time that I
have diſcovered the fallacy, or, to ſay better, the fallacies of this
Argumemtation, founded upon a moſt falſe Hypotheſis, and upon

a Piopoſition of the ſaid Copernicus, underſtood by his
ries, with too punctual a nicity, according to the practiſe of thoſe
pleaders, who finding the flaw to be in the very merit of their
cauſe, keep to ſome one word, fallen unawares from the
ry partie, and fly out into loud and tedious deſcants upon that.
But for your better information; Copernicus having declared
1thoſe admirable conſequences which are derived from the Earths

annual motion, to the other Planets, that is to ſay, of the ^{*}

ons and retrogradations of the three uppermoſt in particular; he
ſubjoyneth, that this apparent mutation (which is diſcerned more
in Mars than in Jupiter, by reaſon Jupiter is more remote, and
yet leſſe in Saturn, by reaſon it is more remote than Jupiter) in
the fixed Stars, did remain imperceptible, by reaſon of their
immenſe remoteneſſe from us, in compariſon of the diſtances of
Jupiter or Saturn. Here the Adverſaries of this opinion riſe up,
and ſuppoſing that fore-named imperceptibility of Copernicus, as
if it had been taken by him, for a real and abſolute thing of
thing, and adding, that a fixed Star of one of the leſſer
tudes, is notwithſtanding perceptible, ſeeing that it cometh
der the ſence of ſeeing, they go on to calculate with the
vention of other falſe aſſumptions, and concluding that it is
ſary by the Copernican Doctrine, to admit, that a fixed Star is much
bigger than the whole grand Orb. Now to diſcover the vanity

of this their whole proceeding, I ſhall ſhew that a fixed Star of the
ſixth magnitude, being ſuppoſed to be no bigger than the Sun,
one may thence conclude with true demonſtrations, that the
ſtance of the ſaid fixed Stars from us, cometh to be ſo great, that
the annual motion of the Earth, which cauſeth ſo great and
notable variations in the Planets, appears ſcarce obſervable in
them; and at the ſame time, I will diſtinctly ſhew the groſs
fallacies, in the aſſumptions of Copernicus his Adverſaries.
Litigious Lawyers
that are
ed in an ill cauſe,
keep cloſe to ſome
expreſſion fallen
from the adverſe
party at unawares.
* Or progreſſions.
The apparent
diverſity of motion
in the Planets, is
inſenſible in the
fixed Start.
Suppoſing that a
fixed Star of the
ſixth magnitude is
no bigger than the
Sun, the diverſitie
which is ſo great
in the Planets, in
the fixed Stars is
almost inſenſible.
And firſt of all, I ſuppoſe with the ſaid Copernicus, and alſo

with his oppoſers, that the Semidiameter of the grand Orb, which
is the diſtance of the Earth from the Sun, containeth 1208
diameters of the ſaid Earth. Secondly, I premiſe with the
ance aforeſaid, and of truth, that the ^{*} apparent diameter of the

Sun in its mean diſtance, to be about half a degree, that is, 30.
min. prim. which are 1800. ſeconds, that is, 108000. thirds.
And becauſe the apparent Diameter of a fixed Star of the firſt

magnitude, is no more than 5. ſeconds, that is, 300. thirds, and
the Diameter of a fixed Star of the ſixth magnitude, 50. thirds,
(and herein is the greateſt errour of the Anti-Copernicans)

fore the Diameter of the Sun, containeth the Diameter of a
fixed Star of the ſixth magnitude 2160 times. And therefore
if a fixed Star of the ſixth magnitude, were ſuppoſed to be really
equal to the Sun, and not bigger, which is the ſame as to ſay, if
the Sun were ſo far removed, that its Diameter ſhould ſeem to
be one of the 2160. parts of what it now appeareth, its diſtance
ought of neceſſity to be 2160. times greater than now in effect it
is, which is as much as to ſay, that the diſtance of the fixed Stars
of the ſixth magnitude, is 2160. Semidiameters of the grand
1Orb. And becauſe the diſtance of the Sun from the Earth,

tains by common conſent 1208. Semidiameters of the ſaid Earth,
and the diſtance of the fixed Stars (as hath been ſaid) 2160.
Semediameters of the grand Orb, therefore the Semediameter of
the Earth is much greater (that is almoſt double) in compariſon
of the grand Orb, than the Semediameter of the grand Orb, in

relation to the diſtance of the Starry Sphære; and therefore the
variation of aſpect in the fixed Stars, cauſed by the Diameter of
the grand Orb, can be but little more obſervable, than that which
is obſerved in the Sun, occaſioned by the Semediameter of the
Earth.
The diſtance of
the Sun, containeth
1208 Semid. of the
Earth.
* The Diameter
of the Sun, half a
degree.
The Diameter
of a fixed Star, of
the firſt
tude, and of one of
the ſixth.
The apparent
Diameter of the
Sun, how much it
is bigger than that
of a fixed ſtar.
The diſtance of
a fixed ſtar of the
ſixth magnitude,
how much it is, the
ſtar being ſuppoſed
to be equal to the
Sun.
In the fixed ſtars
the diverſitie of
ſpect, cauſed by
the grand Orb, is
little more then
that cauſed by the
Earth in the Snn.
SAGR. This is a great fall for the firſt ſtep.
SALV. It is doubtleſſe an errour; for a fixed Star of the ſixth

magnitude, which by the computation of this Authour, ought,
for the upholding the propoſition of Copernicus, to be as big as
the whole grand Orb, onely by ſuppoſing it equal to the Sun,
which Sun is leſſe by far, than the hundred and ſix milionth part
of the ſaid grand Orb, maketh the ſtarry Sphære ſo great and high
as ſufficeth to overthrow the inſtance brought againſt the ſaid
pernicus.
A ſtar of the
ſixth magnitude,
ſuppoſed by Tycho
and the Authour
of the Book of
cluſions, an
dred and ſix
ons of times bigger
than needs.
SAGR. Favour me with this computation.
SALV. The ſupputation is eaſie and ſhort. The Diameter of
the Sun, is eleven ſemediameters of the Earth, and the Diameter

of the grand Orb, contains 2416. of thoſe ſame ſemediameters,
by the aſcent of both parties; ſo that the Diameter of the ſaid
Orb, contains the Suns Diameter 220. times very near. And
becauſe the Spheres are to one another, as the Cubes of their
ameters, let us make the Cube of 220. which is 106480000. and
we ſhall have the grand Orb, an hundred and ſix millions, four
hundred and eighty thouſand times bigger than the Sun, to which
grand Orb, a ſtar of the fixth magnitude, ought to be equal,
cording to the aſſertion of this Authour.
The
on of the
tude of the fixed
Stars, in reſpect to
the grand Orb.
SAGR. The errour then of theſe men, conſiſteth in being
treamly miſtaken, in taking the apparent Diameter of the fixed
Stars.
SALV. This is one, but not the onely errour of them; and

indeed, I do very much admire how ſo many Aſtronomers, and
thoſe very famous, as are Alfagranus, Albategnus, Tebizius, and
much more modernly the Tycho's and Clavius's, and in ſumm,
all the predeceſſors of our Academian, ſhould have been ſo groſly
miſtaken, in determining the magnitudes of all the Stars, as well
ſixed as moveable, the two Luminaries excepted out of that
ber; and that they have not taken any heed to the adventitious
irradiations that deceitfully repreſent them an hundred and more
times bigger, than when they are beheld, without thoſe
1ous rayes, nor can this their inadvertency be excuſed, in regard
that it was in their power to have beheld them at their pleaſure
without thoſe treſſes, which is done, by looking upon them at
their firſt appearance in the evening, or their laſt occultation in

the comming on of day; and if none of the reſt, yet Venus,
which oft times is ſeen at noon day, ſo ſmall, that one muſt
pen the ſight in diſcerning it; and again, in the following night,
ſeemeth a great flake of light, might advertiſe them of their
lacy; for I will not believe that they thought the true Diſcus to
be that which is ſeen in the obſcureſt darkneſſes, and not that
which is diſcerned in the luminous Medium: for our lights, which
ſeen by night afar off appear great, and neer at hand ſhew their
true luſtre to be terminate and ſmall, might have eaſily have
made them cautious; nay, if I may freely ſpeak my thoughts, I
abſolutely believe that none of them, no not Tycho himſelf, ſo
accurate in handling Aſtronomical Inſtruments, and that ſo great
and accurate, without ſparing very great coſt in their
ction, did ever go about to take and meaſure the apparent
meter of any Star, the Sun and Moon excepted; but I think,
that arbitrarily, and as we ſay, with the eye, ſome one of the
more antient of them pronounced the thing to be ſo and ſo, and
that all that followed him afterwards, without more ado, kept
cloſe to what the firſt had ſaid; for if any one of them had
plied himſelf to have made ſome new proof of the ſame, he would
doubtleſſe have diſcovered the fraud.
A common
rour of all the
ſtronomers,
ing the magnitude
of the ſtars.
Venus renders the
errour of
mers in
ing the magnitudes
of ſtars
ble.
SAGR. But if they wanted the Teleſcope, and you have
ready ſaid, that our Friend with that ſame Inſtrument came to
the knowledge of the truth, they ought to be excuſed, and not
accuſed of ignorance.
SALV. This would hold good, if without the Teleſcope the
buſineſſe could not be effected. Its true, that this Inſtrument by
ſhewing the Diſcus of the Star naked, and magnified an
dred or a thouſand times, rendereth the operation much more
ſie, but the ſame thing may be done, although not altogether ſo
exactly, without the Inſtrument, and I have many times done
the ſame, and my method therein was this. I have cauſed a rope

to be hanged towards ſome Star, and I have made uſe of the
Conſtellation, called the Harp, which riſeth between the North
and ^{*} North-eaſt, and then by going towards, and from

the ſaid rope, interpoſed between me and the Star, I have found
the place from whence the thickneſſe of the rope hath juſt hid
the Star from me: this done, I have taken the diſtance from the
eye to the rope, which was one of the ſides including the angle
that was compoſed in the eye, and ^{*} which inſiſteth upon the

thickneſſe of the rope, and which is like, yea the ſame with the
1angle in the Starry Sphere, that inſiſteth upon the diameter of
the Star, and by the proportion of the ropes thickneſſe to the
diſtance from the eye to the rope, by the table of Arches and
Chords, I have immediately found the quantity of the angle;
ſing all the while the wonted caution that is obſerved in taking
angles ſo acute, not to forme the concourſe of the viſive rayes
in the centre of the eye, where they are onely refracted, but
beyond the eye, where really the pupils greatneſſe maketh them
to concur.
A way to
ſure the apparent
diameter of a ſtar.
* Rendred in
Latine Corum, that
is to ſay,
weſt.
* i.e. Is
ded by.
SAGR. I apprehend this your cautelous procedure, albeit I
have a kind of hæſitancy touching the ſame, but that which moſt
puzzleth me is, that in this operation, if it be made in the dark
of night, methinks that you meaſure the diameter of the
ted Diſcus, and not the true and naked face of the Star.
SALV. Not ſo, Sir, for the rope in covering the naked body
of the Star, taketh away the rayes, which belong not to it, but
to our eye, of which it is deprived ſo ſoon as the true Diſcus
thereof is hid; and in making the obſervation, you ſhall ſee, how
unexpectedly a little cord will cover that reaſonable big body of
light, which ſeemed impoſſible to be hid, unleſſe it were with a
much broader Screene: to meaſure, in the next place, and
ctly to find out, how many of thoſe thickneſſes of the rope
poſe in the diſtance between the ſaid rope and the eye, I take not
onely one diameter of the rope, but laying many pieces of the
ſame together upon a Table, ſo that they touch, I take with a
pair of Compaſſes the whole ſpace occupied by fifteen, or
ty of them, and with that meaſure I commenſurate the diſtance
before with another ſmaller cord taken from the rope to the
courſe of the viſive rayes. And with this ſufficiently-exact
ration I finde the apparent diameter of a fixed Star of the firſt
magnitude, commonly eſteemed to be 2 min. pri. and alſo 3 min.
prim. by Tycho in his Aſtronomical Letters, cap. 167. to be no

more than 5 ſeconds, which is one of the 24. or 36. parts of what
they have held it: ſee now upon what groſſe errours their
ctrines are founded.
The diameter of
a fixed ſtar of the
firſt magnitude not
more than five ſec.
min.
SAGR. I ſee and comprehend this very well, but before we
paſſe any further, I would propound the doubt that ariſeth in
me in the finding the concourſe [or interſection] of the viſual
rayes beyond the eye, when obſervation is made of objects
prehended between very acute angles; and my ſcruple proceeds
from thinking, that the ſaid concourſe may be ſometimes more
remote, and ſometimes leſſe; and this not ſo much, by meanes
of the greater or leſſer magnitude of the object that is beheld, as
becauſe that in obſerving objects of the ſame bigneſſe, it ſeems
to me that the concourſe of the rayes, for certain other
1ſpects ought to be made more and leſſe remote from the eye.
SALV. I ſee already, whither the apprehenſion of Sagredus,
a moſt diligent obſerver of Natures ſecrets, tendeth; and I

would lay any wager, that amongſt the thouſands that have
ſerved Cats to contract and inlarge the pupils of their eyes very
much, there are not two, nor haply one that hath obſerved the
like effect to be wrought by the pupils of men in ſeeing, whilſt
the medium is much or little illumin'd, and that in the open light
the circlet of the pupil diminiſheth conſiderably: ſo that in
king upon the face or Diſcus of the Sun, it is reduced to a
neſſe leſſer than a grain of ^{*} Panick, and in beholding objects

that do not ſhine, and are in a leſſe luminous medium, it is
god to the bigneſſe of a Lintel or more; and in ſumme this
expanſion and contraction differeth in more than decuple
portion: From whence it is manifeſt, that when the pupil is
much dilated, it is neceſſary that the angle of the rayes
courſe be more remote from the eye; which happeneth in
holding objects little luminated. This is a Doctrine which
gredus hath, juſt now, given me the hint of, whereby, if we
were to make a very exact obſervation, and of great
quence, we are advertized to make the obſervation of that
courſe in the act of the ſame, or juſt ſuch another operation; but
in this our caſe, wherein we are to ſhew the errour of
mers, this accurateneſſe is not neceſſary: for though we ſhould,
in favour of the contrary party, ſuppoſe the ſaid concourſe to be
made upon the pupil it ſelf, it would import little, their miſtake
being ſo great. I am not certain, Sagredus, that this would have
been your objection.
The circle of the
pupil of the eye
largeth and
tracteth.
+ Panicum, a
ſmall grain like to
Mill, I take it to be
the ſame with that
called Bird Seed.
SAGR. It is the very ſame, and I am glad that it was not
together without reaſon, as your concurrence in the ſame
reth me; but yet upon this occaſion I would willingly hear what
way may be taken to finde out the diſtance of the concourſe of
the viſual rayes.
SALV. The method is very eaſie, and this it is, I take two
long^{*} labels of paper, one black, and the other white, and make

the black half as broad as the white; then I ſtick up the white
gainſt a wall, and far from that I place the other upon a ſtick, or
other ſupport, at a diſtance of fifteen or twenty yards, and
ding from this, ſecond another ſuch a ſpace in the ſame right line,
it is very manifeſt, that at the ſaid diſtance the right lines will
concur, that departing from the termes of the breadth of the
white piece, ſhall paſſe cloſe by the edges of the other label
ced in the mid-way; whence it followeth, that in caſe the eye
were placed in the point of the ſaid concourſe or interſection,
the black ſlip of paper in the midſt would preciſely hide the
1poſite blank, if the ſight were made in one onely point; but if we
ſhould find, that the edges of the white cartel appear diſcovered,
it ſhall be a neceſſary argument that the viſual rayes do not iſſue
from one ſole point. And to make the white label to be hid by
the black, it will be requiſite to draw neerer with the eye:
Therefore, having approached ſo neer, that the intermediate
bel covereth the other, and noted how much the required
proximation was, the quantity of that approach ſhall be the
tain meaſure, how much the true concourſe of the viſive rayes, is
remote from the eye in the ſaid operation, and we ſhall moreover
have the diameter of the pupil, or of that circlet from whence
the viſive rayes proceed: for it ſhall be to the breadth of the
black paper, as is the diſtance from the concourſe of the lines,
that are produced by the edges of the papers to the place where
the eye ſtandeth, when it firſt ſeeth the remote paper to be hid
by the intermediate one, as that diſtance is, I ſay, to the diſtance
that is between thoſe two papers. And therefore when we
would, with exactneſſe, meaſure the apparent diameter of a Star,
having made the obſervation in manner, as aforeſaid, it would be
neceſſary to compare the diameter of the rope to the diameter of
the pupil; and having found v.g. the diameter of the rope to be
quadruple to that of the pupil, and the diſtance of the eye from
the rope to be, for example, thirty yards, we would ſay, that the
true concourſe of the lines produced from the ends or
ties of the diameter of the ſtar, by the extremities of the
meter of the rope, doth fall out to be fourty yards remote from
the ſaid rope, for ſo we ſhall have obſerved, as we ought, the
portion between the diſtance of the rope from the concourſe of
the ſaid lines, and the diſtance from the ſaid concourſe to the
place of the eye, which ought to be the ſame that is between
the diameter of the rope, and diameter of the pupil.
* Striſce.
How to find the
diſtance of the rays
concourſe from the
pupil.
SAGR. I have perfectly underſtood the whole buſineſſe, and
therefore let us hear what Simplicius hath to alledge in defence of
the Anti-Copernicans.
SIMP. Albeit that grand and altogether incredible
nience inſiſted upon by theſe adverſaries of Copernicus be much
moderated and abated by the diſcourſe of Salviatus, yet do I
not think it weakened ſo, as that it hath not ſtrength enough left
to foil this ſame opinion. For, if I have rightly apprehended the
chief and ultimate concluſion, in caſe, the ſtars of the ſixth
nitude were ſuppoſed to be as big as the Sun, (which yet I can
hardly think) yet it would ſtill be true, that the grand Orb [or
Ecliptick] would occaſion a mutation and variation in the ſtarry
Sphere, like to that which the ſemidiameter of the Earth
ceth in the Sun, which yet is obſervable; ſo that neither that, no
1nor a leſſe mutation being diſcerned in the fixed Stars, methinks
that by this means the annual motion of the Earth is deſtroyed
and overthrown.
SALV. You might very well ſo conclude, Simplicius, if we
had nothing elſe to ſay in behalf of Copernicus: but we have
many things to alledge that yet have not been mentioned; and
as to that your reply, nothing hindereth, but that we may
poſe the diſtance of the fixed Stars to be yet much greater than
that which hath been allowed them, and you your ſelf, and
ever elſe will not derogate from the propoſitions admitted by
Piolomy's ſectators, muſt needs grant it as a thing moſt requiſite
to ſuppoſe the Starry Sphere to be very much bigger yet than
that which even now we ſaid that it ought to be eſteemed. For

all Aſtronomers agreeing in this, that the cauſe of the greater
tardity of the Revolutions of the Planets is, the majority of
their Spheres, and that therefore Saturn is more flow than
piter, and Jupiter than the Sun, for that the firſt is to deſcribe a
greater circle than the ſecond, and that than this later, &c.
ſidering that Saturn v.g. the altitude of whoſe Orb is nine times
higher than that of the Sun, and that for that cauſe the time of
one Revolution of Saturn, is thirty times longer than that of a
converſion of the Sun, in regard that according to the Doctrine
of Ptolomy, one converſion of the ſtarry Sphere is finiſhed in
36000. years, whereas that of Saturn is conſummate in thirty,
and that of the Sun in one, arguing with a like proportion, and

ſaying, if the Orb of Saturn, by reaſon it is nine times bigger
than that of the Sun, revolves in a time thirty times longer, by
converſion, how great ought that Orb to be, which revolves
36000. times more ſlowly? it ſhall be found that the diſtance of
the ſtarry Sphere ought to be 10800 ſemidiameters of the grand
Orb, which ſhould be full five times bigger than that, which even
now we computed it to be, in caſe that a fixed Star of the ſixth
magnitude were equal to the Sun. Now ſee how much leſſer yet,
upon this account, the variation occaſioned in the ſaid Stars, by
the annual motion of the Earth, ought to appear. And if at the
ſame rate we would argue the diſtance of the ſtarry Sphere from

Jupiter, and from Mars, that would give it us to be 15000. and
this 27000 ſemidiameters of the grand Orb, to wit, the firſt
ſeven, and the ſecond twelve times bigger than what the
nitude of the fixed Star, ſuppoſed equal to the Sun, did make
it.
All
mers agree that
the greater
tudes of the Orbes
is the cauſe of the
tardity of the
verſions.
By another
poſition taken from
Aſtronomers, the
diſtance of the
ed Stars is
lated to be 10800
ſemidiameters of
the grand Orb.
By the proportion
of Jupiter and of
Mais, the ſtarry
Sphere is found to
be yet more remote.
SIMP. Methinks that to this might be anſwered, that the
tion of the ſtarry Sphere hath, ſince Ptolomy, been obſerved not
to be ſo ſlow as he accounted it; yea, if I miſtake. not, I have
heard that Copernicus himſelf made the Obſervation.
1
SALV. You ſay very well; but you alledge nothing in that
which may favour the cauſe of the Ptolomœans in the leaſt, who
did never yet reject the motion of 36000. years in the ſtarry
Sphere, for that the ſaid tardity would make it too vaſt and
menſe. For if that the ſaid immenſity was not to be ſuppoſed in
Nature, they ought before now to to have denied a converſion
ſo ſlow as that it could not with good proportion adapt it ſelf,
ſave onely to a Sphere of monſtrous magnitude.
SAGR. Pray you, Salviatus, let us loſe no more time in
ceeding, by the way of theſe proportions with people that are apt
to admit things moſt diſ-proportionate; ſo that its impoſſible
to win any thing upon them this way: and what more
tionate proportion can be imagined than that which theſe men
ſwallow down, and admit, in that writing, that there cannot be a
more convenient way to diſpoſe the Cœleſtial Spheres, in order,
than to regulate them by the differences of the times of their
riods, placing from one degree to another the more flow above
the more ſwift, when they have conſtituted the Starry Sphere
higher than the reſt, as being the ſloweſt, they frame another
higher ſtill than that, and conſequently greater, and make it
volve in twenty four hours, whilſt the next below, it moves not
round under 36000. years?
SALV. I could wiſh, Simplicius, that ſuſpending for a time
the affection rhat you bear to the followers of your opinion, you
would ſincerely tell me, whether you think that they do in their
minds comprehend that magnitude, which they reject afterwards
as uncapable for its immenſity to be aſcribed to the Univerſe.
For I, as to my own part, think that they do not; But believe,

that like as in the apprehenſion of numbers, when once a man
begins to paſſe thoſe millions of millions, the imagination is
founded, and can no longer form a conceipt of the ſame, ſo it
happens alſo in comprehending immenſe magnitudes and
ces; ſo that there intervenes to the comprehenſion an effect like
to that which befalleth the ſenſe; For whileſt that in a ſerene
night I look towards the Stars, I judge, according to ſenſe, that
their diſtance is but a few miles, and that the fixed Stars are not a
jot more remote than Jupiter or Saturn, nay than the Moon.
But without more ado, conſider the controverſies that have paſt
between the Aſtronomers and Peripatetick Philoſophers, upon
occaſion of the new Stars of Caſſiopeia and of Sagittary, the
ſtronomers placing them amongſt the fixed Stars, and the
ſophers believing them to be below the Moon. So unable is our
ſenſe to diſtinguiſh great diſtances from the greateſt, though theſe
be in reality many thouſand times greater than thoſe. In a word,
I ask of thee, O fooliſh man! Doth thy imagination comprehend
1that vaſt magnitude of the Univerſe, which thou afterwards
eſt to be too immenſe? If thou comprehendeſt it; wilt thou
hold that thy apprehenſion extendeth it ſelf farther than the
vine Power? wilt thou ſay, that thou canſt imagine greater
things than thoſe which God can bring to paſſe? But if thou
apprehendeſt it not, why wilt thou paſſe thy verdict upon things
beyond thy comprehenſion?
Immenſe
nitudes and
bers are
henſible by our
derſtanding.
SIMP. All this is very well, nor can it be denied, but that
Heaven may in greatneſſe ſurpaſſe our imagination, as alſo that
God might have created it thouſands of times vaſter than now it
is; but we ought not to grant any thing to have been made in
vain, and to be idle in the Univerſe. Now, in that we ſee this
mirable order of the Planets, diſpoſed about the Earth in
ces proportionate for producing their effects for our advantage,
to what purpoſe is it to interpoſe afterwards between the ſublime
Orb of Saturn and the ſtarry Sphere, a vaſt vacancy, without any
ſtar that is ſuperfluous, and to no purpoſe? To what end? For
whoſe profit and advantage?
SALV. Methinks we arrogate too much to our ſelves,
cius, whilſt we will have it, that the onely care of us, is the
æquate work, and bound, beyond which the Divine Wiſdome
and Power doth, or diſpoſeth of nothing. But I will not
ſent, that we ſhould ſo much ſhorten its hand, but deſire that we
may content our ſelves with an aſſurance that God and Nature

are ſo imployed in the governing of humane affairs, that they
could not more apply themſelves thereto, although they had no
other care than onely that of mankind; and this, I think, I am
able to make out by a moſt pertinent and moſt noble example,
taken from the operation of the Suns light, which whileſt it

tracteth theſe vapours, or ſcorcheth that plant, it attracteth, it
ſcorcheth them, as if it had no more to do; yea, in ripening that
bunch of grapes, nay that one ſingle grape, it doth apply it ſelf
ſo, that it could not be more intenſe if the ſum of all its buſineſs
had been the only maturation of that grape. Now if this grape
receiveth all that it is poſſible for it to receive from the Sun, not
ſuffering the leaſt injury by the Suns production of a thouſand
other effects at the ſame time; it would be either envy or folly
to blame that grape, if it ſhould think or wiſh that the Sun would
onely appropriate its rayes to its advantage. I am confident that
nothing is omitted by the Divine Providence, of what concernes
the government of humane affairs; but that there may not be
other things in the Univerſe, that depend upon the ſame infinite
Wiſdome, I cannot, of my ſelf, by what my reaſon holds forth
to me, bring my ſelf to believe. However, if it were not ſo,
yet ſhould I not forbear to believe the reaſons laid before me by
1ſome more ſublime intelligence. In the mean time, if one
ſhould tell me, that an immenſe ſpace interpoſed between the
Orbs of the Planets and the Starry Sphere, deprived of ſtars and
idle, would be vain and uſeleſſe, as likewiſe that ſo great an
immenſity for receipt of the fixed ſtars, as exceeds our utmoſt
comprehenſion would be ſuperfluous, I would reply, that it is
raſhneſſe to go about to make our ſhallow reaſon judg of the
Works of God, and to call vain and ſuperfluous, whatſoever
thing in the Univerſe is not ſubſervient to us.
God & Nature
do imploy
ſelves in caring
for men, as if they
minded nothing
elſe.
An example of
Gods care of
kind taken from
the Sun.
SAGR. Say rather, and I believe you would ſay better, that

we know not what is ſubſervient to us; and I hold it one of the
greateſt vanities, yea follies, that can be in the World, to ſay,
becauſe I know not of what uſe Jupiter or Saturn are to me, that
therefore theſe Planets are ſuperfluous, yea more, that there are
no ſuch things in rerum natura; when as, oh fooliſh man! I
know not ſo much as to what purpoſe the arteries, the griſtles,
the ſpleen, the gall do ſerve; nay I ſhould not know that I have
a gall, ſpleen, or kidneys, if in many deſected Corps, they were
not ſhewn unto me; and then onely ſhall I be able to know what
the ſpleen worketh in me, when it comes to be taken from me.
To be able to know what this or that Cœleſtial body worketh in

me (ſeeing you will have it that all their influences direct
ſelves to us) it would be requiſite to remove that body for ſome
time; and then whatſoever effect I ſhould find wanting in me, I
would ſay that it depended on that ſtar. Moreover, who will
ſume to ſay that the ſpace which they call too vaſt and uſeleſſe
between Saturn and the fixed ſtars, is void of other mundane
dies? Muſt it be ſo, becauſe we do not ſee them? Then the four

Medicean Planets, and the companions of Saturn came firſt
to Heaven, when we began to ſee them, and not before? And
by this rule the innumerable other fixed ſtars had no exiſtence
before that men did look on them? and the cloudy
ons called Nebuloſœ were at firſt only white flakes, but afterwards
with the Teleſcope we made them to become conſtellations of
many lucid and bright ſtars. Oh preſumptious, rather oh raſh
ignorance of man!
It is great
neſſe to cenſure
that to be
ous in the Univerſe,
which we do not
perceive to be made
for us.
By depriving
Heaven of ſome
ſtar, one might
come to know what
influence it hath
upon us.
Many things
may be in Heauen,
that are inviſible
to us
SALV. It's to no purpoſe Sagredus, to ſally out any more into
theſe unprofitable exaggerations: Let us purſue our intended
deſigne of examining the validity of the reaſons alledged on
ther ſide, without determining any thing, remitting the
ment thereof when we have done, to ſuch as are more knowing.
Returning therefore to our natural and humane diſquiſitions, I

ſay, that great, little, immenſe, ſmall, &c. are not abſolute,
but relative terms, ſo that the ſelf ſame thing compared with
divers others, may one while be called immenſe, and another
1while imperceptible, not to ſay ſmall. This being ſo, I demand
in relation to what the Starry Sphere of Copernicus may be
led over vaſt. In my judgment it cannot be compared, or ſaid
to be ſuch, unleſſe it be in relation to ſome other thing of the
ſame kind; now let us take the very leaſt of the ſame kind,

which ſhall be the Lunar Orb; and if the Starry Orb may be ſo
cenſured to be too big in reſpect to that of the Moon, every
ther magnitude that with like or greater proportion exceedeth
another of the ſame kind, ought to be adjudged too vaſt, and
for the ſame reaſon to be denied that they are to be found in the
World; and thus an Elephant, and a Whale, ſhall without more
ado be condemned for Chymæra's, and Poetical fictions,
cauſe that the one as being too vaſt in relation to an Ant, which
is a Terreſtrial animal, and the other in reſpect to the ^{*}Gudgeon,

which is a Fiſh, and are certainly ſeen to be in rerum natura,
would be too immeaſurable; for without all diſpute, the
phant and Whale exceed the Ant and Gudgeon in a much
er proportion than the Starry Sphere doth that of the Moon,
although we ſhould fancy the ſaid Sphere to be as big as the
pernican Syſteme maketh it. Moreover, how hugely big is the

Sphere of Jupiter, or that of Saturn, defigned for a receptacle
but for one ſingle ſtar; and that very ſmall in compariſon of one
of the fixed? Certainly if we ſhould aſſign to every one of the
fixed ſtars for its receptacle ſo great a part of the Worlds ſpace,
it would be neceſſary to make the Orb wherein ſuch innumerable
multitudes of them reſide, very many thouſands of times
ger than that which ſerveth the purpoſe of Copernicus. Beſides,

do not you call a fixed ſtar very ſmall, I mean even one of the
moſt apparent, and not one of thoſe which ſhun our ſight; and
do we not call them ſo in reſpect of the vaſt ſpace circumfuſed?
Now if the whole Starry Sphere were one entire lucid body; who

is there, that doth not know that in an infinite ſpace there might be
aſſigned a diſtance ſo great, as that the ſaid lucid Sphere might
from thence ſhew as little, yea leſſe than a fixed ſtar, now
peareth beheld from the Earth? From thence therefore we
ſhould then judg that ſelf ſame thing to be little, which now from
hence we eſteem to be immeaſurably great.
Great, ſmall,
immenſe, &c. are
relative terms.
Vanity of thoſe
mens diſcour ſewho
judg the ſtarry
ſphere too vaſt in
the Copernican
Hypotheſis.
* Spilloncola, which
is here put for the
leaſt of Fiſhes.
The ſpace
ſigned to a fixed
ſtar, is much ieſſe
than that of a
net.
A ſtar is
led in reſpect of the
ſpace that environs
it.
The whole
ry ſphere beheld
from a great
ſtance might
pear as ſmall as
one ſingle ſtar.
SAGR. Great in my judgment, is the folly of thoſe who
would have had God to have made the World more proportinal
to the narrow capacities of their reaſon, than to his immenſe,
rather infinite power.
SIMP. All this that you ſay is very true; but that upon
which the adverſary makes a ſcruple, is, to grant that a fixed
ſtar ſhould be not onely equal to, but ſo much bigger than the
Sun; when as they both are particular bodies ſituate within the
1Starry Orb: “And indeed in my opinion this Authour very
pertinently queſtioneth and asketh: To what end, and
for whoſe ſake are ſuch huge machines made? Were they

produced for the Earth, for an inconſiderable point? And
why ſo remote? To the end they might ſeem ſo very ſmall,
and might have no influence at all upon the Earth? To

what purpoſe is ſuch a needleſſe monſtrous ^{*} immenſity
tween them and Saturn? All thoſe aſſertions fall to the
ground that are not upheld by probable reaſons.”
Inſtances of the
Authour of the
Concluſions by way
of interrogation.
Or Gulph.
SALV. I conceive by the queſtions which this perſon asketh,

that one may collect, that in caſe the Heavens, the Stars, and
the quantity of their diſtances and magnitudes which he hath
hitherto held, be let alone, (although he never certainly fancied
to himſelf any conceivable magnitude thereof) he perfectly
cerns and comprehends the benefits that flow from thence to the
Earth, which is no longer an inconſiderable thing; nor are they
any longer ſo remote as to appear ſo very ſmall, but big enough to
be able to operate on the Earth; and that the diſtance between
them and Saturn is very well proportioned, and that he, for all
theſe things, hath very probable reaſons; of which I would
ly have heard ſome one: but being that in theſe few words he

confounds and contradicts himſelf, it maketh me think that he
is very poor and ill furniſhed with thoſe probable reaſons, and
that thoſe which he calls reaſons, are rather fallacies, or dreams
of an over-weening fancy. For I ask of him, whether theſe

leſtial bodies truly operate on the Earth, and whether for the
working of thoſe effects they were produced of ſuch and ſuch
magnitudes, and diſpoſed at ſuch and ſuch diſtances, or elſe
whether they have nothing at all to do with Terrene mattets. If
they have nothing to do with the Earth; it is a great folly for us
that are Earth-born, to offer to make our ſelves arbitrators of
their magnitudes, and regulators of their local diſpoſitions,
ing that we are altogether ignorant of their whole buſineſſe and
concerns; but if he ſhall ſay that they do operate, and that they
are directed to this end, he doth affirm the ſame thing which a
little before he denied, and praiſeth that which even now he
condemned, in that he ſaid, that the Celeſtial bodies ſituate ſo
far remote as that they appear very ſmall, cannot have any
fluence at all upon the Earth. But, good Sir, in the Starry Sphere
pre-eſtabliſhed at its preſent diſtance, and which you did
knowledg to be in your judgment, well proportioned to have an
influence upon theſe Terrene bodies, many ſtars appear very
ſmall, and an hundred times as many more are wholly inviſible
unto us (which is an appearing yet leſſe than very ſmall)
therefore it is neceſſary that (contradicting your ſelf) you do
1now deny their operation upon the the Earth; or elſe that (ſtill
contradicting your ſelf) you grant that their appearing very ſmall
doth not in the leaſt leſſen their influence; or elſe that (and this
ſhall be a more ſincere and modeſt conceſſion) you acknowledg
and freely confeſſe, that our paſſing judgment upon their
nitudes and diſtances is a vanity, not to ſay preſumption or
raſhneſſe.
Anſwers to the
interrogatories of
the ſaid Authour.
The Auihour
of the
ons confound and
contradicts
ſelfin his
gations.
Inter ogatories
put to the
thour of the
cluſions, by which
the weakneſſe of
his is made appear.
SIMP. Truth is, I my ſelf did alſo, in reading this paſſage
perceive the manifeſt contradiction, in ſaying, that the Stars. (if
one may ſo ſpeak) of Copernicus appearing ſo very ſmall, could
not operate on the Earth, and not perceiving that he had granted
an influence upon the Earth to thoſe of Ptolomy, and his
tors, which appear not only very ſmall, but are, for the moſt
part, very inviſible.
SALV. But I proceed to another conſideration: What is the
reaſon, doth he ſay, why the ſtars appear ſo little? Is it haply,
becauſe they ſeem ſo to us? Doth not he know, that this

meth from the Inſtrument that we imploy in beholding them, to
wit, from our eye? And that this is true, by changing
ment, we ſhall ſee them bigger and bigger, as much as we will.
And who knows but that to the Earth, which beholdeth them
without eyes, they may not ſhew very great, and ſuch as in
ty they are? But it's time that, omitting theſe trifles, we come
to things of more moment; and therefore I having already
monſtrated theſe two things: Firſt, how far off the Firmament
ought to be placed to make, that the grand Orb cauſeth no
ter difference than that which the Terreſtrial Orb occaſioneth in
the remoteneſſe of the Sun; And next, how likewiſe to make
that a ſtar of the Firmament appear to us of the ſame bigneſſe,
as now we ſee it, it is not neceſſary to ſuppoſe it bigger than the
Sun; I would know whether Tycho, or any of his adherents hath
ever attempted to find out, by any means, whether any
rance be to be diſcovered in the ſtarry Sphere, upon which one
may the more reſolutely deny or admit the annual motion of
the Earth.
That remote
jects appeare ſo
ſmall, is the defect
of the eye, as
demonſtrated.
SAGR. I would anſwer for them, that there is not, no nor is

there any need there ſhould; ſeeing that it is Copernicus himſelf
that ſaith, that no ſuch diverſity is there: and they, arguing ad
hominem, admit him the ſame; and upon this aſſumption they
demonſtrate the improbability that followeth thereupon,
ly, that it would be neceſſary to make the Sphere ſo immenſe,
that a fixed ſtar, to appear unto us as great as it now ſeems, ought
of neceſſity to be of ſo immenſe a magnitude, as that it would
exceed the bigneſſe of the whole grand Orb, a thing, which
withſtanding, as they ſay, is altogether incredible.
1
Tycho nor his
followers ever
tempted to ſee
ther there are any
appearances in the
Firmament for or
against the annual
motion.
SALV. I am of the ſame judgment, and verily believe that
they argue contra hominem, ſtudying more to defend another
man, than deſiring to come to the knowledge of the truth. And

I do not only believe, that none of them ever applied themſelves
to make any ſuch obſervation, but I am alſo uncertain, whether
any of them do know what alteration the Earths annual motion
ought to produce in the fixed ſtars, in caſe the ſtarry Sphere were
not ſo far diſtant, as that in them the ſaid diverſity, by reaſon of
its minuity diſ-appeareth; for their ſurceaſing that inquiſition,
and referring themſelves to the meer aſſertion of Copernicus,
may very well ſerve to convict a man, but not to acquit him of
the fact: For its poſſible that ſuch a diverſity may be, and yet

not have been ſought for; or that either by reaſon of its
ty, or for want of exact Inſtruments it was not diſcovered by
pernicus; for though it were ſo, this would not be the firſt thing,
that he either for want of Inſtruments, or for ſome other defect
hath not known; and yet he proceeding upon other ſolid and
rational conjectures, affirmeth that, which the things by him not
diſcovered do ſeem to contradict: for, as hath been ſaid already,
without the Teleſcope, neither could Mars be diſcerned to
creaſe 60. times; nor Venus 40. more in that than in this
on; yea, their differences appear much leſſe than really they are:
and yet nevertheleſſe it is certainly diſcovered at length, that
thoſe mutations are the ſame, to an hair that the Copernican

ſteme required. Now it would be very well, if with the greateſt
accurateneſſe poſſible one ſhould enquire whether ſuch a
tion as ought to be diſcoverable in the fixed ſtars, ſuppoſing the
annual motion of the Earth, would be obſerved really and in
effect, a thing which I verily believe hath never as yet been done
by any; done, ſaid I? no, nor haply (as I ſaid before) by many
well underſtood how it ought to be done. Nor ſpeak I this at
randome, for I have heretofore ſeen a certain Manuſcript of
one of theſe Anti-Copernicans, which ſaid, that there would
ceſſarily follow, in caſe that opinion were true, a continual
ſing and falling of the Pole from ſix moneths to ſix moneths,
cording as the Earth in ſuch a time, by ſuch a ſpace as is the
meter of the grand Orb, retireth one while towards the North, and
another while towards the South; and yet it ſeemed to him
nable, yea neceſſary, that we, following the Earth, when we were
towards the North ſhould have the Pole more elevated than when
we are towards the South. In this very error did one fall that was
otherwiſe a very skilful Mathematician, & a follower of Copernic.

as Tycho relateth in his ^{*}Progymnaſma. pag 684. which ſaid, that he
had obſerved the Polar altitude to vary, and to differ in Summer
from what it is in Winter: and becauſe Tycho denieth the merit
1of the cauſe, but findeth no fault with the method of it; that
is, denieth that there is any mutation to be ſeen in the altitude of
the Pole, but doth not blame the inquiſition, for not being
ted to the finding of what is ſought, he thereby ſheweth, that he
alſo eſtecemed the Polar altitude varied, or not varied every ſix
moneths, to be a good teſtimony to diſprove or inferre the annual
motion of the Earth.
A ſtronomeys,
perhaps, have not
known what
pearances ought to
follow upon the
nual motion of the
Earth.
Copernicus
derſtood not ſome
things for want of
Inſtruments.
Tycho and
thers argue
gainſt the annual
motion, from the
invariable
tion of the Pole.
* Chriſiophoius
Rothmannus.
SIMP. In truth, Salviatus, my opinion alſo tells me, that the
ſame muſt neceſſarily enſue: for I do not think that you will
ny me, but that if we walk only 60. miles towards the North,
the Pole will riſe unto us a degree higher, and that if we move
60. miles farther Northwards, the Pole will be elevated to us a
degree more, &c. Now if the approaching or receding 60. miles
onely, make ſo notable a change in the Polar altitudes, what
alteration would follow, if the Earth and we with it, ſhould
be tranſported, I will not ſay 60. miles, but 60. thouſand miles
that way.
SALV. It would follow (if it ſhould proceed in the ſame
proportion) that the Pole ſhall be elevated a thouſand degrees.
See, Simplicius, what a long rooted opinion can do. Yea, by
reaſon you have fixed it in your mind for ſo many years, that it
is Heaven, that revolveth in twenty four hours, and not the
Earth, and that conſequently the Poles of that Revolution are in
Heaven, and not in the Terreſtrial Globe, cannot now, in an
hours time ſhake off this habituated conceipt, and take up the
contrary, fancying to your ſelf, that the Earth is that which
veth, only for ſo long time as may ſuffice to conceive of what
would follow, thereupon ſhould that lye be a truth. If the Earth
Simplicius, be that which moveth in its ſelf in twenty four hours,
in it are the Poles, in it is the Axis, in it is the Equinoctial, that
is, the grand Circle, deſcribed by the point, equidiſtant from the
Poles, in it are the inſinite Parallels bigger and leſſer deſcribed by
the points of the ſuperficies more and leſſe diſtant from the Poles,
in it are all theſe things, and not in the ſtarry Sphere, which, as
being immoveable, wants them all, and can only by the
tion be conceived to be therein, prolonging the Axis of the Earth
ſo far, till that determining, it ſhall mark out two points placed
right over our Poles, and the plane of the Equinoctial being
tended, it ſhall deſcribe in Heaven a circle like it ſelf. Now if the
true Axis, the true Poles, the true Equinoctial, do not change
in the Earth ſo long as you continue in the ſame place of the
Earth, and though the Earth be tranſported, as you do pleaſe,
yet you ſhall not change your habitude either to the Poles, or to
the circles, or to any other Earthly thing; and this becauſe, that
that tranſpoſition being common to you and to all Terreſtrial
1things; and that motion where it is common, is as if it never

were; and as you change not habitude to the Terreſtrial Poles
(habitude I ſay, whether that they riſe, or deſcend) ſo neither
ſhall you change poſition to the Poles imagined in Heaven;
wayes provided that by Celeſtial Poles we underſtand (as hath
been already defined) thoſe two points that come to be marked
out by the prolongation of the Terreſtrial Axis unto that length.
Tis true thoſe points in Heaven do change, when the Earths
ſportment is made after ſuch a manner, that its Axis cometh to
paſſe by other and other points of the immoveable Celeſtial
Sphere, but our habitude thereunto changeth not, ſo as that the
ſecond ſhould be more elevated to us than the firſt. If any one
will have one of the points of the Firmament, which do anſwer
to the Poles of the Earth to aſcend, and the other to deſcend,
he muſt walk along the Earth towards the one, receding from the
other, for the tranſportment of the Earth, and with it us our
ſelves, (as I told you before) operates nothing at all.
Motion where
it is common, is as
if it never were.
SAGR. Permit me, I beſeech you Salviatus, to make this a
little more clear by an example, which although groſſe, is
commodated to this purpoſe. Suppoſe your ſelf, Simplicius, to

be aboard a Ship, and that ſtanding in the Poope, or Hin-deck;
you have directed a Quadrant, or ſome other Aſtronomical
ſtrument, towards the top of the Top-gallant-Maſt, as if you
would take its height, which ſuppoſe it were v. gr. 40. degrees,

there is no doubt, but that if you walk along the ^{*} Hatches
wards the Maſt 25. or 30. paces; and then again direct the ſaid
Inſtrument to the ſame Top-Gallant-Top. You ſhall find its
vation to be greater, and to be encreaſed v. gr. 10. degrees; but
if inſtead of walking thoſe 25. or 30. paces towards the Maſt,
you ſtand ſtill at the Sterne, and make the whole Ship to move
thitherwards, do you believe that by reaſon of the 25. or 30.
paces that it had paſt, the elevation of the Top-Gallant-Top
would ſhew 10. degrees encreaſed?
An example
ted to prove that
the altitude of the
Pole ought not to
vary by means of
the Earths annual
motion.
* Corſia, the bank
or bench on which
ſlaves ſit in a
ly.
SIMP. I believe and know that it would not gain an hairs
breadth in the paſſing of 30. paces, nor of a thouſand, no nor of
an hundred thouſand miles; but yet I believe withal that
ing through the ſights at the Top and Top-Gallant, if I ſhould
find a fixed Star that was in the ſame elevation, I believe I ſay,
that, holding ſtill the Quadrant, after I had ſailed towards the
ſtar 60. miles, the eye would meet with the top of the ſaid
Maſt, as before, but not with the ſtar, which would be
ted to me one degree.
SAGR. Then you do not think that the ſight would fall upon
that point of the Starry Sphere, that anſwereth to the direction
of the Top-Gallant Top?
1
SIMP. No: For the point would be changed, and would be
beneath the ſtar firſt obſerved.
SAGR. You are in the right. Now like as that which in this
example anſwereth to the elevation of the Top-Gallant-Top, is
not the ſtar, but the point of the Firmament that lyeth in a right
line with the eye, and the ſaid top of the Maſt, ſo in the caſe
exemplified, that which in the Firmament anſwers to the Pole
of the Earth, is not a ſtar, or other fixed thing in the
ment; but is that point in which the Axis of the Earth
ed ſtreight out, till it cometh thither doth determine, which point
is not fixed, but obeyeth the mutations that the Pole of the
Earth doth make. And therefore Tycho, or who ever elſe that

did alledg this objection, ought to have ſaid that upon that
ſame motion of the Earth, were it true, one might obſerve ſome
difference in the elevation and depreſſion (not of the Pole, but)
of ſome fixed ſtar toward that part which anſwereth to our Pole.
Upon the
al motion of the
Earth, alteration
may enſue in
ſome fixed ſtar,
not in the Pole.
SIMP. I already very well underſtand the miſtake by them
committed; but yet therefore (which to me ſeems very great) of
the argument brought on the contrary is not leſſened,
ſing relation to be had to the variation of the ſtars, and not of
the Pole; for if the moving of the Ship but 60. miles, make a
fixed ſtar riſe to me one degree, ſhall I not find alike, yea and
very much greater mutation, if the Ship ſhould ſail towards the
ſaid ſtar for ſo much ſpace as is the Diameter of the Grand
Orb, which you affirm to be double the diſtance that is between
the Earth and Sun?
SAGR. Herein Simplicius, there is another fallacy, which,

truth is, you underſtand, but do not upon the ſudden think of
the ſame, but I will try to bring it to your remembrance: Tell
me therefore; if when after you have directed the Quadrant to
a fixed ſtar, and found v. g. its elevation to be 40. degrees,
you ſhould without ſtirring from the place, incline the ſide of
the Ouadrant, ſo as that the ſtar might remain elevated above
that direction, would you thereupon ſay that the ſtar had
red greater elevation?
The equivoke of
thoſe who believe
that in the annual
motion great
tations are to be
made about the
elevation of a
ed ſtar, is
ted.
SIMP. Certainly no: For the mutation was made in the
ſtrument and not in the Obſerver, that did change place,
ving towards the ſame.
SAGR. But if you ſail or walk along the ſurface of the
ſtrial Globe, will you ſay that there is no alteration made in the
ſaid Quadrant, but that the ſame elevarion is ſtill retained in
ſpect of the Heavens, ſo long as you your ſelf do not incline it,
but let it ſtand at its firſt conſtitution?
SIMP. Give me leave to think of it. I would ſay without
more ado, that it would not retain the ſame, in regard the
1greſſe I make is not in plano, but about the circumference of the
Terreſtrial Globe, which at every ſtep changeth inclination in
reſpect to Heaven, and conſequently maketh the ſame change
in the Inſtrument which is erected upon the ſame.
SAGR. You ſay very well: And you know withal, that by
how much the bigger that circle ſhall be upon which you move,
ſo many more miles you are to walk, to make the ſaid ſtar to
riſe that ſame degree higher; and that ſinally if the motion
wards the ſtar ſhould be in a right line, you ought to move yet
farther, than if it were about the circumference of never ſo
great a
The right line,
and circumference
of an infinite
cle, are the ſame
thing.
SALV. True: For in ſhort the circumference of an infinite
circle, and a right line are the ſame thing.
SAGR. But this I do not underſtand, nor as I believe, doth
Simplicius apprehend the ſame; and it muſt needs be concealed
from us under ſome miſtery, for we know that Salviatus never
ſpeaks at random, nor propoſeth any Paradox, which doth not
break forth into ſome conceit, not trivial in the leaſt. Therefore
in due time and place I will put you in mind to demonſtrate this,
that the right line is the ſame with the circumference of an
nite circle, but at preſent I am unwilling that we ſhould
rupt the diſcourſe in hand. Returning then to the caſe, I
poſe to the conſideration of Simplicius, how the acceſſion and
receſſion that the Earth makes from the ſaid fixed ſtar which is
neer the Pole can be made as it were by a right line, for ſuch is
the Diameter of the Grand Orb, ſo that the attempting to
gulate the elevation and depreſſion of the Polar ſtar by the
tion along the ſaid Diameter, as if it were by the motion about
the little circle of the Earth, is a great argument of but little
judgment.
SIMP. But we continue ſtill unſatisfied, in regard that the
ſaid ſmall mutation that ſhould be therein, would not be
ned; and if this be null, then muſt the annual motion about
the Grand Orb aſcribed to the Earth, be null alſo.
SAGR. Here now I give Salviatus leave to go on, who as I
believe will not overpaſſe the elevation and depreſſion of the
Polar ſtar or any other of thoſe that are fixed as null, although
not diſcovered by any one, and affirmed by Copernicus himſelf
to be, I will not ſay null, but unobſervable by reaſon of its
minuity.
SALV. I have already ſaid above, that I do not think that

any one did ever ſet himſelf to obſerve, whether in different times
of the year there is any mutation to be ſeen in the fixed ſtars, that
may have a dependance on the annual motion of the Earth, and
added withal, that I doubted leaſt haply ſome might never have
1underſtood what thoſe mutations are, and amongſt what ſtars
they ſhould be diſcerned; therefore it would be neceſſary that
we in the next place narrowly examine this particular. My

ving onely found written in general terms that the annual
on of the Earth about the Grand Orb, ought not to be
ted, becauſe it is not probable but that by means of the ſame
there would be diſcoverd ſome apparent mutation in the fixed
ſtars, and not hearing ſay what thoſe apparent mutations ought to
be in particular, and in what ſtars, maketh me very reaſonably
to infer that they who rely upon that general poſition, have not
underſtood, no nor poſſibly endeavoured to underſtand, how
the buſineſſe of theſe mutations goeth, nor what things thoſe
are which they ſay ought to be ſeen. And to this judgment I am

the rather induced, knowing that the annual motion aſcribed
by Copernicus to the Earth, if it ſhould appear ſenſible in the
Starry Sphere, is not to make apparent mutations equal in
ſpect to all the ſtars, but thoſe appearances ought to be made
in ſome greater, in others leſſer, and in others yet leſſer; and
laſtly, in others abſolutely nothing at all, by reaſon of the
vaſt magnitude that the circle of this annual motion is ſuppoſed
to be of. As for the mutations that ſhould b ſeen, they are of
two kinds, one is the ſaid ſtars changing apparent magnitude,
and the other their variation of altitudes in the Meridian. Upon
which neceſſarily followeth the mutation of riſings and ſettings,
and of their diſtances from the Zenith, &c.
Enquiry is made
what mutations, &
in what ſtars, are to
be diſcovered, by
means of the
nual motion of the
Earth.
Aſtronomers
ving omitted to
ſtance what
rations thoſe are
that may be
ved from the
nual motion of the
Earth, do thereby
teſtifie that they
never rightly
derſtood the ſame.
The mutations
of the fixed ſtars
ought to be in ſome
greater, in others
leſſer, and in others
nothing at all.
SAGR. Methinks I ſee preparing for me ſuch a skean of theſe
revolutions, that I wiſh it may never be my task to diſ-intangle
them, for to confeſſe my infirmity to Salviatus, I have
times thought thereon, but could never find the ^{*} Lay-band of

it, and I ſpeak not ſo much of this which pertains to the fixed
ſtars, as of another more terrible labour which you bring to my
remembrance by maintaining theſe Meridian Altitudes, Ortive
Latitudes and diſtances from the Vertex, &c. And that which

puzzleth my brains, ariſeth from what I am now about to tell
you. Copernicus ſuppoſeth the Starry Sphere immoveable, and
the Sun in the centre thereof immoveable alſo. Therefore
ry mutation which ſeemeth unto us to be made in the Sun or in
the fixed ſtars, muſt of neceſſity befall the Earth and be ous.
But the Sun riſeth and declineth in our Meridian by a very great
arch of almoſt 47. degrees, and by arches yet greater and
greatet, varieth its Ortive and Occidual Latitudes in the oblique

Horizons. Now how can the Earth ever incline and elevate ſo
notably to the Sun, and nothing at all to the fixed ſtars, or ſo
little, that it is not to be perceived? This is that knot which
could never get thorow my ^{*} Loom-Combe; and if you ſhall
1untie it, I ſhall hold you for more than an Alexander.
* Bandola that
end of a skeen
where with
wives faſten their
hankes of yarn,
thread or ſilk.
The grand
ficulty in
nicus his Doctrine,
is that which
cerns the
mena of the Sun
and fixed ſtars.
* Pettine, it is
the ſtay in a
vets Loom, that
permitteth no knot
or ſnarle to paſſe
it, called by them
the Combe of the
Loom.
SALV. Theſe are ſcruples worthy of the ingenuity of
dus, and this doubt is ſo intricate, that even Copernicus himſelf
almoſt deſpaired of being able to explain the ſame, ſo as to
render it intelligible, which we ſee as well by his own confeſſion
of its obſcurity, as alſo by his, at two ſeveral times, taking two
different wayes to make it out. And, I ingenuouſly confeſſe that
I underſtood not his explanation, till ſuch time as another
thod more plain and manifeſt, had rendred it intelligible; and
yet neither was that done without a long and laborious
tion of my thoughts to the ſame.
SIMP. Ariſtotle ſaw the ſame ſcruple, and makes uſe

of to oppoſe certain of the Ancients, who held that the Earth
was a Planet; againſt whom he argueth, that if it were ſo, it
would follow that it alſo, as the reſt of the Planets, ſhould have a
plurality of motions, from whence would follow theſe
ons in the riſings and ſettings of the fixed ſtars, and likewiſe in
the Meridian Altitudes. And in regard that he propoundeth the
difficulty, and doth not anſwer it, it muſt needs be, if not
poſſible, at leaſt very difficult to be reſolved.
Ariſtotles
ment againſt the
Ancients, who held
that the Earth
was a Planet.
SALV. The ſtreſſe and ſtrength of the knot rendereth the
ſolution thereof more commendable and admirable; but I do
not promiſe you the ſame at this time, and pray you to diſpenſe
with me therein till too morrow, and for the preſent we will go
conſidering and explaining thoſe mutations and differences that
by means of the annual motion ought to be diſcerned in the
ed ſtars, like as even now we ſaid, for the explication whereof
certain preparatory points offer themſelves, which may
tate the anſwer to the grand objection. Now reaſſuming the
two motions aſcribed to the Earth (two I ſay, for the third is
no motion, as in its place I will declare) that is the annual and

diurnal, the firſt is to be underſtood to be made by the centre of
the Earth in or about the circumference of the grand Orb, that
is of a very great circle deſcribed in the plain of the fixed and
immutable Ecliptick; the other, namely the diurnal, is made
by the Globe of the Earth in it ſelf about its own centre, and
own Axis, not erect, but inclined to the Plane of the Ecliptick,
with the inclination of 23. degrees and an half, or thereabouts,
the which inclination is maintained all the year about, and that
which ought eſpecially to be obſerved, is alwayes ſituate
wards the ſame point of Heaven: in ſo much that the Axis of the

diurnal motion doth alwayes remain parallel to it ſelf; ſo that
if we imagine that ſame Axis to be continued out until it reach
the fixed ſtars, whilſt the centre of the Earth is encircling the
whole Ecliptick in a year, the ſaid Axis deſcribeth the
1ficies of an oblique Cylinder, which hath for one of its baſes
the ſaid annual circle, and for the other a like circle
rily deſcribed by its extremity, or, (if you will) Pole, amongſt
the fixed ſtars. And this ſame cylinder is oblique to the Plane of
the Ecliptick, according to the inclination of the Axis that
ſcribeth it, which we have ſaid to be 23 degrees and an half,
the which continuing perpetually the ſame (ſave onely, that in
many thouſands of years it maketh ſome very ſmall mutation,
which nothing importeth in our preſent buſineſſe) cauſeth that

the Terreſtrial Globe doth never more incline or elevate, but
ſtill conſerveth the ſame ſtate without mutation. From whence
enſueth, that as to what pertaineth to the mutations to be
ſerved in the fixed ſtars dependant on the ſole annual motion,
the ſame ſhall happen to any point whatſoever of the Earths
ſurface, as befalleth unto the centre of the Earth it ſelf; and
therefore in the preſent explanations we will make uſe of the
centre, as if it were any whatſoever point of the ſuperficies.
And for a more facile underſtanding of the whole, let us deſign

the ſame in lineal figures: And firſt of all let us deſcribe in the
Plane of the Ecliptick the circle A N B O [in Fig. 7.] and let
us underſtand the points A and B, to be the extreams towards
the North and South; that is, the beginning of [or entrance into]
Cancer or Capricorn, and let us prolong the Diameter A B,
determinately by D and C towards the Starry Sphere. I ſay
now in the firſt place, that none of the fixed ſtars placed in the
Ecliptick, ſhall ever vary elevation, by reaſon of any
ever mutation made by the Earth along the ſaid Plane of the
Ecliptick, but ſhall alwayes appear in the ſame ſuperficies,
though the Earth ſhall approach and recede as great a ſpace as is
that of the diameter of the Grand Orb, as may plainly be
ſeen in the ſaid figure. For whether the Earth be in the point
A or in B, the ſtar C alwayes appeareth in the ſame line A B C;
although the diſtance B C, be leſſe than A C, by the whole
diameter A B. The moſt therefore that can be diſcovered in the
ſtar C, and in any other placed in the Ecliptick, is the
mented or diminiſhed apparent magnitude, by reaſon of the
proximation or receſſion of the Earth.
The annual
tion made by the
centre of the Earth
under the
tick and the
nal motion made
by the Earth about
its own centre.
The axis of the
Earth continueth
alwayes parallel to
it ſelf, and
beth a
cal ſuperficies,
clining to the
grand Orb.
The Orb of the
Earth never
neth, but is
mutably the ſame.
The fixed ſtars
placed in the
cliptick never
vate nor deſcend,
on account of the
annual motion, but
yet approach and
recede.
SAGR. Stay a while I pray you, for I meet with a certain
ſcruple, which much troubleth me, and it is this: That the ſtar
C may be ſeen by the ſame line A B C, as wel when the Earth
is in A, as when it is in B, I underſtand very well, as alſo
thermore I apprehend that the ſame would happen in all the

points of the line A B, ſo long as the Earth ſhould paſſe from A
to B by the ſaid line; but it paſſing thither, as is to be ſuppoſed,
by the arch A N B, it is manifeſt that when it ſhall be in the
1point N, and in any other except thoſe two A and B, the ſaid
ſtar ſhall no longer be obſerved in the line A B; but in others.
So that, if the appearing under ſeveral lines ought to cauſe
apparent mutations, ſome difference muſt needs appear in
this caſe. Nay more, I will ſpeak it with that Philoſophical
freedom, which ought to be allowed amongſt Philoſophick
friends, methinks that you, contradicting your ſelf, deny that
now, which but even now to our admiration, you proved to be
really true, and conſiderable; I mean that which happeneth in
the Planets, and particularly in the three ſuperiour ones, that
being conſtantly in the Ecliptick, or very near unto it, do not
onely ſhew themſelves one while near unto us, and another
while remote, but ſo deformed in their regular motions, that
they ſeem ſometimes immoveable, and ſometimes many
grees retrograde; and all upon no other occaſion than the
nual motion of the Earth.
Objections againſt
the Earths annual
motion taken from
the fixed stars
placed in the
cliptick.
SALV. Though by a thouſand accidents I have been
fore aſſured of the wittineſſe of Sagredus, yet I had a deſire by
this one experiment more to aſcertain me of what I may expect
from his ingenuity, and all this for my own intereſt, for in caſe
my Propoſitions ſtand but proof againſt the hammer and
nace of his judgment, I ſhall be confident that they will abide

the ^{*} teſt of all Touch-ſtones. I ſay therefore that I had
poſely diſſembled this objection, but yet not with any intent to
deceive you, and to put any falſhood upon you, as it might
have happened if the objection by me diſguiſed, and by you
ver-lookt, had been the ſame in effect as it ſeemed to be in
pearance, that is, really valid and concluſive; but it is not ſo;
nay I rather ſuſpect that to try me, you make as if you did not
ſee its nullity. But I will herein be too hard for you, and force
from your tongue, that which you would ſo artificially conceal;
and therefore tell me, what that thing ſhould be, whereby you
come to know the ſtation and retrogradation of the Planets,
which is derived from the annual motion, aud which is ſo great,
that at leaſt ſome foot-ſteps of ſuch an effect ought to appear in
the ſtars of the Ecliptick?
* Or will prove
of good alloy.
SAGR. This demand of yours containeth two queſtions, to
which it is neceſſary that I make reply; the firſt relates to the
imputation which you lay upon me of a Diſſembler; the other
concerneth that which may appear in the ſtars, &c. As to the
firſt, I will ſay with your permiſſion, that it is not true, that I
have diſſembled my knowing the nullity of that objection; and
to aſſure you of the ſame, I now tell you that I very well
ſtand the nullity thereof.
SALV. But yet I do not underſtand how it can be, that you
1ſpake not friendly, when you ſaid you did not know that ſame
fallacy which you now confeſſe that you know very well.
SAGR. The very confeſſion of knowing it may aſſure you
that I did not diſſemble, when I ſaid that I did not underſtand it;
for if I had had a mind, and would diſſemble, who could
der me from continuing in the ſame ſimulation, and denying ſtill
that I underſtand the fallacy? I ſay therefore that I underſtood
not the ſame, at that time, but that I do now at this preſent
prehend it, for that you have prompted my intellect, firſt by
telling me reſolutely that it is null, and then by beginning to
queſtion me ſo at large what thing that might be, whereby I
might come to know the ſtation and retrogradation of the

nets; and becauſe this is known by comparing them with the
ed ſtars, in relation to which, they are ſeen to vary their
tions, one while towards the Weſt, and another towards the
Eaſt, and ſometimes to abide immoveable; and becauſe there
is not any thing above the Starry Sphere, immenſely more remote
from us, and viſible unto us, wherewith we may compare our
fixed ſtars, therefore we cannot diſcover in the fixed ſtars any
foot-ſteps of what appeareth to us in the Planets. This I believe
is the ſubſtance of that which you would force from me.
The ſtation,
rection and
gradation of the
Planets is known,
in relation to the
fixed ſtars.
SALV. It is ſo, with the addition moreover of your

rable ingenuity; and if with half a word I did open your eyes,
you by the like have remembred me that it is not altogether
poſſible, but that ſometime or other ſomething obſervable may
be found amongſt the fixed ſtars, by which it may be gathered
wherein the annual converſion reſides, ſo as that they alſo no
leſſe than the Planets and Sun it ſelf, may appear in judgment to
bear witneſſe of that motion, in favour of the Earth; for I do not
think that the ſtas are ſpread in a ſpherical ſuperficies equally
mote from a common centre, but hold, that their diſtances from
us are ſo various, that ſome of them may be twice and thrice as
remote as others; ſo that if with the Teleſcope one ſhould
ſerve a very ſmall ſtar neer to one of the bigger, and which
therefore was very exceeding high, it might happen that ſome
ſenſible mutation might fall out between them, correſpondent
to that of the ſuperiour Planets. And ſo much ſhall ſerve to have
ſpoken at this time touching the ſtars placed in the Ecliptick.

Let us now come to the fixed ſtars, placed out of the Ecliptick,
and let us ſuppoſe a great circle erect upor [i. e. at right angles
to] the Plane of the ^{*} ſame; and let it, for example, be a cir­
cle that in the Starry Sphere anſwers to the Solſtitial Colure,

and let us mark it C E H [in Fig. 8.] which ſhall happen to be
withal a Meridian, and in it we will take a ſtar without the
tick, which let be E. Now this ſtar will indeed vary its
1on upon the Earths motion; for from the Earth in A it ſhall be
ſeen according to the ray A E, with the elevation of the angle
E A C; but from the Earth placed in B, it ſhall be ſeen
cording to the ray B E, with the elevation of the angle E B C,
bigger than the other E A C, that being extern, and this
tern and oppoſite in the triangle E A B, the diſtance therefore
of the ſtar E from the Ecliptick, ſhall appear changed; and
likewiſe its altitude in the Meridian ſhall become greater in the
poſition B, than in the place A, according as the angle E B C
exceeds the angle E A C, which exceſſe is the quantity of the
angle A E B: For in the triangle E A B, the ſide A B being
continued to C, the exteriour angle E B C (as being equal to
the two interiour and oppoſite E and A) exceedeth the ſaid
gle A, by the quantity of the angle E. And if we ſhould take
another ſtar in the ſame Meridian, more remote from the
ptick, as for inſtance the ſtar H, the diverſity in it ſhall be
greater by being obſerved from the two ſtations A and B,
ding as the angle A H B is greater than the other E; which
gle ſhall encreaſe continually according as the obſerved ſtar ſhall
be farther and farther from the Ecliptick, till that at laſt the
greateſt mutation will appear in that ſtar that ſhould be placed in
the very Pole of the Ecliptick. As for a full underſtanding
of we thus demonſtrate. Suppoſe the diameter of the Grand
Orb to be A B, whoſe centre [in the ſame Figure] is G, and
let it be ſuppoſed to be continued out as far as the Starry Sphere
in the points D and C, and from the centre G let there be erected
the Axis of the Ecliptick G F, prolonged till it arrive at the ſaid
Sphere, in which a Meridian D F C is ſuppoſed to be deſcribed,
that ſhall be perpendicular to the Plane of the Ecliptick; and
in the arch F C any points H and E, are imagined to be taken,
as places of fixed ſtars: Let the lines F A, F B, A H, H G,
H B, A E, G E, B E, be conjoyned. And let the angle of
ference, or, if you will, the Parallax of the ſtar placed in the
Pole F, be A F B, and let that of the ſtar placed in H, be the
angle A H B, and let that of the ſtar in E, be the angle
A E B. I ſay, that the angle of difference of the Polar ſtar F, is
the greateſt, and that of the reſt, thoſe that are nearer to the
greateſt are bigger than the more remote; that is to ſay, that the
angle F is bigger than the angle H, and this bigger than the angle
E. Now about the triangle F A B, let us ſuppoſe a circle to be
ſcribed. And becauſe the angle F is acute, (by reaſon that its baſe
AB is leſſe than the diameter DC, of the ſemicircle D F C) it ſhall
be placed in the greater portion of the circumſcribed circle cut
by the baſe A B. And becauſe the ſaid A B is divided in the
midſt, and at right angles by F G, the centre of the
1bed circle ſhall be in the line F G, which let be the point I; and
becauſe that of ſuch lines as are drawn from the point G, which
is not the centre, unto the circumference of the circumſcribed
circle, the biggeſt is that which paſſeth by the centre, G F ſhall
be bigger than any other that is drawn from the point G, to the
circumference of the ſaid circle; and therefore that
rence will cut the line G H (which is equal to the line G F) and
cutting G H, it will alſo cut A H. Let it cut it in L, and
joyn the line L B. Theſe two angles, therefore, A F B and A L B
ſhall be equal, as being in the ſame portion of the circle
cumſcribed. But A L B external, is bigger than the internal H;
therefore the angle F is bigger than the angle H. And by the
ſame method we might demonſtrate the angle H to be bigger
than the angle E, becauſe that of the circle deſcribed about the
triangle A H B, the centre is in the perpendicular G F, to which
the line G H is nearer than the line G E, and therefore the
cumference of it cutteth G E, and alſo A E, whereupon the
poſition is manifeſt. We will conclude from hence, that the
ference of appearance, (which with the proper term of art, we
might call the Parallax of the fixed ſtars) is greater, or leſſe,
cording as the Stars obſerved are more or leſſe adjacent to the
Pole of the Ecliptick, ſo that, in concluſion of thoſe Stars that
are in the Ecliptick it ſelf, the ſaid diverſity is reduced to nothing.
In the next place, as to the Earths acceſſion by that motion to,

or receſſion from the Stars, it appeareth to, and recedeth from
thoſe that are in the Ecliptick, the quantity of the whole
ter of the grand Orb, as we did ſee even now, but that acceſſion
or receſſion to, or from the ſtars about the Pole of the Ecliptick,
is almoſt nothing; and in going to and from others, this
rence groweth greater, according as they are neerer to the
tick. We may, in the third place, know, that the ſaid difference

of Aſpect groweth greater or leſſer, according as the Star
ved ſhall be neerer to us, or farther from us. For if we draw
nother Meridian, leſſe diſtant from the Earth; as for example,
this D F I [in Fig. 7.] a Star placed in F, and ſeen by the ſame
ray A F E, the Earth being in A, would, in caſe it ſhould be
ſerved from the Earth in B, appear according to the ray B F, and
would make the angle of difference, namely, B F A, bigger
than the former A E B, being the exteriour angle of the
gle B F E.
An Indice in
the fixed ſtars like
to that which is
ſeen in the
nets, is an
ment of the Earths
annual motion.
The fixed ſtars
without the
tick elevate and
deſcend more or
leſſe, according to
their diſtance from
the ſaid Ecliptick.
* i. e. of the
cliptick.
The Earth
proacheth or
deth from the
ed ſtars of the
cliptick, the
tity of the
ter of the Grand
Orb.
The ſtars
er to us make
greater differences
than the more
more.
SAGR. With great delight, and alſo benefit have I heard
your diſcourſe; and that I may be certain, whether I have

ly underſtood the ſame, I ſhall give you the ſumme of the
cluſions in a few words. As I take it, you have explained to us
the different appearances, that by means of the Earths annual
1tion, may be by us obſerved in the fixed ſtars to be of two
kinds: The one is, that of their apparent magnitudes varied,
cording as we, tranſported by the Earth, approach or recede
from the ſame: The other (which likewiſe dependeth on the
ſame acceſſion and reeeſſion) their appearing unto us in the
ſame Meridian, one while more elevated, and another while leſſe.
Moreover, you tell us (and I underſtand it very well) that the
one and other of theſe mutations are not made alike in all the
ſtars, but in ſome greater, and in others leſſer, and in others not
at all. The acceſſion and receſſion whereby the ſame ſtar ought
to appear, one while bigger, and another while leſſer, is
ble, and almoſt nothing in the ſtars neer unto the pole of the
cliptick, but is greateſt in the ſtars placed in the Ecliptick it ſelf,
and indifferent in the intermediate: the contrary happens in the
other difference, that is, the elevation or depreſſion of the ſtars
placed in the Ecliptick is nothing at all, greateſt in thoſe neereſt
to the Pole of the ſaid Ecliptick, and indifferent in the
diate. Beſides, both theſe differences are more ſenſible in the
Stars neereſt to us, in the more remote leſſe ſenſible, and in
thoſe that are very far diſtant wholly diſappear. This is, as to
what concerns my ſelf; it remaineth now, as I conceive, that
ſomething be ſaid for the ſatisfaction of Simplicius, who, as I
believe, will not eaſily be made to over-paſſe thoſe differences,
as inſenſible that are derived from a motion of the Earth ſo vaſt,
and from a mutation that tranſports the Earth into places twice
as far diſtant from us as the Sun.
The Epilogue of
the Phænomena
of the fixed ſtars
cauſed by the
nual motion of the
Earth.
SIMP. Truth is, to ſpeak freely, I am very loth to confeſſe, that
the diſtance of the fixed Stars ought to be ſuch, that in them the
fore-mentioned differences ſhould be wholly imperceptible.
SALV. Do notthrow your ſelf into abſolute deſpair,
cius, for there may perhaps yet ſome qualification be found for
your difficulties. And firſt, that the apparent magnitude of the
ſtars is not ſeen to make any ſenſible alteration, ought not to be
judged by you a thing improbable, in regard you ſee the gueſſes
of men in this particular to be ſo groſſely erroneous, eſpecially in
looking upon ſplendid objects; and you your ſelf beholding
v. g. a lighted Torch at the diſtance of 200 paces, if it

proach nearer to you 3. or 4. yards, do you think that it will
ſhew any whit encreaſed in magnitude? I for my part ſhould
not perceive it certainly, although it ſhould approach 20. or
30. yards nearer; nay it hath ſometimes happened that in ſeeing
ſuch a light at that diſtance I know not how to reſolve whether
it came towards me, or retreated from me, when as it did in
reality approach nearer to me. But what need I ſpeak of this?
If the ſelf ſame acceſſion and receſſion (I ſpeak of a diſtance
1twice as great as that from the Sun to us) in the ſtar of Saturn is
almoſt totally imperceptible, and in Jupiter not very
ble, what ſhall we think of the fixed ſtars, which I believe you
will not ſcruple to place twice as far off as Saturn? In Mars,
which for that it is nearer to us -------
In objects far
remote, and
nous, a ſmall
proach or receſſion
is imperceptible.
SIMP. Pray Sir, put your ſelf to no farther trouble in this
particular, for I already conceive that what hath been ſpoken
touching the unaltered apparent magnitude of the fixed ſtars may
very well come to paſſe, but what ſhall we ſay of the other
ficulty that proceeds from not perceiving any variation in the
mutation of aſpect?
SALV. We will ſay that which peradventure may ſatisfie
you alſo in this particular. And to make ſhort, would you not
be ſatisfied if there ſhould be diſcovered in the ſtars face
tions that you think ought to be diſcovered, in caſe the annual
motion belonged to the Earth?
SIMP. I ſhould ſo doubtleſſe, as to what concerns this
ticular.
SALV. I could wiſh you would ſay that in caſe ſuch a

rence were diſcovered, nothing more would remain behind, that
might render the mobility of the Earth queſtionable. But
though yet that ſhould not ſenſibly appear, yet is not its
bility removed, nor its immobility neceſſarily proved, it being
poſſible, (as Copernicus affirmeth) that the immenſe diſtance of
the Starry Sphere rendereth ſuch very ſmall Phænomena
vable; the which as already hath been ſaid, may poſſibly not
have been hitherto ſo much as ſought for, or if ſought for, yet
not ſought for in ſuch a way as they ought, to wit, with that

exactneſſe which to ſo minute a punctuality would be neceſſary;
which exactneſſe is very difficult to obtain, as well by reaſon of the
deficiency of Aſttonomical Inſtruments, ſubject to many
tions, as alſo through the fault of thoſe that manage them with leſs
diligence then is requiſite. A neceſſary argument how little
dit is to be given to thoſe obſervations may be deduced from the
differences which we find amongſt Aſtronomers in aſſigning the
places, I will not ſay, of the new Stars or Comets, but of the fixed
ſtars themſelves, even to the altitudes of the very Poles, in
which, moſt an end, they are found to differ from one another
many minutes. And to ſpeak the truth, who can in a Quadrant,
or Sextant, that at moſt ſhall have its ſide ^{*} 3. or 4. yards long,

aſcertain himſelf in the incidence of the perpendicular, or in the
direction of the ſights, not to erre two or three minutes, which
in its circumference ſhall not amount to the breadth of a grain of
^{*}Mylet? Beſides that, it is almoſt impoſſible, that the Inſtrument

ſhould be made, and kept with abſolute exactneſſe. Ptolomey
1
ſheweth his diſtruſt of a Spherical Inſtrument compoſed by
chimedes hiſmelf to take the Suns ingreſſion into the

If in the fixed
ſtars one ſhould
diſcover any
nual mutation, the
motion of the
Earth would be
undeniable.
It is proved what
ſmall credit is to be
given to
mical Inſtruments
in minute
tions.
* Braceia Italian.
* Or Mill.
Ptolomy did not
truſt to an
ment made by
chimedes.
Inſtruments of
Tycho made with
great expence.
SIMP. But if the Inſtruments be ſo ſuſpitious, and the
vations ſo dubious, how can we ever come to any certainty of
things, or free our ſelves from miſtakes? I have heard ſtrange
things of the Inſtruments of Tycho made with extraordinary coſt,
and of his ſingular diligence in obſervations.
SALV. All this I grant you; but neither one nor other of
theſe is ſufficient to aſcertain us in a buſineſſe of this importance.

I deſire that we may make uſe of Inſtruments greater by far, and
by far certainer than thoſe of Tycho, made with a very ſmall
charge; the ſides of which are of 4. 6. 20. 30. and 50. miles, ſo

as that a degree is a mile broad, a minute prim. 50 ^{*} yards, a
ſecond but little leſſe than a yard, and in ſhort we may without
a farthing expence procure them of what bigneſſe we pleaſe. I

being in a Countrey Seat of mine near to Florence, did plainly
obſerve the Suns arrival at, and departure from the Summer
Solſtice, whilſt one Evening at the time of its going down it
peared upon the top of a Rock on the Mountains of Pictrapana,
about 60. miles from thence, leaving diſcovered of it a ſmall
ſtreak or filament towards the North, whoſe breadth was not
the hundredth part of its Diameter; and the following Evening
at the like ſetting, it ſhew'd ſuch another part of it, but notably
more ſmall, a neceſſary argument, that it had begun to recede
from the Tropick; and the regreſſion of the Sun from the firſt to
the ſecond obſervation, doth not import doubtleſſe a ſecond

nute in the Eaſt. The obſervation made afterwards with an
quiſite Teleſcope, and that multiplyeth the Diſcus of the Sun
more than a thouſand times, would prove eaſie, and with all
delightful. Now with ſuch an Inſtrument as this, I would have
obſervations to be made in the fixed ſtars, making uſe of ſome
of thoſe wherein the mutation ought to appear more
ous, ſuch as are (as hath already been declared) the more
mote from the Ecliptick, amongſt which the Harp a very great
ſtar, and near to the Pole of the Ecliptick, would be very
per in Countries far North, proceeding according to the
ner that I ſhall ſhew by and by, but in the uſe of another ſtar;
and I have already fancied to my ſelf a place very well adapted
for ſuch an obſervation. The place is an open Plane, upon
which towards the North there riſeth a very eminent Mountain,
in the apex or top whereof is built a little Chappel, ſituate Eaſt
and Weſt, ſo as that the ridg of its Roof may interſect at right
angles, the meridian of ſome building ſtanding in the Plane. I
will place a beam parallel to the ſaid ridg, or top of the Roof,
1and diſtant from it a yard or thereabouts. This being placed, I
will ſeek in the Plain the place from whence one of the ſtars of
Charls's Waine, in paſſing by the Meridian, cometh to hide it
ſelf behind the beam ſo placed, or in caſe the beam ſhould not
be ſo big as to hide the ſtar, I will finde a ſtation where one
may ſee the ſaid beam to cut the ſaid ſtar into two equal parts;
an effect that with an ^{*} exquiſite Teleſcope may be perfectly
diſcerned. And if in the place where the ſaid accident is
ed, there were ſome building, it will be the more commodious;
but if not, I will cauſe a Pole to be ſtuck very faſt in the
ground, with ſome ſtanding mark to direct where to place the
eye anew, when ever I have a mind to repeat the obſervation.
The firſt of which obſervations I will make about the Summer
Solſtice, to continue afterwards from Moneth to Moneth, or
when I ſhall ſo pleaſe, to the other Solſtice; with which
vation one may diſcover the elevation and depreſſion of the ſtar,
though it be very ſmall. And if in that operation it ſhall
pen, that any mutation ſhall diſcover it ſelf, what and how great
benefit will it bring to Aſtronomy? Seeing that thereby, beſides
our being aſſured of the annual motion, we may come to know
the grandure and diſtance of the ſame ſtar.
What
ments are apt for
moſt exact
vation.
* Italian braces.
An exquiſite
obſervation of the
approach and
parture of the Sun
from the Summer
Solſtice.
A place
modated for the
obſervation of the
fixed ſtars, as to
what concers the
annual motion of
the Earth.
SAGR. I very well comprehend your whole proceedings;
and the operation ſeems to me ſo eaſie, and ſo commodious for
the purpoſe, that it may very rationally be thought, that either
Copernicus himſelf, or ſome other Aſtronomer had made trial
of it.
SALV. But I judg the quite contrary, for it is not probable,
that if any one had experimented it, he would not have
tioned the event, whether it fell out in favour of this, or that
opinion; beſides that, no man that I can find, either for this,
or any other end, did ever go about to make ſuch an
on; which alſo without an exact Teleſcope could but badly be
effected.
SIMP. I am fully ſatisfied with what you ſay. But ſeeing
that it is a great while to night, if you defire that I ſhall paſſe
the ſame quietly, let it not be a trouble to you to explain unto
us thoſe Problems, the declaration whereof you did even now
requeſt might be deferred until too morrow. Be pleaſed to grant
us your promiſed indulgence, and, laying aſide all other
ſes, proceed to ſhew us, that the motions which Copernicus aſſigns
to the Earth being taken for granted, and ſuppoſing the Sun
and fixed ſtars immoveable, there may follow the ſame
dents touching the elevations and depreſſions of the Sun,
ing the mutations of the Seaſons, and the inequality of dayes
and nights, &c. in the ſelf ſame manner, juſt as they are with
1facility apprehended in the Prolomaick Syſteme.
SALV. I neither ought, nor can deny any thing that Sagredus
ſhall requeſt: And the delay by me deſired was to no other end,
ſave only that I might have time once again to methodize thoſe
prefatory points, in my fancy, that ſerve for a large and plain
claration of the manner how the forenamed accidents follow, as
well in the Copernican poſition, as in the Ptolomaick: nay, with

much greater facility and ſimplicity in that than in this. Whence
one may manifeſtly conceive that Hypotheſis to be as eaſie to be
effected by nature, as difficult to be apprehended by the
ſtanding: yet nevertheleſſe, I hope by making uſe of another

kind of explanation, than that uſed by Copernicus, to render
wiſe the apprehending of it ſomewhat leſſe obſcure. Which
that I may do, I will propoſe certain ſuppoſitions of themſelves
known and manifeſt, and they ſhall be theſe that follow.
The
can Syſteme
cult to be
ſtood, but eaſie to
be effected.
Neceſſary
poſitions for the
better conceiving
of the conſequences
of the Earths
tion.
Firſt, I ſuppoſe that the Earth is a ſpherical body, turning
round upon its own Axis and Poles, and that each point aſſigned
in its ſuperficies, deſcribeth the circumference of a circle,
er or leſſer, according as the point aſſigned ſhall be neerer or
farther from the Poles: And that of theſe circles the greateſt is
that which is deſcribed by a point equidiſtant from the ſaid Poles;
and all theſe circles are parallel to each other; and Parallels we
will call them.
Secondly, The Earth being of a Spherical Figure, and of an
pacous ſubſtance, it is continually illuminated by the Sun,
ding to the half of its ſurface, the other half remaining obſcure,
and the boundary that diſtinguiſheth the illuminated part from
the dark being a grand circle, we will call that circle the
nator of the light.
Thirdly, If the Circle that is terminator of the light ſhould
paſſe by the Poles of the Earth, it would cut (being a grand
and principal circle) all the parallels into equal parts; but not
paſſing by the Poles, it would cut them all in parts unequal,
cept only the circle in the middle, which, as being a grand circle
will be cut into equal parts.
Fourthly, The Earth turning round upon its own Poles, the
quantities of dayes and nights are termined by the arches of the
Parallels, interſected by the circle, that is, the terminator of the
light, and the arch that is ſcituate in the illuminated Hemiſphere
preſcribeth the length of the day, and the remainer is the
tity of the night.
Theſe things being preſuppoſed, for the more clear

ſtanding of that which remaines to be ſaid, we will lay it down
in a Figure. And firſt, we will draw the circumference of a
circle, that ſhall repreſent unto us that of the grand Orb
1bed in the plain of the Ecliptick, and this we will divide into
four equal parts with the two diameters Capricorn Cancer, and
Libra Aries, which, at the ſame time, ſhall repreſent unto us the
four Cardinal points, that is, the two Solſtices, and the two
quinoctials; and in the centre of that circle we will place the
Sun O, fixed and immoveable.
A plain Scheme
repreſenting the
Copernican
theſis, and its
ſequences.
20[Figure 20]
Let us next draw about the four points, Capricorn, Cancer,
Libra and Aries, as centres, four equal circles, which repreſent
unto us the Earth placed in them at four ſeveral times of the
year. The which, with its centre, in the ſpace of a year, paſſeth
through the whole circumference, Capricorn, Aries, Cancer,
bra, moving from Eaſt to Weſt, that is, according to the order
of the Signes. It is already manifeſt, that whilſt the Earth is in
Capricorn, the Sun will appear in Cancer, and the Earth moving

along the arch Capricorn Aries, the Sun will ſeem to move along
the arch Cancer Libra, and in ſhort, will run thorow the Zodiack
according to the order of the Signes, in the ſpace of a year; and
by this firſt aſſumption, without all queſtion, full ſatisfaction is
given for the Suns apparent annual motion under the Ecliptick.
Now, coming to the other, that is, the diurnal motion of the
Earth in it ſelf, it is neceſſary to eſtabliſh its Poles and its Axis,
the which muſt be underſtood not to be erect perpendicularly
upon the plain of the Ecliptick, that is, not to be parallel to the
Axis of the grand Orb, but declining from a right angle 23
grees and an half, or thereabouts, with its North Pole towards
1the Axis of the grand Orb, the Earths centre being in the
tial point of Capricorn. Suppoſing therefore the Terreſtrial
Globe to have its centre in the point Capricorn, we will deſcribe
its Poles and Axis A B, inclined upon the diameter Capricorn
Cancer 23 degrees and an half; ſo that the angle A Capricorn
Cancer cometh to be the complement of a Quadrant or Radius,
that is, 66 degrees and an half; and this inclination muſt be
derſtood to be immutable, and we will ſuppoſe the ſuperiour
Pole A to be Boreal, or North, and the other Auſtral, or South.
Now imagining the Earth to revolve in it ſelf about the Axis A B
in twenty four hours, from Weſt to Eaſt, there ſhall by all the
points aſſigned in its ſuperſicies, be circles deſcribed parallel to
each other. We will draw, in this firſt poſition of the Earth,
the greateſt C D, and thoſe two diſtant from it gr. 23. and an
half, E F above, and G M beneath, and the other two extream
ones I K and L M remote, by thoſe intervals from the Poles A
and B; and as we have marked theſe five, ſo we may imagine
numerable others, parallel to theſe, deſcribed by the
ble points of the Terreſtrial ſurface. Next let us ſuppoſe the
Earth, with the annual motion of its centre, to transferre it ſelf
into the other places already marked; but to paſſe thither in ſuch
a manner, that its own Axis A B ſhall not only not change
nation upon the plain of the Ecliptick, but ſhall alſo never vary
direction; ſo that alwayes keeping parallel to it ſelf, it may
continually tend towards the ſame part of the Univerſe, or, if
you will, of the Firmament, whereas, if we do but ſuppoſe it
prolonged, it will, with its extream termes, deſigne a Circle
rallel and equal to the grand Orb, Libra Capricorn Aries Cancer,
as the ſuperiour baſe of a Cylinder deſcribed by it ſelf in the
nual motion above the inferiour baſe, Libra Capricorn Aries
Cancer. And therefore this immutability of inclination
nuing, we will deſign theſe other three figures about the centres
Aries, Cancer, and Libra, alike in every thing to that firſt
ſcribed about the centre Capricorn. Now we will conſider the
firſt figure of the Earth, in which, in regard the Axis A B is
clined from perpendicularity upon the diameter Capricorn
cer 23 degrees and an half towards the Sun O, and the arch A I
being alſo 23 degrees and an half, the illumination of the Sun
will illuſtrate the Hemiſphere of the Terreſtrial Globe expoſed
towards the Sun (of which, in this place, half is to be ſeen)
vided from the obſcure part by the Terminator of the light
I M, by which the parallel C D, as being a grand circle, ſhall
come to be divided into equal parts, but all the reſt into parts
equal; being that the terminator of the light I M paſſeth not
by their Poles A B, and the parallel I K, together with all the reſt
1deſcribed within the ſame, and neerer to the pole A, ſhall wholly
be included in the illuminated part; as on the contrary, the
poſite ones towards the Pole B, contained within the
lel L M, ſhall remain in the dark. Moreover, the arch A I
ing equal to the arch F D, and the arch A F, common to them
both, the two arches I K F and A F D ſhall be equal, and each
a quadrant or 90 degrees. And becauſe the whole arch I F M
is a ſemicircle, the arch F M ſhall be a quadrant, and equal to
the other F K I; and therefore the Sun O ſhall be in this ſtate
of the Earth vertical to one that ſtands in the point F. But by
the revolution diurnal about the ſtanding Axis A B, all the points
of the parallel E F paſſe by the ſame point F: and therefore in
that ſame day the Sun, at noon, ſhall be vertical to all the
bitants of the Parallel E F, and will ſeem to them to deſcribe in its
apparent motion the circle which we call the Tropick of Cancer.
But to the inhabitants of all the Parallels that are above the
rallel E F, towards the North pole A, the Sun declineth from
their Vertex or Zenith towards the South; and on the contrary,
to all the inhabitants of the Parallels that are beneath E F,
wards the Equinoctial C D, and the South Pole B, the Meridian
Sun is elevated beyond their Vertex towards the North Pole A.
Next, it is viſible that of all the Parallels, only the greateſt C D
is cut in equal parts by the Terminator of the light I M. But
the reſt, that are beneath and above the ſaid grand circle, are all
interſected in parts unequal: and of the ſuperiour ones, the
midiurnal arches, namely thoſe of the part of the Terreſtrial
face, illuſtrated by the Sun, are bigger than the ſeminocturnal
ones that remain in the dark: and the contrary befalls in the
remainder, that are under the great one C D, towards the pole B,
of which the ſemidiurnal arches are leſſer than the ſeminocturnal,
It is likewiſe apparently manifeſt, that the differences of the ſaid
arches go augmenting, according as the Parallels are neerer to
the Poles, till ſuch time as the parallel I K comes to be wholly in
the part illuminated, and the inhabitants thereof have a day of
twenty four hours long, without any night; and on the contrary,
the Parallel L M, remaining all in obſcurity, hath a night of
twenty four hours, without any day. Come we next to the
third Figure of the Earth, placed with its centre in the point
Cancer, where the Sun ſeemeth to be in the firſt point of
pricorn. We have already ſeen very manifeſtly, that by reaſon
the Axis A B doth not change inclination, but continueth
lel to it ſelf, the aſpect and ſituation of the Earth is the ſame to
an hair with that in the firſt Figure; ſave onely that that
ſphere which in the firſt was illuminated by the Sun, in this
maineth obtenebrated, and that cometh to be luminous, which in
1the firſt was tenebrous: whereupon that which happened before
concerning the differences of dayes and nights, touching the
dayes being greater or leſſer than the nights, now falls out quite
contrary. And firſt, we ſee, that whereas in the firſt Figure the
circle I K was wholly in the light, it is now wholly in the dark;
and the oppoſite arch L M is now wholly in the light, which
was before wholly in the dark. Of the parallels between the
grand circle C D, and the Pole A, the ſemidiurnal arches are now
leſſer than the ſeminocturnal, which before were the contrary.
Of the others likewiſe towards the Pole B, the ſemidiurnal
es are now bigger than the ſeminocturnal, the contrary to what
happened in the other poſition of the Earth. We now ſee the
Sun made vertical to the inhabitants of the Tropick G N, and to
be depreſſed towards the South, with thoſe of the Parallel E F,
by all the arch E C G, that is, 47 degrees; and in ſumme, to have
paſſed from one to the other Tropick, traverſing the Equinoctial,
elevating and declining in the Meridians the ſaid ſpace of 47
grees. And all this mutation is derived not from the inclination
or elevation of the Earth, but on the contrary, from its not
clining or elevating at all; and in a word, by continuing always
in the ſame poſition, in reſpect of the Univerſe, onely with
ing about the Sun ſituate iu the midſt of the ſaid plane, in which
it moveth it ſelf about circularly with its annual motion. And

here is to be noted an admirable accident, which is, that like as
the Axis of the Earth conſerving the ſame direction towards the
Univerſe, or we may ſay, towards the higheſt Sphere of the fixed
ſtars, cauſeth the Sun to appear to elevate and incline ſo great a
ſpace, namely, for 47 degrees, and the fixed Stars to incline or
levate nothing at all; ſo, on the contrary, if the ſame Axis of
the Earth ſhould maintain it ſelf continually in the ſame
tion towards the Sun, or, if you will, towards the Axis of the
Zodiack, no mutation would appear to be made in the Sun about
its elevating or declining, whereupon the inhabitants of one and
the ſame place would alwayes have one and the ſame difference
of dayes and nights, and one and the ſame conſtitution of
ſons, that is, ſome alwayes Winter, others alwayes Summer,
others Spring, &c. but, on the contrary, the alterations in the
fixed Stars would appear very great, as touching their elevation,
and inclination to us, which would amount to the ſame 47
grees. For the underſtanding of which let us return to conſider
the poſition of the Earth, in its firſt Figure, where we ſee the
Axis A B, with the ſuperiour Pole A, to incline towards the Sun;
but in its third Figure, the ſame Axis having kept the ſame
ction towards the higheſt Sphere, by keeping parallel to it ſelf,
inclines no longer towards the Sun with its ſuperiour Pole A, but
1on the contrary reclines from its former poſition gr. 47. and
clineth towards the oppoſite part, ſo that to reſtore the ſame
clination of the ſaid Pole A towards the Sun, it would be
ſite by turning round the Terreſtrial Globe, according to the
circumference A C B D, to tranſport it towards E thoſe ſame
gr. 47. and for ſo many degrees, any whatſoever fixed ſtar
ſerved in the Meridian, would appear to be elevated, or inclined.
Let us come now to the explanation of that which remains, and
let us conſider the Earth placed in the fourth Figure, that is,
with its centre in the firſt point of Libra; upon which the Sun
will appear in the beginning of Aries. And becauſe the Axis of
21[Figure 21]
the Earth, which in the firſt Figure is ſuppoſed to be inclined
on the diameter Capricorn Cancer, and therefore to be in that
ſame plane, which cutting the plane of the grand Orb,
ding to the line Capricorn Cancer, was erected perpendicularly
upon the ſame, tranſpoſed into the fourth Figure, and
ned, as hath alwayes been ſaid, parallel to it ſelf, it ſhall come
to be in a plane in like manner erected to the ſuperficies of
the Grand Orbe, and parallel to the plane, which at right
angles cuts the ſame ſuperficies, according to the diameter
pricorn Cancer. And therefore the line which goeth from
the centre of the Sunne to the centre of the Earth, that is,
O Libra, ſhall be perpendicular to the Axis BA: but the
ſame line which goeth from the centre of the Sunne to the
centre of the Earth, is alſo alwayes perpendicular to the
1circle that is the Terminator of the light; therefore this ſame
circle ſhall paſſe by the Poles A B in the fourth figure, and
in its plain the Axis A B ſhall fall, but the greateſt circle paſſing
by the Poles of the Parallels, divideth them all in equal parts;
therefore the arches I K, E F, C D, G N, L M, ſhall be all
ſemicircles, and the illumin'd Hemiſphere ſhall be this which
looketh towards us, and the Sun, and the Terminator of the
light ſhall be one and the ſame circle A C B D, and the Earth
being in this place ſhall make it Equinoctial to all its Inhabitants.
And the ſame happeneth in the ſecond figure, where the Earth
having its illuminated Hemiſphere towards the Sun, ſheweth us
the other that is obſcure, with its nocturnal arches, which in
like manner are all ſemicircles, and conſequently, here alſo it
maketh the Equinoctial. And laſtly in regard that the line
duced from the centre of the Sun to the centre of the Earth, is
perpendicular to the Axis A B, to which the greateſt circle of
the parallels C D, is likewiſe erect, the ſaid line O Libra ſhall
paſſe of neceſſity by the ſame Plain of the parallel C D, cutting
its circumference in the midſt of the diurnal arch C D; and
therefore the Snn ſhall be vertical to any one that ſhall ſtand
where that interſection is made; but all the Inhabitants of that
Parallel ſhall paſſe the ſame, as being carried about by the
Earths diurnal converſion; therefore all theſ upon that day
ſhall have the Meridian Sun in their vertex. And the Sun at the
ſame time to all the Inhabitants of the Earth ſhall ſeem to
ſcribe the Grand Parallel called the Equinoctial. Furthermore,
foraſmuch as the Earth being in both the Solſtitial points of the
Polar circles I K and L M, the one is wholly in the light, and
the other wholly in the dark; but when the Earth is in the
noctial points, the halves of thoſe ſame polar circles are in the
light, the remainder of them being in the dark; it ſhould not
be hard to underſtand, how that the Earth v. gr. from Cancer
(where the parallel I K is wholly in the dark) to Leo, one part of
the parallel towards the point I, beginneth to enter into the light,
and that the Terminator of the light I M beginneth to retreat
wards the Pole AB, interſecting the circle ACBD nolonger in IM,
but in two other points falling between the terms I A and MB, of
the arches IA and M B; whereupon the Inhabitants of the circle
begin to enjoy the light, and the other Inhabitants of the circle
L M to partake of night. And thus you ſee that by two ſimple
motions made in times proportionate to their bigneſſes, and not
contrary to one another, but performed, as all others that
long to moveable mundane bodies, from Weſt to Eaſt aſſigned
to the Terreſtrial Globe, adequate reaſons are rendred of all
thoſe Phænomena or appearances, for the accommodating of
1which to the ſtability of the Earth it is neceſſary (forſaking that
Symetry which is obſerved to be between the velocities and
nitudes of moveables) to aſcribe to a Sphere, vaſt above all
others, an unconceiveable celerity, whilſt the other leſſer
Spheres move extream ſlowly; and which is more, to make that
motion contrary to all their motions; and, yet again to adde to
the improbability, to make that ſuperiour Sphere forcibly to
tranſport all the inferionr ones along with it contrary to their
proper inclination. And here I refer it to your judgment to
termine which of the two is the moſt probable.
The Suns
nual motion, how
it comes to paſſe,
according to
pernicus.
An admirable
accident depending
on the not inclining
of the Earths axis
SAGR. To me, as far as concerneth ſenſe, there appeareth
no ſmall difference betwixt the ſimplicity and facility of
ting effects by the means aſſigned in this new conſtitution, and
the multiplicity, conſufion, and difficulty, that is found in the
ancient and commonly received Hypotheſis. For if the Univerſe
were diſpoſed according to this multiplicity, it would be
ceſſary to renounce many Maximes in Philoſophy commonly

ceived by Philoſophers, as for inſtance, That Nature doth
not multiply things without neceſſity; and, That She makes uſe
of the moſt facile and ſimple means in producing her effects;
and, That She doth nothing in vain, and the like. I do confeſſe
that I never heard any thing more admirable than this, nor can I
believe that Humane Underſtanding ever penetrated a more
ſublime ſpeculation. I know not what Simplicius may think
of it.
Axiomes
monly admitted by
all Philoſophers.
SIMP. Theſe (if I may ſpeak my judgment freely) do ſeem

to me ſome of thoſe Geometrical ſubtilties which Ariſtotle finds
fault with in Plato, when he accuſeth him that by his too
much ſtudying of Geometry he forſook ſolid Philoſophy; and I
have known and heard very great Peripatetick Philoſophers to
diſſwade their Scholars from the Study of the Mathematicks, as
thoſe that render the wit cavilous, and unable to philoſophate
well; an Inſtitute diametrically contrary to that of Plato, who
admitted uone to Philoſophy, unleſſe he was firſt well entered in
Geometry.
Ariſtotle
eth Plato for being
too ſtudious of
ometry.
SALV. I commend the policy of theſe your Peripateticks, in

dehorting their Diſciples from the Study of Geometry, for that
there is no art more commodious for detecting their fallacies; but
ſee how they differ from the Mathematical Philoſophers, who
much more willingly converſe with thoſe that are well verſt in
the commune Peripatetick Philoſophy, than with thoſe that are
deſtitute of that knowledg, who for want thereof cannot
ſtinguiſh between doctrine and doctrine. But paſſing by this, tell
me I beſeech you, what are thoſe extravagancies and thoſe too
affected ſubtilties that make you think this Copernican Syſteme
the leſſe plauſible?
1
Peripatetick
loſophers condemn
the Study of
metry, and why.
SIMP. To tell you true, I do not very well know; perhaps,
becauſe I have not ſo much as learnt the reaſons that are by
my produced, of thoſe effects, I mean of thoſe ſtations,
dations, acceſſions, receſſions of the Planets; lengthenings and
ſhortnings of dayes, changes of ſeaſons, &c. But omitting the
conſequences that depend on the firſt ſuppoſitions, I find in the
ſuppoſitions themſelves no ſmall difficulties; which ſuppoſitions,
if once they be overthrown, they draw along with them the ruine
of the whole fabrick. Now foraſmuch as becauſe the whole
module of Copernicus ſeemeth in my opinion to be built upon
firm foundations, in that it relyeth upon the mobility of the earth,
if this ſhould happen to be diſproved, there would be no need of
farther diſpute. And to diſprove this, the Axiom of Ariſtotle
is in my judgment moſt ſufficient, That of one ſimple body,
one ſole ſimple motion can be natural: but here in this caſe, to

the Earth, a ſimple body, there are aſſigned 3. if not 4. motions,
and all very different from each other. For beſides the light
motion, as a grave body towards its centre, which cannot be
nied it, there is aſſigned to it a circular motion in a great circle
about the Sun in a year, and a vertiginous converſion about its
own centre in twenty four hours. And that in the next place
which is more exorbitant, & which happly for that reaſon you paſs
over in ſilence, there is aſcribed to it another revolution about
its own centre, contrary to the former of twenty four hours,
and which finiſheth its period in a year. In this my
ing apprehendeth a very great
Four ſeveral
motions aſſigned to
the Earth.
The motion of
deſcent belongs not
to the terreſtrial
Globe, but to its
parts.
SALV. As to the motion of deſcent, it hath already been
cluded not to belong to the Terreſtrial Globe which did never
move with any ſuch motion, nor never ſhall do; but is (if there be
ſuch a thing) that propenſion of its parts to reunite themſelves
to their whole. As, in the next place, to the Annual motion,

and the Diurnal, theſe being both made towards one way, are
very compatible, in the ſame manner juſt as if we ſhould let a
Ball trundle downwards upon a declining ſuperficies, it would in
its deſcent along the ſame ſpontaneouſly revolve in it ſelf. As
to the third motion aſſigned it by Copernicus, namely about it
ſelf in a year, onely to keep its Axis inclined and directed
towards the ſame part of the Firmament, I will tell you a thing
worthy of great conſideration: namely ut tantum abeſt (although
it be made contrary to the other annual) it is ſo far from having
any repugnance or difficulty in it, that naturally and without any

moving cauſe, it agreeth to any whatſoever ſuſpended and
ted body, which if it ſhall be carried round in the circumference
of a circle, immediate of it ſelf, it acquireth a converſion about
its own centre, contrary to that which carrieth it about, and of
1ſuch velocity, that they both finiſh one revolution in the ſame
time preciſely. You may ſee this admirable, and to our

poſe accommodate experience, if putting in a Baſon of water a
Ball that will ſwim; and holding the Baſon in your hand, you
turn round upon your toe, for you ſhall immediatly ſee the Ball
begin to revolve in it ſelf with a motion, contrary to that of the
Baſon, and it ſhall finiſh its revolution, when that of the Baſon it
ſhall finiſh. Now what other is the Earth than a penſil Globe
librated in tenuous and yielding aire, which being carried
bout in a year along the circumference of a great circle, muſt

needs acquire, without any other mover, a revolution about its
own centre, annual, and yet contrary to the other motion in like
manner annual? You ſhall ſee this effect I ſay, but if afterwards
you more narrowly conſider it, you ſhall find this to be no real
thing, but a meer appearance; and that which you think to be
a revolution in it ſelf, you will find to be a not moving at all,
but a continuing altogether immoveable in reſpect of all that
which without you, and without the veſſel is immoveable: for if in
that Ball you ſhall make ſome mark, and conſider to what part of
the Room where you are, or of the Field, or of Heaven it is
ſituate, you ſhall ſee that mark in yours, and the veſſels
tion to look alwayes towards that ſame part; but comparing it to
the veſſel and to your ſelf that are moveable, it will appear to go
altering its direction, and with a motion contrary to yours, and
that of the veſſel, to go ſeeking all the points of its
tion; ſo that with more reaſon you and the baſon may be ſaid
to turn round the immoveable Ball, than that it moveth round
in the baſon. In the ſame manner the Earth ſuſpended and
brated in the circumference of the Grand Orbe, and ſcituate in
ſuch ſort that one of its notes, as for example, its North Pole,
keth towards ſuch a Star or other part of the Firmament, it always
keepeth directed towards the ſame, although carried round by
the annual motion about the circumference of the ſaid Grand
Orbe. This alone is ſufficient to make the Wonder ceaſe, and
to remove all difficulties. But what will Simplicius ſay, if to
this non-indigence of the co-operating cauſe we ſhould adde
an admirable intrinſick vertue of the Terreſtrial Globe, of

ing with its determinate parts towards determinate parts of the
Firmament, I ſpeak of the Magnetick vertue conſtantly
pated by any whatſoever piece of Loade-ſtone. And if every
minute particle of that S one have in it ſuch a vertue, who will

queſtion but that the ſame more powerfully reſides in this whole
Terreſtrial Globe, abounding in that Magnetick matter, and
which happily it ſelf, as to its internal and primary ſubſtance, is
nothing elſe but a huge maſſe of Loade-ſtone.
1
The annual and
diurnal motion are
compatible in the
Earth.
Every penſil and
librated, body
ryed round in the
circumference of a
circle, acquireth of
it ſelf a motion in
it ſelf contrary to
that.
An Experiment
which ſenſibly
ſhews that two
trary motions may
naturally agree
the ſame
able.
The third motion
aſcribed to the
Earth is rather
reſting
able.
An admirable
intern vertœe of the
terreſtrial Globe of
alwayes beholding
the ſame part of
Heaven.
The terreſtriæl
Globe made of
Loade-ſtone.
SIMP. Then you are one of thoſe it ſeems that hold the

netick Phyloſophy William ^{*} Gilbert.
An eminent
Doctor of Phyſick,
our Countreyman,
born at Coloheſter,
and famous for this
his learned
tiſe, publiſhed
bout 60 years ſince
at London, The
Magnetick
loſophy of William
Gilbert.
SALV. I am for certain, and think that all thoſe that have
ſeriouſly read his Book, and tried his experiments, will bear me
company therein; nor ſhould I deſpair, that what hath befallen
me in this caſe, might poſſibly happen to you alſo, if ſo be a
rioſity, like to mine, and a notice that infinite things in Nature
are ſtill conceal'd from the wits of mankind, by delivering you
from being captivated by this or that particular writer in natural
things, ſhould but ſlacken the reines of your Reaſon, and
lifie the contumacy and tenaceouſneſſe of your ſenſe; ſo as that
they would not refuſe to hearken ſometimes to novelties never

before ſpoken of. But (permit me to uſe this phraſe) the
nimity of vulgar Wits is come to that paſſe, that not only like
blind men, they make a gift, nay tribute of their own aſſent to
whatſoever they find written by thoſe Authours, which in the
infancy of their Studies were laid before them, as authentick by
their Tutors, but refuſe to hear (not to ſay examine) any new
Propoſition or Probleme, although it not only never hath been
confuted, but not ſo much as examined or conſidered by their
Authours. Amongſt which, one is this, of inveſtigating what is
the true, proper, primary, interne, and general matter and
ſtance of this our Terreſtrial Globe; For although it never came
into the mind either of Ariſtotle, or of any one elſe, before
liam Gilbert to think that it might be a Magnet, ſo far are
ſtotle and the reſt from confuting this opinion, yet nevertheleſſe
I have met with many, that at the very firſt mention of it, as a
Horſe at his own ſhadow, have ſtart back, and refuſed to
courſe thereof, and cenſured the conceipt for a vain Chymæra,
yea, for a ſolemn madneſſe: and its poſſible the Book of Gilbert
had never come to my hands, if a Peripatetick Philoſopher, of great
fame, as I believe, to free his Library from its contagion, had not
given it me.
The
mity of Popular
Wits.
SIMP. I, who ingenuouſly confeſſe my ſelf to be one of
thoſe vulgar Wits, and never till within theſe few dayes that I
have been admitted to a ſhare in your conferences, could I
tend to have in the leaſt withdrawn from thoſe trite and
lar paths, yet, for all that, I think I have advantaged my ſelf ſo
much, as that I could without much trouble or difficulty, maſter
the roughneſſes of theſe novel and fantaſtical opinions.
SALV. If that which Gilbert writeth be true, then is it no
pinion, but the ſubject of Science; nor is it new, but as antient
as the Earth it ſelf; nor can it (being true) be rugged or
cult, but plain and eaſie; and when you pleaſe I ſhall make you
feel the ſame in your hand, for that you of your ſelf fancy it to
1be a Ghoſt, and ſtand in fear of that which hath nothing in it of
dreadfull, like as a little child doth fear the Hobgoblin, without
knowing any more of it, ſave the name; as that which beſides
the name is nothing.
SIMP. I ſhould be glad to be informed, and reclaimed from
an errour.
SALV. Anſwer me then to the queſtions that I ſhall ask you.
And firſt of all, Tell me whether you believe, that this our Globe,
which we inhabit and call Earth, conſiſteth of one ſole and
ple matter, or elſe that it is an aggregate of matters different
from each other.
SIMP. I ſee it to be compoſed of ſubſtances and bodies very

different; and firſt, for the greateſt parts of the compoſition,
I ſee the Water and the Earth, which extreamly differ from one
another.
The Terreſtrial
Globe compoſed of
ſundry matters.
SAIV. Let us, for this once, lay aſide the Seas and other
ters, and let us conſider the ſolid parts, and tell me, if you think
them one and the ſame thing, or elſe different.
SIMP. As to appearance, I ſee that they are different things,
there being very great heaps of unfruitful ſands, and others of
fruitful ſoiles; There are infinite ſharp and ſteril mountains, full
of hard ſtones and quarries of ſeveral kinds, as Porphyre,
blaſter, Jaſper, and a thouſand other kinds of Marbles: There
are vaſt Minerals of ſo many kinds of metals; and in a word,
ſuch varieties of matters, that a whole day would not ſuffice
ly to enumerate them.
SALV. Now of all theſe different matters, do you think,
that in the compoſition of this grand maſſe, there do concur
tions, or elſe that amongſt them all there is one part that far
ceeds the reſt, and is as it were the matter and ſubſtance of the
immenſe lump?
SIMP. I believe that the Stones, Marbles, Metals, Gems, and
the ſo many other ſeveral matters are as it were Jewels, and
teriour and ſuperficial Ornaments of the primary Globe, which
in groſſe, as I believe, doth without compare exceed all theſe
things put together.
SALV. And this principal and vaſt maſſe, of which thoſe
things above named are as it were excreſſences and ornaments, of
what matter do you think that it is compoſed?
SIMP. I think that it is the ſimple, or leſſe impure element of
Earth.
SALV. But what do you underſtand by Earth? Is it haply
that which is diſperſed all over the fields, which is broke up with
Mattocks and Ploughs, wherein we ſowe corne, and plant fruits,
and in which great boſcages grow up, without the help of
1ture, and which is, in a word, the habitation of all animals, and
the womb of all vegetables?
SIMP. Tis this that I would affirm to be the ſubſtance of this
our Globe.
SALV. But in this you do, in my judgment, affirm that which
is not right: for this Earth which is broke up, is ſowed, and is
fertile, is but one part, and that very ſmall of the ſurface of the
Globe, which doth not go very deep, yea, its depth is very ſmall,
in compariſon of the diſtance to the centre: and experience
ſheweth us, that one ſhall not dig very low, but one ſhall finde
matters very different from this exteriour ſcurf, more ſolid, and
not good for the production of vegetables. Beſides the interne
parts, as being compreſſed by very huge weights that lie upon
them, are, in all probability, ſlived, and made as hard as any
hard rock. One may adde to this, that fecundity would be in
vain conferred upon thoſe matters which never were deſigned to
bear fruit, but to reſt eternally buried in the profound and dark
abyſſes of the Earth.
SIMP. But who ſhall aſſure us, that the parts more inward
and near to the centre are unfruitful? They alſo may, perhaps,
have their productions of things unknown to us?
SALV. You may aſwell be aſſured thereof, as any man elſe,
as being very capable to comprehend, that if the integral bodies
of the Univerſe be produced onely for the benefit of Mankind,
this above all the reſt ought to be deſtin d to the ſole
ces of us its inhabitants. But what beneſit can we draw from
matters ſo hid and remote from us, as that we ſhall never be

ble to make uſe of them? Therefore the interne ſubſtance of
this our Globe cannot be a matter frangible, diſſipable, and
coherent, like this ſuperficial part which we call ^{*} EARTH: but

it muſt, of neceſſity, be a moſt denſe and ſolid body, and in a
word, a moſt hard ſtone. And, if it ought to be ſo, what reaſon
is there that ſhould make you more ſcrupulous to believe that it
is a Loadſtone than a Porphiry, a Jaſper, or other hard
ble? Happily if Gilbert had written, that this Globe is all

pounded within of ^{*} Pietra Serena, or of Chalcedon, the paradox
would have ſeemed to you leſſe exorbitant?
The interne parts
of the terreſtrial
Globe muſt of
ceſſity be ſolid.
* Or MOULD.
Of which with
the Latin
tour, I muſt once
more profeſſe my
ſelf ignorant.
SIMP. That the parts of this Globe more intern are more
compreſſed, and ſo more ſlived together and ſolid, and more
and more ſo, according as they lie lower, I do grant, and ſo
likewiſe doth Ariſtotle, but that they degenerate and become
other than Earth, of the ſame ſort with this of the ſuperficial
parts, I ſee nothing that obliege h me to believe.
SALV. I undertook not this diſcourſe with an intent to prove
demonſtratively that the primary and real ſubſtance of this our
1Globe is Load-ſtone; but onely to ſhew that no reaſon could be
given why one ſhould be more unwilling to grant that it is of
Load-ſtone, than of ſome other matter. And if you will but

ſeriouſly conſider, you ſhall find that it is not improbable, that
one ſole, pure, and arbitrary name, hath moved men to think
that it conſiſts of Earth; and that is their having made uſe
monly from the beginning of this word Earth, as well to
ſie that matter which is plowed and ſowed, as to name this our
Globe. The denomination of which if it had been taken from
ſtone, as that it might as well have been taken from that as
from the Earth; the ſaying that its primary ſubſtance was ſtone,
would doubtleſſe have found no ſcruple or oppoſition in any
man. And is ſo much the more probable, in that I verily
lieve, that if one could but pare off the ſcurf of this great Globe,
taking away but one full thouſand or two thouſand yards; and
afterwards ſeperate the Stones from the Earth, the
on of the ſtones would be very much biger than that of the
tile Mould. But as for the reaſons which concludently prove de
facto, that is our Globe is a Magnet, I have mentioned none of
them, nor is this a time to alledg them, and the rather, for that
to your benefit you may read them in Gilbert; onely to
rage you to the peruſal of them, I will ſet before you, in a

litude of my own, the method that he obſerved in his
phy. I know you underſtand very well how much the
ledg of the accidents is ſubſervient to the inveſtigation of the
ſubſtance and eſſence of things; therefore I deſire that you
would take pains to informe your ſelf well of many accidents and
properties that are found in the Magnet, and in no other ſtone,

or body; as for inſtance of attracting Iron, of conferring
on it by its ſole preſence the ſame virtue, of communicating
likewiſe to it the property of looking towards the Poles, as it
alſo doth it ſelf; and moreover endeavour to know by trial,
that it containeth in it a virtue of conferring upon the magnetick
needle not onely the direction under a Meridian towards the
Poles, with an Horizontal motion, (a property a long time ago
known) but a new found accident, of declining (being ballanced
under the Meridian before marked upon a little ſpherical
net) of declining I ſay to determinate marks more or leſſe,
cording as that needle is held nearer or farther from the Pole,
till that upon the Pole it ſelf it erecteth perpendicularly,
as in the middle parts it is parallel to the Axis. Furthermore
cure a proof to be made, whether the virtue of attracting Iron,
reſiding much more vigorouſly about the Poles, than about the
middle parts, this force be not notably more vigorous in one
Pole than in the other, and that in all pieces of Magnet; the
1ſtronger of which Poles is that which looketh towards the South.
Obſerve, in the next place, that in a little Magnet this South and
more vigorous Pole, becometh weaker, when ever it is to take
up an iron in preſence of the North Pole, of another much
ger Magnet: and not to make any tedious diſcourſe of it,
tain your ſelf, by experience, of theſe and many other properties
deſcribed by Gilbert, which are all ſo peculiar to the Magnet, as

that none of them agree with any other matter. Tell me now,
Simplicius, if there were laid before you a thouſand pieces of
ſeveral matters, but all covered and concealed in a cloth, under
which it is hid, and you were required, without uncovering them,
to make a gueſſe, by external ſignes, at the matter of each of
them, and that in making trial, you ſhould hit upon one that
ſhould openly ſhew it ſelf to have all the properties by you
dy acknowledged to reſide onely in the Magnet, and in no other
matter, what judgment would you make of the eſſence of ſuch a
body? Would you ſay, that it might be a piece of Ebony, or
Alablaſter, or Tin.
Our Globe would
have been called
ſtone, in ſtead of
Earth, if that
name had been
uen it in the
ginning.
The method of
Gilbert in his
loſophy.
Many
ties in the
net.
An Argument
proving the
ſtrial Globe to be
a Magnet.
SIMP. I would ſay, without the leaſt hæſitation, that it was a
piece of Load-ſtone.
SALV. If it be ſo, ſay reſolutely, that under this cover and
ſcurf of Earth, ſtones, metals, water, &c. there is hid a great
Magnet, foraſmuch as about the ſame there may be ſeen by any
one that will heedfully obſerve the ſame, all thoſe very accidents
that agree with a true and viſible Globe of Magnet; but if no
more were to be ſeen than that of the Declinatory Needle, which
being carried about the Earth, more and more inclineth, as it
proacheth to the North Pole, and declineth leſſe towards the
quinoctial, under which it finally is brought to an Æquilibrium,
it might ſerve to perſwade even the moſt ſcrupulous judgment. I
forbear to mention that other admirable effect, which is ſenſibly
obſerved in every piece of Magnet, of which, to us inhabitants
of the Northern Hemiſphere, the Meridional Pole of the ſaid
net is more vigorous than the other; and the difference is found
greater, by how much one recedeth from the Equinoctial; and
under the Equinoctial both the parts are of equal ſtrength, but
notably weaker. But, in the Meridional Regions, far diſtant
from the Equinoctial, it changeth nature, and that part which to
us was more weak, acquireth more ſtrength than the other: and
all this I confer with that which we ſee to be done by a ſmall
piece of Magnet, in the preſence of a great one, the vertue of
which ſuperating the leſſer, maketh it to become obedient to it,
and according as it is held, either on this or on that ſide the
noctial of the great one, maketh the ſelf ſame mutations,
which I have ſaid are made by every Magnet, carried on this
1ſide, or that ſide of the Equinoctiall of the Earth.
SAGR. I was perſwaded, at the very firſt reading of the Book
of Gilbertus; and having met with a moſt excellent piece of

Magnet, I, for a long time, made many Obſervations, and all
worthy of extream wonder; but above all, that ſeemeth to me
very ſtupendious of increaſing the faculty of taking up Iron ſo
much by arming it, like as the ſaid Authour teacheth; and with
arming that piece of mine, I multiplied its force in octuple
tion; and whereas unarmed it ſcarce took up nine ounces of
Iron, it being armed did take up above ſix pounds: And, it
may be, you have ſeen this Loadſtone in the ^{*} Gallery of your

Moſt Serene Grand Duke (to whom I preſented it) upholding
two little Anchors of Iron.
|The Magnet
armed takes up
much more Iron,
than when
med.
+ Or Cloſet of
rarities.
SALV. I ſaw it many times, and with great admiration, till
that a little piece of the like ſtone gave me greater cauſe of
der, that is in the keeping of our Academick, which being no
more than of ſix ounces weight, and ſuſtaining, when unarmed,
hardly two ounces, doth, when armed, take up 160. ounces, ſo
as that it is of 80. times more force armed than unarmed, and
takes up a weight 26. times greater than its own; a much greater
wonder than Gilbert could ever meet with, who writeth, that he
could never get any Loadſtone that could reach to take up four
times its own weight.
SAGR. In my opinion, this Stone offers to the wit of man a
large Field to Phyloſophate in; and I have many times thought
with my ſelf, how it can be that it conferreth on that Iron, which
armeth it, a ſtrength ſo ſuperiour to its own; and finally, I finde
nothing that giveth me ſatisfaction herein; nor do I find any
thing extraordinary in that which Gilbert writes about this
cular; I know not whether the ſame may have befallen
you.
SALV. I extreamly praiſe, admire, and envy this Authour,
for that a conceit ſo ſtupendious ſhould come into his minde,
touching a thing handled by infinite ſublime wits, and hit upon
by none of them: I think him moreover worthy of
nary applauſe for the many new and true Obſervations that he
made, to the diſgrace of ſo many fabulous Authours, that write
not only what they do not know, but what ever they hear
ken by the fooliſh vulgar, never ſeeking to aſſure themſelves of
the ſame by experience, perhaps, becauſe they are unwilling to
diminiſh the bulk of their Books. That which I could have
ſired in Gilbert, is, that he had been a little greater
an, and particularly well grounded in Geometry, the practice
whereof would have rendered him leſs reſolute in accepting thoſe
reaſons for true Demonſtrations, which he produceth for true
1cauſes of the true concluſions obſerved by himſelf. Which
ſons (freely ſpeaking) do not knit and bind ſo faſt, as thoſe
doubtedly ought to do, in that of natural, neceſſary, and laſting
concluſions may be alledged. And I doubt not, but that in
ceſſe of time this new Science will be perfected with new
vations, and, which is more, with true and neceſſary

tions. Nor ought the glory of the firſt Inventor to be thereby
diminiſhed, nor do I leſſe eſteem, but rather more admire, the
Inventor of the Harp (although it may be ſuppoſed that the
ſtrument at firſt was but rudely framed, and more rudely
ed) than an hundred other Artiſts, that in the inſuing Ages
ced that profeſſion to great perfection. And methinks, that
tiquity had very good reaſon to enumerate the firſt Inventors of
the Noble Arts amongſt the Gods; ſeeing that the common wits
have ſo little curioſity, and are ſo little regardful of rare and
gant things, that though they ſee and hear them exercirated by
the exquifite profeſſors of them, yet are they not thereby
ſwaded to a deſire of learning them. Now judge, whether
cities of this kind would ever have attempted to have found out
the making of the Harp, or the invention of Muſick, upon the
hint of the whiſtling noiſe of the dry ſinews of a Tortois, or
from the ſtriking of four Hammers. The application to great
inventions moved by ſmall hints, and the thinking that under a
primary and childiſh appearance admirable Arts may lie hid, is
not the part of a trivial, but of a ſuper-humane ſpirit. Now
ſwering to your demands, I ſay, that I alſo have long thought
upon what might poſſibly be the cauſe of this ſo tenacious and
potent union, that we ſee to be made between the one Iron that
armeth the Magnet, and the other that conjoyns it ſelf unto it.

And firſt, we are certain, that the vertue and ſtrength of the ſtone
doth not augment by being armed, for it neither attracts at
greater diſtance, nor doth it hold an Iron the faſter, if between it,
and the arming or cap, a very fine paper, or a leaf of beaten gold,
be interpoſed; nay, with that interpoſition, the naked ſtone
takes up more Iron than the armed. There is therefore no
ration in the vertue, and yet there is an innovation in the effect.

And becauſe its neceſſary, that a new effect have a new cauſe, if
it be inquired what novelty is introduced in the act of taking up
with the cap or arming, there is no mutation to be diſcovered, but
in the different contact; for whereas before Iron toucht
ſtone, now Iron toucheth Iron. Therefore it is neceſſary to
clude, that the diverſity of contacts is the cauſe of the diverſity

of effects. And for the difference of contacts it cannot, as I ſee,
be derived from any thing elſe, ſave from that the ſubſtance of
the Iron is of parts more ſubtil, more pure, and more
1ed than thoſe of the Magnet, which are more groſſe, impure, and
rare. From whence it followeth, that the ſuperficies of two
rons that are to touch, by being exquiſitely plained, filed, and
burniſhed, do ſo exactly conjoyn, that all the infinite points of
the one meet with the infinite points of the other; ſo that the
filaments, if I may ſo ſay, that collegate the two Irons, are many
more than thoſe that collegate the Magnet to the Iron, by reaſon
that the ſubſtance of the Magnet is more porous, and leſſe
pact, which maketh that all the points and filaments of the
ſtone do not cloſe with that which it unites unto. In the next
place, that the ſubſtance of Iron (eſpecially the well refined, as
namely, the pureſt ſteel) is of parts much more denſe, ſubtil,
and pure than the matter of the Loadſtone, is ſeen, in that one
may bring its edge to an extraordinary ſharpneſſe, ſuch as is that
of the Raſor, which can never be in any great meaſure effected in
a piece of Magnet. Then, as for the impurity of the Magnet, and

its being mixed with other qualities of ſtone, it is firſt ſenſibly
diſcovered by the colour of ſome little ſpots, for the moſt part
white; and next by preſenting a needle to it, hanging in a
thread, which upon thoſe ſtonyneſſes cannot find repoſe, but
being attracted by the parts circumfuſed, ſeemeth to fly from

^{*} thoſe, and to leap upon the Magnet contiguous to them: and
as ſome of thoſe Heterogeneal parts are for their magnitude
ry viſible, ſo we may believe, that there are others, in great
bundance, which, for their ſmallneſſe, are imperceptible, that are
diſſeminated throughout the whole maſſe. That which I ſay,
(namely, that the multitude of contacts that are made between
Iron and Iron, is the cauſe of the ſo ſolid conjunction) is
firmed by an experiment, which is this, that if we preſent the
ſharpned point of a needle to the cap of a Magnet, it will ſtick
no faſter to it, than to the ſame ſtone unarmed: which can
proceed from no other cauſe, than from the equality of the
tacts that are both of one ſole point. But what then? Let a
^{*} Needle be taken and placed upon a Magnet, ſo that one of its

extremities hang ſomewhat over, and to that preſent a Nail; to
which the Needle will inſtantly cleave, inſomuch that
ing the Nail, the Needle will ſtand in ſuſpenſe, and with its two
ends touching the Magnet and the Iron; and withdrawing the
Nail yet a little further, the Needle will forſake the Magnet;
provided that the eye of the Needle be towards the Nail, and
the point towards the Magnet; but if the eye be towards the
Loadſtone, in withdrawing the Nail the Needle will cleave to
the Magnet; and this, in my judgment, for no other reaſon,
ſave onely that the Needle, by reaſon it is bigger towards the
eye, toucheth in much more points than its ſharp point doth.
1
The firſt
vers and inventers
of things ought to
be admired.
The true cauſe
of the
tion of vertue in
the Magnet, by
means of the
ming.
Of a new effect
its neceſſary that
the cauſe be
wiſe new.
It is proved,
that Iron conſists
of parts more
til, pure, and
pact than the
net.
A ſenſible proof
of the impurity of
the Magnet.
* The
hereby
that the
doth not all
ſiſt of magnetick
matter, but that
the whiter ſpecks
being weak, thoſe
other parts of the
Loadſtone of a
more dark &
ſtant colour,
tain all that vertue
wherewith bodies
are attracted.
* A common
ſewing needle.
SAGR. Your whole diſcourſe hath been in my judgment very
concluding, and this experiment of the Needle hath made me
think it little inferiour to a Mathematical Demonſtration; and
I ingenuouſly confeſſe, that in all the Magnetick Philoſophy, I
never heard or read any thing, that with ſuch ſtrong reaſons
gave account of its ſo many admirable accidents, of which, if the
cauſes were with the ſame perſpicuity laid open, I know not
what ſweeter food our Intellects could deſire.
SALV. In ſeeking the reaſons of concluſions unknown unto
us, it is requiſite to have the good fortune to direct the
courſe from the very beginning towards the way of truth; in
which if any one walk, it will eaſily happen, that one ſhall meet
with ſeveral other Propoſitions known to be true, either by
putes or experiments, from the certainty of which the truth of
ours acquireth ſtrength and evidence; as it did in every reſpect
happen to me in the preſent Probleme, for being deſirous to
ſure my ſelf, by ſome other accident, whether the reaſon of the
Propoſition, by me found, were true; namely, whether the
ſtance of the Magnet were really much leſſe continuate than that
of Iron or of Steel, I made the Artiſts that work in the Gallery
of my Lord the Grand Duke, to ſmooth one ſide of that piece
of Magnet, which formerly was yours, and then to poliſh and
burniſh it; upon which to my ſatisfaction I found what I deſired.
For I diſcovered many ſpecks of colour different from the reſt,
but as ſplendid and bright, as any of the harder ſort of ſtones;
the reſt of the Magnet was polite, but to the tact onely, not
being in the leaſt ſplendid; but rather as if it were ſmeered over
with ſoot; and this was the ſubſtance of the Load ſtone, and
the ſhining part was the fragments of other ſtones intermixt
therewith, as was ſenſibly made known by preſenting the face
thereof to filings of Iron, the which in great number leapt to
the Load-ſtone, but not ſo much as one grain did ſtick to the
ſaid ſpots, which were many, ſome as big as the fourth part of
the nail of a mans finger, others ſomewhat leſſer, the leaſt of
all very many, and thoſe that were ſcarce viſible almoſt
merable. So that I did aſſure my ſelf, that my conjecture was
true, when I firſt thought that the ſubſtance of the Magnet
was not cloſe and compact, but porous, or to ſay better,
gy; but with this difference, that whereas the ſponge in its
cavities and little cels conteineth Air or Water, the Magnet hath
its pores full of hard and heavy ſtone, as appears by the
ſite luſtre which thoſe ſpecks receive. Whereupon, as I have ſaid
from the beginning, applying the ſurface of the Iron to the
perficies of the Magnet the minute particles of the Iron, though
perhaps more continuate than theſe of any other body (as its
1ſhining more than any other matter doth ſhew) do not all, nay
but very few of them incounter pure Magnet; and the contacts
being few, the union is but weak. But becauſe the cap of the
Load-ſtone, beſides the contact of a great part of its ſuperficies,
inveſts its ſelf alſo with the virtue of the parts adjoyning,
though they touch not; that ſide of it being exactly ſmoothed
to which the other face, in like manner well poliſht of the Iron to
be attracted, is applyed, the contact is made by
ble minute particles, if not haply by the infinite points of both
the ſuperficies, whereupon the union becometh very ſtrong.
This obſervation of ſmoothing the ſurfaces of the Irons that are
to touch, came not into the thoughts of Gilbert, for he makes
the Irons convex, ſo that their contact is very ſmall; and
upon it cometh to paſſe that the tenacity, wherewith thoſe Irons
conjoyn, is much leſſer.
SAGR. I am, as I told you before, little leſſe ſatisfied with
this reaſon, that if it were a pure Geometrical Demonſtration;
and becauſe we ſpeak of a Phyſical Problem, I believe that alſo
Simplicius will find himſelf ſatisfied as far as natural ſcience
mits, in which he knows that Geometrical evidence is not to be
required.
SIMP. I think indeed, that Salviatus with a fine

cution hath ſo manifeſtly diſplayed the cauſe of this effect, that
any indifferent wit, though not verſt in the Sciences, may
prehend the ſame; but we, confining our ſelves to the terms of
Art, reduce the cauſe of theſe and other the like natural effects
to Sympathy, which is a certain agreement and mutual appetite
which ariſeth between things that are ſemblable to one another
in qualities; as likewiſe on the contrary that hatred & enmity for
which other things ſhun & abhor one another we call Antipathy.
Sympathy and
Antipathy, terms
uſed by
phers to give a
ſon eaſily of
ny narural effests.
SAGR. And thus with theſe two words men come to render
reaſons of a great number of accidents and effects which we ſee
not without admiration to be produced in nature. But this kind
of philoſophating ſeems to me to have great ſympathy with a

certain way of Painting that a Friend of mine uſed, who writ
upon the Tele or Canvaſſe in chalk, here I will have the
tain with Diana and her Nimphs, there certain Hariers, in this
corner I will have a Huntſ-man with the Head of a Stag, the reſt
ſhall be Lanes, Woods, and Hills; and left the remainder for
the Painter to ſet forth with Colours; and thus he perſwaded
himſelf that he had painted the Story of Acteon, when as he had
contributed thereto nothing of his own more than the names.
But whether are we wandred with ſo long a digreſſion, contrary
to our former reſolutions? I have almoſt forgot what the point
was that we were upon when we fell into this magnetick
1courſe; and yet I had ſomething in my mind that I intended to
have ſpoken upon that ſubject.
A pleaſant
ampleaeclaring the
invalidity of ſome
Phyloſophical
gumentations.
SALV. We were about to demonſtrate that third motion
ſcribed by Copernicus to the Earth to be no motion but a
ſcence and maintaining of it ſelf immutably directed with its
terminate parts towards the ſame & determinate parts of the
verſe, that is a perpetual conſervation of the Axis of its diurnal
revolution parallel to it ſelf, and looking towards ſuch and ſuch
fixed ſtars; which moſt conſtant poſition we ſaid did naturally
agree with every librated body ſuſpended in a fluid and yielding
medium, which although carried about, yet did it not change
rectionin reſpect of things external, but onely ſeemed to revolve in
its ſelf, in reſpect of that which carryed it round, and to the
veſſel in which it was tranſported. And then we added to this
ſimple and natural accident the magnetick virtue, whereby the
ſelf Terreſtrial Globe might ſo much the more conſtantly keep it
immutable, -----
SAGR. Now I remember the whole buſineſſe; and that which
then came into my minde, & which I would have intimated, was a
certain conſideration touching the ſcruple and objection of
plicius, which he propounded againſt the mobility of the Earth,

taken from the multiplicity of motions, impoſſible to be aſſigned
to a ſimple body, of which but one ſole and ſimple motion,
cording to the doctrine of Ariſtotle, can be natural; and that
which I would have propoſed to conſideration, was the Magnet,
to which we manifeſtly ſee three motions naturally to agree:
one towards the centre of the Earth, as a Grave; the ſecond is
the circular Horizontal Motion, whereby it reſtores and
ſerves its Axis towards determinate parts of the Univerſe; and
the third is this, newly diſcovered by Gilbert, of inclining its
Axis, being in the plane of a Meridian towards the ſurface of the
Earth, and this more and leſſe, according as it ſhall be diſtant
from the Equinoctial, under which it is parallel to the Axis of
the Earth. Beſides theſe three, it is not perhaps improbable,
but that it may have a fourth, of revolving upon its own Axis, in
caſe it were librated and ſuſpended in the air or other fluid and
yielding Medium, ſo that all external and accidental impediments
were removed, and this opinion Gilbert himſelf ſeemeth alſo to
applaud. So that, Simplicius, you ſee how tottering the Axiome
of Ariſtotle is.
The ſeveral
tural motions of
the Magnet.
SIMP. This doth uot only not make againſt the Maxime, but
not ſo much as look towards it: for that he ſpeaketh of a fimple
body, and of that which may naturally conſiſt therewith; but
you propoſe that which befalleth a mixt body; nor do you tell
us of any thing that is new to the doctrine of Ariſtotle, for that
1he likewiſe granteth to mixt bodies compound motions by -----
SAGR. Stay a little, Simplicius, & anſwer me to the queſtions
I ſhall ask you. You ſay that the Load-ſtone is no ſimple body,

now I defire you to tell me what thoſe ſimple bodies are, that
mingle in compoſing the Load-ſtone.
Ariſtole grants
a compound motion
to mixt bodies.
SIMP. I know not how to tell you th'ingredients nor ſimples
preciſely, but it ſufficeth that they are things elementary.
SALV. So much ſufficeth me alſo. And of theſe ſimple
mentary bodies, what are the natural motions?
SIMP. They are the two right and ſimple motions, ſurſum
and deorſum.
SAGR. Tell me in the next place? Do you believe that the
motion, that ſhall remain natural to that ſame mixed body, ſhould
be one that may reſult from the compoſition of the two ſimple
natural motions of the ſimple bodies compounding, or that it
may be a motion impoſſible to be compoſed of
The motion of
mixt bodies ought
to be ſuch as may
reſult from the
compoſition of the
motions of the
ple bodies
pounding.
SIMP. I believe that it ſhall move with the motion reſulting
from the compoſition of the motions of the ſimple bodies
pounding, and that with a motion impoſſible to be compoſed of
theſe, it is impoſſible that it ſhould move.
SAGR. But, Simplicius, with two right and ſimple motions, you
ſhall never be able to compoſe a circular motion, ſuch as are the

two, or three circular motions that the magnet hath: you ſee
then into what abſurdities evil grounded Principles, or, to ſay

better, the ill-inferred conſequences of good Principles carry a
man; for you are now forced to ſay, that the Magnet is a
ture compounded of ſubſtances elementary and cœleſtial, if you
will maintain that the ſtraight motion is a peculiar to the
ments, and the circular to the cœleſtial bodies. Therefore if
you will more ſafely argue, you muſt ſay, that of the integral
bodies of the Univerſe, thoſe that are by nature moveable, do all
move circularly, and that therefore the Magnet, as a part of the

true primary, and integral ſubſtance of our Globe, pertaketh of
the ſame qualities with it. And take notice of this your fallacy,
in calling the Magnet a mixt body, and the Terreſtrial Globe a
ſimple body, which is ſenſibly perceived to be a thouſand times
more compound: for, beſides that it containeth an hundred an
hundred matters, exceeding different from one another, it
taineth great abundance of this which you call mixt, I mean
of the Load-ſtone. This ſeems to me juſt as if one ſhould call

bread a mixt body, and ^{*} Pannada a ſimple body, in which there
is put no ſmall quantity of bread, beſides many other things
ble. This ſeemeth to me a very admirable thing, amongſt others
1
of the Peripateticks, who grant (nor can it be denied) that our
Terreſtrial Globe is, de facto, a compound of infinite different
matters; and grant farther that of compound bodies the motion
ought to be compound: now the motions that admit of
ſition are the right and circular: For the two right motions, as
being contrary, are incompatible together, they affirm, that the
pure Element of Earth is no where to be found; they confeſſe,
that it never hath been moved with a local motion; and yet they
will introduce in Nature that body which is not to be found, and
make it move with that motion which it never exerciſed, nor
ver ſhall do, and to that body which hath, and ever had a being,
they deny that motion, which before they granted, ought
rally to agree therewith.
With two right
motions one cannot
compoſe circular
motions.
Philoſophers are
forced to confeſſe
that the Magnet
is compounded of
cœleſtial
ces, and of
tary.
The errour of
thoſe who call the
Magnet a mixt
body, and the
reſtrial Globe
ſimble body.
* Ogliopotrida
a Spaniſh diſh of
many ingredients
boild together.
The Diſcourſes
of Peripateticks,
full of errours and
contradictions.
SALV. I beſeech you, Sagredus, let us not weary our ſelves
any more about theſe particulars, and the rather, becauſe you
know that our purpoſe was not to determine reſolutely, or to
accept for true, this or that opinion, but only to propoſe for our
divertiſement ſuch reaſons, and anſwers as may be alledged on
the one ſide, or on the other; and Simplicius maketh this
ſwer, in defence of his Peripateticks, therefore let us leave the
judgment in ſuſpenſe, and remit the determination into the
hands of ſuch as are more known than we. And becauſe I think
that we have, with ſufficient prolixity, in theſe three dayes,
courſed upon the Syſteme of the Univerſe, it will now be
nable, that we proceed to the grand accident, from whence our
Diſputations took beginning, I mean, of the ebbing and flowing
of the Sea, the cauſe whereof may, in all probability, be referred
to the motion of the Earth. But that, if you ſo pleaſe, we will
reſerve till to morrow. In the mean time, that I may not forget
it, I will ſpeak to one particular, to which I could have wiſhed,
that Gilbert had not lent an ear; I mean that of admitting, that

in caſe a little Sphere of Loadſtone might be exactly librated, it
would revolve in it ſelf; becauſe there is no reaſon why it ſhould
do ſo; For if the whole Terreſtrial Globe hath a natural
ty of revolving about its own centre in twenty four hours, and
that all its parts ought to have the ſame, I mean, that faculty of
turning round together with their whole, about its centre in
ty four hours; they already have the ſame in effect, whilſt that,
being upon the Earth, they turn round along with it: And the
aſſigning them a revolution about their particular centres, would
be to aſcribe unto them a ſecond motion much different from the
firſt; for ſo they would have two, namely, the revolving in
ty four hours about the centre of their whole; and the turning
about their own: now this ſecond is arbitrary, nor is there any
1reaſon for the introducing of it: If by pluoking away a piece
of Loadſtone from the whole natural maſſd, it were deprived of
the faculty of following it, as it did, whilſt it was unitedy thereto,
ſo that it is thereby deprived of the revodution about the
ſal centre of the Terreſtrial Globe, it might Chaply, with
what greater probability be thought by ſome, that the ſaid
net was to appropriate to it ſelf a new converſion about its
cular centre; but if it do no leſſe, when ſeparated, than when
conjoyned, continue always to purſue its firſt, eternal, and
ral courſe, to what purpoſe ſhould we go about to obtrude upon
it another new one?
An
ble effect admired
by Gilbertus in the
Loadſtone.
SAGR. I underſtand you very well, and this puts me in mind
of a Diſcourſe very like to this for the vanity of it, falling from

certain Writers upon the Sphere, and I think, if I well
ber, amongſt others from Sacroboſco, who, to ſhew how the
lement of Water, doth, together with the Earth, make a
pleat Spherical Figure, and ſo between them both compoſe this
our Globe, writeth, that the ſeeing the ſmall ^{*} particles of water
ſhape themſelves into rotundity, as in the drops, and in the dew
daily apparent upon the leaves of ſeveral herbs, is a ſtrong
gument; and becauſe, according to the trite Axiome, there is
the ſame reaſon for the whole, as for the parts, the parts affecting
that ſame figure, it is neceſſary that the ſame is proper to the
whole Element: and truth is, methinks it is a great overſight
that theſe men ſhould not perceive ſo apparent a vanity, and
ſider that if their argument had run right, it would have
ed, that not only the ſmall drops, but that any whatſoever greater
quantity of water ſeparated from the whole Element, ſhould be
duced into a Globe: Which is not ſeen to happen; though indeed
the Senſes may ſee, and the Underſtanding perceive that the
lement of Water loving to form it ſelf into a Spherical Figure
about the common centre of gravity, to which all grave
dies tend (that is, the centre of the Terreſtrial Globe) it
therein is followed by all its parts, according to the Axiome;
ſo that all the ſurfaces of Seas, Lakes, Pools, and in a word,
of all the parts of Waters conteined in veſſels, diſtend
themſelves into a Spherical Figure, but that Figure is an arch
of that Sphere that hath for its centre the centre of the
reſtrial Globe, and do not make particular Spheres of
ſelves.
The vain
mentation of ſome
to prove the
ment of Water to
be of a Spherical
ſuper ficies.
SALV. The errour indeed is childiſh; and if it had
been onely the ſingle miſtake of Sacroboſco, I would eaſily
have allowed him in it; but to pardon it alſo to his
mentators, and to other famous men, and even to Ptolomy
1himſelfe; this I cannot do, without bluſhing for their
tation. But it is high time to take leave, it row being
very late, and we being to meet again to morrow,
at the uſual hour, to bring all the foregoing
Diſcourſes to a final
122[Figure 22]23[Figure 23]24[Figure 24]25[Figure 25]26[Figure 26]27[Figure 27]28[Figure 28]29[Figure 29]
Place this Plate
at the end of
the thirdDialogue
1
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1
GALILÆUS
Gailæus Lyncæus,
HIS
SYSTEME
OF THE
WORLD.
The Fourth Dialogue.
INTERLOCVTORS.
SALVIATUS, SAGREDUS, & SIMPLICIUS.
SAGR. I know not whether your return to our
accuſtomed conferences hath really been
later than uſual, or whether the deſire
of hearing the thoughts of Salviatus,
touching a matter ſo curious, hath
made me think it ſo: But I have
ried a long hour at this window,
cting every moment when the Gondola
would appear that I ſent to fetch you.
SALV. I verily believe that your imagination more than our
tarriance hath prolonged the time: and to make no longer

murre, it would be well, if without interpoſing more words, we
came to the matter it ſelf; and did ſhew, that nature hath
mitted (whether the buſineſs in rei veritate be ſo, or elſe to play
1and ſport with our Fancies) hath, I ſay, hath permitted that the

motions for every other reſpect, except to reſolve the ebbing and
flowing of the Sea, aſſigned long ſince to the earth, ſhould be found
now at laſt to anſwer exactly to the cauſe thereof; and, as it

were, with mutual a emulation, the ſaid ebbing and flowing
to appear in confirmation of the Terreſtrial motion: the judices
whereof have hitherto been taken from the cœleſtial Phænomena,
in regard that of thoſe things that happen on Earth, not any one
was of force to prove one opinion more than another, as we
ready have at large proved, by ſhewing that all the terrene
rences upon which the ſtability of the Earth and mobility of the
Sun and Firmament is commonly inferred, are to ſeem to us
formed in the ſame manner, though we ſuppoſed the mobility of
the Earth, and the immobility of them. The Element of
ter onely, as being moſt vaſt, and which is not annexed and
catenated to the Terreſtrial Globe as all its other ſolid parts are;
yea, rather which by reaſon of its fluidity remaineth apart ſui
juris, and free, is to be ranked amongſt thoſe ſublunary things,
from which we may collect ſome hinte and intimation of what the
Earth doth in relation to motion and reſt. After I had many
and many a time examined with my ſelf the effects and accidents,
partly ſeen and partly underſtood from others, thar are to be
ſerved in the motions of waters: and moreover read and heard
the great vanities produced by many, as the cauſes of thoſe
dents, I have been induced upon no ſlight reaſons to omit theſe

two concluſions (having made withal the neceſſary
ſals) that in caſe the terreſtrial Globe be immoveable, the flux
and reflux of the Sea cannot be natural; and that, in caſe thoſe
motions be conferred upon the ſaid Globe, which have been long
ſince aſſigned to it, it is neceſſary that the Sea be ſubject to
bing and flowing, according to all that which we obſerve to
pen in the ſame.
Nature in ſport
maketh the ebbing
and flowing of the
Sea, to approve the
Earths mobility.
The tide, and
mobility of the
Earth mutually
confirm each other
All terrene
fects, indifferently
confirm the motion
or reſt of the
Earth, except the
ebbing and flowing
of the Sea.
The firſt
ral concluſion of
the impoſſibility of
the ebbing and
flowing the
bility of the
ſtrial Globe being
granted.
SAGR. The Propoſition is very conſiderable, as well for it
ſelf as for what followeth upon the ſame by way of conſequence,
ſo that I ſhall the more intenſly hearken to the explanation and
confirmation of
The knowledge
of the offests
tributes to the
veſtigation of the
cauſes.
SALV. Becauſe in natural queſtions, of which number this
which we have in hand is one, the knowledge of the effects is a
means to guide us to the inveſtigation and diſcovery of the
ſes, and without which we ſhould walk in the dark, nay with
more uncertainty, for that we know not whither we would go,
whereas the blind, at leaſt, know where they deſire to arrive;
fore firſt of all it is neceſſary to know the effects whereof we
quire the cauſes: of which effects you, Sagredus, ought more
abundantly and more certainly to be informed than I am,
1as one, that beſides your being born, and having, for a long
time, dwelt in Venice, where the Tides are very notable for their
greatneſſe, have alſo ſailed into Syria, and, as an ingenuous and
apprehenſive wit, muſt needs have made many Obſervations
on this ſubject: whereas I, that could onely for a time, and that
very ſhort, obſerve what happened in theſe extream parts of the
Adriatick Gulph, and in our Seas below about the Tyrrhene
ſhores, muſt needs take many things upon the relation of
thers, who, for the moſt part, not very well agreeing, and
ſequently being very uncertain, contribute more of confuſion
than confirmation to our ſpeculations. Nevertheleſſe, from thoſe
that we are ſure of, and which are the principal, I think I am
ble to attain to the true and primary cauſes; not that I pretend
to be able to produce all the proper and adequate reaſons of
thoſe effects that are new unto me, and which conſequently I
could never have thought upon. And that which I have to ſay,
I propoſe only, as a key that openeth the door to a path never
yet trodden by any, in certain hope, that ſome wits more
lative than mine, will make a further progreſſe herin, and
trate much farther than I ſhall have done in this my firſt
very: And although that in other Seas, remote from us, there may
happen ſeveral accidents, which do not happen in our
ranean Sea, yet doth not this invalidate the reaſon and cauſe that
I ſhall produce, if ſo be that it veriſie and fully reſolve the
cidents which evene in our Sea: for that in concluſion there can
be but one true and primary cauſe of the effects that are of the
ſame kind. I will relate unto you, therefore, the effects that I
know to be true, and aſſigne the cauſes thereof that I think
to be true, and you alſo, Gentlemen, ſhall produce ſuch
others as are known to you, beſides mine, and then we will
try whether the cauſe, by me alledged, may ſatisfie them
alſo.
Three Periods
of ebbings and
flowings, diurnal,
monethly, and
nual.
I therefore affirm the periods that are obſerved in the fluxes
and refluxes of the Sea-waters to be three: the firſt and
pal is this great and moſt obvious one; namely, the diurnal,
ding to which the intervals of ſome hours with the waters flow and
ebbe; and theſe intervals are, for the moſt part, in the
rane from ſix hours to ſix hours, or thereabouts, that is, they for
ſix hours flow, and for ſix hours ebbe. The ſecond period is
monethly, and it ſeemes to take its origen from the motion of
the Moon, not that it introduceth other motions, but only
tereth the greatneſſe of thoſe before mentioned, with a notable
difference, according as it ſhall wax or wane, or come to the
Quadrature with the Sun. The third Period is annual, and is
ſeen to depend on the Sunne, and onely altereth the diurnal
1motions, by making them different in the times of the
ſtices, as to greatneſſe, from what they are in the Equinoxes.
We will ſpeak (in the firſt place, of the diurnal motion, as
being the principal, and upon which the Moon and Sun ſeem to
exerciſe their power ſecondarily, in their monethly and annual

alterations. Three differences are obſervable in theſe horary
mutations; for in ſome places the waters riſe and fall, without
making any progreſſive motion; in others, without riſing or
ling they run one while towards the Eaſt, and recur another
while towards the Weſt; and in others they vary the heights
and courſe alſo, as happeneth here in Venice, where the Tides in
coming in riſe, and in going out fall; and this they do in the
termities of the lengths of Gulphs that diſtend from Weſt to
Eaſt, and terminate in open ſhores, up along which ſhores the
Tide at time of flood hath room to extend it ſelf: but if the
courfe of the Tide were iutercepted by Cliffes and Banks of
great height and ſteepneſſe, there it will flow and ebbe without
any progreſſive motion. Again, it runs to and again, without
changing height in the middle parts of the Mediterrane, as

bly happeneth in the ^{*} Faro de Meſſina, between Scylla and
rybdis, where the Currents, by reaſon of the narrowneſſe of
the Channel, are very ſwift; but in the more open Seas, and
about the Iſles that ſtand farther into the Mediterranean Sea, as

the Baleares, Corſica, Sardignia, ^{*} Elba, Sicily towards the Affrican

Coaſts, Malta, ^{*} Candia, &c. the changes of watermark are
very ſmall; but the currents indeed are very notable, and
cially when the Sea is pent between Iſlands, or between them
and the Continent.
Varieties that
happen in the
nal period.
* A Strait, ſo
called.
* Or Ilva.
* Or Creta.
Now theſe onely true and certain effects, were there no more
to be obſerved, do, in my judgment, very probably perſwade
any man, that will contain himſelf within the bounds of
ral cauſes, to grant the mobility of the Earth: for to make the
veſſel (as it may be called) of the Mediterrane ſtand ſtill, and to
make the water contained therein to do, as it doth, exceeds my
imagination, and perhaps every mans elſe, who will but pierce
beyond the rinde in theſe kind of inquiries.
SIMP. Theſe accidents, Salviatus, begin not now, they are
moſt ancient, and have been obſerved by very many, and ſeveral
have attempted to aſſigne, ſome one, ſome another cauſe for the
ſame: and there dwelleth not many miles from hence a famous
Peripatetick, that alledgeth a cauſe for the ſame newly fiſhed out

of a certain Text of Ariſtotle, not well underſtood by his
poſitors, from which Text he collecteth, that the true cauſe of
theſe motions doth only proceed from the different profundities
of Seas: for that the waters of greateſt depth being greater in
1abundance, and therefore more grave, drive back the Waters
of leſſe depth, which being afterwards raiſed, deſire to
ſcend, and from this continual colluctation or conteſt proceeds

the ebbing and flowing. Again thoſe that referre the ſame to the
Moon are many, ſaying that ſhe hath particular Dominion over
the Water; and at laſt a certain Prelate hath publiſhed a little
Treatiſe, wher in he ſaith that the Moon wandering too and
fro in the Heavens attracteth and draweth towards it a Maſſe of
Water, which goeth continually following it, ſo that it is full Sea
alwayes in that part which lyeth under the Moon; and becauſe,
that though ſhe be under the Horizon, yet nevertheleſſe the Tide
returneth, he ſaith that no more can be ſaid for the ſalving of that
particular, ſave onely, that the Moon doth not onely naturally
retain this faculty in her ſelf; but in this caſe hath power to
fer it upon that degree of the Zodiack that is oppoſite unto it.
Others, as I believe you know, do ſay that the Moon is able

with her temperate heat to rarefie the Water, which being
refied, doth thereupon flow. Nor hath there been wanting ſome
that ----
The cauſe of the
abbing and flowing
alledged by a
tain modern
loſopher.
The cauſe of
the ebbing and
flowing aſcribed to
the Moon by a
certain Prelate.
Hieronymus
rius and other
ripateticks refer it
to the temperate
heat of the Moon.
SAGR. I pray you Simplicius let us hear no more of them,
for I do not think it is worth the while to waſt time in relating
them, or to ſpend our breath in confuting them; and for your
part, if you gave your aſſent to any of theſe or the like
ries, you did a great injury to your judgment, which
leſſe I acknowledg to be very piercing.
SALV. But I that am a little more flegmatick than you, Sagre-

dus, will ſpend a few words in favour of Simplicius, if haply
he thinks that any probability is to be found in thoſe things that
he hath related. I ſay therefore: The Waters, Simplicius, that
have their exteriour ſuperficies higher, repel thoſe that are
riour to them, and lower; but ſo do not thoſe Waters that are
of greateſt profundity; and the higher having once driven back
the lower, they in a ſhort time grow quiet and ^{*} level. This

your Peripatetick muſt needs be of an opinion, that all the Lakes
in the World that are in a calme, and that all the Seas where
the ebbing and flowing is inſenſible, are level in their bottoms;
but I was ſo ſimple, that I perſwaded my ſelf that had we no

ther plummet to ſound with, the Iſles that advance ſo high
bove Water, had been a ſufficient evidence of the unevenneſſe
of their bottomes. To that Prelate I could ſay that the Moon
runneth every day along the whole Mediterrane, and yet its
Waters do not riſe thereupon ſave onely in the very extream
bounds of it Eaſtward, and here to us at Venice. And for thoſe
that make the Moons temperate heat able to make the Water
ſwell, bid them put fire under a Kettle full of Water, and hold
1their right hand therein till that the Water by reaſon of the heat
do riſe but one ſole inch, and then let them take it out, and
write off the tumefaction of the Sea. Or at leaſt deſire them to
ſhew you how the Moon doth to rarefie a certain part of the
Waters, and not the remainder; as for inſtance, theſe here of
Venice, and not thoſe of Ancona, Naples, Genova: the truth is

Poetick Wits are of two kinds, ſome are ready and apt to
invent Fables, and others diſpoſed and inclined to believe them.
Anſwers to the
vanities alledged
as cauſes of the
bing and flowing.
+ Or rather
ſmooth.
The Iſles are
kens of the
venneſſe of the
bottomes of Seas.
Poetick wits of
two kinds.
SIMP. I believe that no man believeth Fables, ſo long as he
knows them to be ſo; and of the opinions concerning the cauſes
of ebbing and flowing, which are many, becauſe I know that of
one ſingle effect there is but one ſingle cauſe that is true and
mary, I underſtand very well, and am certain that but one alone
at the moſt can be true, and for all the reſt I am ſure that they are
fabulous, and falſe; and its poſſible that the true one may not be
among thoſe that have been hitherto produced; nay I verily
lieve that it is not, for it would be very ſtrange that the truth

ſhould have ſo little light, as that it ſhould not be viſible amongſt
the umbrages of ſo many falſhoods. But this I ſhall ſay with the
liberty that is permitted amongſt us, that the introduction of the
Earths motion, and the making it the cauſe of the ebbing and
flowing of Tides, ſeemeth to me as yet a conjecture no leſſe
bulous than the reſt of thoſe that I have heard; and if there
ſhould not be propoſed to me reaſons more conformable to
ral matters, I would without any more ado proceed to believe
this to be a ſupernatural effect, and therefore miraculous, and
unſearchable to the underſtandings of men, as infinite others there
are, that immediately depend on the Omnipotent hand of
Truth hath not
ſo little light as
not to be
ed amidſt the
brages of
ſhoods.
Ariſtotle holdeth
thoſe effects to be
miraculous, of
which the cauſes
are unknown.
SAGR. You argue very prudently, and according to the
Doctrine of Ariſtotle, who you know in the beginning of his
mechanical queſtions referreth thoſe things to a Miracle, the
cauſes whereof are occult. But that the cauſe of the ebbing and
flowing is one of thoſe that are not to be found out, I believe
you have no greater proof than onely that you ſee, that amongſt
all thoſe that have hitherto been produced for true cauſes
of, there is not one wherewith, working by what artifice you
will, we are able to repreſent ſuch an effect; in regard that
ther with the light of the Moon nor of the Sun, nor with
temperate heats, nor with different profundities, ſhall one ever
artificially make the Water conteined in an immoveable Veſſel
to run one way or another, and to ebbe and flow in one place,
and not in another. But if without any other artifice, but with
the onely moving of the Veſſel, I am able punctually to
ſent all thoſe mutations that are obſerved in the Sea Water, why
will you refuſe this reaſon and run to a Miracle?
1
SIMP. I will run to a Miracle ſtill, if you do not with ſome
other natural cauſes, beſides that of the motion of the Veſſels of
the Sea-water diſſwade me from it; for I know that thoſe Veſſels
move not, in regard that all the entire Terreſtrial Globe is
rally immoveable.
SALV. But do not you think, that the Terreſtrial Globe might
ſupernaturally, that is, by the abſolute power of God, be made
moveable? SIMP. Who doubts it?
SALV. Then Simplicius, ſeeing that to make the flux and
reflux of the Sea, it is neceſſary to introduce a Miracle, let us
ſuppoſe the Earth to move miraculouſly, upon the motion of
which the Sea moveth naturally: and this effect ſhall be alſo the
more ſimple, and I may ſay natural, amongſt the miraculous
perations, in that the making a Globe to move round, of which
kind we ſee many others to move, is leſſe difficult than to make
an immenſe maſſe of water go forwards and backwards, in one
place more ſwiftly, and in another leſſe, and to riſe and fall in
ſome places more; in ſome leſſe, and in ſome not at all: and to
work all theſe different effects in one and the ſame Veſſel that
containeth it: beſides, that theſe are ſeveral Miracles, and that
is but one onely. And here it may be added, that the Miracle
of making the water to move is accompanied with another,
namely, the holding of the Earth ſtedfaſt againſt impetuosities
of the water, able to make it ſwage ſometimes one way, and
ſometimes another, if it were not miraculouſly kept to rights.
SAGR. Good Simplicius, let us for the preſent ſuſpend our
judgement about ſentencing the new opinion to be vain that
viatus is about to explicate unto us, nor let us ſo haſtily flye out
into paſſion like the ſcolding overgrown Haggs: and as for the
Miracle, we may as well recurre to it when we have done
ring the Diſcourſes contained within the bounds of natural
ſes: though to ſpeak freely, all the Works of nature, or rather
of God, are in my judgement miraculous.
SALV. And I am of the ſame opinion; nor doth my ſaying,
that the motion of the Earth is the Natural cauſe of the ebbing
and flowing, hinder, but that the ſaid motion of the Earth may
be miraculous. Now reaſſuming our Argument, I apply, and
once again affirm, that it hath been hitherto unknown how it
might be that the Waters contained in our Mediterranean
Straights ſhould make thoſe motions, as we ſee it doth, if ſo be
the ſaid Straight, or containing Veſſel were immoveable. And
that which makes the difficulty, and rendreth this matter
cable, are the things which I am about to ſpeak of, and which
are daily obſerved. Therefore lend me your attention.
We are here in Venice, where at this time the Waters are low,
1

the Sea calm, the Air tranquil; ſuppoſe it to be young flood,
and that in the term of five or ſix hours the water do riſe ten
^{*} hand breadths and more; that riſe is not made by the firſt
water, which was ſaid to be rarefied, but it is done by the
ſion of new Water: Water of the ſame ſort with the former,

of the ſame brackiſhneſs, of the ſame denſity, of the ſame
weight: Ships, Simplicius, float therein as in the former,
out drawing an hairs breadth more water; a Barrel of this ſecond
doth not weigh one ſingle grain more or leſs than ſuch another
quantity of the other, and retaineth the ſame coldneſs without
the leaſt alteration: And it is, in a word, Water newly and

bly entred by the Channels and Mouth of the ^{*} Lio. Conſider
now, how and from whence it came thither. Are there happly
hereabouts any Gulphs or Whirle pools in the bottom of the
Sea, by which the Earth drinketh in and ſpueth out the Water,
breathing as it were a great and monſtruous Whale? But if this
be ſo, how comes it that the Water doth not flow in the ſpace of
ſix hours in Ancona, in ^{*} Raguſa, in Corfu, where the Tide is
ry ſmall, and happly unobſervable? Who will invent a way to
pour new Water into an immoveable Veſſel, and to make that
it riſe onely in one determinate part of it, and in other places
not? Will you ſay, that this new Water is borrowed from the
Ocean, being brought in by the Straight of Gibraltar? This
will not remove the doubt aforeſaid, but will beget a greater.
And firſt tell me what ought to be the current of that Water,
that entering at the Straights mouth, is carried in ſix hours to
the remoteſt Creeks of the Mediterrane, at a diſtance of two
or three thouſand Miles, and that returneth the ſame ſpace again
in a like time at its going back? What would Ships do that lye out
at Sea? What would become of thoſe that ſhould be in the
Straights-mouth in a continual precipice of a vaſt accumulation of
Waters, that entering in at a Channel but eight Mile, broad, is to
give admittance to ſo much Water as in ſix hours over-floweth a
tract of many hundred Miles broad, & thouſands in length? What
Tygre, what Falcon runneth or flyeth with ſo much ſwiftneſs?
With the ſwiftneſs, I ſay, of above 400 Miles an hour. The
rents run (nor can it be denied) the long-wayes of the Gulph, but
ſo ſlowly, as that a Boat with Oars will out-go them, though
deed not without defalking for their wanderings. Moreover, if this
Water come in at the Straight, the other doubt yet remaineth,
namely, how it cometh to flow here ſo high in a place ſo remote,
without firſt riſing a like or greater height in the parts more
cent? In a word, I cannot think that either obſtinacy, or ſharpneſs
of wit can ever find an anſwer to theſe Objections, nor
quently to maintain the ſtability of the Earth againſt them,
ing within the bounds of Nature.
1
It is proved
impoſſible that
there ſhould
rally be any ebbing
and flowing, the
Earth being
moveable.
* Palms.
+ Lio is a fair
Port in the
tian Gulph, lying
N. E. from the
City.
SAGR. I have all the while perfectly apprehended you in this;
and I ſtand greedily attending to hear in what manner theſe
ders may occur without obſtruction from the motion already
ſigned to the Earth.
SALV. Theſe effects being to enſue in conſequence of the
tions that naturally agree with the Earth, it is neceſſary that they
not onely meet with no impediment or obſtacle, but that they do
follow eaſily, & not onely that they follow with facility, but with
neceſſity, ſo as that it is impoſſible that it ſhould ſucceed otherwiſe,
for ſuch is the property & condition of things natural & true.

ving therefore ſhewen the impoſſibility of rendring a reaſon of the
motions diſcerned in the Waters, & at the ſame time to maintain
the immobility of the veſſel that containeth them: we may proceed
to enquire, whether the mobility of the Container may produce
the required effect, in the manner that it is obſerved to evene.
True and
ral effects follow
without difficulty.
Two kinds of motions may be conferred upon a Veſſel,

by the Water therein contained, may acquire a faculty of
ctuating in it, one while towards one ſide, and another while
towards another; and there one while to ebbe, and another
while to flow. The firſt is, when firſt one, and then another of
thoſe ſides is declined, for then the Water running towards the
inclining ſide, will alternately be higher and lower, ſometimes
on one ſide, and ſometimes on another. But becauſe that this
riſing and abating is no other than a receſſion and acceſſion to the
centre of the Earth, ſuch a motion cannot be aſcribed to the
ties of the ſaid Earth, that are the Veſſels which contain the
ters; the parts of which Veſſel cannot by any whatſoever motion
aſſigned to the Earth, be made to approach or recede from the

centre of the ſame: The other ſort of motion is, when the
Veſſel moveth (without inclining in the leaſt) with a progreſſive
motion, not uniform, but that changeth velocity, by ſometimes
accellerating, and other times retarding: from which diſparity

it would follow, that the Water contained in the Veſſel its true,
but not fixed faſt to it, as its other ſolid parts, but by reaſon of
its fluidity, as if it were ſeparated and at liberty, and not
ged to follow all the mutations of its Container, in the retardation
of the Veſſel, it keeping part of the impetus before conceived,
would run towards the the preceding part, whereupon it would
of neceſſity come to riſe; and on the contrary, if new velocity
ſhould be added to the Veſſel, with retaining parts of its tardity,
ſtaying ſomewhat behind, before it could habituate it ſelf to the
new impetus, it would hang back towards the following part,
where it would come to riſe ſomething. The which effects we
may plainly declare and make out to the Senſe by the example of
one of thoſe ſame Barks yonder, which continually come from
1
^{*} Lizza-Fuſina, laden with freſh water, for the ſervice of the City.
Let us therefore fancy one of thoſe Barks, to come from thence
with moderate velocity along the Lake, carrying the water gently,
of which it is full: and then either by running a ground, or by
ſome other impediment that it ſhall meet with, let it be notably
retarded. The water therein contained ſhall not, by that means,
loſe, as the Bark doth, its pre-conceived impetus, but retaining
the ſame, ſhall run forwards towards the prow, where it ſhall
riſe notably, falling as much a ſtern. But if, on the contrary,
the ſaid Bark, in the midſt of its ſmooth courſe, ſhall have a new
velocity, with notable augmentation added to it, the water
tained before it can habituate it ſelf thereto, continuing in its
tardity, ſhall ſtay behinde, namely a ſtern, where of
quence it ſhall mount, and abate for the ſame at the prow. This
effect is undoubted and manifeſt, and may hourly be
ted; in which I deſire that for the preſent three particulars may
be noted. The flrſt is, that to make the water to riſe on one
ſide of the veſſel, there is no need of new water, nor that it run
thither, forſaking the other ſide. The ſecond is, that the water
in the middle doth not riſe or fall notably, unleſſe the courſe of
the Bark were not before that very ſwift, and the ſhock or other
arreſt that held it exceeding ſtrong and ſudden, in which caſe its
poſſible, that not only all the water might run forwards, but
that the greater part thereof might iſſue forth of the Bark: and
the ſame alſo would enſue, whilſt that being under ſail in a
ſmooth courſe, a moſt violent impetus ſhould, upon an inſtant,
overtake it: But when to its calme motion there is added a
derate retardation or incitation, the middle parts (as I ſaid)
obſervedly riſe and fall: and the other parts, according as they
are neerer to the middle, riſe the leſſe; and the more remote,
more. The third is, that whereas the parts about the midſt do
make little alteration in riſing and falling, in reſpect of the
ters of the ſides; on the contrary, they run forwards and
wards very much, in compariſon of the extreams. Now, my
Maſters, that which the Bark doth, in reſpect of the water by it
contained, and that which the water contained doth, in
ſpect of the Bark its container, is the ſelf-ſame, to an hair, with
that which the Mediterranean Veſſel doth, in reſpect of the
ters in it contained, and that which the waters contained do, in

reſpect of the Mediterranean Veſſel their container. It
eth now that we demonſtrate how, and in what manner it is true,
that the Mediterrane, and all the other Straits; and in a word,
all the parts of the Earth do all move, with a motion notably
uneven, though no motion that is not regular and uniforme, is
thereby aſſigned to all the ſaid Globe taken collectively.
1
Two ſorts of
motions of the
taining Veſſel, may
make the
ned water to riſe
and fall.
The Cavities of
the Earth cannot
approach or go
ther from the
tre of the ſame.
The progpeſſive
and uneven motion
may make the
ter contained in a
Veſſel to run to
and fro.
+ A Town
ing S. E. of Venice
The parts of the
terreſtrial Globe
accelerate and
tard in their
on.
SIMP. This Propoſition, at firſt ſight to me, that am neither
Geometrician nor Aſtronomer, hath the appearance of a very
great Paradox; and if it ſhould be true, that the motion of the
whole, being regular, that of the parts, which are all united to
their whole, may be irregular, the Paradox will overthrow the
Axiome that affirmeth, Eandem eſſe rationem totius &
tium.
SALV. I will demonſtrate my Paradox, and leave it to your
care, Simplicius, to defend the Axiome from it, or elſe to
concile them; and my demonſtration ſhall be ſhort and
miliar, depending on the things largely handled in our
dent conferences, without introducing the leaſt ſyllable, in
vour of the flux and reflux.
We have ſaid, that the motions aſſigned to the Terreſtrial

Globe are two, the firſt Annual, made by its centre about the
circumference of the Grand Orb, under the Ecliptick, according
to the order of the Signes, that is, from Weſt to Eaſt; the other
made by the ſaid Globe revolving about its own centre in twenty
four hours; and this likewiſe from Weſt to Eaſt: though
bout an Axis ſomewhat inclined, and not equidiſtant from that
of the Annual converſion. From the mixture of theſe two
tions, each of it ſelf uniform, I ſay, that there doth reſult an
uneven and deformed motion in the parts of the Earth. Which,
that it may the more eaſily be underſtood, I will explain, by
drawing a Scheme thereof. And firſt, about the centre A [in
Fig. 1. of this Dialogue] I will deſcribe the circumference of

the Grand Orb B C, in which any point being taken, as B,
about it as a centre we will deſcribe this leſſer circle D E F G,
repreſenting the Terreſtrial Globe; the which we will ſuppoſe
to run thorow the whole circumference of the Grand Orb, with
its centre B, from the Weſt towards the Eaſt, that is, from the
part B towards C; and moreover we will ſuppoſe the
ſtrial Globe to turn about its own centre B likewiſe from Weſt
to Eaſt, that is, according to the ſucceſſion of the points
D E F G, in the ſpace of twenty four hours. But here we
ought carefully to note, that a circle turning round upon its
own centre, each part of it muſt, at different times, move with
contrary motions: the which is manifeſt, conſidering that whilſt
the parts of the circumference, about the point D move to the
left hand, that is, towards E, the oppoſite parts that are about F,
approach to the right hand, that is, towards G; ſo that when
the parts D ſhall be in F, their motion ſhall be contrary to what
it was before. when it was in D. Furthermore, the ſame time
that the parts E deſcend, if I may ſo ſpeak, towards F, thoſe in
G aſcend towards D. It being therefore preſuppoſed, that
1
there are ſuch contrarieties of motions in the parts of the
ſtrial Surface, whilſt it turneth round upon its own centre, it is
neceſſary, that in conjoyning this Diurnal Motion, with the other
Annual, there do reſult an abſolute motion for the parts of the
ſaid Terreſtrial Superficies, one while very accelerate, and
ther while as ſlow again. The which is manifeſt, conſidering
firſt the parts about D, the abſolute motion of which ſhall be
extream ſwift, as that which proceedeth from two motions made
both one way, namely, towards the left hand; the firſt of
which is part of the Annual Motion, common to all the parts of
the Globe, the other is that of the ſaid point D., carried likewiſe
to the left, by the Diurnal Revolution; ſo that, in this caſe, the
Diurnal motion increaſeth and accelerateth the Annual. The
contrary to which happeneth in the oppoſite part F, which, whilſt
it is by the common annual motion carried, together with the
whole Globe, towards the left, it happeneth to be carried by the
Diurnal converſion alſo towards the right: ſo that the
nal motion by that means detracteth from the Annual,
upon the abſolute motion, reſulting from the compoſition of both
the other, is much retarded. Again, about the points E and G,
the abſolute motion becometh in a manner equal to the ſimple
Annual one, in regard that little or nothing increaſeth or
niſheth it, as not tending either to the left hand, or to the right,
but downwards and upwards. We will conclude therefore, that
like as it is true, that the motion of the whole Globe, and of
each of its parts, would be equal and uniforme, in caſe they did
move with one ſingle motion, whether it were the meer Annual,
or the ſingle Diurnal Revolution, ſo it is requiſite, that mixing
thoſe two motions together, there do reſult thence for the parts
of the ſaid Globe irregular motions, one while accelerated, and
another while retarded, by means of the additions or
ons of the Diurnal converſion from the annual circulation. So
that, if it be true (and moſt true it is, as experience proves) that
the acceleration and retardation of the motion of the
ſel, makes water contained therein to run to and again the long
waves of it, and to riſe and fall in its extreames, who will make
ſcruple of granting, that the ſaid effect may, nay ought to
ceed in the Sea-waters, contained within their Veſſels, ſubject to
ſuch like alterations, and eſpecially in thoſe that diſtend
ſelves long-wayes from Weſt to Eaſt, which is the courſe that

the motion of thoſe ſame Veſſels ſteereth? Now this is the
moſt potent and primary cauſe of the ebbing and flowing,
out the which no ſuch effect would enſue. But becauſe the
ticular accidents are many and various, that in ſeveral places and
times are obſerved, which muſt of neceſſity have dependance
1on other different concomitant cauſes, although they ought all
to have connexion with the primary; therefore it is convenient
that we propound and examine the ſeveral accidents that may
be the cauſes of ſuch different effects.
Demonſtrations
how the parts of
the terreſtriall
Globe accelerats
and ratard.
The parts of a
Circle regularly
moved about its
own centre move in
divers times with
contrary motions.
The mixture of
the two motions
annnal and
nal, cauſeth the
inequality in the
motion of the parts
of the terreſtrial
Globe.
The moſt potent
and primary cauſe
of the ebbing and
flowing.
The firſt of which is, that when ever the water, by means of a

notable retardation or acceleration of the motion of the Veſſel,
its container, ſhall have acquired a cauſe of running towards this

or that extream, and ſhall be raiſed in the one, and abated in the

other, it ſhall not nevertheleſſe continue, for any time in that
ſtate, when once the primary cauſe is ceaſed: but by vertue of
its own gravity and natural inclination to level and grow, even it
ſhall ſpeedily return backwards of its own accord, and, as being
grave and fluid, ſhall not only move towards Æquilibrium; but
being impelled by its own impetus, ſhall go beyond it, riſing in
the part, where before it was loweſt; nor ſhall it ſtay here, but
returning backwards anew, with more reiterated reciprocations of
its undulations, it ſhall give us to know, that it will not from a
velocity of motion, once conceived, reduce it ſelf, in an inſtant,
to the privation thereof, and to the ſtate of reſt, but will
ſively, by decreaſing a little and a little, reduce it ſelf unto the
ſame, juſt in the ſame manner as we ſee a weight hanging at a
cord, after it hath been once removed from its ſtate of reſt, that
is, from its perpendicularity, of its own accord, to return thither
and ſettle it ſelf, but not till ſuch time as it ſhall have often
paſt to one ſide, and to the other, with its reciprocall
brations.
Sundry accidents
that happen in the
ebbings & flowings
The first
dent.
The Water
ſed in one end of
the Veſſel
eth of its ſelf to
Æquilibrium.
The ſecond accident to be obſerved is, that the

declared reciprocations of motion come to be made and repeated
with greater or leſſer frequency, that is, under ſhorter or longer
times, according to the different lengths of the Veſſels
ing the waters; ſo that in the ſhorter ſpaces the
ons are more frequent, and in the longer more rare: juſt as in
the former example of pendent bodies, the vibrations of thoſe
that are hanged to longer cords are ſeen to be leſſe frequent,
than thoſe of them that hang at ſhorter ſtrings.
In the ſhorter
Viſſels the
tions of waters are
more frequent.
And here, for a third obſervation, it is to be noted, that not

onely the greater or leſſer length of the Veſſel is a cauſe that
the water maketh its reciprocations under different times; but
the greater or leſſer profundity worketh the ſame effect. And
it happeneth, that of waters contained in receptacles of equall
length, but of unequal depth, that which ſhall be the deepeſt,
maketh its undulations under ſhorter times, and the
ons of the ſhallower waters are leſſe frequent.
The greater
profundity maketh
the undulations of
waters more
quent.
Fourthly, there are two effects worthy to be noted, and
ligently obſerved, which the water worketh in thoſe its
1
tions; the one is its riſing and falling alternately towards the
one and other extremity; the other is its moving and running, to
ſo ſpeak, Horizontally forwards and backwards. Which two
ferent motions differently reſide in divers parts of the Water:
for its extream parts are thoſe which moſt eminently riſe and fall;
thoſe in the middle never abſolutely moving upwards and
wards, of the reſt ſucceſſively thoſe that are neereſt to the
treams riſe and fall proportionally more than the remote: but on
the contrary, touching the other progreſſive motion forwards
and backwards, the middle parts move notably, going and
turning, and the waters that are in the extream parts gain no
ground at all; ſave onely in caſe that in their riſing they
flow their banks, and break forth of their firſt channel and
ceptacle; but where there is the obſtacle of banks to keep them
in, they onely riſe and fall; which yet hindereth not the waters
in the middle from fluctuating to and again; which likewiſe
the other parts do in proportion, undulating more or leſſe,
according as they are neerer or more remote from the
Water riſeth &
falleth in the
tream parts of the
Veſſel, and runneth
to and fro in the
midst.
An accident of
the Earths motions
impoſſible to be
duced to practice
by art.
The fifth particular accident ought the more attentively to be
conſidered, in that it is impoſſible to repreſent the effect
of by an experiment or example; and the accident is this. In
the veſſels by us framed with art, and moved, as the
named Bark, one while more, and another while leſſe ſwiftly,
the acceleration and retardation is imparted in the ſame manner
to all the veſſel, and to every part of it; ſo that whilſt v. g. the
Bark forbeareth to move, the parts precedent retard no more
than the ſubſequent, but all equally partake of the ſame
tardment; and the ſelf-ſame holds true of the acceleration,
namely, that conferring on the Bark a new cauſe of
ter velocity, the Prow and Poop both accelerate in one and
the ſame manner. But in huge great veſſels, ſuch as are the very
long bottomes of Seas, albeit they alſo are no other than
tain cavities made in the ſolidity of the Terreſtrial Globe,
it alwayes admirably happeneth, that their extreams do not
unitedly equall, and at the ſame moments of time increaſe
and diminiſh their motion, but it happeneth that when one of its
extreames hath, by vertue of the commixtion of the two
Motions, Diurnal, and Annual, greatly retarded its velocity,
the other extream is animated with an extream ſwift motion.
Which for the better underſtanding of it we will explain,
ſuming a Scheme like to the former; in which if we do but
poſe a tract of Sea to be long, v. g. a fourth part, as is the arch
B C [in Fig. 2.] becauſe the parts B are, as hath been already
declared, very ſwift in motion, by reaſon of the union of the
two motions diurnal and annual, towards one and the ſame way,
1but the part C at the ſame time is retarded in its motion, as be
ing deprived of the progreſſion dependant on the diurnal motion:
If we ſuppoſe, I ſay, a tract of Sea as long as the arch B C, we
have already ſeen, that its extreams ſhall move in the ſame time
with great inequality. And extreamly different would the
cities of a tract of Sea be that is in length a ſemicircle, and
ced in the poſition B C D, in regard that the extream B would
be in a moſt accelerate motion, and the other D, in a moſt ſlow
one; and the intermediate parts towards C, would be in a
moderate motion. And according as the ſaid tracts of Sea ſhall
be ſhorter, they ſhall leſſe participate of this extravagant
dent, of being in ſome hours of the day with their parts diverſly
affected by velocity and tardity of motion. So that, if, as in the firſt
caſe, we ſee by experience that the acceleration and retardation,
though equally imparted to all the parts of the conteining Veſſel,
is the cauſe that the water contained, fluctuates too and again, what
may we think would happen in a Veſſel ſo admirably diſpoſed,
that retardation and acceleration of motion is very unequally
contributed to its parts? Certainly we muſt needs grant that
greater and more wonderful cauſes of the commotions in the
Water ought to be looked for. And though it may ſeem
poſſible to ſome, that in artificial Machines and Veſſels we ſhould
be able to experiment the effects of ſuch an accident; yet
vertheleſſe it is not abſolutely impoſſible to be done; and I have
by me the model of an Engine, in which the effect of theſe
rable commixtions of motions may be particularly obſerved. But
as to what concerns our preſent purpoſe, that which you may
have hitherto comprehended with your imagination may
fice.
SAGR. I for my own particular very well conceive that this
admirable accident ought neceſſarily to evene in the Straights of
Seas, and eſpecially in thoſe that diſtend themſelves for a great
length from Weſt to Eaſt; namely according to the courſe of
the motions of the Terreſtrial Globe; and as it is in a certain
manner unthought of, and without a preſident among the
ons poſſible to be made by us, ſo it is not hard for me to believe,
that effects may be derived from the ſame, which are not to be
mitated by our artificial experiments.
SALV. Theſe things being declared, it is time that we
ceed to examine the particular accidents, which, together with
their diverſities, are obſerved by experience in the ebbing and
flowing of the waters. And firſt we need not think it hard to

gueſſe whence it happeneth, that in Lakes, Pooles, and alſo in the
leſſer Seas there is no notable flux and reflux; the which hath
two very ſolid reaſons. The one is, that by reaſon of the
1
neſſe of the Veſſel, in its acquiring in ſeveral hours of the day
ſeveral degrees of velocity, they are with very little difference
acquired by all its parts; for as well the precedent as the
quent, that is to ſay, both the Eaſtern and Weſtern parts, do
accelerate and retard almoſt in the ſame manner; and withal
making that alteration by little and little, and not by giving the
motion of the conteining Veſſel a ſudden check, and
ment, or a ſudden and great impulſe or acceleration; both it
and all its parts, come to be gently and equally impreſſed with
the ſame degrees of velocity; from which uniformity it
eth, that alſo the conteined water with but ſmall reſiſtance and
oppoſition, receiveth the ſame impreſſions, and by conſequence
doth give but very obſcure ſignes of its riſing or falling, or of its
running towards one part or another. The which effect is likewiſe
manifeſtly to be ſeen in the little artificial Veſſels, wherein the
contained water doth receive the ſelf ſame impreſſions of
ty; when ever the acceleration and retardation is made by gentle
and uniform proportion. But in the Straights and Bays that for a
great length diſtend themſelves from Eaſt to Weſt, the
ration and retardation is more notable and more uneven, for
that one of its extreams ſhall be much retarded in motion, and
the other ſhall at the ſame time move very ſwiftly: The
procal libration or levelling of the water proceeding from the
petus that it had conceived from the motion of its container.
The which libration, as hath been noted, hath its undulations
very frequent in ſmall Veſſels; from whence enſues, that though
there do reſide in the Terreſtrial motions the cauſe of
ring on the waters a motion onely from twelve hours to twelve
hours, for that the motion of the conteining Veſſels do
treamly accelerate and extreamly retard but once every day,
and no more; yet nevertheleſſe this ſame ſecond cauſe
ing on the gravity of the water which ſtriveth to reduce it ſelf to
equilibration, and that according to the ſhortneſſe of the
ſel hath its reciprocations of one, two, three, or more hours, this
intermixing with the firſt, which alſo it ſelf in ſmall Veſſels is
very little, it becommeth upon the whole altogether inſenſible.
For the primary cauſe, which hath the periods of twelve hours,
having not made an end of imprinting the precedent
on, it is overtaken and oppoſed by the other ſecond,
dant on the waters own weight, which according to the brevity
and profundity of the Veſſel, hath the time of its undulations of
one, two, three, four, or more hours; and this contending
with the other former one, diſturbeth and removeth it, not
mitting it to come to the height, no nor to the half of its
on; and by this conteſtation the evidence of the ebbing and
1flowing is wholly annihilated, or at leaſt very much obſcured.
I paſſe by the continual alteration of the air, which diſquieting
the water, permits us not to come to a certainty, whether any,
though but ſmall, encreaſe or abatement of half an inch, or
leſſe, do reſide in the Straights, or receptacles of water not
bove a degree or two in length.
Reaſons
ed of the
lar accidents
ſerved in the
bings and flowings.
Second cauſes
why in ſmall Seas
and in Lakes there
are no ebbings and
flowings.
I come in the ſecond place to reſolve the queſtion, why, there

not reſiding any vertue in the primary principle of commoving
the waters, ſave onely every twelve hours, that is to ſay, once
by the greateſt velocity, and once by the greateſt tardity of
motion; the ebbings and flowings ſhould yet nevertheleſſe
pear to be every ſix hours. To which is anſwered, that this
termination cannot any wayes be taken from the primary cauſe
onely; but there is a neceſſity of introducing the ſecondary
ſes, as namely the greater or leſſe length of the Veſſels, and
the greater or leſſe depth of the waters in them conteined.
Which cauſes although they have not any operation in the
ons of the waters, thoſe operations belonging to the ſole
ry cauſe, without which no ebbing or flowing would happen,
yet nevertheleſſe they have a principal ſhare in determining the
times or periods of the reciprocations, and herein their
ence is ſo powerful, that the primary cauſe muſt of force give
way unto them. The period of ſix hours therefore is no more
proper or natural than thoſe of other intervals of times, though
indeed its the moſt obſerved, as agreeing with our Mediterrane,
which was the onely Sea that for many Ages was navigated:
though neither is that period obſerved in all its parts; for
that in ſome more anguſt places, ſuch as are the
ſpont, and the Ægean Sea, the periods are much ſhorter,
and alſo very divers amongſt themſelves; for which
ſities, and their cauſes incomprehenſible to Ariſtotle, ſome
ſay, that after he had a long time obſerved it upon ſome
cliffes of Negropont, being brought to deſperation, he threw
himſelf into the adjoyning Euripus, and voluntarily drowned
himſelf.
The reaſon
ven, why the
bings and flowings,
for the moſt part,
are every ſix
hours.
In the third place we have the reaſon ready at hand, whence

it commeth to paſſe, that ſome Seas, although very long, as is
the Red Sea, are almoſt altogether exempt from Tides, which
happeneth becauſe their length extendeth not from Eaſt to
Weſt, but rather tranſverſly from the Southeaſt to the
weſt; but the motions of the Earth going from Weſt to Eaſt;
the impulſes of the water, by that means, alwayes happen to fall
in the Meridians, and do not move from parallel to parallel;
inſomuch that in the Seas that extend themſelves athwart
wards the Poles, and that the contrary way are narrow, there is
1no cauſe of ebbing and flowing, ſave onely by the participation
of another Sea, wherewith it hath communication, that is
ject to great
The cauſe why
ſome Seas, though
very long, ſuffer
no ebbing and
flowing.
Ebbings and
flowings why
teſt in the
mities of gulphs,
and leaſt in the
middle parts.
In the fourth place we ſhall very eaſily find out the reaſon
why the fluxes and refluxes are greateſt, as to the waters riſing
and falling in the utmoſt extremities of Gulphs, and leaſt in the
intermediate parts; as daily experience ſheweth here in Venice,
lying in the farther end of the Adriatick Sea, where that
rence commonly amounts to five or ſix feet; but in the places
of the Mediterrane, far diſtant from the extreams, that
on is very ſmall, as in the Iſles of Corſica and Sardinnia, and
in the Strands of Rome and Ligorne, where it exceeds not half a
foot; we ſhall underſtand alſo, why on the contrary, where
the riſings and fallings are ſmall, the courſes and recourſes are
great: I ſay it is an eaſie thing to underſtand the cauſes of theſe
accidents, ſeeing that we meet with many manifeſt occurrences
of the ſame nature in every kind of Veſſel by us artificially
poſed, in which the ſame effects are obſerved naturally to
low upon our moving it unevenly, that is, one while faſter, and
another while ſlower.
Why in narrow
places the courſe
of the waters is
more ſwift than in
larger.
Moreover, conſidering in the fifth place, that the ſame
quantity of Water being moved, though but gently, in a ſpatious
Channel, comming afterwards to go through a narrow paſſage,
will of neceſſity run, with great violence, we ſhall not finde it hard
to comprehend the cauſe of the great Currents that are made
in the narrow Channel that ſeparateth Calabria from Sicilia:
for that all the Water that, by the ſpaciouſneſſe of the Iſle,
and by the Ionick Gulph, happens to be pent in the Eaſtern
part of the Sea, though it do in that, by reaſon of its largeneſs,
gently deſcend towards the Weſt, yet nevertheleſſe, in that it
is pent up in the Boſphorus, it floweth with great violence
tween Scilla and Caribdis, and maketh a great agitation. Like to
which, and much greater, is ſaid to be betwixt Africa and the
great Iſle of St. Lorenzo, where the Waters of the two vaſt
Seas, Indian and Ethiopick, that lie round it, muſt needs be
ſtraightned into a leſſe Channel between the ſaid Iſle and the
Ethiopian Coaſt. And the Currents muſt needs be very great
in the Straights of Magellanes, which joyne together the
vaſt Oceans of Ethiopia, and Del Zur, called alſo the Pacifick
Sea.
A diſcuſſion of
ſome more abſtruſe
accidents obſerved
in the ebbing and
flowing.
It follows now, in the ſixth place, that to render a reaſon of
ſome more abſtruſe and incredible accidents, which are
ved upon this occaſion, we make a conſiderable reflection upon
the two principal cauſes of ebbings and flowings, afterwards
compounding and mixing them together. The firſt and ſimpleſt
1of which is (as hath often been ſaid) the determinate
tion and retardation of the parts of the Earth, from whence
the Waters have a determinate period put to their decurſions
towards the Eaſt, and return towards the Weſt, in the time of
twenty ſour hours. The other is that which dependeth on the
per gravity of the Water, which being once commoved by the
primary cauſe, ſeeketh, in the next place, to reduce it ſelf to
quilibrium, with iterated reciprocations; which are not
mined by one ſole and prefixed time; but have as many
ties of times as are the different lengths and profundities of the
receptacles, and Straights of Seas; and by what dependeth on
this ſecond principle, they would ebbe. and flow, ſome in one
hour, others in two, in four, in ſix, in eight, in ten, &c. Now if
we begin to put together the firſt cauſe, which hath its ſet Period
from twelve hours to twelve hours, with ſome one of the
dary, that hath its Period verb. grat. from five hours to five
hours, it would come to paſſe, that at ſometimes the primary
cauſe and ſecondary would accord to make impulſes both one
and the ſame way; and in this concurrency, and (as one may call
it) unanimous conſpiration the flowings ſhall be great. At other
times it happening that the primary impulſe doth, in a certain
manner, oppoſe that which the ſecondary Period would make,
and in this conteſt one of the Principles being taken away, that
which the other would give, will weaken the commotion of the
Waters, and the Sea will return to a very tranquil State, and
almoſt immoveable. And at other times, according as the two
aforeſaid Principles ſhall neither altogether conteſt, nor
ther concur, there ſhall be other kinds of alterations made in
the increaſe and diminution of the ebbing and flowing. It may
likewiſe fall out that two Seas, conſiderably great and which
communicate by ſome narrow Channel, may chance to have, by
reaſon of the mixtion of the two Principles of motion, one
cauſe to flow at the time that the other hath cauſe to move a
contrary way; in which caſe in the Channel, whereby they
imbogue themſelves into each other, there do extraordinary
conturbations inſue, with oppoſite and vortick motions, and
moſt dangerous boilings and breakings, as frequent relations
and experiences do aſſure us. From ſuch like diſcordant
ons, dependent not onely on the differenr poſitions and
tudes, but very much alſo upon the different profundities of the
Seas, which have the ſaid intercourſe there do happen at
times different commotions in the Waters, irregular, and that
can be reduced to no rules of obſervation, the reaſons of which
have much troubled, and alwayes do trouble Mariners, for that
they meet with them without ſeeing either impulſe of winds, or
1other eminent aereal alteration that might occaſion the ſame; of
which diſturbance of the Air we ought to make great account
in other accidents, and to take it for a third and accidental
cauſe, able to alter very much the obſervation of the effects
pending on the ſecondary and more eſſential cauſes. And it is
not to be doubted, but that impetuous windes, continuing to
blow, for example, from the Eaſt, they ſhall retein the Waters
and prohibit the reflux or ebbing; whereupon the ſecond and
third reply of the flux or tide overtaking the former, at the
hours prefixed, they will ſwell very high; and being thus born
up for ſome dayes, by the ſtrength of the Winds, they ſhall riſe
more than uſual, making extraordinary inundations.
We ought alſo, (and this ſhall ſerve for a ſeventh Probleme)
to take notice of another cauſe of motion dependant on the
great abundance of the Waters of great Rivers that diſcharge

themſelves into Seas of no great capacity, whereupon in the
Straits or Boſphori that communicate with thoſe Seas, the Waters
are ſeen to run always one way: as it happeneth in the
an Boſphorus below Conſtantinople, where the water alwayes
runneth from the Black-Sea, towards the Propontis: For in the
ſaid Black-Sea by reaſon of its ſhortneſſe, the principal cauſes
of ebbing and flowing are but of ſmall force. But, on the
trary, very great Rivers falling into the ſame, thoſe huge
fluxions of water being to paſſe and diſgorge themſelves by the

the Straight, the ^{*}courſe is there very notable and alwayes
wards the South. Where moreover we ought to take notice, that
the ſaid Straight or Channel, albeit very narrow, is not ſubject
to perturbations, as the Straight of Soilla and Carybdis; for that
that hath the Black-Sea above towards the North, and the
pontis, the Ægean, and the Mediterranean Seas joyned unto it,
though by a long tract towards the South; but now, as we have
obſerved, the Seas, though of never ſo great length, lying North
and South, are not much ſubject to ebbings and flowings; but
becauſe the Sicilian Straight is ſituate between the parts of the
Mediterrane diſtended for a long tract or diſtance from Weſt to
Eaſt, that is, according to the courſe of the fluxes and refluxes,
therefore in this the agitations are very great; and would be
much more violent between Hercules Pillars, in caſe the
Straight of Gibraltar did open leſſe; and thoſe of the Straight of
Magellanes are reported to be extraordinary violent.
The cauſe why,
in ſome narrow
Channels, we ſee
the Sea-waters run
alwayes one way.
* Or current.
This is what, for the preſent, cometh into my mind to ſay unto
you about the cauſes of this firſt period diurnal of the Tide, and
its various accidents, touching which, if you have any thing to
offer, you may let us hear it, that ſo we may afterwards
ceed to the other two periods, monethly and annual.
1
SIMP. In my opinion, it cannot be denied, but that your
courſe carrieth with it much of probability, arguing, as we ſay,
ex ſuppoſitione, namely, granting that the Earth moveth with
the two motions aſſigned it by Copernicus: but if that motion

be diſproved, all that you have ſaid is vain, and inſignificant:
and for the diſproval of that Hypotheſis, it is very manifeſtly
hinted by your Diſcourſe it ſelf. You, with the ſuppoſition of
the two Terreſtrial motions, give a reaſon of the ebbing and
flowing; and then again, arguing circularly, from the ebbing
and flowing, draw the reaſon and confirmation of thoſe very
motions; aud ſo proceeding to a more ſpecious Diſcourſe, you
ſay that the Water, as being a fluid body, and not tenaciouſly
annexed to the Earth, is not conſtrained punctually to obey
ry of its motions, from which you afterwards infer its ebbing
and flowing, Now I, according to your own method, argue
the quite contrary, and ſay; the Air is much more tenuous, and
fluid than the Water, and leſſe annexed to the Earths
es, to which the Water, if it be for nothing elſe, yet by reaſon
of its gravity that preſſeth down upon the ſame more than the
light Air, adhereth; therefore the Air is much obliged to
low the motions of the Earth: and therefore were it ſo, that the
Earth did move in that manner, we the inhabitants of it, and
carried round with like velocity by it, ought perpetually to feel
a Winde from the Eaſt that beateth upon us with intolerable
force. And that ſo it ought to fall out, quotidian experience
ſureth us: for if with onely riding poſt, at the ſpeed of eight or
ten miles an hour in the tranquil Air, the incountering of it with
our face ſeemeth to us a Winde that doth not lightly blow upon
us, what ſhould we expect from our rapid courſe of 800. or a
thouſand miles an hour, againſt the Air, that is, free from that
motion? And yet, notwithſtanding we cannot perceive any
thing of that nature.
The Hypotheſir
of the Earths
bility taken in
vour of the Tide,
oppoſed.
SALV. To this objection that hath much of likelihood in it, I

reply, that its true, the Air is of greater tenuity and levity; and,
by reaſon of its levity, leſſe adherent to the Earth than Water ſo
much more grave and ^{*}bulky; but yet the conſequence is falſe
that you infer from theſe qualities; namely, that upon account

of that its levity, tenuity, and leſſe adherence to the Earth, it
ſhould be more exempt than the Water from following the
Terreſtrial Motions; ſo as that to us, who abſolutely pertake of
of them, the ſaid exemption ſhould be ſenſible and manifeſt;
nay, it happeneth quite contrary; for, if you well remember, the
cauſe of the ebbing and flowing of the Water aſſigned by us,
conſiſteth in the Waters not following the unevenneſſe of the
motion of its Veſſel, but retaining the impetus conceived before,
1without diminiſhing or increaſing it according to the preciſe rate
of its diminiſhing or increaſing in its Veſſel. Becauſe therefore

that in the conſervation and retention of the impetus before
ceived, the diſobedience to a new augmentation or diminution of
motion conſiſteth, that moveable that ſhall be moſt apt for ſuch
a retention, ſhall be alſo moſt commodious to demonſtrate the
effect that followeth in conſequence of that retention. Now how
much the Water is diſpoſed to maintain ſuch a conceived
tion; though the cauſes ceaſe that impreſs the ſame, the
ence of the Seas extreamly diſturbed by impetuous Winds
eth us; the Billows of which, though the Air be grown calm, and
the Wind laid, for a long time after continue in motion: As the
Sacred Poet pleaſantly ſings,
The anſwer to
the objections
made againſt the
motion of the
reſtrial Globe.
+ Corpulenta.
The Water more
apt to conſerve an
impetus conceived,
then the Air.
Qual l'alto Egeo, &c.----------
And that long continuing rough after a ſtorm, dependeth on

the gravity of the water: For, as I have elſewhere ſaid, light
dies are much eaſier to be moved than the more grave, but yet
are ſo much the leſs apt to conſerve the motion imparted, when
once the moving cauſe ceaſeth. Whence it comes that the Aire,
as being of it ſelf very light and thin, is eaſily mov'd by any very
ſmall force, yet it is withall very unable to hold on its motion,
the Mover once ceaſing. Therefore, as to the Aire which
rons the Terreſtrial Globe, I would fay, that by reaſon of its
adherence, it is no leſſe carried about therewith then the Water;
and eſpecially that part which is contained in its veſſels; which

veſſels are the valleys encloſed with Mountains. And we may
with much more reaſon affirm that this ſame part of the Air is
carried round, and born forwards by the rugged parts of the
Earth, than that the higher is whirl'd about by the motion of the
Heavens, as ye Peripateticks maintain.
Light bodies eaſier
to be moved than
beavy, but leſs aut
to conſerve the
tion.
Its more rational
that the Air be
commoved by the
rugged ſurface of
the Earth than
by the Celeſtial
motion.
What hath been hitherto ſpoken, ſeems to me a ſufficient

ſwer to the allega ion of Simputius; yet nevertheleſs with a new
inſtance and ſolution, founded upon an admirable experiment, I
will ſuperabundantly ſatisfie him, and confirm to Sagredus the
mobility of the Earth. I have told you that the Air, and in
ticular that part of it which aſcendeth not above the tops of the
higheſt Mountains, is carried round by the uneven parts of the
Earths ſurface: from whence it ſhould ſeem, that it muſt of
ſequence come to paſſe, that in caſe the ſuperficies of the Earth
were not uneven, but ſmooth and plain, no cauſe would remain
for drawing the Air along with it, or at leaſt for revolving it with
ſo much uniformity. Now the ſurface of this our Globe, is not
all craggy and rugged, but there are exceeding great tracts very
1even, to wit, the ſurfaces of very vaſt Seas, which being alſo far
remote from the continuate ledges of Mountains which environ
it, ſeem to have no faculty of carrying the ſuper-ambient Air
along therewith: and not carrying it about, we may perceive what
will of conſequence enſue in thoſe places.
The revolution of
the Earth
firmed by a new
argument taken
from the Air.
SIMP. I was about to propoſe the very ſame difficulty, which
I think is of great validity.
SALV. You ſay very well Simplicius, for from the not finding
in the Air that which of conſequence would follow, did this our
Globe move round; you argue its immoveableneſſe. But in caſe
that this which you think ought of neceſſary conſequence to be
found, be indeed by experience proved to be ſo; will you accept
it for a ſufficient teſtimony and an argument for the mobility of
the ſaid Globe?
SIMP. In this caſe it is not requiſite to argue with me alone,
for if it ſhould ſo fall out, and that I could not comprehend the
cauſe thereof, yet haply it might be known by others.
SALV. So that by playing with you, a man ſhall never get, but
be alwayes on the loſing hand; and therefore it would be better
to give over: Nevertheleſs, that we may not cheat our third man
we will play on. We ſaid even now, and with ſome addition we
reitterate it, that the Ayr as if it were a thin and fluid body, and
not ſolidly conjoyned with the Earth, ſeem'd not to be
tated to obey its motion; unleſſe ſo far as the craggineſs of the
terreſtrial ſuperficies, tranſports and carries with it a part
of contigious thereunto; which doth not by any great ſpace
ceed the greateſt altitude of Mountains: the which portion of Air
ought to be ſo much leſs repugnant to the terreſtrial converſion,

by how much it is repleat with vapours, fumes, and exhalations,
matters all participating of terrene qualities, and conſequently
apt of their own nature to the ſame motions. But where there are
wanting the cauſes of motion, that is, where the ſurface of the
Globe hath great levels, and where there is leſs mixture of the
terrene vapours, there the cauſe whereby the ambient Air is
ſtrained to give entire obedience to the terreſtrial converſion will
ceaſe in part; ſo that in ſuch places, whilſt the Earth revolveth
wards the Eaſt, there will be continually a wind perceived which
will beat upon us, blowing from the Eaſt towards the Weſt:
and ſuch gales will be the more ſenſible, where the revolution of
the Globe is moſt ſwift; which will be in places more remote from
the Poles, and approaching to the greateſt Circle of the diurnal
converſion. But now de facto experience much confi meth this
Phyloſophical argumentation; for in the ſpatious Seas, and in their
parts moſt remote from Land, and ſituate under the Torrid Zone,
that is bounded by the Tropicks, where there are none of thoſe
1
ſame terreſtrial evaporations, we finde a perpetual gale move
from the Eaſt with ſo conſtant a blaſt, that ſhips by favour
of ſail proſperouſly to the West-India's. And from the ſame
coaſting along the Mexican ſhore, they with the ſame felicity paſs
the Pacifick Ocean towards the India's; which to us are Eaſt, but

to them are Weſt. Whereas on the contrary the Courſe from
thence towards the Eaſt is difficult and uncertain, and not to be
made by the ſame Rhumb, but muſt vere more to Land-ward, to
recover other Winds, which we may call accidentary and
tuary, produced from other Principles, as thoſe that inhabit the
continent find by experience. Of which productions of Winds,
the Cauſes are many and different, which ſhall not at this time be

mentioned. And theſe accidentary Winds are thoſe which blow
indifferently from all parts of the Eatth, and make rough the Seas
remote from the Equinoctial, and environed by the rugged
face of the Earth; which is as much as to ſay environ'd with
thoſe perturbations of Air, that confound that primary Gale.
The which, in caſe theſe accidental impediments were removed,
would be continually felt, and eſpecially upon the Sea. Now
ſee how the effect of the Water and Air ſeem wonderfully to
cord with the Celeſtial obſervations, to confirm the mobility of
our Terreſtrial
The vaporous
parts of the earth,
partake of its
tions.
Conſtant gales
within the
pieks blow towards
the Weſt.
The courſe to the
Weſt-India's
ſie, the return
ficult.
Winds from Land
make rough the
Seas.
Another
tion taken from the
Air in
on of the motion of
the Earth.
SAGR. I alſo for a final cloſe will relate to you one particular,
which as I believe is unknown unto you, and which likewiſe may
ſerve to confirm the ſame concluſion: You Salviatus alledged,
That Accident which Sailers meet with between the Tropicks;
I mean that perpetual Gale of Winde that beats upon them from
the Eaſt, of which I have an account from thoſe that have many
times made the Voyage: And moreover (which is very
vable) I underſtand that the Mariners do not call it a Wind, but

by another ^{*} name, which I do not now remember, taken haply
from its ſo fixed and conſtant Tenor; which when they have met
with, they tie up their ſhrouds and other cordage belonging to
the Sails, and without any more need of touching them, though
they be in a ſleep, they can continue their courſe. Now this conſtant
Trade-wind was known to be ſuch by its continual blowing
out interruptions; for if it were interrupted by other Windes, it
would not have been acknowledged for a ſingular Effect, and
different from the reſt: from which I wlll infer, That it may be
that alſo our Mediterranean Sea doth partake of the like accident;
but it is not obſerved, as being frequently altered by the
ence of other windes. And this I ſay, not without good grounds,
yea upon very probable conjectures whch came unto my
ledge, from that which tendred it ſelf to my notice on occaſion of
the voyage that I made into Syria, going Conſul for this Nation
1to Aleppo, and this it is: That keeping a particular account and

memorial of the dayes of the departure and arrival of the Ships in
the Ports of Alexandria, of Alexandretta, and this of Venice; in
comparing ſundry of them, which I did for my curioſity, I found
that in exactneſs of account the returns hither, that is the voiages
from Eaſt to Weſt along the Mediterrane, are made in leſs time
then the contrary courſes by 25. in the Hundred: So that we ſee
that one with another, the Eaſtern windes are ſtronger then the
Weſtern.
Which Wind
with our Engliſh
Mariners is called
the Trade-wind.
The voiages in the
Mediterrane from
Eaſt to Weſt are
made in ſhorter
times than from
Weſt to Eaſt.
SALV. I am very glad I know this particular, which doth not
a little make for the confirmation of the Earths mobility. And
although it may be alledged, That all the Water of the
rane runs perpetually towards the Straits-mouth, as being to
diſimbogue into the Ocean, the waters of as many Rivers, as do
diſcharge themſelves into the ſame; I do not think that that
rent can be ſo great, as to be able of it ſelf alone to make ſo
table a difference: which is alſo manifeſt by obſerving that the
water in the Pharo of Sicily runneth back again no leſs towards
the Eaſt, than it runneth forwards towards the Weſt.
SAGR. I, that have not as Simplicius, an inclination to
fie any one beſides my ſelf, am ſatisfied with what hath been ſaid
as to this firſt particular: Therefore Salviatus, when you think
it fit to proceed forward, I am prepared to hear you.
SALV. I ſhall do as you command me, but yet I would fain
hear the opinion alſo of Simplicius, from whoſe judgement I can
argue how much I may promiſe to my ſelf touching theſe
courſes from the Peripatetick Schools, if ever they ſhould come
to their ears.
SIMP. I deſire not that my opinion ſhould ſerve or ſtand for
a meaſure, whereby you ſhould judge of others thoughts; for
as I have often ſaid, I am inconſiderable in theſe kinde of ſtudies,
and ſuch things may come into the mindes of thoſe that are
ed into the deepeſt paſſages of Philoſophy, as I could never think
of; as having (according to the Proverb) ſcarce kiſt her Maid:
yet nevertheleſs, to give you my ſudden thoughts, I ſhall tell
you, That of thoſe effects by you recounted, and particularly the
laſt, there may in my judgement very ſufficient Reaſons be given
without the Earths mobility, by the mobility of the Heavens
ly; never introducing any novelty more, than the inverſion of
that which you your ſelf propoſe unto us. It hath been received

by the Peripatetick Schools, that the Element of Fire, and alſo a
great part of the Aire is carried about according to the Diurnal
converſion from Eaſt to Weſt, by the contact of the Concave of
the Lunar Orb, as by the Veſſel their container. Now without
going out of your track, I will that we determine the Quantity of
1
the Aire which partaketh of that motion to diſtend ſo low as to
the Tops of the higheſt Hills, and that likewiſe they would reach
to the Earth, if thoſe Mountains did not impede them, which
agreeth with what you ſay: For as you affirm, the Air, which is
invironed by ledges of Mountains, to be carried about by the
aſperity of the moveable Earth; we on the contrary ſay, That
the whole Element of Air is carried about by the motion of
Heaven, that part only excepted which lyeth below thoſe bodies,
which is hindred by the aſperity of the immoveable Earth. And
whereas you ſaid, That in caſe that aſperity ſhould be removed,
the Air would alſo ceaſe to be whirld about; we may ſay,
That the ſaid aſperity being removed, the whole Aire would
tinue its motion. Whereupon, becauſe the ſurfaces of ſpacious
Seas are ſmooth, and even; the Airs motion ſhall continue upon
thoſe, alwaies blowing from the Eaſt: And this is more ſenſibly
perceived in Climates lying under the Line, and within the
picks, where the motion of Heaven is ſwifter; and like as that
Celeſtial motion is able to bear before it all the Air that is at
liberty, ſo we may very rationally affirm that it contributeth the
ſame motion to the Water moveable, as being fluid and not
nected to the immobility of the Earth: And with ſo much the

more confidence may we affirm the ſame, in that by your
feſſion, that motion ought to be very ſmall in reſect of the efficient
Cauſe; which begirting in a natural day the whole Terreſtrial
Globe, paſſeth many hundreds of miles an hour, and eſpecially
towards the Equinoctial; whereas in the currents of the open Sea,
it moveth but very few miles an hour. And thus the voiages
wards the Weſt ſhall come to be commodious and expeditious,
not onely by reaſon of the perpetual Eaſtern Gale, but of the
courſe alſo of the Waters; from which courſe alſo perhaps the
Ebbing and Flowing may come, by reaſon of the different

ation of the Terreſtrial Shores: againſt which the Water coming
to beat, may alſo return backwards with a contrary motion, like
as experience ſheweth us in the courſe of Rivers; for according as
the Water in the unevenneſs of the Banks, meeteth with ſome
parts that ſtand out, or make with their Meanders ſome Reach or
Bay, here the Water turneth again, and is ſeen to retreat back
a conſiderable ſpace. Upon this I hold, That of thoſe effects
from which you argue the Earths mobility, and alledge it as a
cauſe of them, there may be aſſigned a cauſe ſufficiently valid,
retaining the Earth ſtedfaſt, and reſtoring the mobility of
Heaven.
It is
ted inverting the
argument, that
the perpetual
tion of the Air
from Eaſt to Weſt
cometh from the
motion of Heaven?
It is demonſtrated
inverting the
gument, that the
perpetual motion of
the Air from Eaſt
to Weſt, cometh
from the motion of
Heaven.
The motion of the
Water dependeth
on the motion of
Heaven.
The flux and
flux may depend
on the diurual
tion of Heaven.
SALV. It cannot be denied, but that your diſcourſe is ingenious,
& hath much of probability, I mean probability in appearance, but
not in reality & exiſtence: It conſiſteth of two parts: In the firſt it
1aſſignes a reaſon of the continual motion of the Eaſtern Winde,
and alſo of a like motion in the Water. In the ſecond, It would
draw from the ſame Sourſe the cauſe of the Ebbing and Flowing.
The firſt part hath (as I have ſaid) ſome appearance of
lity, but yet extreamly leſs then that which we take from the
Terreſtrial motion. The ſecond is not onely wholly improbable,
but altogether impoſſible and falſe. And coming to the firſt,

whereas it is ſaid that the Concave of the Moon carrieth about
the element of Fire, and the whole Air, even to the tops of the
higher Mountains. I anſwer firſt, that it is dubious whether
there be any element of Fire: But ſuppoſe there be, it is much
doubted of the Orbe of the Moon, as alſo of all the reſt; that is,
Whether there be any ſuch ſolid bodies and vaſt, or elſs, Whether
beyond the Air there be extended a continuate expanſion of a
ſubſtance of much more tenuity and purity than our Air, up and
down which the Planets go wandring, as now at laſt a good part
of thoſe very Phyloſophers begin to think: But be it in this or in

that manner, there is no reaſon for which the Fire, by a ſimple
contract to a ſuperficies, which you your ſelf grant to be ſmooth
and terſe, ſhould be according to its whole depth carried round in
a motion different from its natural inclination; as hath been
fuſely proved, and with ſenſible reaſons demonſtrated by^{+} Il Sag-

giatore: Beſides the other improbability of the ſaid motions
transfuſing it ſelf from the ſubtileſt Fire throughout the Air, much
more denſe; and from that alſo again to the Water. But that
a body of rugged and mountainous ſurface, by revolving in it
ſelf, ſhould carry with it the Air contiguous to it, and againſt
which its promontaries beat, is not onely probable but neceſſary,
and experience thereof may be daily ſeen; though without
ing it, I believe that there is no judgement that doubts thereof.
As to the other part, ſuppoſing that the motion of Heaven did
carry round the Air, and alſo the Water; yet would that motion
for all that have nothing to do with the Ebbing and Flowing.
For being that from one onely and uniform cauſe, there can

low but one ſole and uniform effect; that which ſhould be
vered in the Water, would be a continuate and uniform courſe
from Eaſt to Weſt; and in that a Sea onely, which running
paſs environeth the whole Globe. But in determinate Seas, ſuch
as is the Mediterrane ſhut up in the Eaſt, there could be no ſuch
motion. For if its Water might be driven by the courſe of
Heaven towards the Weſt, it would have been dry many ages
ſince: Beſides that our Water runneth not onely towards the
Weſt, But returneth backwards towards the Eaſt, and that in
dinal Periods: And whereas you ſay by the example of Rivers,
that though the courſe of the Sea were Originally that onely
1from Eaſt to Weſt, yet nevertheleſs the different Poſition of the
Shores may make part of the Water regurgitate, and return
backwards: I grant it you, but it is neceſſary that you take
tice my Simplicius, that where the Water upon that account
returneth backwards, it doth ſo there perpetually; and where
it runneth ſtraight forwards, it runneth there alwayes in the ſame
manner; for ſo the example of the Rivers ſhewes you: But in the
caſe of the ebbing and flowing, you muſt finde and give us ſome
reaſon why it doth in the ſelf ſame place run one while one way,
and another while another; Effects that being contrary & irregular,
can never be deduced from any uniform and conſtant Cauſe:
And this Argument, that overthrows the Hypotheſis of the
tion contributed to the Sea from the Heavens diurnal motion,
doth alſo confute that Poſition of thoſe who would admit the ſole
diurnal motion of the Earth, and believe that they are able with
that alone to give a reaſon of the Flux and Reflux: Of which
effect ſince it is irregular, the cauſe muſt of neceſſity be irregular
and alterable.
A reaſon of the
continual motion of
the Air and
ter may be given,
making the Earth
moveable, then by
making it
able.
Its improbable that
the element of Fire
ſhould be carried
round by the
cave of the Moon.
+ A Treatiſe of our
Author formerly
cited.
The Ebbing and
Flowing cannot
pend on the motion
of Heaven.
SIMP. I have nothing to reply, neither of my own, by reaſon
of the weakneſs of my underſtanding; nor of that of others, for
that the Opinion is ſo new: But I could believe that if it were
ſpread amongſt the Schools, there would not want Phyloſophers
able to oppoſe it.
SAGR. Expect ſuch an occaſion; and we in the mean time
if it ſeem good to Salviatus, will proceed forward.
SALV. All that which hath been ſaid hitherto, pertaineth to
the diurnal period of the ebbing and flowing; of which we have in
the firſt place demonſtrated in general the primary and univerſal
Cauſe, without which, no ſuch effect would follow: Afterw ds
paſſing to the particular Accidents, various, and in a certain ſort
irregular, that are obſerved therein: We have handled the
dary and concommitant Cauſes upon which they depend. Now
follow the two other Periods, Monethly, and Annual, which do
not bring with them new and different Accidents, other than
thoſe already conſidered in the diurnal Period; but they
rate on the ſame Accidents, by rendring them greater and leſſer
in ſeveral parts of the Lunar Moneth, and in ſeveral times of
the Solar Year; as if that the Moon and Sun did each conceive
it ſelf apart in operating and producing of thoſe Effects; a thing
that totally claſheth with my underſtanding, which ſeeing how
that this of Seas is a local and ſenſible motion, made in an
menſe maſs of Water, it cannot be brought to ſubſcribe to
Lights, to temperate Heats, to predominacies by occult
ties, and to ſuch like vain Imaginations, that are ſo far from
ing, or being poſſible to be Cauſes of the Tide; that on the
1trary, the Tide is the cauſe of them, that is, of bringing them
into the brains more apt for loquacity and oſtentation, than for
the ſpeculation and diſcovering of the more abſtruſe ſecrets of
Nature; which kind of people, before they can be brought to
prononnce that wiſe, ingenious, and modeſt ſentence, I know it
not, ſuffer to eſcape from their mouths and pens all manner of
travagancies. And the onely obſerving, that the ſame Moon, and
the ſame Sun operate not with their light with their motion, with
great heat, or with temperate, on the leſſer reeeptaces of Water,
but that to effect their flowing by heat, they muſt be reduced to
little leſſe than boiling, and in ſhort, we not being able artificially
to imitate any way the motions of the Tide, ſave only by the
tion of the Veſſel, ought it not to ſatisfie every one, that all
the other things alledged, as cauſes of thoſe eſſects, are
vaine fancies, and altogether eſtranged from the Truth. I

ſay, therefore, that if it be true, that of one effect there is but
one ſole primary cauſe, and that between the cauſe and effect,
there is a firm and conſtant connection; it is neceſſary that
ſoever there is ſeen a firm and conſtant alteration in the effect,
there be a firm and conſtant alteration in the cauſe. And
cauſe the alterations that happen in the ebbing and flowing in
ſeveral parts of the Year and Moneths, have their periods firm and
conſtant, it is neceſſary to ſay, that a regular alteration in thoſe
ſame times happeneth in the primary cauſe of the ebbings and
flowings. And as for the alteration that in thoſe times happens

in the ebbings and flowings conſiſteth onely in their greatneſs;
that is, in the Waters riſing and falling more or leſſe, and in
running with greater or leſſe impetus; therefore it is neceſſary,
that that which is the primary cauſe of the ebbing and flowing,
doth in thoſe ſame determinate times increaſe and diminiſh its
force. But we have already concluded upon the inequality and
irregularity of the motion of the Veſſels containing the Water to
be the primary cauſe of the ebbings and flowings. Therefore
it is neceſſary, that that irregularity, from time to time,
ſpondently grow more irregular, that is, grow greater and leſſer.
Now it is requiſite, that we call to minde, that the irregularity,
that is, the different velocity of the motions of the Veſſels, to
wit, of the parts of the Terreſtrial Superficies, dependeth on
their moving with a compound motion, reſulting from the
mixtion of the two motions, Annual and Diurnal, proper to the
whole Terreſtrial Globe; of which the Diurnal converſion, by
one while adding to, and another while ſubſtracting from, the
Annual motion, is that which produceth the irregularity in the
compound motion; ſo that, in the additions and ſubſtractions,
that the Diurnal revolution maketh from the Annual motion,
1conſiſteth the original cauſe of the irregular motion of the
ſels, and conſequently of the Ebbing and Flowing: inſomuch

that if theſe additions and ſubſtractions ſhould alwayes proceed
in the ſame proportion, in reſpect of the Annual motion, the
cauſe of the Ebbing and Flowing would indeed continue, but
yet ſo as that they would perpetually return in the ſelf ſame
ner: But we are to finde out the cauſe of making the ſame
bings and Flowings in divers times greater and leſſer:
fore we muſt (if we will retain the identity of the cauſe) find the
alteration in theſe additions and ſubſtractions, that make them
more & leſs potent, in producing thoſe effects which depend
upon. But I ſee not how that potency and impotence can be
duced, unleſſe by making the ſame additions and ſubſtractions,
one while greater, and another while leſſer; ſo that the
tion and the retardment of the compound motion, may be made,
ſometimes in greater, and ſometimes in leſſer proportion.
The alterations
in the effects argue
alteration in the
cauſe.
The cauſes at
large aſſigned of
the Periods
nethly and
al of the ebbing
and flowing.
The monethly
and annual
tions of the tide can
depend upon
thing, ſave on the
alteration of the
additions &
ſtractions of the
diurnal period from
the annual.
SAGR. I feel my ſelf very gently led, as it were, by the hand,
and though I finde no rubs in the way, yet nevertheleſſe, like a
blind man, I ſee not whether your Clue leadeth me, nor can I
imagine where ſuch a Journey will end.
SALV. Though there be a great difference between my ſlow
pac't Philoſophy, and your more nimble Reaſon, yet
leſſe, in this particular which we are now upon, I do not much
wonder, if the apprehenſiveneſſe of your wit be a little
red by the dark and thick miſt that hides the mark, at which we
aime: and that which leſſeneth my admiration is, the
brance of the many hours, many dayes, yea more, many nights
that I have conſumed in this contemplation, and of the many
times that, deſpairing to bring it to a period, I have, for an
couragement of my ſelf, indeavoured to believe, by the
ple of the unfortunate Orlando, that that might not poſſibly be
true, which yet the teſtimony of ſo many credible men ſet
fore my eyes: wonder not, therefore, if this once, contrary to
your cuſtome, you do not foreſee what I intend: and if you will
needs admire, I believe that the event, as far as I can judge
expected, will make you ceaſe your wonderment.
SAGR. I thank God, that he did not permit that deſperation
of yours to end in the Exit that is fabled of the miſerable
lando, nor in that which haply is no leſſe fabulouſly related of
Ariſtotle,, that ſo neither my ſelf nor others ſhould be deprived
of the diſcovery of a thing, as abſtruſe as it was deſirable: I
beſeech you, therefore, to ſatisfie my eager appetite as ſoon as
you can.
SALV. I am ready to ſerve you: We were upon an inquiry
in what manner the additions and ſubſtractions of the
1all converſion from the Annual motion, could be made, one
while in a greater, and another while in a leſſer proportion;
which diverſity, and no other thing, could be aſſigned for the
cauſe of the alterations, Monethly and Annual, that are ſeen in
the greatneſſe of the Ebbings and Flowings. I will now
ſider how this proportion of the additions and ſubſtractions of

the Diurnal Revolution, and Annual motion may grow greater
and leſſer three ſeveral wayes. One is by increaſing and
niſhing the velocity of the Annual motion, retaining the
ons and ſubſtractions made by the Diurnal converſion in the
ſame greatneſſe, becauſe the Annual motion being about three
times greater, that is, more velocious than the Diurnal motion
(conſidered likewiſe in the Grand Circle) if we increaſe it
anew, the additions and ſubſtractions of the Diurnal motion
will occaſion leſſe alteration therein: but, on the other ſide,
making it more ſlow, it will be altered in greater proportion, by
that ſame diurnal motion, juſt as the adding or ſubſtracting
four degrees of velocity from one that moveth with twenty
grees, altereth his courſe leſſe, than thoſe very four degrees would
do, added or ſubſtracted from one that ſhould move onely with
ten degrees. The ſecond way would be, by making the
ons and ſubſtractions greater and leſſer, retaining the annual
tion in the ſame velocity; which is as eaſie to be underſtood, as it
is manifeſt, that a velocity v. gr. of 20. degr. is more altered by the
addition or ſubſtraction of 10. deg. than by the addition or
ction of 4. The third way would be, in caſe theſe two were joyned
together, diminiſhing the annual motion, & increaſing the diurnal
additions and ſubſtractions. Hitherto, as you ſee, it was no
hard matter to attain, but yet it proved to me very hard to find
by what means this might be effected in Nature. Yet in the end,

I finde that ſhe doth admirably make uſe thereof, and in wayes
almoſt incredible: I mean, admirable and incredible to us, but
not to her, who worketh even thoſe very things, which, to our
capacity, are of infinite wonder, with extraordinary facility and
ſimplicity: and that which it is hard for us to underſtand, is
ſie for her to effect. Now to proceed, having ſhewn that the
proportion between the additions and ſubſtractions of the
nal converſion and Annual motion may be made greater and
ſer, two wayes, (and I ſay two, becauſe the third is comprized in
the two firſt) I adde, that Nature maketh uſe of them both:
and farthermore, I ſubjoyn, that if ſhe did make uſe but of one
alone, it would be neceſſary to take away one of the two
dical alterations. That of the Monethly Period would ceaſe, if

the annual motion ſhould not alter. And in caſe the additions
and ſubſtractions of the diurnal revolution ſhould continually
1be equal, the alterations of the annual Period would fail.
Three wayes of
altering the
portion of the
ditions of the
nal Revolution to
the annual motion.
That which
us is hard to be
derſtood, is with
Nature eaſie to be
effected.
If the Diurnal
motion ſhould not
alter, the annual
Period would ceaſe
SAGR. It ſeems then, that the Monethly alteration of
bings and flowings dependeth on the alteration of the annual
motion of the Earth? And the annual alteration of thoſe
bings and flowings do, it ſeems, depend on the additions and
ſubſtractions of the diurnal converſion? And here now I finde
my ſelf worſe puzzled than before, and more out of hope of
being able to comprehend how this intricacy may be, which is
more inextricable, in my judgment, than the Gordian knot. And
I envy Simplicius, from whoſe ſilence I argue that he doth
prehend the whole buſineſſe, and is acquit of that confuſion
which greatly puzzleth my brains.
SIMP. I believe verily, Sagredus, that you are put to a
a ſtand; and I believe that I know alſo the cauſe of your
fuſion, which, if I miſtake not, riſeth from your underſtanding
part of thoſe particulars but even now alledged by Salviatus,
and but a part. It is true likewiſe that I find my ſelf free from the
like confuſion; but not for that cauſe as you think, to wit,
cauſe I apprehend the whole, nay it happens upon the quite
contrary account; namely, from my not comprehending any
thing; and confuſion is in the plurality of things, and not in
nothing.
SAGR. You ſee Salviatus, how a few checks given to
cius in the dayes preceding, have rendered him gentle, and
brought him from the capriol to the amble. But I beſeech you
without farther delay, put us both out of ſuſpence.
SALV. I will endeavour it to the utmoſt of my harſh way of
expreſſing my ſelf, the obtuſeneſſe of which, the acuteneſſe of
your wit ſhall ſupply. The accidents of which we are to enquire
the cauſes are two: The firſt reſpecteth the varieties that happen
in the ebbings and flowings in the Monethly Period; and the
thr relateth to the Annual. We will firſt ſpeak of the
ly, and then treat of the Annual; and it is convenient that we
reſolve them all according to the Fundamentals and Hypotheſis
already laid down, without introducing any novelty either in
ſtronomy, or in the Univerſe, in favour of the ebbings and
ings; therefore let us demonſtrate that of all the ſeveral
dents in them obſerved, the cauſes reſide in the things already

known, and received for true and undoubted. I ſay therefore,
that it is a truly natural, yea neceſſary thing, that one and the ſame
moveable made to move round by the ſame moving virtue in a
longer time, do make its courſe by a greater circle, rather than
by a leſſer; and this is a truth received by all, and
firmed by all experiments, of which we will produce a few.

In the wheel-clocks, and particularly in the great ones, to
1derate the time, the Artificers that make them accomodate a
tain voluble ſtaffe horozontally, and at each end of it they
ſten two Weights of Lead, and when the time goeth too ſlow,
by the onely removing thoſe Leads a little nearer to the centre
of the ſtaffe, they render its vibrations more frequent; and on
the contrary to retard it, it is but drawing thoſe Weights more
towards the ends; for ſo the vibrations are made more ſeldome,
and conſequently the intervals of the hours are prolonged.
The true
theſis may diſpatch
its revolutions in a
ſhorter time, in
leſſer circles than
in greater; the
which is proved by
two examples.
The firſt
ample.
Here the movent vertue is the ſame, namely the counterpoiſe,

the moveables are thoſe ſame Weights of lead, and their
brations are more frequent when they are neerer to the centre,
that is, when they move by leſſer circles. Hanging equal
Weights at unequal cords, and being removed from their
pendicularity, letting them go; we ſhall ſee thoſe that are
dent at the ſhorter cords, to make their vibrations under ſhorter
times, as thoſe that move by leſſer circles. Again, let ſuch a
kind of Weight be faſtened to a cord, which cord let play upon
a ſtaple faſtened in the Seeling, and do you hold the other end
of the cord in your hand, and having given the motion to the
pendent Weight, whilſt it is making its vibrations, pull the
end of the cord that you hold in your hand, ſo that the Weight
may riſe higher and higher: In its riſing you ſhall ſee the
quency of its vibrations encreaſe, in regard that they are made
ſucceſſively by leſſer and leſſer circies. And here I deſire you to

take notice of two particulars worthy to be obſerved. One is
that the vibrations of one of thoſe plummets are made with ſuch
a neceſſity under ſuch determinate times, that it is altogether
impoſſible to cauſe them to be made under other times, unleſſe
it be by prolonging, or abreviating the cord; of which you
may alſo at this very inſtant aſcertain your ſelves by experience,
tying a ſtone to a pack-threed, and holding the other end in
your hand, trying whether you can ever by any artifice be able
to ſwing it this way and that way in other than one determinate
time, unleſſe by lengthening or ſhortening the ſtring, which
you will find to be abſolutely impoſſible. The other particular
truly admirable is, that the ſelf ſame pendulum makes its
tions with one and the ſame frequency, or very little, and as it
were inſenſibly different, whether they be made by very great,
or very ſmall arches of the ſelf-ſame circumference. I mean that
whether we remove the pendulum from perpendicularity one, two,
or three degrees onely, or whether we remove it 70. 80. nay to
an entire quadrant, it being let go, will in the one caſe and in
the other make its vibrations with the ſame frequency, as well
the former where it is to move by an arch of but four or ſix
grees, as the ſecond, where it is to paſſe arches of 160. or more
1degrees. Which may the better be ſeen, by hanging two weights
at two ſtrings of equal length, and then removing them from
pendicularity, one a little way, and the other very far; the which
being ſet at liberty, will go & return under the ſame times, the one
by arches very ſmall, & the other by very great ones, from whence
followeth the concluſion of an admirable Problem; which is,

That a Quadrant of a Circle being given (take a little diagram of
the ſame, [in Fig. 3.]) as for inſtance: A B erect to the Hori­
zon, ſo as that it reſt upon the plain touching in the point B. and
an Arch being made with a Hoop well plained and ſmoothed in
the concave part, bending it according to the curvity of the
cumference A D B. So that a Bullet very round and ſmooth
may freely run to and again within it (the rim of a Sieve is very
proper for the experiment) I ſay, that the Bullet being put in any
what ever place, neer or far from the loweſt term B. As for
ſtance, putting it in the point C, or here in D, or in E; and then
let go, it will in equal times, or inſenſibly different arrive at the
term B, departing from C, or from D, or from E, or from
ever other place; an accident truly wonderfull. We may add
another accident no leſs ſtrange than this, which is, That
over by all the cords drawn from the point B to the points C,
D, E; and to any other whatſoever, taken not onely in the
drant B A, but in all the whole circumference of the Circle the
ſaid moveable ſhall deſcend in times abſolutely equal; inſomuch
that it ſhall be no longer in deſcending by the whole Diameter
erect perpendicularly upon the point B, then it ſhall in
ing by B. C. although it do ſublend but one ſole degree, or a
ſer Arch. Let us add the other wonder, which is, That the
tions of the falling bodies made by the Arches of the Quadrant
A B; are made in ſhorter times than thoſe that are made by the
cords of thoſe ſame Arches; ſo that the ſwifteſt motion, and
made by a moveable in the ſhorteſt time, to arrive from the
point A, to the term B, ſhall be that which is made, not by the
right line A, B, (although it be the ſhorteſt of all thoſe that can
de drawn between the points A. B.) but by the circumference
A D B. And any point being taken in the ſaid Arch; as for
example: The point D. and two cords drawn A D, and D. B.
the moveable departing from the qoint A, ſhall in a leſs time
come to B, moving by the two cords A D and D B. than by the
ſole cord A, B. But the ſhorteſt of all the times ſhall be that of
the fall by the Arch A D B. And the ſelf ſame accidents are
to be underſtood of all the other leſſer Arches taken from the
lowermoſt term B. upwards.
The ſecond
ample.
Two particular
notable accidents
in the penduli and
their vibrations.
Admirable
blems of
bles deſcending by
the Quadrant of a
Circle, and of thoſe
deſcending by all
the cords of the
whole Circle.
SAGR. No more, no more; for you ſo confund and fill me
with Wonders, and diſtract my thoughts ſo many ſeveral wayes,
1that I fear I ſhall have but a ſmall part of it left free and
gaged, to apply to the principal matter that is treated of, and
which of it ſelf is but even too obſcure and intricate: So that
I intreat you to vouchſafe me, having once diſpatcht the buſineſs
of the ebbings and flowings, to do this honour to my houſe (and
yours) ſome other dayes, and to diſcourſe upon the ſo many other
Problems that we have left in ſuſpence; and which perhaps are
no leſs curious and admirable, than this that hath been diſcuſſed
theſe dayes paſt, and that now ought to draw to a
cluſion.
SALV. I ſhall be ready to ſerve you, but we muſt make more
than one or two Seſſions; if beſides the other queſtions reſerved
to be handled apart, we would diſcuſſe thoſe many that pertain
to the local motion, as well of natural moveables, as of the
ed: an Argument largely treated of by our Lyncean
mick. But turning to our firſt purpoſe, where we were about to
declare, That the bodies moving circularly by a movent virtue,
which continually remaineth the ſame, the times of the
tions were prefixt and determined, and impoſſible to be made
longer or ſhorter, having given examples, and produced
ments thereof, ſenſible, and feaſible, we may confirm the ſame
truth by the experiences of the Celeſtial motions of the Planets;
in which we ſee the ſame rule obſerved; for thoſe that move by
greater Circles, confirm longer times in paſſing them. A moſt
pertinent obſervation of this we have from the Medicæan
nets, which in ſhort times make their revolutions about Jupiter:
Inſomuch that it is not to be queſtioned, nay we may hold it for
ſure and certain, that if for example, the Moon continuing to be
moved by the ſame movent faculty, ſhould retire by little and
little in leſſer Circles, it would acquire a power of abreviating
the times of its Periods, according to that Pendulum, of which in
the courſe of its vibrations, we by degrees ſhortned the cord, that
is contracted the Semidiameter of the circumferences by it paſſed.
Know now that this that I have alledged an example of it in the
Moon, is ſeen and verified eſſentially in fact. Let us call to mind,
that it hath been already concluded by us, together with Coperni-

cus, That it is not poſſible to ſeparate the Moon from the Earth,
about which it without diſpute revolveth in a Moneth: Let us
remember alſo that the Terreſtrial Globe, accompanyed alwayes
by the Moon, goeth along the circumference of the Grand Orb
about the Sun in a year, in which time the Moon revolveth about
the Earth almoſt thirteen times; from which revolution it
eth, that the ſaid Moon ſometimes is found near the Sun; that is,
when it is between the Sun and the Earth, and ſometimes
much more remote, that is, when the Earth is ſituate between
1the Moon and Sun; neer, in a word, at the time of its conjun
ction and change; remote, in its Full and Oppoſition; and the
greateſt vicinity differ the quantity of the Diameter of the
nar Orb. Now if it be true that the virtue which moveth the
Earth and Moon, about the Sun, be alwayes maintained in
the ſame vigour; and if it be true that the ſame moveable
moved by the ſame virtue, but in circles unequal, do in ſhorter
times paſſe like arches of leſſer circles, it muſt needs be granted,
that the Moon when it is at a leſſe diſtance from the Sun, that is
in the time of conjunction, paſſeth greater arches of the Grand
Orb, than when it is at a greater diſtance, that is in its Opppſition
and Full. And this Lunar inequality muſt of neceſſity be imparted
to the Earth alſo; for if we ſhall ſuppoſe a right line produced from
the centre of the Sun by the centre of the Terreſtrial Globe, and
prolonged as far as the Orb of the Moon, this ſhall be the
diameter of the Grand Orb, in which the Earth, in caſe it were
alone, would move uniformly, but if in the ſame ſemidiameter we
ſhould place another body to be carried about, placing it one
while between the Earth and Sun, and another while beyond
the Earth, at a greater diſtance from the Sun, it is neceſſary,
that in this ſecond caſe the motion common to both, according
to the circumference of the great Orb by means of the diſtance
of the Moon, do prove a little ſlower than in the other caſe,
when the Moon is between the Earth and Sun, that is at a leſſer
diſtance. So that in this buſineſſe the very ſame happeneth that
befals in the time of the clock; that lead which is placed one
while farther ſrom the centre, to make the vibrations of the
ſtaffe or ballance leſſe frequent, and another while nearer, to
make them thicker, repreſenting the Moon. Hence it may be
manifeſt, that the annual motion of the Earth in the Grand
Orb, and under the Ecliptick, is not uniform, and that its
regularity proceedeth from the Moon, and hath its Monethly
Periods and Returns. And becauſe it hath been concluded, that
the Monethly and Annual Periodick alterations of the ebbings
and flowings, cannot be deduced from any other cauſe than
from the altered proportion between the annual motion and the
additions and ſubſtractions of the diurnal converſion; and that
thoſe alterations might be made two wayes, that is by altering
the annual motion, keeping the quantity of the additions
altered, or by changing of the bigneſſe of theſe, reteining the
uniformity of annual motion. We have already found the firſt
of theſe, depending on the irregularity of the annual motion
occaſioned by the Moon, and which hath its Monethly Periods.
It is therefore neceſſary, that upon that account the ebbings
and flowings have a Monethly Period in which they do grow
1greater and leſſer. Now you ſee that the cauſe of the Monethly
Period reſideth in the annual motion; and withal you ſee how
much the Moon is concerned in this buſineſs, and how it is
with interrupted apart, without having any thing to do with either,
with Seas or Waters.
The Earths
nual motion by the
Ecliptick, unequal
by means of the
Moons motion.
SAGR. If one that never had ſeen any kinde of Stairs or
der, were ſhewed a very high Tower, and asked if ever he hoped
to climb to the top of it, I verily believe that he would anſwer he
did not, not conceiving how one ſhould come thither any way
except by flying; but ſhewing him a ſtone of but a foot high, and
asking him whether he thought he could get to the top of that,
I am certain that he would anſwer he could; and farther, that he
would not deny, but that it was not onely one, but ten, twenty,
and an hundred times eaſier to climb that: But now if he ſhould
be ſhewed the Stairs, by means whereof, with the facility by him
granted, it is poſſible to get thither, whither he a little before had
affirmed it was impoſſible to aſcend, I do think that laughing at
himſelf he would confeſs his dulneſs of apprehenſion. Thus,
Salviatus, have you ſtep by ſtep ſo gently lead me, that, not
without wonder, I finde that I am got with ſmall pains to that
height which I deſpaired of arriving at. 'Tis true; that the
caſe having been dark, I did not perceive that I was got nearer
to, or arrived at the top, till that coming into the open Air I
covered a great Sea, and ſpacious Country: And as in aſcending
one ſtep, there is no labour; ſo each of your propoſitions by it
ſelf ſeemed to me ſo plain, that thinking I heard but little or
thing that was new unto me, I conceived that my benefit thereby
had been little or none at all: Whereupon I was the more
zed at the unexpected exit of this diſcourſe, that hath guided me
to the knowledge of a thing which I held impoſſible to be
monſtrated. One doubt onely remains, from which I deſire to
be freed, and this it is; Whether that if the motion of the Earth
together with that of the Moon under the Zodiack are irregular
motions, thoſe irregularities ought to have been obſerved and
ken notice of by Aſtronomers, which I do not know that they
are: Therefore I pray you, who are better acquainted with theſe
things than I, to free me from this doubt, and tell me how the
caſe ſtands.
SALV. You ask a rational queſtion, and anſwering to the

jection, I ſay; That although Aſtronomy in the courſes of many
ages hath made a great progreſs in diſcovering the conſtitution
and motions of the Celeſtial bodies, yet is it not hitherto arrived
at that height, but that very many things remain undecided, and
haply many others alſo undiſcovered. It is to be ſuppoſed that the
firſt obſervers of Heaven knew no more but one motion common
1to all the Stars, as is this diurnal one: yet I believe that in few
dayes they perceived that the Moon was inconſtant in keeping
company with the other Stars; but yet withal, that many years
paſt, before that they diſtinguiſhed all the Planets: And in
ticular, I conceit that Saturn by its ſlowneſs, and Mercury by

ſon of its ſeldom appearing, were the laſt that were obſerved to
be wandring and errant. It is to be thought that many more
years run out before the ſtations and retrogradations of the three
ſuperiour Planets were known, as alſo their approximations and
receſſions from the Earth, neceſſary occaſions of introducing the
Eccentrix and Epicicles, things unknown even to Ariſtotle, for
that he makes no mention thereof. Mercury, and Venus, with
their admirable apparitions; how long did they keep
mers in ſuſpence, before that they could reſolve (not to ſpeak of
any other of their qualities) upon their ſituation? Inſomuch
that the very order onely of the Mundane bodies, and the
gral ſtructure of the parts of the Univerſe by us known, hath been
doubted of untill the time of Copernicus, who hath at laſt given
us notice of the true conſtitution, and real ſyſteme, according to
which thoſe parts are diſpoſed; ſo that at length we are certain
that Mercury, Venus, and the other Planets do revolve about
the Sun; and that the Moon revolveth about the Earth. But

how each Planet governeth it ſelf in its particular revolution, and
how preciſely the ſtructure of its Orb is framed; which is that
which is vulgarly called the Theory of the Planets, we cannot as
yet undoubtedly reſolve. Mars, that hath ſo much puzled our
Modern Aſtronomers, is a proof of this: And to the Moon her
ſelf there have been aſſigned ſeveral Theories, after that the ſaid
Copernicus had much altered it from that of Ptolomy. And to
deſcend to our particular caſe, that is to ſay, to the apparent
tion of the Sun and Moon; touching the former, there hath been
obſerved a certain great irregularity, whereby it paſſeth the two

ſemicircles of the Ecliptick, divided by the points of the
noxes in very different times; in paſſing one of which, it
eth about nine dayes more than in paſſing the other; a difference,
as you ſee, very great and notable. But if in paſſing ſmall arches,
ſuch for example as are the twelve Signs, he maintain a moſt
gular motion, or elſe proceed with paces, one while a little more
ſwift, and another more ſlow, as it is neceſſary that it do, in caſe
the annual motion belong to the Sun onely in appearance, but
in reality to the Earth in company with the Moon, it is what hath
not hitherto been obſerved, nor it may be, ſought. Touching

the Moon in the next place, whoſe reſtitutions have been
cipally lookt into an account of the Eclipſes, for which it is
ficient to have an exact knowledge of its motion about the Earth,
1it hath not been likewiſe with a perfect curioſity inquired, what
its courſe is thorow the particular arches of the Zodiack. That
therefore the Earth and Moon in running through the Zodiack,
that is round the Grand Orb, do ſomewhat accellerate at the
Moons change, and retard at its full, ought not to be doubted;
for that the ſaid difference is not manifeſt, which cometh to be
unobſerved upon two accounts; Firſt, Becauſe it hath not been
lookt for. Secondly, Becauſe that its poſſible it may not be very
great. Nor is there any need that it ſhould be great, for the
ducing the effect that we ſee in the alteration of the greatneſs of
ebbings and flowings. For not onely thoſe alterations, but the

Tides themſelves are but ſmall matters in reſpect of the grandure
of the ſubjects on which they work; albeit that to us, and to our
littleneſs they ſeem great. For the addition or ſubduction of
one degree of velocity where there are naturally 700, or 1000,
can be called no great alteration, either in that which conferreth
it, or in that Which receiveth it: the Water of our Mediterrane
carried about by the diurnal revolution, maketh about 700 miles
an hour, (which is the motion common to the Earth and to it, and
therefore not perceptible to us) & that which we ſenſibly diſcern
to be made in the ſtreams or currents, is not at the rate of full one
mile an hour, (I ſpeak of the main Seas, and not of the Straights)
and this is that which altereth the firſt, naturall, and grand
tion; and this motion is very great in reſpect of us, and of Ships:
for a Veſſel that in a ſtanding Water by the help of Oares can
make v. g. three miles an hour, in that ſame current will row
twice as far with the ſtream as againſt it: A notable difference
in the motion of the Boat, though but very ſmall in the motion
of the Sea, which is altered but its ſeven hundredth part. The
like I ſay of its riſing, and falling one, two, or three feet; and
ſcarcely four or five in the utmoſt bounds of a ſtreight, two
ſand, or more miles long, and where there are depths of hundreds
of feet; this alteration is much leſs than if in one of the Boats
that bring us freſh Water, the ſaid Water upon the arreſt of the
Boat ſhould riſe at the Prow the thickneſs of a leaf. I conclude
therefore that very ſmall alterations in reſpect of the immenſe
greatneſs, and extraordinary velocity of the Seas, is ſufficient to
make therein great mutations in relation to our ſmallneſs, and to
our accidents.
Many things
may remain as yet
unobſerved in
ſtronomy.
Saturn for its
ſlowneſs, and
cury for its
neſs of appearing
were amongſt thoſe
that were laſt
ſerved.
Particular
ctures of the Orbs
of the Planets not
yet well reſolved.
The Sun
eth one half of the
Zodiack nine days
ſooner than the
other.
The Moons
tion principally
ſought in the
count of Eclipſes.
Ebbings and
flowings are petty
things in
ſon of the vaſtneſs
of Seas, and of the
velocity of the
tion of the
ſtrial Globe.
SAGR. I am fully ſatisfied as to this particular; it remains to
declare unto us how thoſe additions and ſubſtractions derived
from the diurnal Vertigo are made one while greater, and
ther while leſſer; from which alterations you hinted that the
nual period of the augmentations and diminutions of the
bings and flowings did depend.
1
SALV. I will uſe my utmoſt endeavours to render my ſelf

intelligible, but the difficulty of the accident it ſelf, and the
great attention of mind requiſite for the comprehending of it,
conſtrains me to be obſcure. The unequalities of the additions
and ſubſtractions, that the diurnal motion maketh to or from
the annual dependeth upon the inclination of the Axis of the
urnal motion upon the plane of the Grand Orb, or, if you pleaſe,
of the Ecliptick; by means of which inclination the Equinoctial
interſecteth the ſaid Ecliptick, remaining inclined and oblique
upon the ſame according to the ſaid inclination of Axis. And the
quantity of the additions importeth as much as the whole
ter of the ſaid Equinoctial, the Earths centre being at the ſame
time in the Solſtitial points; but being out of them it importeth
leſſe and leſſe, according as the ſaid centre ſucceſſively
cheth to the points of the Equinoxes, where thoſe additions are
leſſer than in any other places. This is the whole buſineſſe, but
wrapt up in the obſcurity that you ſee.
The cauſes of
the inequality of
the additions and
ſubſtractions of the
diurnal converſion
from the annual
motion.
SAGR. Rather in that which I do no not ſee; for hitherto I
comprehend nothing at all.
SALV. I have already foretold it. Nevertheleſſe we will try
whether by drawing a Diagram thereof, we can give ſome
ſmall light to the ſame; though indeed it might better be ſet
forth by ſolid bodies than by bare Schemes; yet we will help our
ſelves with Perſpective and fore-ſhortning. Let us draw
fore, as before, the circumference of the Grand Orb, [as in
Fig. 4.] in which the point A is underſtood to be one of the
Solſtitials, and the diameter A P the common Section of the
Solſtitial Colure, and of the plane of the Grand Orb or
tick; and in that ſame point A let us ſuppoſe the centre of the
Terreſtrial Globe to be placed, the Axis of which C A B,
clined upon the Plane of the Grand Orb, falleth on the plane of
the ſaid Colure that paſſeth thorow both the Axis of the
ctial, and of the Ecliptick. And for to prevent confuſion, let
us only draw the Equinoctial circle, marking it with theſe
cters D G E F, the common ſection of which, with the plane of
the grand Orb, let be the line D E, ſo that half of the ſaid
quinoctial D F E will remain inclined below the plane of the
Grand Orb, and the other half D G E elevated above. Let
now the Revolution of the ſaid Equinoctial be made, according
to the order of the points D G E F, and the motion of the
tre from A towards E. And becauſe the centre of the Earth
being in A, the Axis C B (which is erect upon the diameter of
the Equinoctial D E) falleth, as hath been ſaid, in the
tial Colure, the common Section of which and of the
Grand Orb, is the diameter P A, the ſaid line P A ſhall
1be perpendicular to the ſame D E, by reaſon that the Colure is
erect upon the grand Orb; and therefore the ſaid D E,
ſhall be the Tangent of the grand Orb in the point A.
So that in this Poſition the motion of the Centre by the arch
A E; that is, of one degree every day differeth very little; yea,
is as if it were made by the Tangent D A E. And becauſe by
means of the diurnal motion the point D, carried about by G,
unto E, encreaſeth the motion of the Centre moved almoſt in the
ſame line D E, as much as the whole diameter D E amounts
unto; and on the other ſide diminiſheth as much, moving about
the other ſemicircle E F D. The additions and ſubductions
in this place therefore, that is in the time of the ſolſtice, ſhall be
meaſured by the whole diameter D E.
Let us in the next place enquire, Whether they be of the ſame
bigneſs in the times of the Equinoxes; and tranſporting the
Centre of the Earth to the point I, diſtant a Quadrant of a
Circle from the point A. Let us ſuppoſe the ſaid Equinoctial
to be G E F D, its common ſection with the grand Orb D E, the
Axis with the ſame inclination C B; but the Tangent of the grand
Orb in the point I ſhall be no longer D E, but another which
ſhall cut that at right Angles; and let it be this marked H I L,
according to which the motion of the Centre I, ſhall make its
greſs, proceeding along the circumference of this grand Orb.
Now in this ſtate the Additions and Subſtractions are no longer
meaſured by the diameter D E, as before was done; becauſe that
diameter not diſtending it ſelf according to the line of the annual
motion H L, rather cutting it at right angles, thoſe terms D E, do
neither add nor ſubſtract any thing; but the Additions and
Subſtractons are to be taken from that diameter that falleth
in the plane that is errect upon the plane of the grand Orb, and
that interſects it according to the line H L; which diameter in this
caſe ſhall be this G F and the Adjective, if I may ſo ſay, ſhall
be that made by the point G, about the ſemicircle G E F, and the
Ablative ſhall be the reſt made by the other ſemicircle F D G.
Now this diameter, as not being in the ſame line H L of the
annual motion, but rather cutting it, as we ſee in the point I, the
term G being elevated above, and E depreſſed below the plane
of the grand Orb, doth not determine the Additions and
ſtractions according to its whole length, but the quantity of thoſe
firſt ought to be taken from the part of the line H L, that is
tercepted between the perpendiculars drawn upon it from the
terms G F; namely, theſe two G S, and F V: So that the
ſure of the additions is the line S V leſſer then G F, or then D E;
which was the meaſure of the additions in the Solſtice A. And
ſo ſucceſſively, according as the centre of the Earth ſhall be
1ſtituted in other points of the Quadrant A I, drawing the
gents in the ſaid points, and the perpndiculars upon the ſame
ling from the terms of the diameters of the Equinoctial drawn
from the errect planes by the ſaid Tangents to the plane of the
grand Orb; the parts of the ſaid Tangents (which ſhall
nually be leſſer towards the Equinoctials, and greater towards the
Solſtices) ſhall give us the quantities of the additions and
ctions. How much in the next place the leaſt additions differ from
the greateſt, is eaſie to be known, becauſe there is the ſame
ference betwixt them, as between the whole Axis or Diameter of
the Sphere, and the part thereof that lyeth between the
Circles; the which is leſs than the whole diameter by very near a
twelfth part, ſuppoſing yet that we ſpeak of the additions and
ſubſtractions made in the Equinoctial; but in the other
lels they are leſſer, according as their diameters do diminiſh.
This is all that I have to ſay upon this Argument, and all perhaps
that can fall under the comprehenſion of our knowledge, which,
as you well know, may not entertain any concluſions, ſave onely
thoſe that are firm and conſtant, ſuch as are the three kinds of
riods of the ebbings and flowings; for that they depend on cauſes
that are invariable, ſimple, and eternal. But becauſe that
condary and particular cauſes, able to make many alterations,
termix with theſe that are the primary and univerſal; and theſe
ſecondary cauſes being part of them inconſtant, and not to be
obſerved; as for example, The alteration of Winds, and part
(though terminate and fixed) unobſerved for their multiplicity,
as are the lengths of the Straights, their various inclinations
wards this or that part, the ſo many and ſo different depths of the
Waters, who ſhall be able, unleſs after very long obſervations, and
very certain relations, to frame ſo expeditious Hiſtories thereof, as
that they may ſerve for Hypoth eſes, and certain ſuppoſitions to
ſuch as will by their combinations give adequate reaſons of all the
appearances, and as I may ſay, Anomalie, and particular
rities that may be diſcovered in the motions of the Waters? I
will content my ſelf with advertiſing you, that the accidental
cauſes are in nature, and are able to produce many alterations;
for the more minute obſervations, I remit them to be made by
thoſe that frequent ſeveral Seas: and onely by way of a
ſion to this our conference, I will propoſe to be conſidered, how
that the preciſe times of the fluxes and refluxes do not onely
pen to be altered by the length of Straights, and by the
rence of depths; but I believe that a notable alteration may alſo
proceed from the comparing together of ſundry tarcts of Sea,
different in greatneſs; and in poſition, or, if you will,
tion; which difference happeneth exactly here in the Adriatick
1Gulph, leſſe by far than the reſt of the Mediterrane, and placed in
ſo different an inclination, that whereas that hath its bounds that
incloſeth it on the Eaſtern part, as are the Coaſts of Syria, this is
ſhut up in its more Weſterly part: and becauſe the ebbings and
flowings are much greater towards the extremities, yea, becauſe
the Seas riſings and fallings are there onely greateſt, it may
bably happen that the times of Flood at Venice may be the time of
low Water in the other Sea, which, as being much greater, and
diſtended more directly from Weſt to Eaſt, cometh in a certain
ſort to have dominion over the Adriatick: and therefore it
would be no wonder, in caſe the effects depending on the
mary cauſes, ſhould not hold true in the times that they ought,
and that correſpond to the periods in the Adriatick, as it doth
in the reſt of the Mediterrane. But theſe Particularities require
long Obſervations, which I neither have made as yet, nor ſhall I
ever be able to make the ſame for the future.
SAGR. You have, in my opinion, done enough in opening us
the way to ſo lofty a ſpeculation, of which, if you had given us
no more than that firſt general Propoſition that ſeemeth to me to
admit of no reply, where you declare very rationally, that the
Veſſels containing the Sea-waters continuing ſtedfaſt, it would
be impoſſible, according to the common courſe of Nature, that
thoſe motions ſhould follow in them which we ſee do follow;
and that, on the other ſide, granting the motions aſcribed, for
ther reſpects, by Copernicus to the Terreſtrial Globe, theſe ſame
alterations ought to enſue in the Seas, if I ſay you had told us no
more, this alone in my judgment, ſo far exceeds the vanities
troduced by ſo many others, that my meer looking on them
makes me nauſeate them, and I very much admire, that among
men of ſublime wit, of which nevertheleſs there are not a few,
not one hath ever conſidered the incompatibility that is between
the reciprocal motion of the Water contained, and the
lity of the Veſſel containing, which contradiction ſeemeth to me
now ſo manifeſt.
SALV. It is more to be admired, that it having come into the

thoughts of ſome to refer the cauſe of the Tide to the motion of
the Earth, therein ſhewing a more than common apprehenſion,
they ſhould, in afterwards driving home the motion cloſe with
no ſide; and all, becauſe they did not ſee that one ſimple and
uniform motion, as v. gr. the ſole diurnal motion of the
ſtrial Globe, doth not ſuffice, but that there is required an
ven motion, one while accelerated, and another while retarded:
for when the motion of the Veſſels are uniforme, the waters
contained will habituate themſelves thereto, without ever
king any alteration. To ſay alſo (as it is related of an ancient
1
Mathematician) that the motion of the Earth meeting with the
motion of the Lunar Orb, the concurrence of them occaſioneth
the Ebbing and Flowing, is an abſolute vanity, not onely
cauſe it is not expreſt, nor ſeen how it ſhould ſo happen, but the
falſity is obvious, for that the Revolution of the Earth is not
trary to the motion of the Moon, but is towards the ſame way.
So that all that hath been hitherto ſaid, and imagined by others,
is, in my judgment, altogether invalid. But amongſt all the
famous men that have philoſophated upon this admirable effect

of Nature, I more wonder at Kepler than any of the reſt, who
being of a free and piercing wit, and having the motion
bed to the Earth, before him, hath for all that given his ear and
aſſent to the Moons predominancy over the Water, and to
cult properties, and ſuch like trifles.
One ſingle
on of the
al Globe ſufficeth
not to produce the
Ebbing & Flowing
The opinion of
Seleucus the
thematician
red.
Kepler is with
veſpect blamed.
SAGR. I am of opinion, that to theſe more ſpaculative
ſons the ſame happened, that at preſent befalls me, namely, the
not underſtanding the intricate commixtion of the three Periods
Annual, Monethly, and Diurnal; And how their cauſes ſhould
ſeem to depend on the Sun, and on the Moon, without the Suns
or Moons having any thing to do with the Water; a buſineſſe,
for the full underſtanding of which I ſtand in need of a little
longer time to conſider thereof, which the novelty and difficulty
of it hath hitherto hindred me from doing: but I deſpair not, but
that when I return in my ſolitude and ſilence to ruminate that
which remaineth in my fancy, not very well digeſted, I ſhall
make it my own. We have now, from theſe four dayes
courſe, great atteſtations, in favour of the Copernican Syſteme,
amongſt which theſe three taken: the firſt, from the Stations and
Retrogradations of the Planets, and from their approaches, and
receſſions from the Earth; the ſecond, from the Suns revolving
in it ſelf, and from what is obſerved in its ſpots; the third, from
the Ebbing and Flowing of the Sea do ſhew very rational and
concluding.
SALV. To which alſo haply, in ſhort, one might adde a
fourth, and peradventure a fifth; a fourth, I ſay, taken from
the fixed ſtars, ſeeing that in them, upon exact obſervations, thoſe
minute mutations appear, that Copernicus thought to have been
inſenſible. There ſtarts up, at this inſtant, a fifth novelty, from
which one may argue mobility in the Terreſtrial Globe, by

means of that which the moſt Illuſtrious Signore Cæſare, of the
noble Family of the Marſilii of Bologna, and a Lyncean
demick, diſcovereth with much ingenuity, who in a very learned
Tract of his, ſheweth very particularly how that he had obſerved
a continual mutation, though very ſlow in the Meridian line,
of which Treatiſe, at length, with amazement, peruſed by me,
1I hope he will communicate Copies to all thoſe that are Students
of Natures Wonders.
Sig. Cæſare
ſilius obſerveth the
Meridian to be
moveable.
SAGR. This is not the firſt time that I have heard ſpeak of
the exquiſite Learning of this Gentleman, and of his ſhewing
himſelf a zealous Patron of all the Learned, and if this, or any
other of his Works ſhall come to appear in publique, we may be
aforehand aſſured, that they will be received, as things of great
value.
SALV. Now becauſe it is time to put an end to our
ſes, it remaineth, that I intreat you, that if, at more leaſure
ing over the things again that have been alledged you meet
with any doubts, or ſcruples not well reſolved, you will excuſe
my overſight, as well for the novelty of the Notion, as for the
weakneſſe of my wit, as alſo for the grandure of the Subject,
as alſo finally, becauſe I do not, nor have pretended to that
ſent from others, which I my ſelf do not give to this conceit,
which I could very eaſily grant to be a Chymæra, and a meer
paradox; and you Sagredus, although in the Diſcourſes paſt
you have many times, with great applauſe, declared, that you
were pleaſed with ſome of my conjectures, yet do I believe, that
that was in part more occaſioned by the novelty than by the
tainty of them, but much more by your courteſie, which did
think and deſire, by its aſſent, to procure me that content which
we naturally uſe to take in the approbation and applauſe of our
own matters: and as your civility hath obliged me to you; ſo
am I alſo pleaſed with the ingenuity of Simplicius. Nay, his
conſtancy in maintaining the Doctrine of his Maſter, with ſo
much ſtrength & undauntedneſs, hath made me much to love him.
And as I am to give you thanks, Sagredus, for your courteous
fection; ſo of Simplicius, I ask pardon, if I have ſometimes
moved him with my too bold and reſolute ſpeaking: and let him
be aſſured that I have not done the ſame out of any inducement
of ſiniſter affection, but onely to give him occaſion to ſet before
us more lofty fancies that might make me the more knowing.
SIMP. There is no reaſon why you ſhould make all theſe
cuſes, that are needleſſe, and eſpecially to me, that being
ſtomed to be at Conferences and publique Diſputes, have an
hundred times ſeen the Diſputants not onely to grow hot and
gry at one another, but likewiſe to break forth into injurious
words, and ſometimes to come very neer to blows. As for the
paſt Diſcourſes, and particulatly in this laſt, of the reaſon of
the Ebbing and Flowing of the Sea, I do not, to ſpeak the truth,
very well apprehend the ſame, but by that ſlight Idea, what
ver it be, that I have formed thereof to my ſelf, I confeſſe that
your conceit ſeemeth to me far more ingenuous than any of all
1thoſe that I ever heard beſides, but yet nevertheleſſe I eſteem it
not true and concluding: but keeping alwayes before the eyes
of my mind a ſolid Doctrine that I have learn't from a moſt
learned and ingenuous perſon, and with which it is neceſſary to
ſit down; I know that both you being asked, Whether God, by
his infinite Power and Wiſdome might confer upon the Element
of Water the reciprocal motion which we obſerve in the ſame in
any other way, than by making the containing Veſſel to move; I
know, I ſay, that you will anſwer, that he might, and knew how
to have done the ſame many wayes, and thoſe unimaginable to
our ſhallow underſtanding: upon which I forthwith conclude,
that this being granted, it would be an extravagant boldneſſe
for any one to goe about to limit and confine the Divine
Power and Wiſdome to ſome one particular conjecture of
his own.
SALV. This of yours is admirable, and truly Angelical
ctrine, to which very exactly that other accords, in like manner
divine, which whilſt it giveth us leave to diſpute, touching the
conſtitution of the World, addeth withall (perhaps to the end,
that the exerciſe of the minds of men might neither be
raged, nor made bold) that we cannot find out the works made
by his hands. Let therefore the Diſquiſition permitted and
dain'd us by God, aſſiſt us in the knowing, and ſo much more
admiring his greatneſſe, by how much leſſe we finde our ſelves
too dull to penetrate the profound Abyſſes of his infinite
dome.
SAGR. And this may ſerve for a final cloſe of our four dayes
Diſputations, after which, if it ſeem good to Salviatus, to take
ſome time to reſt himſelf, our curioſity muſt, of neceſſity, grant
him the ſame, yet upon condition, that when it is leſſe
dious for him, he will return and ſatisfie my deſire in particular
concerning the Problemes that remain to be diſcuſt, and that I
have ſet down to be propounded at one or two other
ces, according to our agreement: and above all, I ſhall very
impatiently wait to hear the Elements of the new Science of our
Academick about the natural and violent local Motions. And
in the mean time, we may, according to our cuſtome, ſpend an
hour in taking the Air in the Gondola that waiteth for us.
FINIS.
130[Figure 30]31[Figure 31]32[Figure 32]33[Figure 33]
Place this Plate
at the end of
the fourth
Dialogue
1
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1
THE
Ancient and Modern
DOCTRINE
OF
Holy Fathers,
AND
Iudicious Divines,
CONCERNING
The raſh citation of the Teſtimony of SACRED
SCRIPTURE, in Concluſions meerly Natural, and
that may be proved by Senſible Experiments, and
Neceſſary Demonſtrations.
Written, ſome years ſince, to Gratifie The moſt SERENE
CHRISTINA LOTHARINGA, Arch­
Dutcheſs of TVSCANR;
By GALILÆO GALILÆI, A Gentleman of
Florence, and Chief Philoſopher and Mathematician to
His moſt Serene Highneſs the Grand DVKE.
And now rendred into Engliſh from the Italian,
BY
THOMAS SALUSBURY.
Naturam Rerum invenire, difficile; & ubi inveneris, indicare
in vulgus, nefas. Plato.
LONDON,
Printed by WILLIAM LEYBOURN, 1661.
1
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1
TO
Her moſt Serene
HIGHNES
THE
Gran Ducheſs Mother.
Some years ſince, as Your moſt Serene Highneſs well
knoweth, I did diſcover many particulars in Hea­
ven that had been unſeen and unheard of untill
this our Age; which, as well for their Novelty, as
for certain conſequences which depend upon
them, claſhing with ſome Phyſical Propoſitions commonly recei­
ved by the Schools, did ſtir up againſt me no ſmall number of
ſuch as profeſſed the vulgar Philoſophy in the Univerſities; as if
I had with my own hand newly placed theſe things in Heaven to
obſcure and diſturb Nature and the Sciences: who forgetting
that the multitude of Truths contribute, and concur to the inve­
ſtigation, augmentation, and eſtabliſhment of the Arts, and not to
their diminution, and deſtruction; and at the ſame time ſhewing
themſelves more affectionate to their own Opinions, than to
Truth, went about to deny, and to diſprove thoſe Novelties; of
which their very ſenſe, had they but pleaſed to have intenſly be­
held them, would have rendered them thorowly aſſured. And
to this purpoſe they alledged ſundry things, and publiſhed cer­
tain Papers fraughted with vain diſcourſes; and which was a
more groſs errour, interwoven with the atteſtations of the Sacred
Scriptures, taken from places by them not rightly underſtood,
and which did not any thing concern the point for which they
were produced Into which errour perhaps they would not
have run, if they had but been advertiſed of a moſt profitable
Document which S. Auguſtine giveth us, concerning our pro­
ceeding warily, in making poſitive determinations in points that
1are obſcure and hard to be underſtood by the meer help of
ratiocination; where treating (as we) of a certain natural conclu­
ſion concerning Celeſtial Bodies, he thus writes: (a) But now

having evermore a reſpect to the moderation of pious Gravity,
we ought to believe nothing unadviſedly in a doubtful point; leſt
we conceive a prejudice againſt that, in favour to our Errour,
which Truth hereafter may diſcover to be no wiſe contrary to the
Sacred Books either of the Old, or New Teſtament.
(a) Nunc au­
tem, ſervatâ ſem­
per moderatione piæ
gravitatis, nihil
credere de re ob­
ſcurâ temerè de­
bemus, ne fortè,
quod poſtea veritas
patefecerit, quam­
vis Libris Sanct is,
ſive Teſtamenti
Veteris, ſive No­
vi, nisllo modo eſſe
poſſit adverſum,
tamen propter a­
morem noſtri erro­
ris, oderimus.
It hath ſince come to paſs, that Time hath by degrees diſco­
vered to every one the truths before by me indicated: and to­
gether with the truth of the fact, a diſcovery hath been made of
the difference of humours between thoſe who ſimply and with­
out paſſion did refuſe to admit ſuch like Phænomena for true, and
thoſe who to their incredulity had added ſome diſcompoſed af­
fection: For as thoſe who were better grounded in the Science of

Aſtronomy, and Natural Philoſophy, became ſatisfied upon my
firſt ntimation of the news; ſo all thoſe who ſtood not in the
Negative, or in doubt for any other reaſon, but becauſe it was
an unlookt-for-Novelty, and becauſe they had not an occaſion of
ſeeing a ſensible experiment thereof, did by degrees come to ſa­
risfie themſelves: But thoſe, who beſides the love they bore to
their firſt Errour, have I know not what imaginary intereſs to
render them diſaffected; not ſo much towards the things, as to­
wards the Author of them, not being able any longer to deny
them, conceal themſelves under an obſtinate ſilence; and being
exaſperated more than ever by that whereby thoſe others were
ſatisfied and convinced, they divert their thoughts to other pro­
jects, and ſeek to prejudice me ſome other wayes: of whom I
proreſs that I would make no more account than I have done of
thoſe who heretofore have contradicted me (at whom I alwaies
laugh, as being aſſured of the iſſue that the buſineſs is to have)
but that I ſee that thoſe new Calumnies and Perſecutions do not
determine in our greater or leſier Learning (in which I will ſcarce
pretend to any thing) but extend ſo far as to attempt to aſperſe
me with Crimes which ought to be, and are more abhorred by me
than Death it ſelf: Nor ought I to content my ſelf that they
are known to be unjuſt by thoſe onely who know me and them,
but by all men whatſoever. They perſiſting therefore in their
firſt Reſolution, Of ruining me and whatſoever is mine, by all
imaginable waies; and knowing how that I in my Studies of
Aſtronomy and Philoſophy hold, as to the Worlds Syſteme,
That the Sun, without changing place, is ſituate in the Centre
of the Converſion of the Celeſtial Orbes; and that the Earth,
convertible about its own Axis, moveth it ſelf about the Sun:
And moreover underſtanding, that I proceed to maintain this Po­
1ſition, not onely by refuting the Reaſons of Ptolomy and Ariſto­
tle, but by producing many on the contrary; and in particular,
ſome Phyſical pertaining to Natural Effects, the cauſes of which
perhaps can be by no other way aſſigned; and others Aſtrono­
mical depending upon many circumſtances and encounters of
new Diſcoveries in Heaven, which manifeſtly confute the Ptolo­
maick Syſteme, and admirably agree with and confirm this other
Hypotheſis: and poſſibly being aſhamed to ſee the known truth
of other Poſitions by me aſſerted, different from thoſe that have
been commonly received; and therefore diſtruſting their de­
fence ſo long as they ſhould continue in the Field of Philoſo­
phy: for theſe reſpects, I ſay, they have reſolved to try whe­
ther they could make a Shield for the fallacies of their Argu­
ments of the Mantle of a feigned Religion, and of the Autho­
rity of the Sacred Scriptures, applyed by them with little judg­
ment to the confutation of ſuch Reaſons of mine as they had
neither underſtood, nor ſo much as heard.
Lib_{+} 2. Geneſi
ad Literam in
fine.
And firſt, they have indeavoured, as much as in them lay, to
divulge an opiniou thorow the Univerſe, that thoſe Propoſitions
are contrary to the Holy Letters, and conſequently Damnable
and Heretical: And thereupon perceiving, that for the moſt
part, the inclination of Mans Nature is more prone to imbrace
thoſe enterprizes, whereby his Neighbour may, although un­
juſtly, be oppreſſed, than thoſe from whence he may receive
juſt incouragement; it was no hard matter to find thoſe Com­
plices, who for ſuch (that is, for Damnable and Heretical) did
from their Pulpits with unwonted confidence preach it, with but
an unmerciful and leſs conſiderate injury, not only to this Do­
ctrine, and to its followers, but to all Mathematicks and Ma­
thematicians together. Hereupon aſſuming greater confidence,
and vainly hoping that that Seed which firſt took root in their un­
ſound mindes, might ſpread its branches, and aſcend towards
Heaven, they went ſcattering rumours up and down among the
People, That it would, ere long be condemned by Supreme Au­
thority: and knowing that ſuch a Cenſure would ſupplant
not onely theſe two Concluſions of the Worlds Syſteme, but
would make all other Aſtronomical and Phyſical Obſervations
that have correſpondence and neceſſary connection therewith to
become damnable, to facilitate the buſineſs they ſeek all they
can to make this opinion (at leaſt among the vulgar) to ſeem new,
and peculiar to my ſelf, not owning to know that Nicholas Coper­
nicus was its Authour, or rather Reſtorer and Confirmer: a per­
ſon who was not only a Catholick, but a Prieſt, Canonick, and
ſo eſteemed, that there being a Diſpute in the Lateran Council,
under Leo X. touching the correction of the Eccleſiaſtick Ca­
1lendar, he was ſent for to Rome from the remoteſt parts of
Germany, for to aſſiſt in this Reformation, which for that time
was left imperfect, onely becauſe as then the true meaſure of
the Year and Lunar Moneth was not exactly known: whereupon
it was given him in charge by the Biſhop of Sempronia, at that
time Super-intendent in that Affair, to ſearch with reiterated
ſtudies and pains for greater light and certainty, touching thoſe
Cœleſtial Motions. Upon which, with a Labour truly Atlantick
and with his admirable Wit, ſetting himſelf again to that Study,
he made ſuch a progreſs in theſe Sciences, and reduced the
knowledge of the Cœleſtial Motions to ſuch exactneſſe, that he
gained the title of an Excellent Aſtronomer. And, according
unto his Doctrine, not only the Calendar hath been ſince regu­
lated, but the Tables of all the Motions of the Planets have al­
ſo been calculated: and having reduced the ſaid Doctrine into
ſix Books, he publiſhed them to the World at the inſtance of
the Cardinal of Capua, and of the Biſhop of Culma. And in
regard that he had re-aſſumed this ſo laborious an enterprize by
the order of The Pope; he dedicated his Book De Revolutioni­
bus Cœleſtibus to His Succeſſour, namely Paul III. which, being
then alſo Printed, hath been received by The Holy Church, and
read and ſtudied by all the World, without any the leaſt um­
brage of ſcruple that hath ever been conceived at his Doctrine;
The which, whilſt it is now proved by manifeſt Experiments and
neceſſary Demonſtrations to have been well grounded, there
want not perſons that, though they never ſaw that ſame Book in­
tercept the reward of thoſe many Labours to its Authour, by
cauſing him to be cenſured and pronounced an Heretick; and
this, only to ſatisfie a particular diſpleaſure conceived, without
any cauſe, againſt another man, that hath no other intereſt in
Copernicus, but only as he is an approver of his Doctrine.
Now in regard of theſe falſe aſperſions, which they ſo unjuſtly
ſeek to throw upon me, I have thought it neceſſary for my juſti­
fication before the World (of whoſe judgment in matters of
Religion and Reputation I ought to make great eſteem) to
diſcourſe concerning thoſe Particulars, which theſe men produce
to ſcandalize and ſubvert this Opinion, and in a word, to con­
demn it, not only as falſe, but alſo as Heretical; continually
making an Hipocritical Zeal for Religion their Shield; going a­
bout moreover to intereſt the Sacred Scriptures in the Diſpute,
and to make them in a certain ſenſe Miniſters of their deceiptful
purpoſes: and farthermore deſiring, if I miſtake not, contrary to
the intention of them, and of the Holy Fathers to extend (that I
may not ſay abuſe) their Authority, ſo as that even in Concluſions
meerly Natural, and not de Fide, they would have us altogether
1leave Senſe and Demonſtrative Reaſons, for ſome place of Scri­
pture which ſometimes under the apparent words may contain
a different ſenſe. Now I hope to ſhew with how much
greater Piety and Religious Zeal I proceed, than they do, in that
I propoſe not, that the Book of Copernicus is not to be condemn­
ed, but that it is not to be condemned, as they would have it;
without underſtanding it, hearing it, or ſo much as ſeeing it;
and eſpecially he being an Author that never treateth of matters
of Religion or Faith; nor by Reaſons any way depending on the
Authority of Sacred Scripoures whereupon he may have erroni­
ouſly interpreted them; but alwaies inſiſts upon Natural Conclu­
ſions belonging to the Celeſtial Motions, handled with Aſtrono­
mical and Geometrical Demonſtrations. Not that he had not a

reſpect to the places of the Sacred Leaves, but becauſe he knew
very well that his ſaid Doctrine being demonſtrated, it could
not contradict the Scriptures, rightly, and according to their true
meaning underſtood. And therefore in the end of his Epiſtle
Dedicatory, ſpeaking to The Pope, he ſaith thus: (b) If there
ſhould chance to be any Matæologiſts, who though ignorant in all
the Mathematicks, yet pretending a skill in thoſe Learnings,
ſhould dare, upon the authority of ſome place of Scripture wreſted
to their purpoſe, to condemn and cenſure this my Hypotheſis, I
value them not, but ſhall ſlight their inconſiderate Judgement. For
it is not unknown, that Lactantius (otherwiſe a Famous Author,
though mean Mathematician) writeth very childiſhly touching the
Form of the Earth, when he ſcoffs at thoſe who affirm the Earth to
be in Form of a Globe. So that it ought not to ſeem ſtrange to the
Ingenious, if any ſuch ſhould likewiſe now deride us. The Ma­
thematicks are written for Mathematitians, to whom (if I deceive
not my ſelf) theſe Labours of mine ſhall ſeem to add ſomething,
as alſo to the Common-weale of the Church, whoſe Government is
now in the hands of Your Holineſs.
(c) Si fort aſſeerunt
Matæologi, qui
cum omnium Ma­
thematicum igna­
ri ſint, tamen de tis
judicium aſſu­
munt, propter ali­
quem locum Scri­
ptur æ, malè ad ſu­
um propoſitum, de­
tortum, auſi fue­
rint hoc meum in­
ſtitutum reprehen­
dere ac inſectari,
illos nihil moror,
adeò ut etiam illo­
rum judicium, tan­
guam temera ium
contemnam. Non
enim obſcurum eſt,
Lact antium, cele­
lebrem alioqui
Scriptorem, ſed
Mathematicum
parvum, admodum
pueriliter de forma
Terræ loqui, cùm
deridet eos, qui
Terram, Globi for­
mam habere prodi­
derunt. Itaque non
debet mirum vide­
ri ſtudioſis, ſi qui
tales, nos ettam ri­
debunt. Mathema­
ta Mathematicis
ſcribuntur; quibus
& hi noſtri labo­
res, (ſi me non fal­
lit opinio) vide­
buntur etiam Rei­
publicæ Eccleſia­
ſticæ conducere a­
liquid, cujus Prin­
cipatum Tua San­
ctitas nunc teness.
And of this kinde do theſe appear to be who indeavour to
perſwade that Copernicus may be condemned before his Book is
read; and to make the World believe that it is not onely lawfull
but commendable ſo to do, produce certain Authorities of the
Scripture, of Divines, and of Councils; which as they are by me
had in reverence, and held of Supream Authority, inſomuch that
I ſhould eſteem it high temerity for any one to contradict them
whilſt they are uſed according to the In ſtitutes of Holy Church,
ſo I believe that it is no errour to ſpeak, ſo long as one hath rea­
ſon to ſuſpect that a perſon hath a deſire, for ſome concern of
his own, to produce and alledge them, to purpoſes different from
thoſe that are in the moſt Sacred intention of The Holy Church.
Therefore I not onely proteſt (and my ſincerity ſhall manifeſt it
1ſelf) that I intend to ſubmit my ſelf freely to renounce thoſe et­
rors, into which, through ignorance, I may run in this Diſcourſe
of matters pertaining to Religion; but I farther declare, that I
deſire not in theſe matters to engage diſpute with any one, al­
though it ſhould be in points that are diſputable: for my end
endeth onely to this, That if in theſe conſiderations, beſides my
own profeſſion, amongſt the errours that may be in them, there
be any thing apt to give others an hint of ſome Notion beneficial
to the Holy Church, touching the determining about the Coper­
nican Syſteme, it may be taken and improved as ſhall ſeem beſt
to my Superiours: If not, let my Book be torn and burnt; for
that I do neither intend, nor pretend to gain to my ſelf any fruit
from my writings, that is not Pious and Catholick. And more­
over, although that many of the things that I obſerve have been
ſpoken in my own hearing, yet I ſhall freely admit and grant to
thoſe that ſpake them, that they never ſaid them, if ſo they
pleaſe, but confeſs that I might have been miſtaken: And
therefore what I ſay, let it be ſuppoſed to be ſpoken not by them,
but by thoſe which were of this opinion.
The motive therefore that they produce to condemn the Opi­
nion of the Mobility of the Earth, and Stability of the Sun, is, that
reading in the Sacred Leaves, in many places, that the Sun mo­
veth, that the Earth ſtandeth ſtill; and the Scripture not being
capable of lying, or erring, it followeth upon neceſſary conſe­
quence, that the Poſition of thoſe is Erronious and Heretical, who
maintain that the Sun of it ſelf is immoveable, and the Earth
moveable.
Touching this Reaſon I think it fit in the firſt place, to con­
ſider, That it is both piouſly ſpoken, and prudently affirmed, That
the Sacred Scripture can never lye, when ever its true meaning is
underſtood: Which I believe none will deny to be many times
very abſtruce, and very different from that which the bare ſound
of the words ſignifieth. Whence it cometh to paſs, that if ever
any one ſhould conſtantly confine himſelf to the naked Gram­
matical Sence, he might, erring himſelf, make not only Contra­
dictions and Propoſitions remote from Truth to appear in the
Scriptures, but alſo groſs Hereſies and Blaſphemies: For that we
ſhould be forced to aſſign to God feet, and hands, and eyes, yea
more corporal and humane affections, as of Anger, of Repen­
tance, of Hatred, nay, and ſometimes the Forgetting of things
paſt, and Ignorance of thoſe to come: Which Propoſitions, like
as (ſo the Holy Ghoſt affirmeth) they were in that manner pro­
nounced by the Sacred Scriptures, that they might be accommo­
dated to the Capacity of the Vulgar, who are very rude and un­
learned; ſo likewiſe, for the ſakes of thoſe that deſerve to be di­
1ſtinguiſhed from the Vulgar, it is neceſſary that grave and skilful
Expoſitors produce the true ſenſes of them, and ſhew the parti­
cular Reaſons why they are dictated under ſuch and ſuch words.
And this is a Doctrine ſo true and common amongſt Divines,
that it would be ſuperfluous to produce any atteſtation
thereof.
Hence methinks I may with much more reaſon conclude, that
the ſame holy Writ, when ever it hath had occaſion to pronounce
any natural Concluſion, and eſpecially, any of thoſe which are
more abſtruce, and difficult to be underſtood, hath not failed to
obſerve this Rule, that ſo it might not cauſe confuſion in the
mindes of thoſe very people, and render them the more contu­
macious againſt the Doctrines that were more ſublimely myſteri­
ous: For (like as we have ſaid, and as it plainly appeareth) out
of the ſole reſpect of condeſcending to Popular Capacity, the
Scripture hath not ſcrupled to ſhadow over moſt principal and
fundamental Truths, attributing, even to God himſelf, qualities
extreamly remote from, and contrary unto his Eſſence. Who
would poſitively affirm that the Scripture, laying aſide that re­
ſpect, in ſpeaking but occaſionally of the Earth, of the Water, of
the Sun, or of any other Creature, hath choſen to confine it
ſelf, with all rigour, within the bare and narrow literal ſenſe of
the words? And eſpecially, in mentioning of thoſe Crea­
tures, things not at all concerning the primary Inſtitution of
the ſame Sacred Volume, to wit, the Service of God, and the
ſalvation of Souls, and in things infinitely beyond the appre­
henſion of the Vulgar?
This therefore being granted, methinks that in the Diſcuſſion
of Natural Problemes, we ought not to begin at the authority
of places of Scripture; but at Senſible Experiments and Ne­
ceſſary Demonſtrations: For, from the Divine Word, the
Sacred Scripture and Nature did both alike proceed; the firſt,
as the Holy Ghoſts Inſpiration; the ſecond, as the moſt obſer­
vant Executrix of Gods Commands: And moreover it being
convenient in the Scriptures (by way of condeſcenſion to the
underſtanding of all men) to ſpeak many things different, in
appearance; and ſo far as concernes the naked ſigniſication of
the words, from abſolute truth: But on the contrary, Nature
being inexorable and immutable, and never paſſing the bounds
of the Laws aſſigned her, as one that nothing careth whether
her abſtruſe reaſons and methods of operating be, or be not ex­
poſed to the Capacity of Men; I conceive that that, concer­
ning Natural Effects, which either Senſible Experience ſets be­
fore our eyes, or Neceſſary Demonſtrations do prove unto us,
ought not, upon any account, to be called into queſtion, much
1leſs condemned upon the teſtimony of Texts of Scripture, which
may, under their words, couch Senſes ſeemingly contrary there­
to; In regard that every Expreſſion of Scripture is not tied to
ſo ſtrict conditions, as every Effect of Nature: Nor doth God
leſs admirably diſcover himſelf unto us in Nature's Actions, than
in the Scriptures Sacred Dictions. Which peradventure Tertul-

lian intended to expreſs in thoſe words: (c) We conclude, God
is known; firſt, by Nature, and then again more particularly
known by Doctrine: by Nature, in his Works; by Doctrine, in his
Word preached.
Nos definimus,
Deum, primò N.­
tura cognoſcen­
dum; Deinde, Do­
ctrina recognoſcen­
dum: Natura ex
operibus; Doctri­
na ex pr ædicatio­
nibus.
But I will not hence affirm, but that we ought to have an ex­
traordinary eſteem for the Places of Sacred Scripture, nay, being

come to a certainty in any Natural Concluſions, we ought
to make uſe of them, as moſt appoſite helps to the true Expo­
ſition of the ſame Scriptures, and to the inveſtigation of thoſe
Senſes which are neceſſarily conteined in them, as moſt true, and
concordant with the Truths demonſtrated.
Tertul. adver.
Marcion. lib. 1.
cap. 18.
This maketh me to ſuppoſe, that the Authority of the Sacred
Volumes was intended principally to perſwade men to the be­
lief of thoſe Articles and Propoſitions, which, by reaſon they
ſurpaſs all humane diſcourſe, could not by any other Science, or
by any other means be made credible, than by the Mouth of
the Holy Spirit it ſelf. Beſides that, even in thoſe Propoſitions,
which are not de Fide, the Authority of the ſame Sacred Leaves
ought to be preferred to the Authority of all Humane Sciences
that are not written in a Demonſtrative Method, but either with
bare Narrations, or elſe with probable Reaſons; and this I hold
to be ſo far convenient and neceſſary, by how far the ſaid Di­
vine Wiſdome ſurpaſſeth all humane Judgment and Conjecture.
But that that ſelf ſame God who hath indued us with Senſes,
Diſcourſe, and Underſtanding hath intended, laying aſide the
uſe of theſe, to give the knowledg of thoſe things by other means,
which we may attain by theſe, ſo as that even in thoſe Natural
Concluſions, which either by Senſible Experiments or Neceſſary
Demonſtrations are ſet before our eyes, or our Underſtanding, we
ought to deny Senſe and Reaſon, I do not conceive that I am
bound to believe it; and eſpecially in thoſe Sciences, of which
but a ſmall part, and that divided into Concluſions is to be
found in the Scripture: Such as, for inſtance, is that of Aſtro­
nomy, of which there is ſo ſmall a part in Holy Writ, that it doth
not ſo much as name any of the Planets, except the Sun and the
Moon, and once or twice onely Venus under the name of Luci­
fer. For if the Holy Writers had had any intention to perſwade
People to believe the Diſpoſitions and Motions of the Cœleſtial
Bodies; and that conſequently we are ſtill to derive that know­
1ledge from the Sacred Books they would not, in my opinion, have
ſpoken ſo little thereof, that it is as much as nothing, in compa­
riſon of the infinite admirable Concluſions, which in that Sci­
ence are comprized and demonſtrated Nay, that the Authours
of the Holy Volumes did not only not pretend to teach us the
Conſtitutions and Motions of the Heavens and Stars, their Fi­
gures, Magnitudes, and Diſtances, but that intentionally (al­
beit that all theſe things were very well known unto them) they

forbore to ſpeak of them, is the opinion of the Moſt Holy & Moſt
Learned Fathers: and in S. Auguſtine we read the following words.
(c) It is likewiſe commonly asked, of what Form and Figure
we may believe Heaven to be, according to the Scriptures: For
many contend much about thoſe matters, which the greater pru­
dence of our Authors hath forborn to ſpeak of, as nothing further­
ing their Learners in relation to ableſſed life; and, (which is
the chiefeſt thing) taking up much of that time which ſhould be
ſpent in holy exerciſes. For what is it to me whether Heaven, as
a Sphere, doth on all ſides environ the Earth, a Maſs ballanced in
the middle of the World; or whether like a Diſh it doth onely cover
or overcaſt the ſame? But becauſe belief of Scripture is urged for
that cauſe, which we have oft mentioned, that is, That none through
ignorance of Divine Phraſes, when they ſhall find any thing of this
nature in, or hear any thing cited out of our Bibles which may ſeem
to oppoſe manifeſt Concluſions, ſhould be induced to ſuſpect their
truth, when they admoniſh, relate, & deliver more profitable matters
Briefly be it ſpoken, touching the Figure of Heaven, that our Au­
thors knew the truth: But the H. Spirit would not, that men ſhould
learn what is profitable to none for ſalvation.
(c) Quæri etiam
ſolet, quæ forma &
figura Cæli cre­
denda ſit ſecun­
dum Scripturas
noſtras: Multi e­
nim multum diſ­
put ant de iis rebus,
quas majori pru­
dentia noſtri Auto­
res omiſerunt, ad
beatam vitam non
profutur as diſcen­
libus, & occupan­
tes (quod prius eſt)
multum prolixa,
& rebus ſalubri­
bus impendenda
temporum ſpatia.
Quid enim ad me
pertinet, utrum
Cælum, ſicut Sphæ­
ra, undique conclu­
dat Terram, in
media. Mundi mo­
le libratam; an
eam ex una par­
te deſuper, ve­
lut diſcus, ope­
riat? Sed quia de Fide agitur S cripiurærum, propter illam cauſam, quam non ſemel commemoravimus, Ne ſcilicet
quiſquam eloquia divina non intelligens, cum de his rebus tale aliquid vel invenerit in Libris Noſtris, vel ex illis
audiverit, quod perceptis aſſertionibus adver ſari videatur, nullo modo eis, cetera utilia monentibus, vel narrantibus,
vel pranuntiantibus, credat: Breviter diſcendum eſt, de figura Cæli, hoc ſciſſe Autores noſtros, quod verit as ha­
bet: Sed Spiritum Dei, qui per ipſos loquebstur, noluiſſe iſta docere homines, nulli ad ſalutem profutura. D.
Auguſt. Lib. 2. De Gen. ad literam, Cap. 9. Idem etiam legitur apud Petrum Lombardum Magiſtrum Sententiarum.
And the ſame intentional ſilence of theſe ſacred Penmen in
determining what is to be believed of theſe accidents of the Ce­
leſtial Bodies, is again hinted to us by the ſame Father in the en­
ſuing 10. Chapter upon the Queſtion, Whether we are to believe
that Heaven moveth, or ſtandeth ſtill, in theſe words: (d) There

are ſome of the Brethren that ſtart a queſtion concerning the motion
of Heaven, Whether it be fixed, or moved: For if it be moved
(ſay they) how is it a Firmament? If it ſtand ſtill, how do theſe
Stars which are held to be fixed go round from Eaſt to Weſt, the
more Norchern performing ſhorter Circuits near the Pole; ſo that
Heaven, if there be another Pole, to us unknown, may ſeem to re­
volve upon ſome other Axis; but if there be not another Pole, it
may be thought to move as a Diſcus? To whom I reply, That
1theſe points require many ſubtil and profound Reaſons, for the
making out whether they be really ſo, or no; the undertakeing and
diſeuſſing of which is neither conſiſtent with my leaſure, nor their
duty, vvhom I deſire to inſtruct in the neceſſary matters more di­
rectly conducing to their ſalvation, and to the benefit of The Holy
Church.
(d) De Motu
etiam Cæli, non­
nulli fratres quæ­
ſtionem movent, u­
trum ſtet, an mo­
veatur; quia ſi mo­
vetur, inquiunt,
quomodo Firma­
mentum eſt? Si
autem ſtat, quomo­
do Sydera quæ in
ipſo fixa credun­
tur, ab Oriente in
Occidentem circum
eunt, Septentrio­
nalibus breviores
gyros juxta cardi­
nem perag entibus;
ut Cælum, ſi est a­
lius nobis occultus
cardo, ex alio ver­
tice, ſicut Sphæra;
ſi autem nullus a­
lius cardo eſt, vel
uti diſcus rotari
videatur? Quibus
reſpondeo, Multum
ſubtilibus & labo­
rioſis rationibus
iſta perquiri, ut ve­
re percipiatur, u­
trum ita, an non
ita ſit, quibus ine­
undis atque tra­
ctandis, nec mihi
jam tempus eſt, nec
illis eſſe debet, quos
ad ſalutem ſuam,
è Sanctæ Eccleſiæ
neceſſaria utilitate
cupimus informa­
ri:
From which (that we may come nearer to our particular caſe)
it neceſſarily followeth, that the Holy Ghoſt not having intend­
ed to teach us, whether Heaven moveth or ſtandeth ſtill; nor
whether its Figure be in Form of a Sphere, or of a Diſcus, or di­
ſtended in Planum: Nor whether the Earth be contained in the
Centre of it, or on one ſide; he hath much leſs had an intention
to aſſure us of other Concluſions of the ſame kinde, and in ſuch
a manner, connected to theſe already named, that without the
dedermination of them, one can neither affirm one or the other
part; which are, The determining of the Motion and Reſt of the
ſaid Earth, and of the Sun. And if the ſame Holy Spirit hath
purpoſely pretermitted to teach us thoſe Propoſitions, as nothing
concerning his intention, that is, our ſalvation; how can it be af­
firmed, that the holding of one part rather than the other, ſhould
be ſo neceſſary, as that it is de Fide, and the other erronious?
Can an Opinion be Heretical, and yet nothing concerning the
ſalvation of ſouls? Or can it be ſaid that the Holy Ghoſt purpo­
ſed not to teach us a thing that concerned our ſalvation? I might

here inſert the Opinion of an Eccleſiaſtical ^{*} Perſon, raiſed to the

degree of Eminentiſſimo, to wit, That the intention of the Holy
Ghoſt, is to teach us how we ſhall go to Heaven, and not how Hea­
ven goeth.
* Card. Baronius.
Spiritu ſancti
mentem fuiſſe, nos
docere, quomodo ad
Cælum eatur: non
autem, quomodo
Cælum gradiatur.
Cardinal. Bar.
But let us return to conſider how much neceſſary Demonſtra­
tions, and ſenſible Experiments ought to be eſteemed in Natural
Concluſions; and of what Authority Holy and Learned Divines
have accounted them, from whom amongſt an hundred other atte­

ſtations, we have theſe that follow: (e) We must alſo carefully
heed and altogether avoid in handling the Doctrine of Moſes, to
avouch or ſpeak any thing affirmatively and confidently which
contradicteth the manifeſt Experiments and Reaſons of Philoſo­
phy, or other Sciences. For ſince all Truth is agreeable to Truth,
the Truth of Holy Writ cannot be contrary to the ſolid Reaſons
and Experiments of Humane Learning.
(e) Illud etiam
diligenter caven­
dum, & emnino
fugiendum eſt, ne
in tractanda Mo­
ſis Dectrina, quic­
quam affirmate &
aſſeveranter ſen­
tiamus & dica­
mus, quod repug­
net manifeſtis ex­
perimentis & rationibus Philoſophiæ, vel aliarum Diſciplinarum. Namque cum Verum omne ſemper cum Vero
congruat, non poteſt Verit as Sacrarum Litterarum, Veris Rationibus & Experimentis Humanarum Doctrina­
rum eſſe contraria. Perk. in Gen. circa Principium.
(f) Si manife­
ſtæ certæque Rati­
oni, velut ſancta­
rum Litterarum
objicitur autori­
ritas, non intelli­
git, qui hoc facit;
& non Scripturæ
ſenſum (ad quem
penetrare non po­
tuit) ſed ſuum po­
tius objicit verita­
ti: nec id quod in
sa, ſed quod in ſe­
ipſo velue pro ea
invenit, opponit.
And in St. Auguſtine we read: (f) If any one ſhall object
the Authority of Sacred Writ, againſt clear and manifeſt Reaſon,
he that doth ſo, knows not what he undertakes: For he objects
1againſt the Truth, not the ſenſe of the Scripture (which is be­
yond his comprehenſion) but rather his own; not what is in it, but
what, finding it in himſelf, he fancyed to be in it.
This granted, and it being true, (as hath been ſaid) that two
Truths cannot be contrary to each other, it is the office of a
Judicious Expoſitor to ſtudy to finde the true Senſes of Sacred
Texts, which undoubtedly ſhall accord with thoſe Natural Con­
cluſions, of which manifeſt Senſe and Neceſſary Demonſtrations

had before made us ſure and certain. Yea, in regard that the
Scriptures (as hath been ſaid) for the Reaſons alledged, admit in
many places Expoſitions far from the Senſe of the words; and
moreover, we not being able to affirm, that all Interpreters
ſpeak by Divine Inſpiration; For (if it were ſo) then there
would be no difference between them about the Senſes of the
ſame places; I ſhould think that it would be an act of great pru­
dence to make it unlawful for any one to uſurp Texts of Scri­
pture, and as it were to force them to maintain this or that Natu­
rall Concluſion for truth, of which Sence, & Demonſtrative, and
neceſſary Reaſons may one time or other aſſure us the contrary.
For who will preſcribe bounds to the Wits of men? Who will
aſſert that all that is ſenſible and knowable in the World is al­
ready diſcovered and known? Will not they that in other points
diſagree with us, confeſs this (and it is a great truth) that Ea
quæ ſcimus, ſint minima pars eorum quæ ignoramus? That thoſe
Truths which we know, are very few, in compariſon of thoſe
which we know not? Nay more, if we have it from the Mouth

of the Holy Ghoſt, that Deus tradidit Mundum diſputationi
eorum, ut non inveniat homo opus, quod operatus eſt Deus ab
initio ad finem: One ought not, as I conceive, to ſtop the way
to free Philoſophating, touching the things of the World, and of
Nature, as if that they were already certainly found, and all ma­
nifeſt: nor ought it to be counted raſhneſs, if one do not fit
down ſatisfied with the opinions now become as it were com­
mune; nor ought any perſons to be diſpleaſed, if others do not
hold, in natural Diſputes to that opinion which beſt pleaſeth
them; and eſpecially touching Problems that have, for thouſands
of years, been controverted amongſt the greateſt Philoſophers, as is
the Stability of the Sun, and Mobility of the Earth, an opinion
held by Pythagoras, and by his whole Sect; by Heraclides Pon­
ticus, who was of the ſame opininion; by Phylolaus, the Maſter
of Plato; and by Plato himſelf, as Ariſtotle relateth, and of
which Plutarch writeth in the life of Numa, that the ſaid Plato,
when he was grown old, ſaid, It is a moſt abſurd thing to think
otherwiſe: The ſame was believed by Ariſtarchus Samius, as
we have it in Archimedes; and probably by Archimedes him­
1ſelf; by Nicetas the Philoſopher, upon the teſtimony of Scicero,
and by many others. And this opinion hath, finally, been am­
plified, and with many Obſervations and Demonſtrations con­
firmed by Nicholaus Copernicus. And Seneca, a moſt eminent
Philoſopher, in his Book De Cometis, advertizeth us that we
ought, with great diligence, ſeek for an aſſured knowledge,
whether it be Heaven, or the Earth, in which the Diurnal Con­
verſion reſides.
Epiſt. 7. ad Mar­
cellinum.
Eccleſiaſt. cap. 3.
And for this cauſe, it would probably be prudent and proſi­
table counſel, if beſides the Articles which concern our Salvati­
on, and the eſtabliſhment of our Faith (againſt the ſtability of
which there is no fear that any valid and ſolid Doctrine can e­
ver riſe up) men would not aggregate and heap up more, with­
out neceſſity: And if it be ſo, it would certainly be a prepoſte­
rous thing to introduce ſuch Articles at the requeſt of perſons
who, beſides that we know not that they ſpeak by inſpiration
of Divine Grace, we plainly ſee that there might be wiſhed in
them the underſtanding which would be neceſſary firſt to enable
them to comprehend, and then to diſcuſs the Demonſtrations
wherewith the ſubtiler Sciences proceed in confirming ſuch like
Concluſions. Nay, more I ſhould ſay, (were it lawful to ſpeak
my judgment freely on this Argument) that it would haply
more ſuit with the Decorum and Majeſty of thoſe Sacred Vo­
lumes, if care were taken that every ſhallow and vulgar Writer
might not authorize his Books (which are not ſeldome grounded
upon fooliſh fancies) by inſerting into them Places of Holy Scri­
pture, interpreted, or rather diſtorted to Senſes as remote from
the right meaning of the ſaid Scripture, as they are neer to deri­
riſion, who not without oſtentation flouriſh out their Writings
therewith. Examples of ſuch like abuſes there might many be
produced, but for this time I will confine my ſelf to two, not
much beſides theſe matters of Aſtronomy: One of which, is that
of thoſe Pamphlets which were publiſhed againſt the Medicean
Planets, of which I had the fortune to make the diſcovery; a­
gainſt the exiſtence of which there were brought many places of
Sacred Sctipture: Now, that all the World ſeeth them to be
Planets, I would gladly hear with what new interpretations
thoſe very Antagoniſts do expound the Scripture, and excuſe their
own ſimplicity. The other example is of him who but very
lately hath Printed againſt Aſtronomers and Philoſophers, that
the Moon doth not receive its light from the Sun, but is of its own
nature reſplendent: which imagination he in the cloſe confirm­
eth, or, to ſay better, perſwadeth himſelf that he confirmeth by
ſundry Texts of Scripture, which he thinks cannot be reconciled
unleſſe his opinion ſhould be true and neceſſary. Nevertheleſſe,
1the Moon of it ſelf is Tenebroſe, and yet it is no leſſe lucid than
the Splendor of the Sun.
Hence it is manifeſt, that theſe kinde of Authors, in regard they
did not dive into the true Sence of the Scriptures, would (in caſe
their authority were of any great moment) have impoſed a neceſ­
ſity upon others to believe ſuch Concluſions for true as were re­
pugnant to manifeſt Reaſon, and to Senſe. Which abuſe Deus
avertat, that it do not gain Countenance and Authority; for if it
ſhould, it would in a ſhort time be neceſſary to proſcribe and in­
hibit all the Contemplative Sciences. For being that by nature
the number of ſuch as are very unapt to underſtand perfectly
both the Sacred Scriptures, and the other Sciences is much great­
er than that of the skilfull and intelligene; thoſe of the firſt ſort
ſuperficially running over the Scriptures, would arrogate to them­
ſelves an Authority of decreeing upon all the Queſtions in Na­
ture, by vertue of ſome Word by them miſonderſtood, and pro­
duced by the Sacred Pen-men to another purpoſe: Nor would
the ſmall number of the Intelligent be able to repreſs the furious
Torrent of thoſe men, who would finde ſo many the more fol­
lowers, in that the gaining the reputation of Wiſe men without
pains or Study, is far more grateful to humane Nature, than the
conſuming our ſelves with reſtleſs contemplations about the moſt
painfull Arts. Therefore we ought to return infinite thanks to
Almighty God, who of his Goodneſs freeth us from this fear, in
that he depriveth ſuch kinde of perſons of all Authority and, re­
poſeth the Conſulting, Reſolving, and Decreeing upon ſo im­
portant Determinations in the extraordinary Wiſdom and Can­
dor of moſt Sacred Fathers; and in the Supream Authority of
thoſe, who being guided by his Holy Spirit, cannot but determin
Holily: So ordering things, that of the levity of thoſe other men,
there is no account made. This kinde of men are thoſe, as I be­
lieve, againſt whom, not without Reaſon, Grave, and Holy Wri­
ters do ſo much inveigh; and of whom in particular S. Hierom

writeth: (g) This (Scilicet the Sacred Scripture) the talking
old woman, the doting old man, the talkative Sophiſter, all venture
upon, lacerate, teach, and that before they have learnt it. Others
induced by Pride, diving into hard words, Philoſophate amongſt
Women, touching the Holy Scriptures. Others (Oh ſhame­
ful!) Learn of Women what they teach to Men; and, as if this
were nothiug, in a certain facility of words, I may ſay of confi­
dence, expound to others what they underſtand not themſelves. I
forbear to ſpeak of thoſe of my own Profeſſion, who, if after Hu­
mane Learning they chance to attain to the Holy Scriptures, and
tickle the ears of the people with affected and Studied expreſſions,
they affirm that all they ſay, is to be entertained as the Law of God;
1and not ſtooping to learn what the Prophets and Apoſtles held,
they force incongruous teſtimonies to their own Senſe: As if it
were the genuine, and not corrupt way of teaching to deprave Sen­
tences, and Wreſt the Scripture according to their own ſingular and
contradictory humour.
(g) Hanc (Sci­
licer Sacram Scri­
pturam) garrula
arus, hanc deli­
rus ſenex hanc So­
phiſta verboſus,
h univerſi præ­
ſumunt, lacerant,
docent, anteguans
diſcant. Alij,
addacto ſupercilio,
grandia verba
trutinantes, inter
mulierculas, de
Sacris Litteris
Philoſophantur.
Alij diſcunt, prob
pudor! à fæminis,
quod viros docent,
& ne parum hoc
ſit, quadam faci­
litate verborum,
imo audaciâ, ediſ­
ſerunt aliis, quod
ipſi non intelli­
gunt. Taceo de
mei ſimilibus, qui
ſi fortè ad Scriptu­
ras Sanctas, poſt
ſeculares litteras
venerint, & ſer­
mone compoſito,
aurem populi mul­
ſerint; quicquid
dixerint, hoc le­
gem Dei putant:
nec ſcire dignan­
tur, quid Prophe­
tæ, quid Apoſtoli
ſenſerint, ſed ad
ſenſum ſuum, in­
congrua aptant te­
ſtimonia: Quaſi
grande ſit, & non
vitiociſſimum do­
cendi genus, de­
pravare ſententi­
as, & ad volun­
tatem ſuam Scri­
pturamtrahere re­
pugnantem. Je­
ron. Epiſt. ad
Paul. 103.
I will not rank among theſe ſame ſecular Writers any Theo­
logiſts, whom I repute to be men of profound Learning, and ſo­
ber Manners, and therefore hold them in great eſteem and vene­
ration: Yet I cannot deny but that I have a certain ſcruple in
my mind, and conſequently am deſirous to have it removed,
whilſt I hear that they pretend to a power of conſtraining others
by Authority of the Scriptures to follow that opinion in Natu­
ral Diſputations, which they think moſt agreeth with the Texts
of that: Holding withall, that they are not bound to anſwer
the Reaſons and Experiments on the contrary: In Explication
and Confirmation of which their judgement they ſay, That The­
ologie being the Queen of all the Sciences, ſhe ought not upon
any account to ſtoop to accomodate her ſelf to the Poſitions of
the reſt, leſs worthy, and inferior to her: But that they ought
to refer themſelves to her (as to their Supream Empereſs) and
change and alter their Concluſions, according to Theological
Statutes and Decrees. And they further add, That if in the
inferior Science there ſhould be any Concluſion certain by ver­
tue of Demonſtrations or experiments, to which there is found
in Scripture another Concluſion repugnant; the very Profeſſors
of that Science ought of themſelves to reſolve their Demonſtrati­
ons, and diſcover the falacies of their own Experiments, without
repairing to Theologers and Textuaries, it not ſuiting (as hath
been ſaid) with the dignity of Theologie to ſtoop to the inveſtiga­
tion of the falacies of the inferior Sciences: But it ſufficeth her,
to determine the truth of the Concluſion with her abſolute Au­
thority, and by her infallibility. And then the Natural Conclu­
ſions in which they ſay that we ought to bide by the meer Au­
thority of the Scripture, without gloſſing, or expounding it to
Senſes different from the Words, they affirm to be Thoſe of
which the Scripture ſpeaketh alwaies in the ſame manner; and
the Holy Fathers all receive, and expound to the ſame
Senſe.
Now as to theſe Determinations, I have had occaſion to conſi­
der ſome particulars (which I will purpoſe) for that I was made
cautious thereof, by thoſe who underſtand more than I in theſe
buſineſſes, and to whoſe judgments I alwaies ſubmit my ſelf.
And firſt I could ſay, that there might poſſibly a certain kinde of
equivocation interpoſe, in that they do not diſtinguiſh the prehe­
minences whereby Sacred Theologie meriteth the Title of Queen.
1For it might be called ſo, either becauſe that that which is taught
by all the other Sciences, is found to be comprized and demonſtra­
ted in it, but with more excellent means, and with more ſublime
Learning; in like manner, as for example; The Rules of meaſuring
of Land, & of Accountantſhip are much more excellently contain­
ed in the Arithmatick and Geometry of Euclid, than in the Practi­
ſes of Surveyours and Accomptants: Or becauſe the Subject about
which Theologie is converſant, excelleth in Dignity all the other
Subjects, that are the Matters of other Sciences: As alſo becauſe
its Documents are divulged by nobler waies. That the Title
and Authority of Queen belongeth to Theologie in the firſt
Senſe, I think that no Theologers will affirm, that have but any
in-ſight into the other Sciences; of which there are none (as I be­
lieve) that will ſay that Geometry, Aſtronomy Muſick, and Me­
dicine are much more excellently and exactly contained in the
Sacred Volumes, than in the Books of Archimedes, in Ptolomy, in
Boetius, and in Galen. Therefore it is probable that the Regal
Preheminence is given her upon the ſecond account, namely, By
reaſon of the Subject, and the admirable communicating of the
Divine Revelations in thoſe Concluſions which by other means
could not be conceived by men, and which chiefly concern the
acquiſt of eternal Beatitude. Now if Theologie being conver­
ſant about the loftieſt Divine Contemplation, and reſiding for
Dignity in the Regal Throne of the Sciences, (whereby ſhe be­
cometh of higheſt Authority) deſcendeth not to the more mean
and humble Speculations of the inferior Sciences: Nay; (as hath
been declared above) hath no regard to them, as not concerning
Bearitude; the Profeſſors thereof ought not to arrogate to them­
ſelves the Authority to determin of Controverſies in thoſe Pro­
feſſions which have been neither practiſed nor ſtudied by them.
For this would be as if an Abſolute Prince, knowing that he
might freely command, and cauſe himſelf to be obeyed, ſhould
(being neither Phiſitian nor Architect) undertake to adminiſter
Medicines, and erect Buildings after his own faſhion, to the great
endangering af the lives of the poor Patients, and to the manifeſt
deſtruction of the Edifices.
Again, to command the very Profeſſors of Aſtronomy, that
they of themſelves ſee to the confuting of their own Obſerva­
tions and Demonſtrations, as thoſe that can be no other but
Falacies and Sophiſmes, is to enjoyn a thing beyond all poſſibi­
lity of doing: For it is not onely to command them that they do
not ſee that which they ſee, and that they do not underſtand
that which they underſtand; but that in ſeeking, they finde the
contrary of that which they happen to meet with. Therefore be­
fore that this is to be done, it would be neceſſary that they were
1ſhewed the way how to make the Powers of the Soul to command
one another, and the inferior the Superior; ſo that the imaginati­
on and will might, and ſhould believe contrary to what the Intel­
lect underſtands: I ſtill mean in Propoſitions purely Natural, and
which are not de Fide, and not in the Supernatural, which are
de Fide.
I would entreat theſe Wiſe and Prudent Fathers, that they
would withal diligence conſider the difference that is between
Opinable and Demonſtrative Doctrines: To the end, that well
weighing in their minds with what force Neceſſary Illations ob­
lige, they might the better aſcertain themſelves, that it is not in
the Power of the Profeſſors of Demonſtrative Sciences to change
their Opinions at pleaſure, and apply themſelves one while to
one ſide, and another while to another; and that there is a great
difference between commanding a Methametitian or a Philoſo­
pher, and the diſpoſing of a Lawyer or a Merchant; and that the
demonſtrated Concluſions touching the things of Nature and of
the Heavens cannot be changed with the ſame facility, as the
Opinions are touching what is lawful or not in a Contract, Bar­
gain, or Bill of Exchange. This difference was well underſtood
by the Learned and Holy Fathers, as their having been at great
pains to confute many Arguments, or to ſay better, many Phi­

loſophical Fallacies, doth prove unto us; and as may expreſly be
read in ſome of them, and particularly we have in S. Auguſtine
the following words: (g) This is to be held for an undoubt­
ed Truth, That we may be confident, that whatever the Sages of
this World have demonſtrated touching Natural Points, is no waies
contrary to our Bibles: And in caſe they teach any thing in their
Books that is contrary to the Holy Scriptures, we may without any
ſcruple conclude it to be moſt falſe; And aceording to our ability
let us make the ſame appear: And let us ſo keep the Faith of our
Lord, in whom are hidden all the Treaſures of Wiſdom; that we
be neither ſeduced with the Loquacity of falſe Philoſophy, nor
ſcared by the ſuperſtition of a counterfeit Religion.
(g) Hoc indu­
bitanter tenendum
eſt, ut quicquid
Sapientes hujus
Mundi, de Natu­
ra rerum veraci­
ter demonſtrare
potuerint, oſtenda­
mus, noſtris libris
non eſſe contrari­
um: quicquid au­
tem illi, in ſuis vo­
lumintbus, contra­
rium Sacris Lit­
teris docent, ſine
ulla dubitatione
credamus, id falſiſ­
ſimum eſſe, & quo­
quo modo poſſu­
mus, etiam oſten­
damus; atque it a
teneamus Fidem
Domini noſtri, in
quaſunt abſconditi
omnes theſauri
Sapientiæ, ut ne­
que falſæ Philoſo­
phiæ loquacitate
ſeducamur, neque
ſimulata Religio­
nis ſuperſtitione
terreamur.
From which words, I conceive that I may collect this Do­
ctrine, namely, That in the Books of the Wiſe of this World,
there are contained ſome Natural truths that are ſolidly demon­
ſtrated, and others again that are barely taught; and that as to
the firſt ſort, it is the Office of wiſe Divines to ſhew that they
are not contrary to the Sacred Scriptures; As to the reſt, taught,
but not neceſſarily demonſtrated, if they ſhall contain any thing
contrary to the Sacred Leaves, it ought to be held undoubtedly
falſe, and ſuch it ought by all poſſible waies to be demon­
ſtrated.
Gen. ad Litteram.
lib I. Cap. 25.
If therefore Natural Concluſions veritably demonſtrated, are
1not to be poſtpoſed to the Places of Scripture, but that it ought
to be ſhewn how thoſe Places do not interfer with the ſaid Con­
cluſions; then its neceſſary before a Phyſical Propoſition be
condemned, to ſhew that it is not neceſſarily demonſtrated; and
this is to be done not by them who hold it to be true, but by thoſe
who judge it to be falſe. And this ſeemeth very reaſonable,
and agreeable to Nature; that is to ſay, that they may much
more eaſily find the fallacies in a Diſcourſe, who believe it to be
falſe, than thoſe who account it true and concludent. Nay, in
this particular it will come to paſſe, that the followers of this o­
pinion, the more that they ſhall turn over Books, examine the
Arguments, repeat the Obſervations, and compare the Experi­
ments, the more ſhall they be confirmed in this belief. And your
Highneſs knoweth what happened to the late Mathematick Pro­
feſſor in the Univerſity of Piſa, Who betook himſelf in his old
age to look into the Doctrine of Copernicus, with hope that he
might be able ſolidly to confute it (for that he held it ſo far to
be falſe, as that he had never ſtudied it) but it was his fortune,
that as ſoon as he had underſtood the grounds, proceedings, and
demonſtrations of Copernicus, he found himſelf to be perſwaded,
and of an oppoſer became his moſt confident Defender. I
might alſo nominate other ^{*} Mathematicians, who being moved

by my laſt Diſcoveries, have confeſſed it neceſsary to change the
formerly received Conſtitution of the World, it not being able
by any means to ſubſiſt any longer.
* P. Clavius the
Jeſuite.
If for the baniſhing this Opinion and Hypotheſis out of the
World, it were enough to ſtop the mouth of one alone, as it
may be they perſwade themſelves who meaſuring others judge­
ments by their own, think it impoſſible that this Doctrine ſhould
be able to ſubſiſt and finde any followers, this would be very ea­
ſie to be done, but the buſineſs ſtandeth otherwiſe: For to
execute ſuch a determination, it would be neceſſary to prohibite
not onely the Book of Copernicus, and the Writings of the o­
ther Authors that follow the ſame opinion, but to interdict the
whole Science of Aſtronomy; and which is more, to forbid men
looking towards Heaven, that ſo they might not ſee Mars and
Venus at one time neer to the Earth, and at another farther off,
with ſuch a difference that the latter is found to be fourty times,
and the former ſixty times bigger in ſurface at one time than at
another; and to the end, that the ſame Venus might not be
diſcovered to be one while round, and another while forked, with
moſt ſubtil hornes: and many other ſenſible Obſervations which
can never by any means be reconciled to the Ptolomaick Syſteme,
but are unanſwerable Arguments for the Copernican.
But the prohibiting of Copernicus his Book, now that by many
1new Obſervations, and by the application of many of the Lear­
ned to the reading of him, his Hypotheſis and Doctrine doth
every day appear to be more true, having admitted and tolerated
it for ſo many years, whilſt he was leſſe followed, ſtudied, and
confirmed, would ſeem, in my judgment, an affront to Truth,
and a ſeeking the more to obſcure and ſuppreſſe her, the more
ſhe ſheweth her ſelf clear and perſpicuous.
The aboliſhing and cenſuring, not of the whole Book, but
onely ſo much of it as concerns this particular opinion of the
Earths Mobility, would, if I miſtake not, be a greater detriment
to ſouls, it being an occaſion of great ſcandal, to ſee a Poſition
proved, and to ſee it afterwards made an Hereſie to believe it.
The prohibiting of the whole Science, what other would it
be but an open contempt of an hundred Texts of the Holy Scri­
ptures, which teach us, That the Glory, and the Greatneſſe of
Almighty God is admirably diſcerned in all his Works, and di­
vinely read in the Open Book of Heaven? Nor let any one
think that the Lecture of the lofty conceits that are written in
thoſe Leaves finiſh in only beholding the Splendour of the Sun,
and of the Stars, and their riſing and ſetting, (which is the term
to which the eyes of bruits and of the vulgar reach) but there
are couched in them myſteries ſo profound, and conceipts ſo ſub­
lime, that the vigils, labours, and ſtudies of an hundred and an
hundred acute Wits, have not yet been able thorowly to dive
into them after the continual diſquiſition of ſome thouſands of
years. But let the Unlearned believe, that like as that which
their eyes diſcern in beholding the aſpect of a humane body, is
very little in compariſon of the ſtupendious Artifices, which an
exquiſite and curious Anatomiſt or Philoſopher finds in the ſame
when he is ſearching for the uſe of ſo many Muſcles, Tendons,
Nerves, and Bones; and examining the Offices of the Heart,
and of the other principal Members, ſeeking the ſeat of the vi­
tal Faculties, noting and obſerving the admirable ſtructures of
the Inſtruments of the Senſes, and, without ever making an end
of ſatisfying his curioſity and wonder, contemplating the Re­
ceptacles of the Imagination, of the Memory, and of the Un­
derſtanding; So that which repreſents it ſelf to the meer ſight,
is as nothing in compariſon and proportion to the ſtrange Won­
ders, that by help of long and accurate Obſervations the Wit
of Learned Men diſcovereth in Heaven. And this is the ſub­
ſtance of what I had to conſider touching this particular.
In the next place, as to thoſe that adde, That thoſe Natural
Propoſitions of which the Scripture ſtill ſpeaks in one conſtant
tenour, and which the Fathers all unanimouſly receive in the
ſame ſenſe, ought to be accepted according to the naked and
1literal ſenſe of the Words, without gloſſes and interpretations;
and received and held for moſt certain and true; and that con­
ſequently the Mobility of the Sun, and Stability of the Earth,
as being ſuch, are de Fide to be held for true, and the contrary
opinion to be deemed Heretical: I ſhall propoſe to conſidera­
tion, in the firſt place, That of Natural Propoſitions, ſome there
are, of which all humane Science and Diſcourſe can furniſh us
only with ſome plauſible opinion, and probable conjecture ra­
ther than with any certain and demonſtrative knowledge; as for
example, whether the Stars be animated: Others there are, of
which we have, or may confidently believe that we may have,
by Experiments, long Obſervations, and Neceſſary Demonſtra­
tions an undubitable aſſurance; as for inſtance, whether the
Earth and Heavens move, or not; whether the Heavens are
Spherical, or otherwiſe. As to the firſt ſort, I doubt not in the
leaſt, that if humane Ratiocinations cannot reach them, and
that conſequently there is no Science to be had of them, but on­
ly an Opinion or Belief, we ought fully and abſolutely to com­
ply with the meer Verbal Senſe of the Scripture: But as to the
other Poſitions, I ſhould think (as hath been ſaid above) That
we are firſt to aſcertain our ſelves of the fact it ſelf, which will
aſſiſt us in finding out the true ſenſes of the Scriptures; which
ſhall moſt certainly be found to accord with the fact demonſtra­
ted, for two truths can never contradict each other. And
this I take to be a Doctrine orthodox and undoubted, for that I
ſinde it written in Saint Auguſtine, who ſpeaking to our point
of the Figure of Heaven, and what it is to be believed to be, in
regard that which Aſtronomers affirm concerning it ſeemeth to
be, contrary to the Scripture, (they holding it to be rotund,
and the Scripture calling it as it were a ^{*} Curtain, determi­

neth that we are not at all to regard that the Scripture contra­
dicts Aſtronomers; but to believe its Authority, if that which
they ſay ſhall be falſe, and founded, only on the conjectures of
humane infirmity: but if that which which they affirm be pro­
ved by indubitable Reaſons, this Holy Father doth not ſay,
that the Aſtronomers are to be enjoyned, that they themſelves
reſolving and renouncing their Demonſtrations do declare their
Concluſion to be falſe, but ſaith, that it ought to be de­
monſtrated, That what is ſaid in Scripture of a Curtain is not
contrary to their true Demonſtrations. Theſe are his words:

(h) But ſome object; How doth it appear, that the ſaying in our
Bibles, Who ſtretcheth out the Heaven as a Curtain, maketh
not againſt thoſe who maintain the Heavens to be in figure of a
Sphere? Let it be ſo, if that be falſe which they affirme: For
that is truth which is ſpoke by Divine Authority, rather than
1that which proceeds from Humane Inſirmity. But if peradven­
ture they ſhould be able to prove their Poſition by ſuch Experiments
as puts it out of queſtion, it is to be proved, that what is ſaid in
Scripture concerning a Curtain, doth in no wiſe contradict
their manifeſt Reaſons.
* Pelle, a Skin in
the Original, out
in our Bibles a
Curtain.
(h) Sed ait ali­
quis, quomodo non
eſt coutrarium iis,
qui figur am Sphæ­
ræ Cœlo tribunt,
quod ſcriptum eſt
en Libris Noſtris,
Qui extendit Cœ­
lum, ſicut pellem?
Stt ſane contrari­
um, ſi falſum eſt,
quod illi dicunt:
hoc enim verum
eſt, quod Divina
dicit authoritas,
potius quans illud,
quod humana in­
firmitas conjicit.
Sed ſi forte illud
talibus illi docu­
mentis probare po­
tuerint, at dubi­
tari inde non debe­
at; demonſtrandum
eſt, hoc quod apud
nos eſt de Pelle di­
ctum, veris illis
rationibus non eſſe
contrarium.
He proceedeth afterwards to admoniſh us that we ought to be
no leſs careful and obſervant in reconciling a Text of Scripture
with a demonſtrated Natural Propoſition, than with another
Text of Scripture which ſhould ſound to a contrary Senſe. Nay
methinks that the circumſpection of this Saint is worthy to be ad­
mired and imitated, who even in obſcure Concluſions, and of
which we may aſſure our ſelves that we can have no knowledge
or Science by humane demonſtration, is very reſerved in deter­
mining what is to be believed, as we ſee by that which he wri­
teth in the end of his ſecond Book, de Geneſi ad Litteram, ſpeak­
ing, whether the Stars are to be believed animate: (i) Which

particular, although (at preſent) it cannot eaſily be comprehended,
yet I ſuppoſe in our farther Progreſs of bandling the Scriptures,
we may meet with ſome more pertinent places, upon which it will
be permitted us (if not to determin any thing for certain, yet) to
ſuggeſt ſomewhat concerning this matter, according to the dictates
of Sacred Authority. But now, the moderation of pious gravity
being alwaies obſerved, we ought to receive nothing raſhly in
a doubtful point, leaſt perhaps we reject that out of reſpect to
our Errour, which hereafter Truth may diſcover, to be in no
wiſe repugnant to the Sacred Volumes of the Old and New Te­
ſtament.
(i) Quod licet in
praſenti facile non
poſſit comprehendi;
arbitror tamen, in
proceſſis tract an­
dærum Scriptura­
rum, opportuntora
loca poſſe occurre­
re, ubinobis de hac
re, ſecundum San­
ctæ auctoritatis
Litteras, etſi non
oſtendere certum
aliquid, tamen cre­
dere licebit. Nunc
autem, ſervat â
ſemper moderatio­
ne piæ gravitatis,
nihil credere dere
obſcura temere
debemus; ne fortè,
quoà poſtea verit as
patefecerit, quam­
vis Libris San­
ctis, ſive Teſta­
menti veteris, ſive,
novi nullo modo eſ­
ſe poſſit æeverſum,
tamen propter a­
morem noſtri er­
roris, oderimus.
By this and other places (if I deceive not my ſelf) the intent
of the Holy Fathers appeareth to be, That in Natural queſtions,
and which are not de Fide, it is firſt to be conſidered, whether
they be indubitably demonſtrated, or by ſenſible Experiments
known; or whether ſuch a knowledge and demonſtration is to be
had; which having obtained, and it being the gift of God, it
ought to be applyed to find out the true Sences of the Sacred Pa­
ges in thoſe places, which in appearance might ſeem to ſpeak to
a contrary meaning: Which will unqueſtionably be pierced into
by Prudent Divines, together with the occaſions that moved the

Holy Ghoſt, (for our exerciſe, or for ſome other reaſon to me un­
known) to veil it ſelf ſometimes under words of different ſigni­
fications.
Id. D Aug. in
Gen. ad Lute­
ram, lib. 1. in fine.
As to the other point, Of our regarding the Primary Scope of
thoſe Sacred Volumes, I cannot think that their having ſpoken
alwaies in the ſame tenour, doth any thing at all diſturb this
Rule. For if it hath been the Scope of the Scripture by way of
condeſcention to the capacity of the Vulgar at any time, to
1preſs a Propoſition in words, that bear a ſenſe different from the
Eſſence of the ſaid Propoſition; why might it not have obſerved
the ſame, and for the ſame reſpect, as often as it had occaſion to
ſpeak of the ſame thing? Nay I conceive, that to have done
otherwiſe, would but have encreaſed the confuſion, and dimi­
niſhed the credit that theſe Sacred Records ought to have a­
mongſt the Common People.
Again, that touching the Reſt and Motion of the Sun and
Earth, it was neceſſary, for accommodation. to Popular Capa­
city, to aſſert that which the Litteral ſenſe of the Scripture im­
porteth, experience plainly proveth: For that even to our dayes
people far leſs rude, do continue in the ſame Opinion upon Rea­
ſons, that if they were well weighed and examined, would be
found to be extream trivial, and upon Experiments, either whol­
ly falſe, or altogether beſides the purpoſe. Nor is it worth
while to go about to remove them from it, they being incapable
of the contrary Reaſons that depend upon too exquiſite Obſer­
vations, and too ſubtil Demonſtrations, grounded upon Abſtra­
ctions, which, for the comprehending of them, require too ſtrong
an Imagination. Whereupon, although that the Stability of
Heaveu, and Motion of the Earth ſhould be more than certain
and demonſtrated to the Wiſe; yet nevertheleſs it would be
neceſſary, for the conſervation of credit amongſt the Vulgar, to
affirm the contrary: For that of a thouſand ordinary men, that
come to be queſtioned concerning theſe particulars, its probab e
that there will not be found ſo much as one that will not an­
ſwer that he thinketh, and ſo certainly he doth, that the Sun
moveth, and the Earth ſtandeth ſtill. But yet none ought to
take this common Popular Aſſent to be any Argument of the
truth of that which is affirmed: For if we ſhould examine
theſe very men touching the grounds and motives by which they
are induced to believe in that manner; and on the other ſide
ſhould hear what Experiments and Demonſtrationslperſwade
thoſe few others to believe the contrary, we ſhould finde theſe
latter to be moved by moſt ſolid Reaſons, and the former by
ſimple appearances, and vain and ridiculous occurrences. That
therefore it was neceſſary to aſſign Motion to the Sun, and Reſt
to the earth, leſt the ſhallow capacity of the Vulgar ſhould be
confounded, amuſed, and rendred obſtinate and contumacious,
in giving credit to the principal Articles, and which are abſolute­
ly de fide, it is ſufficiently obvious. And if it was neceſſary ſo
to do, it is not at all to be wondred at, that it was with extraor­
dinary Wiſdom ſo done, in the Divine Scriptures.
But I will alledge further, That not onely a reſpect to the
Incapacity of the Vulgar, but the current Opinion of thoſe times
1made the Sacred Writers, in the points that were not neceſſary
to ſalvation, to accommodate themſelves more to the received
uſe, than to the true Eſſence of things: Of which S. Hierom
treating, writeth: (k) As if many things were not ſpoken in

the Holy Scriptures according to the judgement of thoſe times
in which they were acted, and not according to that which
truth contained. And elſewhere, the ſame Saint: (l) It is the cu­
ſtome for the Pen-men of Scripture, to deliver their Judgments in
many things, according to the common received opinion that their
times had of them. And ^{*} S. Thomas Aquinas in Job upon thoſe
words, Qui extendit Aquilonem ſuper vacuum, & appendit

Terram ſuper nihilum: Noteth that the Scripture calleth that
ſpace Vacuum and Nihilum, which imbraceth and invironeth the
Earth, and which we know, not to be empty, bat filled with Air;
Nevertheleſſe, ſaith he, The Scripture to comply with the appre­
henſion of the Vulgar, who think that in that ſame ſpace there
is nothing, calleth it Vacuum and Nihilum. Here the words of

S. Thomas, Quod de ſuperiori Hæmiſphærio Cœli nibil nobis ap­
paret, niſi ſpatium aëre plenum, quod vulgares homines reputant
Vacnum; loquitur enim ſecundum exiſtimationem vulgarium ho­
minum, prout eſt mos in Sacra Scriptura. Now from this Place
I think one may very Logically argue, That the Sacred Scripture
for the ſame reſpect had much more reaſon to phraſe the Sun mo­
veable, and the Earth immoveable. For if we ſhould try the ca­
pacity of the Common People, we ſhould find them much more
unapt to be perſwaded of the ſtability of the Sun, and Motion
of the Earth, than that the ſpace that environeth it is full of Air.
Therefore if the ſacred Authors, in this point, which had not ſo
much difficulty to be beat into the capacity of the Vulgar, have
notwithſtanding forborn to attempt perſwading them unto it, it
muſt needs ſeem very reaſonable that in other Propoſitions much
more abſtruſe they have obſerved the ſame ſtile. Nay Copernicus
himſelf, knowing what power an antiquated cuſtome and way
of conceiving things become familiar to us from our infancy
hath in our Fancy, that he might not increaſe confuſion and dif­
ficulty in our apprehenſions, after he had firſt demonſtrated,
That the Motions which appear to us to belong to the Sun, or to
the Firmament, are really in the Earth; in proceeding after­
wards to reduce rhem into Tables, and to apply them to uſe, he
calleth them the Motions of the Sun, and of the Heaven that is
above the Planets; expreſly terming them the Riſing and Set­
ting of the Sun and Stars; and mutations in the obliquity of
the Zodiack, and variations in the points of the Equinoxes, the
Middle Motion, Anomalia, Proſthaphæreſis of the Sun; and ſuch
other things; which do in reality belong to the Earth: But
1cauſe being joyned to it, and conſequently having a ſhare in eve­
ry of its motions, we cannot immediately diſcern them in her, but
are forced to refer them to the Celeſtial Bodies in which they
appear; therefore we call them as if they were made there, where
they ſeem to us to be made. Whence it is to be noted how ne­
neſſary it is to accommodate our diſcourſe to our old and accu­
ſtomed manner of underſtanding.
(k) Quaſi non
multa in Scriptu­
ris Sanctis dican­
tur juxta opinio­
nem illius tempor is
quo geſt a referant,
& non juxta quod
rei veritas contine­
bat. D. Hiero. in c.
28. Jerem.
(l) Conſuctudi­
nis Scripturarum
eſt, ut opinionem
multarum rerum
ſic narret Hiſtori­
cus, quomodo eo
tempore ab omni­
bus credebatur. In
cap. 13. Matth.
* D. Thomas, in
cap. 26. Job. v. 7.
That, in the next place, the common conſent of Fathers, in re­
ceiving a Natural Propoſition of Scripture, all in the ſame ſenſe
ought to Authorize it ſo far, as to make it become a matter of
Faith to believe it to be ^{*} ſo, I ſhould think that it ought at moſt

to be underſtood of thoſe Concluſions onely, which have beenby
the ſaid Fathers diſcuſſed, and ſifted with all poſſible diligence,
and debated on the one ſide, and on the other, and all things in
the end concurring to diſprove the one, and prove the other. But
the Mobility of the Earth, and Stability of the Sun, are not of
this kinde; For, that the ſaid Opinion was in thoſe times total­
ly buried, and never brought amongſt the Queſtions of the Schools,
and not conſidered, much leſs followed by any one: So that it is to
be believed that it never ſo much as entered into the thought of
the Fathers to diſpute it, the Places of Scripture, their own Opinion,
and the aſſent of men having all concurred in the ſame judgement,
without the contradiction of any one, ſo far as we can finde.
* Namely, ac­
cording to the Lit­
teral Senſe.
Beſides, it is not enough to ſay that the Fathers all admit the
ſtability of the Earth, &c. Therefore to believe it is a matter of
Faith: But its neceſſary to prove that they have condemned the
contrary Opinion: For I may affirm and bide by this, That their
not having occaſion to make ſatisfaction upon the ſame, and to
diſcuſs it, hath made them to omit and admit it, onely as cur­
rent, but not as reſolved and proved And I think I have very
good Reaſon for what I ſay; For either the Fathers did make
reflection upon this Concluſion as controverted, or not: If not,
then they could determin nothing concerning it no not in their
private thoughts; and their incogitance doth not oblige us to
receive thoſe Precepts which they have not, ſo much as in their
intentions enjoyned. But if they did reflect and conſider there­
on, they would long ſince have condemned it, if they had judged
it erroneous; which we do not find that they have done. Nay, after
that ſome Divines have began to conſider it, we find that they
have not deem'd it erroneous; as we read in the Commentaries of
Didacus a Stunica upon Job, in Cap. 9, v. 6. on the words, Qui com­
movet Terram de loco ſuo, &c. Where he at large diſcourſeth upon
the Copernican Hypotheſis, and concludeth, That the Mobility
of the Earth, is not contrary to Scripture.
Withal, I may juſtly queſtion the truth of that determination,
namely, That the Church enjoyneth us to hold ſuch like Natural
1Concluſions as matters of Faith, onely becauſe they bear the
ſtamp of an unanimous Interpretation of all the Fathers: And
I do ſuppoſe that it may poſſibly be, that thoſe who hold in this
manner, might poſſibly have gone about in favour of their own
Opinion, to have amplified the Decretal of the Councils; which
I cannot finde in this caſe to prohibit any other, ſave onely, Per­
verting to Senſes contrary to that of Holy Church, or of the
concurrent conſent of Fathers, thoſe places, and thoſe onely that
do pertain either to Faith or Manners, or concern our edification
in the Doctrine of Chriſtianity: And thus ſpeaks the Council of
Trent. Seſſ. 4. But the Mobility or Stability of the Earth, or

of the Sun, are not matters of Faith, nor contrary to Manners,
nor is there any one, that for the ſtabliſhing of this Opinion,
will pervert places of Scripture in oppoſition to the Holy Church,
or to the Fathers: Nay, Thoſe who have writ of this Doctrine,
did never make uſe of Texts of Scripture; that they might leave
it ſtill in the breaſts of Grave and Prudent Divines to interpret
the ſaid Places, according to their true meaning.
Concil. Trid. Seſſ.
4.
And how far the Decrees of Councills do comply with the Ho­
ly Fathers in theſe particulars, may be ſufficiently manifeſt, in
that they are ſo far from enjoyning to receive ſuch like Natural
Concluſions for matters of Faith, or from cenſuring the contrary
Opinions as erronious; that rather reſpecting the Primitive and
primary intention of the Holy Church, they do adjudge it un­
profitable to be buſied in examining the truth thereof. Let
your Highneſs be pleaſed to hear once again what S. Auguſtine
anſwers to to thoſe Brethren who put the Queſtion, Whether it

be true that Heaven moveth, or ſtandeth ſtill? (*) To theſe I
anſwer, That Points of this nature require a curious and pro­
found examination, that it may truly appear whether they be
true or falſe; a work inconſiſtent with my leaſure to under­
take or go thorow with, nor is it any way neceſſary for thoſe,
whom we deſire to inform of the things that more nearly
concern their own ſalvation and The Churches Be­
nefit.
(*) His re­
ſpondeo, multum
ſubüliter, & labo­
rioſis ratiombus,
iſta perquirere, ut
vere percipiatur,
ntrum ita, an non
ita ſit: quibus in­
eundis atque tra­
ctandis, nec mihi
jam tempus eſt,
nec illis eſſe debet,
quos ad ſalutem
ſuam, Sanctæ Ec­
cleſiæ neceſſariam
utilitatem cupi
mus informari.
But yet although in Natural Propoſitions we were to take the
reſolution of condemning or admitting them from Texts of Scri­
pture unanimouſly expounded in the ſame Senſe by all the Fa­
thers, yet do I not ſee how this Rule can hold in our Caſe; for that
upon the ſame Places we read ſeveral Expoſitions in the Fathers;

(m) Dionyſius Areopagita ſaying, That the Primum Mobile, and
not the Sun ſtand ſtill. Saint Auguſtine is of the ſame Opinion;
(n) All the Celeſtial Bodies were immoveable. And with them

concurreth Abulenſis. But which is more, amongſt the Jewiſh
Authors (whom Joſephus applauds) ſome have held, (o) That
1The Sun did not really ſtand ſtill, but ſeemed ſo to do, during the

ſhort time in which Iſrael gave the overthrow to their Enemies.
So for the Miracle in the time of Hezekiah, Paulus Burgenſis is of
opinion that it was not wrought on the Sun, but on the Diall.
But that, in ſhort, it is neceſſary to Gloſſe and Interpret the
words of the Text in Joſhua, when ever the Worlds Syſteme

is in diſpute, I ſhall ſhew anon. Now finally, granting to theſe
Gentlemen more than they demand, to wit, That we are whol­
ly to acquieſce in the judgment of Judicious Divines, and that
in regard that ſuch a particular Diſquiſition is not found to
have been made by the Ancient Fathers, it may be undertaken
by the Sages of our Age, who having firſt heard the Experiments,
Obſervations, Reaſons, and Demonſtrations of Philolophers and
Aftronomers, on the one ſide, and on the other (ſeeing that the
Controverſie is about Natural Problems, and Neceſſary Dilem­
ma's, and which cannot poſſibly be otherwiſe than in one of
the two manners in controverſie) they may with competent cer­
tainty determine what Divine Inſpirations ſhall dictate to them.
But that without minutely examining and diſcuſſing all the Rea­
ſons on both ſides; and without ever comming to any certainty
of the truth of the Caſe, ſnch a Reſolution ſhould be taken, Is
not to be hoped from thoſe who do not ſtick to hazzard the Ma­
jeſty and Dignity of the Sacred Scripture, in defending the re­
putation of their vain Fancies; Nor to be feared from thoſe
who make it their whole buſineſſe, to examine with all in­
tenſneſs, what the Grounds of this Doctrine are; and that only
in an Holy Zeal for Truth, the Sacred Scriptures, and for the
Majeſty, Dignity, and Authority, in which every Chriſtian
ſhould indeavour to have them maintained. Which Dignity,
who ſeeth not that it is with greater Zeal deſired and procured
by thoſe who, abſolutely ſubmitting themſelves to the Holy
Church, deſire, not that this, or that opinion may be prohibi­
ted, but onely that ſuch things may be propoſed to conſidera­
tion, as may the more aſcertain her in the ſafeſt choice, than by
thoſe who being blinded by their particular Intereſt, or ſtimula­
ted by malitious ſuggeſtions, preach that ſhe ſhould, without
more ado, thunder out Curſes, for that ſhe had power ſo to do:
Not conſidering that all that may be done is not alwayes conve­
nient to be done. The Holy Fathers of old were not of this
opinion, but rather knowing of how great prejudice, and how
much againſt the primary intent of the Catholick Church, it
would be to go about from Texts of Scripture to decide Natu­
ral Concluſions, touching which, either Experiments or neceſſary
Demonſtrations, might in time to come evince the contrary, of
that which the naked ſenſe of the Words ſoundeth, they have
1not only proceeded with great circumſpection, but have left the
following Precepts for the inſtruction of others. (p) In points

obſcure and remote from our Sight, if we come to read any thing
out of Sacred Writ, that, with a Salvo to the Faith that we have
imbued, may correſpond with ſeveral conſtructions, let us not ſo
farre throw our ſelves upon any of them with a precipitous ob­
ſtinacy, as that if, perhaps the Truth being more diligently ſearch't
into, it ſhould juſtly fall to the ground, we might fall together
with it: and ſo ſhew that we contend not for the ſenſe of Divine
Scriptures, but our own, in that we would have that which is
our own to be the ſenſe of Scriptures, when as we ſhould ra­
ther deſire the Scriptures meaning to be ours.
(m) Non Solem, ſed
Primum Mobile
immotum conſti­
tiſſe: Dioniſ.
Areop.
(n) Omnia cor­
pora Cæleſtia, im­
mota ſubſtitiſſe:
(o) Solem re­
vera non ſubſtitiſ­
ſe immorum, ſed
pro brevi tempore,
intra quod Iſræeli­
tæ, hoſtes ſuos fu­
derunt, id ita vi­
ſum eſſe.
Iſa. Cap. 38.
(p) In rebus ob­
ſouris, atque a no­
ſtris oculis remi­
tiſſimis, ſiqua inde
ſcripta etiam divi­
næ legerimus, quæ
poſſint ſalva fide,
qua imbuimur, a­
liis atque altis pa­
rere ſentextiis, in
nullam earum nos
præcipiti affirma­
tione ita projici­
amus, ut ſi forte
ailigentiùs diſcuſ­
ſa veritas eam recte
labefact averit, corruamus: non pro ſententia Divinarum Scripturarum, ſed pro noſtra ita dimicantes, ut eam
velimus Scripturarum eſſe, quæ noſtra eſt, cum potius eam quæ Scripturarum eſt, noſtram eſſe velle debeamus,
Divus Auguſtin. in Gen. ad Litteram, lib. 2. c. 18. & ſeque
He goeth on, and a little after teacheth us, that no Propoſi­
tion can be againſt the Faith, unleſſe firſt it be demonſtrated

falſe; ſaying, (q) Tis not all the while contrary to Faith, until it
be diſproved by moſt certain Truth, which if it ſhould ſo be, the Holy
Scripture affirm'd it not, but Humane Ignorance ſuppoſed it.
Whereby we ſee that the ſenſes which we impoſe on Texts of
Scripture, would be falſe, when ever they ſhould diſagree with
Truths demonſtrated. And therefore we ought, by help of de­
monſtrated Truth, to ſeek the undoubted ſenſe of Scripture:
and not according to the ſound of the words, that may ſeem
true to our weakneſſe, to go about, as it were, to force Na­
ture, and to deny Experiments and Neceſſary Demonſtra­
tions.
(q) Tam diu non
eſt extra fidem, do­
nec Veritate cer­
tiſſima refellatur.
Quod ſi fæctum
fuerit, non hoc ha­
bebut Divina Scri­
ptura, ſed hoc ſen­
ſer at humana Ig­
norantia. Ibid.
Let Your Highneſſe be pleaſed to obſerve farther, with how
great circumſpection this Holy Man proceedeth, before he af­
firmeth any Interpretation of Scripture to be ſure, and in ſuch
wiſe certain, as that it need not fear the encounter of any diffi­
culty that may procure it diſturbance, for not contenting
himſelf that ſome ſenſe of Scripture agreeth with ſome Demon­

ſtration, he ſubjoynes. (r) But if right Reaſon ſhall demon­
ſtrate this to be true, yet is it queſtionable whether in theſe words
of Sacred Scripture the Pen-man would have this to be under­
ſtood, or ſomewhat elſe, no leſſe true. And in caſe the Context
of his Words ſhall prove that he intended not this, yet will not
that which he would have to be underſtood be therefore falſe, but
moſt true, aad that which is more profitable to be known.
(r) Si autem
hoc verum eſſe ve­
ra ratio demon­
ſtraverit, adhuc
incertum erit, u­
trum hoc in illis
verbis Sanctorum
Librorum, Scrip­
tor ſentiri volue­
rit, an aliquid a­
liud non minus ve­
rum. Quod ſi cætera contextio ſermonis non hoc eum voluiſſe probaverit, non ideo falſum erit aliud, quod ipſe
intelligi voluit, ſed & verum, & quod utilius cognoſcatur.
But that which increaſeth our wonder concerning the
1cumſpection, wherewith this Pious Authour proceedeth, is,

that not truſting to his obſerving, that both Demonſtrative
Reaſons, and the ſenſe that the words of Scripture and the reſt
of the Context both precedent and ſubſequent, do conſpire to
prove the ſame thing, he addeth the following words.
(ſ) Si autem con­
textio Scripturæ,
hoc voluiſſe intel­
ligi Scriptorem,
non repugnaverit,
adhuc reſtabit
quærere, utrum &
aliud non potuerit.
(ſ) But if the Context do not hold forth any thing that may

diſprove this to be the Authors Senſé, it yet remains to enquire,
Whether the other may not be intended alſo. And not yet reſolving
to accept of one Senſe, or reject another, but thinking that he
could never uſe ſufficient caution, he proceedeth: (t) But if
ſo be we finde that the other may be alſo meant, it will be doubted
which of them he would have to ſtand; or which in probability he
may be thought to aim at, if the true circumſtances on both ſides be
weighed. And laſtly, intending to render a Reaſon of this his

Rule, by ſhewing us to what perils thoſe men expoſe the Scri­
ptures, and the Church; who, more reſpecting the ſupport of
their own errours, than the Scriptures Dignity, would ſtretch its
Authority beyond the Bounds which it preſcribeth to it ſelf, he
ſubjoyns the enſuing words, which of themſelves alone might
ſuffice to repreſs and moderate the exceſſive liberty, which ſome
think that they may aſſume to themſelves: (u) For it many
times falls out, that a Chriſtian may not ſo fully underſtand a
Point concerning the Earth, lieaven, and the reſt of this Worlds
Elements; the Motion, Converſion, Magnitude, and Diſtances of
the Stars, the certain defects of the Sun and Moon, the Revoluti­
ons of Years and Times, the Nature of Animals, Fruits, Stones,
and other things of like nature, as to defend the ſame by right
Reaſon, or make it out by Experiments. But its too great an ab­
ſurdity, yea moſt pernicious, and chiefly to be avoided, to let an
Infidel finde a Chriſtian ſo ſtupid, that he ſhould argue theſe mat­
ters; as if they were according to Chriſtian Doctrine; and make
him (as the Proverb ſaith) ſcarce able to contain his laughter, ſee­
ing him ſo far from the Mark Nor is the matter ſo much that one
in an errour ſhould be laught at, but that our Authors ſhould be
thought by them that are without, to be of the ſame Opinion, and to
the great prejudice of thoſe, whoſe ſalvation we wait for, ſenſurcd
and rejected as unlearned. For when they ſhal confute any one of the
Chriſtians in that matter, which they themſelvs thorowly under­
ſtand, and ſhall thereupon expreſs their light eſteem of our Books;
how ſhall theſe Volumes be believed touching the Reſurrection of
the Dead, the Hope of eternal Life, and the Kingdom of Heaven;
when, as to theſe Points which admit of preſent Demonſtration,
or undoubted Reaſons, they conceive them to be falſly written.
1
(t) Quod ſi &
aliud potuiſſe inve­
nerimus, incertum
erit; quidnam eo­
rum ille voluerit:
aut utrumque vo­
luiſſe non inconve­
nienter creditur, ſi
utriuſque ſententiæ
certa circumſt an­
tia ſufragatur.
(u) Plerumque
enim accidit, at a­
liquid de Terra, de
Celo, de ceter is hu­
jus mundi elemen­
tis, de motu, con­
verſione, vel ctiam
magnitudine &
intervallis Syde­
rum, de certis de­
fectibus Solis, &
Lunæ, de eircuiti­
bus annorum &
temporum; de Na­
turis animalium,
fruticum, lapidum,
atque bujuſmodi
ceter is, etiam non
Chriſtianus ita no­
verit, ut cirtiſſima
ratione vel experi­
entiâ teneat. Tur­
pe autem eſt nimis
& pernicioſum, ae
maxime caven­
dum, at Chriſtia­
num de his rebus
quaſi ſecundum
Chriſtianaslitter as
loquentem, ita de­
lirare quilibet in­
fiàelis audiat, ut,
quemadmodum di­
citur, toto Cælo er­
ræreconſpiciens, ri­
ſuntenere vix poſſit:
& non tam mole­
ſtum eſt, quod er­
rans homo deride­
retur, ſed quod au­
ctores noſtri, ab tis
qui foris ſunt, ta­
lia ſenſiſſe credun­
tur, & cum magno exitio eorum, de quorum ſalute ſatagimus, tanquam indocti reprehenduntur atque reſpuuntur.
Cum enim quemquam de numero Chriſtiano um eainre, quam ip ſi optime norunt, deprehenderint, & venam ſenten­
tiam ſuam de noſtris libris aſſerent; quo pacto illis Libris credituri ſunt, de Reſurrectione Mortuorum, & de ſpe
vit æ eternæ, Regnoque Celorum; quando de his rebus quas jam experiri, vel indubitatis rationibus percipere potuerunt
fallaciter putaverint eſſe conſcriptos.
And how much the truly Wiſe and Prudent Fathers are diſ­
pleaſed with theſe men, who in defence of Propoſitions which
they do not underſtand, do apply, and in a certain ſenſe pawn
Texts of Scripture, and afterwards go on to encreaſe their firſt
Errour, by producing other places leſs underſtood than the for­
mer. The ſame Saint declareth in the expreſſions following:

(x) What trouble and ſorrow weak undertakers bring upon
their knowing Brethren, is not to be expreſſed; ſince when they
begin to be told and convinced of their falſe and unſound Opinion,
by thoſe who have no reſpect for the Authority of our Scriptures,
in defence of what through a fond Temerity, and moſt manifeſt fal­
ſity, they have urged; they fall to citing the ſaid Sacred Books
for proof of it, or elſe repeat many words by heart out of them,
which they conceive to make for their purpoſe; not knowing
either what they ſay, or whereof they affirm.
(y) Quid enim
moleſtiæ, triſtiæque
ingerant prudenti­
bus fratribus, te­
nerarij præſumpto­
res, ſatis dici non
poteſt, cum, ſi
quando de falſa &
prava opinione ſua
reprehendi & con­
vinci cæperint, ab
iis qui noſtrorum
librorum auctori­
tate, & aperliſſima
falfitate dixerunt,
eoſdnm libros San­
ctos, unde id pro­
bent, proferre co­
nantur; vel etiam
memoriter, quæ ad
teſtimonium vale­
re arbitrantur,
multa inde verba
pronunciant, non
intelligentes, neque
quæ loquuntur, ne­
que de quibus af­
firmant.
In the number of theſe we may, as I conceive, account thoſe,
who, being either unwilling or unable to underſtand the De­
monſtrations and Experiments, wherewith the Author and fol­
lowers of this Opinion do confirm it, run upon all occaſions to
the Scriptures, not conſidering that the more they cite them, and
the more they perſiſt in affirming that they are very clear, and
do admit no other ſenſes, ſave thoſe which they force upon
them, the greater injury they do to the Dignity of them (if we
allowed that their judgments were of any great Authority) in
caſe that the Truth coming to be manifeſtly known to the con­
trary, ſhould occaſion any confuſion, at leaſt to thoſe who are
ſeparated from the Holy Church; of whom yet ſhe is very ſolici­
tous, and like a tender Mother, deſirous to recover them again
into her Lap. Your Highneſs therefore may ſee how præpoſterouſ­
ly thoſe Perſons proceed, who in Natural Diſputations do range
Texts of Scripture in the Front for their Arguments; and ſuch
Texts too many times, as are but ſuperficially underſtood by them.
But if theſe men do verily think, & abſolutely believe that they
have the true ſence of Such a particular place of Scripture, it muſt
needs follow of conſequence, that they do likewiſe hold for certain,
that they have found the abſolute truth of that Natural Concluſi­
on, which they intend to diſpute: And that withall, they do know
that they have a great advantage of their Adverſary, whoſe Lot it
is to defend the part that is falſe; in regard that he who maintain­
eth the Truth, may have many ſenſible experiments, and many ne­
ceſſary Demonſtrations on his ſide; whereas his Antagoniſt can
make uſe of no other than deceitful appearances, Paralogiſms and
Sophiſms. Now if they keeping within natural bounds, & produ­
cing no other Weapons but thoſe of Philoſophy, pretend however,
to have ſo much advantage of their Enemy; why do they
1wards in coming to engage, preſently betake themſelves to a Wea­
pon inevitable & dreadful to terrifie their Opponent with the ſole
beholding of it? But if I may ſpeak the truth, I believe that they are
the firſt that are affrighted, and that perceiving themſelves unable
to bear up againſt the aſſaults of their Adverſary, go about to find
out ways how to keep them far enough off, forbidding unto them
the uſe of the Reaſon which the Divine Bounty had vouchſafed
them, & abuſing the moſt equitable Authority of ſacred Scripture,
which rightly underſtood and applyed, can never, according to
the common Maxime of Divines, oppoſe the Manifeſt Experi­
ments, or Neceſſary Demonſtrations. But theſe mens running
to the Scriptures for a Cloak to their inability to comprehend,
not to ſay reſolve the Reaſons alledged againſt them, ought (if I
be not miſtaken) to ſtand them in no ſtead: the Opinion which
they oppoſe having never as yet been condemned by Holy
Church. So that if they would proceed with Candor, they
ſhould either by ſilence confeſs themſelves unable to handle ſuch
like points, or firſt conſider that it is not in the power of them or
others, but onely in that of the Pope, and of Sacred Councils to

cenſure a Poſition to be Erroneous: But that it is left to their
freedome to diſpute concerning its falſity. And thereupon,
knowing that it is impoſſible that a Propoſition ſhould at the
ſame time be True and Heretical; they ought, I ſay, to imploy
themſelves in that work which is moſt poper to them, namely,
in demonſtrating the falſity thereof: whereby they may ſee
how needleſſe the prohibiting of it is, its falſhood being once
diſcovered, for that none would follow it: or the Prohibition
would be ſafe, and without all danger of Scandal. Therefore
firſt let theſe men apply themſelves to examine the Arguments
of Copernicus and others; and leave the condemning of them
for Erroneous and Heretical to whom it belongeth: But yet let
them not hope ever to finde ſuch raſh and precipitous Determina­
tions in the Wary and Holy Fathers, or in the abſolute Wiſ­
dome of him that cannot erre, as thoſe into which they ſuffer
themſelves to be hurried by ſome particular Affection or Inte­
reſt of their own. In theſe and ſuch other Poſitions, which are
not directly de Fide, certainly no man doubts but His Holineſs
hath alwayes an abſolute power of Admitting or Condemn­
ing them, but it is not in the power of any Creature to make
them to be true or falſe, otherwiſe than of their own nature,
and de facto they are.
If this paſſage
ſeem harſh, the
Reader muſt re­
member that I do
but Tranſlate.
Therefore it is in my judgment more diſcretion to aſſure us
firſt of the neceſſary and immutable Truth of the Fact, (over
which none hath power) than without that certainty by condem­
ning one part to deprive ones ſelf of that authority of freedome
1to elect, making thoſe Determinations to become neceſſary,
which at preſent are indifferent and arbitrary, and reſt in the
will of Supreme Authority. And in a word, if it be not poſ­
ſible that a Concluſion ſhould be declared Heretical, whilſt we
are not certain, but that it may be true, their pains are in vain
who pretend to condemn the Mobility of the Earth and Stabili­
ty of the Sun, unleſſe they have firſt demonſtrated it to be im­
poſſible and falſe.
It remaineth now, that we conſider whether it be true, that
the Place in Joſhuab may be taken without altering the pure ſig­
nification of the words: and how it can be that the Sun, obey­
ing the command of Joſhuah, which was, That it ſhould ſtand
ſtill, the day might thereupon be much lengthened. Which bu­
ſineſſe, if the Celeſtial Motions be taken according to the Ptolo­
maick Syſteme, can never any wayes happen, for that the Sun
moving thorow the Ecliptick, according to the order of the
Signes, which is from Eaſt to Weſt (which is that which maketh
Day and Night) it is a thing manifeſt, that the Sun ceaſing its
true and proper Motion, the day would become ſhorter and not
longer; and that on the contrary, the way to lengthen it would
be to haſten and velocitate the Suns motion; inſomuch that to
cauſe the Sun to ſtay above the Horizon for ſome time, in one
and the ſame place, without declining towards the Weſt, it would
be neceſſary to accelerate its motion in ſuch a manner as that it
might ſeem equal to that of the Primum Mobile, which would be
an accelerating it about three hundred and ſixty times more than
ordinary. If therefore Joſhuah had had an intention that his
words ſhould be taken in their pure and proper ſignification, he
would have bid the Sun to have accelerated its Motion ſo, that
the Rapture of the Primum Mobile might not carry it to the
Weſt: but becauſe his words were heard by people which hap­
ly knew no other Celeſtial Motion, ſave this grand and common
one, from Eaſt to Weſt, ſtooping to their Capacity, and having
no intention to teach them the Conſtitution of the Spheres, but
only that they ſhould perceive the greatneſs of the Miracle
wrought, in the lengthening of the Day, he ſpoke according to
their apprehenſion. Poſſibly this Conſideration moved Diony­
ſius Areopagita to ſay that in this Miracle the Primum Mobile
ſtood ſtill, and this ſtopping, all the Celeſtial Spheres did of
conſequence ſtay: of which opinion is S. Auguſtine himſelf, and
Abulenſis at large confirmeth it. Yea, that Joſhua's intention
was, that the whole Syſteme of the Celeſtial Spheres ſhould
ſtand ſtill, is collected from the command he gave at the ſame
time to the Moon, although that it had nothing to do in the
lengthening of the day; and under the injunction laid upon the
1Moon, we are to underſtand the Orbes of all the other Planets,
paſſed over in ſilence here, as alſo in all other places of the Sacred
Scriptures; the intention of which, was not to reach us the Aſtro­
nomical Sciences. I ſuppoſe therefore, (if I be not deceived)
that it is very plain, that if we allow the Ptolemaick Syſteme, we
muſt of neceſſity interpret the words to ſome ſenſe different from
their ſtrict ſignification. Which Interpretation (being admo­
niſhed by the moſt uſefull precepts of S. Auguſtine) I will not
affirm to be of neceſſity this above-mentioned, ſince that ſome
other man may haply think of ſome other more proper, and more
agreeable Senſe.
But now, if this ſame paſſage may be underſtood in the Coper­
nican Syſteme, to agree better with what we read in Joſhuah,
with the help of another Obſervation by me newly ſhewen in
the Body of the Sun; I will propound it to conſideration, ſpeak­
ing alwaies with thoſe ſafe Reſerves; That I am not ſo affectio­
nate to my own inventions, as to prefer them before thoſe of
other men, and to believe that better and more agreeable to the
intention of the Sacred Volumes cannot be produced.
Suppoſing therefore in the firſt place, that in the Miracle of
Joſhuah, the whole Syſteme of the Celeſtial Revolutions ſtood
ſtill, according to the judgment of the afore-named Authors:
And this is the rather to be admitted, to the end, that by the
ſtaying of one alone, all the Conſtitutions might not be con­
founded, and a great diſorder needleſly introduced in the whole
courſe of Nature: I come in the ſecond place to conſider how the
Solar Body, although ſtable in one conſtant place, doth neverthe­
leſs revolve in it ſelf, making an entire Converſion in the ſpace
of a Month, or thereabouts; as I conceive I have ſolidly demon­
ſtrated in my Letters Delle Machie Solari: Which motion we
ſenſibly ſee to be in the upper part of its Globe, inclined to­
wards the South; and thence towards the lower part, to encline
towards the North, juſt in the ſame manner as all the other Orbs
of the Planets do. Thirdly, If we reſpect the Nobility of the
Sun, and his being the Fountain of Light, by which, (as I neceſ­
ſarily demonſtrate) not onely the Moon and Earth, but all the
other Planets (all in the ſame manner dark of themſelves) become
illuminated; I conceive that it will be no unlogicall Illation to ſay,
That it, as the Grand Miniſter of Nature, and in a certain ſenſe
the Soul and Heart of the World, infuſeth into the other Bodies
which environ it; not onely Light, but Motion alſo; by revol­
ving ^{*} in it ſelf: So that in the ſame manner that the motion of

the Heart of an Animal ceaſing, all the other motions of its
Members would ceaſe; ſo, the Converſion of the Sun ceaſing,
the Converſions of all the Planets would ſtand ſtill. And though
1I could produce the teſtimonies of many grave Writers to prove
the admirable power and influence of the Sun, I will content my
ſelf with one ſole place of Holy Dioniſius Areopagita in his Book

de Divinis Nominibus; who thus writes of the Sun: ^{(*)} His Light
gathereth and converts all things to himſelf, which are ſeen,
moved, illuſtrated, wax hot, and (in a word) thoſe things which
are preſerved by his ſplendor: Wherefore the Sun is called Hλιος,
for that he collecteth and gathereth together all things diſperſed.
And a little after of the Sun again he adds; ^{(*)} If this Sun which
wo ſee, as touching the Eſſences and Qualities of thoſe things
which fall within our Senſe, being very many and different; yet
if he who is one, and equally beſtowes his Light, doth renew,
nouriſh, defend, perfect, divide, conjoyn, cheriſh, make fruitfull,

encreaſe, change, fix, produce, move, and faſhion all living crea­
tures: And every thing in this Vniverſe at his Pleaſure, is par­
taker of one and the ſame Sun; and the cauſes of many things
which participate of him, are equally auticipated in him: Certain­
ly by greater reaſon; &c. The Sun therefore being the Foun­
tain of Light and, Principle of Motion, God intending, that at
the Command of Joſhua, all the Worlds Syſteme, ſhould con­
tinue many hours in the ſame ſtate, it ſufficeth to make the Sun
ſtand ſtill, upon whoſe ſtay (all the other Converſions ceaſing)
the Earth, the Moon, the Sun did abide in the ſame Conſtitution
as before, as likewiſe all the other Planets: Nor in all that time
did the Day decline towards Night, but it was miraculouſly pro­
longed: And in this manner, upon the ſtanding ſtill of the Sun,
without altering, or in the leaſt diſturbing the other Aſpects and
mutual Poſitions of the Stars, the Day might be lengthned on
Earth; which exactly agreeth with the Litteral ſenſe of the Sacred
Text.
* i. i. On its own
Axis.
(*) Lux ejus colli­
git, convertitque ad
ſe omnia, quæ vi­
dentur, quæ mo­
ventur, quæ illu­
ſtrantur, quæ ca­
leſcunt, & uno no­
mine ea, quæ ab e­
jus ſplendore cen­
tinentur. Itaque
Sol Hλι<34> dicitur,
quod omnia con­
greger, colligatque
diſperſa.
(*) Si enim
Sol hic quem vi­
domus, eorum quæ
ſub ſenſum ca­
dunt, eſſentias &
qualitates, quæ que
muliæ ſint ac diſ­
ſimiles, tamen ipſe
qui unus eſt, æqua­
literque lumen
fundit, renovat, a­
lit, tuetur, perficit,
dividit, conjungit,
fovet, fæcunda red­
dit, auget, mutat,
firmat, edit, movet,
vitaliaque facit om­
nia: & unaquæque
res hujus univer­
ſitatis, pro cæptu
ſuo, unius atque e­
juſdem Solis eſt
particeps, cauſæſ­
que multorum,
quæ participant, in
ſe æquabiliter an­
ticipatas habet,
certe majori ratio­
ne, &c.
But that of which, if I be not miſtaken, we are to make no
ſmall account, is, That by help of this Copernican Hypotheſis,
we have the Litteral, apert, and Natural Senſe of another parti­
cular that we read of in the ſame Miracle; which is, That the
Sun ſtood ſtill in Medio Cæli: Upon which paſſage grave Divines
raiſe many queſtions, in regard it ſeemeth very probable, That
when Joſhuah deſired the lengthning of the Day, the Sun was
near ſetting, and not in the Meridian; for if it had been in the
Meridian, it being then about the Summer Solſtice, and con­
ſequently the dayes being at the longeſt, it doth not ſeem likely
that it was neceſſary to pray for the lengthning of the day, to
proſecute Victory in a Battail, the ſpace of ſeven hours and more,
which remained to Night, being ſufficient for that purpoſe.
Upon which Grave Divines have been induced to think that the
Sun was near ſetting: And ſo the words themſelves ſeem to
1ſound, ſaying, Ne movearis Sol, ne movearis. For if it had
been in the Meridian, either it had been needleſs to have asked
a Miracle, or it would have been ſufficient to have onely praid
for ſome retardment. Of this opinion is Cajetan, to which ſub­
ſcribeth Magaglianes, confirming it by ſaying, that Joſhua had
that very day done ſo many other things before his commanding
the Sun, as were not poſſibly to be diſpatch't in half a day.
Whereupon they are forced to read the Words in Medio Cœli
(to confeſs the truth) with a little harſhneſs, ſaying that they
import no more than this: That the Sun ſtood ſtill, being in our
Hemiſphere, that is, above the Horizon. But (if I do not erre)

we ſhall avoid that and all other harſh expoſitions, if according
to the Copernican Syſteme we place the Sun in the midſt, that
is, in the Centre of the Cœleſtial Orbes, and of the Planetary
Converſions, as it is moſt requiſite to do. For ſuppoſing any
hour of the day (either Noon, or any other, as you ſhall pleaſe
neerer to the Evening) the Day was lengthened, and all the
Cœleſtial Revolutions ſtayed by the Suns ſtanding ſtill, In the
midſt, that is, in the Centre of Heaven, where it reſides: A
Senſe ſo much the more accomodate to the Letter (beſides what
hath been ſaid already) in that, if the Text had deſired to have
affirmed the Suns Reſt to have been cauſed at Noon-day, the
proper expreſſion of it had been to ſay, It ſtood ſtill at Noon-day,
or in the Meridian Circle, and not in the midſt of Heaven: In
regard that the true and only Middle of a Spherical Body (as is
Heaven) is the Centre.
Solem ſtetiſſe,
dum adhuc in He­
miſpharto noſtro,
ſupra ſcilicet Ho­
rizontem exiſteret.
Cajetan in loce.
Again, as to other places of Scripture, which ſeem contrary to
this poſition, I do not doubt but that if it were acknowledged
for True and Demonſtrated thoſe very Divines who ſo long as
they repute it falſe, hold thoſe places incapable of Expoſitions
that agree with it would finde ſuch Interpretations for them, as
ſhould very well ſuit therewith; and eſpecially if to the know­
ledge of Divine Learning they would but adde ſome knowledge
of the Aſtronomical Sciences: And as at preſent, whilſt they
deem it falſe they think they meet in Scripture only with ſuch
places as make againſt it, if they ſhall but once have entertained
another conceipt thereof, they would meet peradventure as many
others that accord with it, and haply would judge, that the Holy
Church doth very appoſitly teach, That God placed the Sun in
the Centre of Heaven, and that thereupon by revolving it in it
ſelf, after the manner of a Wheel, He contributed the ordinary
Courſes to the Moon and other Erratick Stars, whilſt that ſhe
Sings,
Cœli Deus ſanctiſſime,
Qui lucidum Centrum Poli,
1
Candore ping is igneo,
Augens decoro lumine,
Quarto die, qui flammeam
Solis rotam conſtituens
Lunœ miniſtras ordinem,
Vagoſque curſus Syderum.
They might ſay, that the Name of Firmament very well a­
greeth, ad literam, to the Starry Sphere, and to all that which
is above the Planetary Converſions; which according to this Hy­
potheſis is altogether firme and immoveable. Ad litteram (the
Earth moving circularly) they might underſtand its Poles,
where it's ſaid, Nec dum Terram fecerat, & flumina, & Cardi­
nes Orbis Terrœ, Which Cardines or ^{*} liinges ſeem to be aſcribed

to the Earth in vain, if it be not to turn upon them.
* Or Poles.
FINIS.
1
AN
ABSTRACT
OF THE
Learned Treatiſe
OF
JOHANNIS KEPLERUS,
The Emperours Mathematician:
ENTITULED
His Introduction upon MARS:
It muſt be confeſſed, that there are very
many who are devoted to Holineſſe,
that diſſent from the Judgment of Co­
pernicus, fearing to give the Lye to the
Holy Ghoſt ſpeaking in the Scriptures,
if they ſhould ſay, that the Earth mo­
veth, and the Sun ſtands ſtill. But let
ſuch conſider, that ſince we judge of ve­
ry many, and thoſe the moſt principal
things by the Senſe of Seeing, it is impoſſible that we ſhould ali­
enate our Speech from this Senſe of our Eyes. Therefore many
things daily occur, of which we ſpeak according to the Senſe of
Sight, when as we certainly know that the things themſelves are
otherwiſe. An Example whereof we have in that Verſe of
Virgil;
Provehimur portu, Terrœque urbeſque recedunt.
So when we come forth of the narrow ſtraight of ſome Val­
ley, we ſay that a large Field diſcovereth it ſelf. So Chriſt to
Peter, Duc in altum; [Lanch forth into the Deep, or on high,]
as if the Sea were higher than its Shores; For ſo it ſeemeth to
the Eye, but the Opticks ſhew the cauſe of this fallacy. Yet
Chriſt uſeth the moſt received Speech, although it proceed from
this deluſion of the Eyes. Thus we conceive of the Riſing and
1Setting of the Stars, that is to ſay, of their Aſcenſion and Deſ­
cenſion; when at the ſame time that we affirm the Sun riſeth, o­
thers ſay, that it goeth down. See my Optices Aſtronomiœ, cap.
10. fol. 327 So in like manner, the Ptolomaicks affirm, that the
Planets ſtand ſtill, when for ſome dayes together they ſeem to be
fixed, although they believe them at that very time to be moved
in a direct line, either downwards to, or upwards from the
Earth. Thus the Writers of all Nations uſe the word Solſtiti­
um, and yet they deny that the Sun doth really ſtand ſtill. Like­
wiſe there will never any man be ſo devoted to Copernicus, but
he will ſay, the Sun entereth into Cancer and Leo, although he
granteth that the Earth enters Capricorn or Aquarius: And ſo
in other caſes of the like nature. But now the Sacred Scriptures,
ſpeaking to men of vulgar matters (in which they were not in­
tended to inſtruct men) after the manner of men, that ſo they
might be underſtood by men, do uſe ſuch Expreſſions as are
granted by all, thereby to inſinuate other things more Myſterious
and Divine. What wonder is it then, if the Scripture ſpeaks
according to mans apprehenſion, at ſuch time when the Truth
of things doth diſſent from the Conception that all men, whe­
ther Learned or Unlearned have of them? Who knows not
that it is a Poetical alluſion, Pſal. 19. where, whilſt under the ſi­
militude of the Sun, the Courſe of the Goſpel, as alſo the Pere­
grination of our Lord Chriſt in this World, undertaken for our
ſakes, is deſcribed, The Sun is ſaid to come forth of his Taberna­
cle of the Horizon, as a Bridegroom out of his Chamber, re­
joycing as a Giant to run a Race? Which Virgil thus imitates;
Tithono croceum linquens Auror a cubile:
For the firſt Poets were amongſt the Jews. The Pſalmiſt knew that
the Sun went not forth of the Horizon, as out of its Tabernacle,
& yet it ſeemeth to the Eye ſo to do: Nor did he believe, that the
Sun moved, for that it appeared to his ſight ſo to do. And yet he
ſaith both, for that both were ſo to his ſeeming. Neither is it
to be adjudged falſe in either Senſe: for the perception of the
Eyes hath its verity, fit for the more ſecret purpoſe of the Pſal­
miſt in ſhadowing forth the current paſſage oſ the Goſpel, as
alſo the Peregrination of the Son of God. Joſhua likewiſe
mentioneth the Vallies on or in, which the Sun and Moon mo­
ved, for that they appeared to him at Jordan ſo to do: And yet
both theſe Pen-men may obtain their ends. David, (and with
him Syracides) the magnificence of God being made known,
which cauſed theſe things to be in this manner repreſented to
ſight, or otherwiſe, the myſtical meaning, by means of theſe
Viſibles being diſcerned: And Joſhua, in that the Sun, as to his
1Senſe of Seeing, ſtaid a whole day in the midſt of Heaven, where­
as at the ſame time to others it lay hid under the Earth. But in­
cogitant perſons onely look upon the contrariety of the words,
The Sun ſtood ſtill, that is, The Earth ſtood ſtill; not conſidering
that this contradiction is confined within the limits of the Op­
ticks and Aſtronomy: For which cauſe it is not outwardly ex­
poſed to the notice and uſe of men: Nor will they underſtand
that the onely thing Joſhuah prayed for, was that the Mountains
might not intercept the Sun from him; which requeſt he expreſ­
ſed in words, that ſuited with his Ocular Senſe: Beſides it had
been very unſeaſonable at that time to think of Aſtronomy, or
the Errours in Sight; for if any one ſhould have told him that
the Sun could not really move upon the Valley of Ajalon,, but
onely in relation to Senſe, would not Joſhuah have replyed, that
his deſire was that the day might be prolonged, ſo it were by
any means whatſoever? In like manner would he have anſwered
if any one had ſtarted a queſtion about the Suns Mobility, and
the Earths Motion. But God eaſily underſtood by Joſhuahs
words what he asked for, and by arreſting the Earths Motion,
made the Sun in his apprehenſion ſeem to ſtand ſtill. For the
ſumm of Joſhuahs Prayer amounts to no more but this, that it
might thus appear to him, let it in the mean time be what it
would of it ſelf. For that its ſo ſeeming, was not in vain and
ridiculous, but accompanied with the deſired effect. But read
the tenth Chap. of my Book, that treats of the Optick part of A­
ſtronomy, where thou ſhalt finde the Reaſons why the Sun doth
in this manner ſeem to all mens thinking to be moved, and not
the Earth; as namely, becauſe the Sun appeareth ſmall; and the
Earth bigg. Again, the Motion of the Sun is not diſcerned by
the eye, by reaſon of his ſeeming tardity, but by ratiocina­
tion onely; in that after ſome time it varieth not its proximity to
ſuch and ſuch Mountains. Therefore it is impoſſible that Rea­
ſon, unleſs it be firſt inſtructed, ſhould frame to it ſelf any other
apprehenſion, than that the Earth with Heavens Arch placed
over it, is as it were a great Houſe, in which, being immoveable,
the Sun like a Bird flying in the Air, paſſeth in ſo ſmall a Species
out of one Climate into another. Which imagination of all
Man-kinde being thus, gave the firſt line in the Sacred Leaves:
^{*} In the beginning (ſaith Moſes) God created the Heaven and the

Earth; for that theſe two are moſt obvious to the eye. As if
Moſes ſhould have ſaid thus to Man; This whole Mundane Fa­
brick which thou ſeeſt, lucid above, and dark, and of a vaſt ex­
tent beneath, wherein thou haſt thy being, and with which thou
art covered, was created by God.
* Gen. Chv. 1.
v. 1.
In another place Man is queſtioned; Whether he can finde out
1the height of Heaven above, or depth of the Earth beneath: for
that each of them appeareth to men of ordinary capacity, to have
equally an infinite extent. And yet no man that is in his right
mind will by theſe words circumſcribe and bound the diligence
of Aſtronomers, whether in demonſtrating the moſt contemptible
Minuity of the Earth, in compariſon of Heaven, or in ſearching
out Aſtronomical Diſtances: Since thoſe words ſpeak not of the
Rational, but real Dimention; which to a Humane Body,
whilſt confin'd to the Earth, and breathing in the open Air, is al­
together impoſſible. Read the whole 38. Chapter of Job, and
compare it with thoſe Points which are diſputed in Aſtronomy,

and Phyſiologie. If any one do alledge from Pſal. 24. That ^{*} The
Earth is founded upon the Seas, to the end that he may thence
infer ſome new Principle in Philoſophy, abſurd to hear; as, That
the Earth doth float upon the Waters; may it not truly be told
him, That he ought not to meddle with the Holy Spirit, nor to
bring him with contempt into the School of Phyſiologie.
For the Pſalmiſt in that place means nothing elſe but
that which men fore-know, and daily ſee by experience; namely,
That the Earth (being lifted up after the ſeparation of the Wa­
ters) doth ſwim between the Grand Oceans, and float about the
Sea. Nor is it ſtrange that the expreſſion ſhould be the ſame
where the Iſraelites ſing, ^{*} That they ſate on the River of Baby­

lon; that is, by the River ſide. or on the Banks of Euphrates and
Tygris.
* Pſal. 24. 2.
Pſal. 137. 1.
If any one receive this Reading without ſcruple, why not the
other; that ſo in thoſe ſame Texts which are wont to be alledged
againſt the Motion of the Earth, we may in like manner turn our
eyes from Natural Philoſophy, to the ſcope and intent of Scri­
pture. One Generation paſſeth away, (ſaith Eccleſiaſtes) and a­

nother Generation cometh: But the Earth abideth for ever. ^{*} As
if Solomon did here diſpute with Aſtronomers, and not rather put
men in minde of their Mutability; when as the Earth, Mankindes
habitation, doth alwaies remain the ſame: The Suns Motion
doth continually return into what it was at firſt: The Wind is
acted in a Circle, and returns in the ſame manner: The Rivers
flow from their Fountains into the Sea, and return again from
thence unto their Fountains: To conclude, The Men of this
Age dying, others are born in their room; the Fable of Life is
ever the ſame; there is nothing new under the Sun. Here is no
reference to any Phyſical Opinion. ονεσὶα is Moral of a thing in it
ſelf manifeſt, and ſeen by the eyes of all, but little regarded: Tis
that therefore which Solomon doth inculcate. For who knows not
that the Earth is alwaies the ſame? Who ſees not that the Sun
dothariſe from the Eaſt; That the Rivers continually run into
1the Sea; That the viciſſitudes of the Windes return into their
primitive State; That ſome men ſucceed others? But who con­
ſidereth that the ſelf-ſame Scene of Life is ever acting, by diffe­
rent perſons; and that nothing is new in humane affairs? There­
fore Solomon inſtancing in thoſe things which all men ſee, doth
put men in minde of that which many thorowly know, but too
ſlightly conſider.
* Chap. 1. v. 4, to
9.
But the 104. Pſalm is thought by ſome to contain a Diſcourſe
altogether Phyſical, in regard it onely concerns Natural Philoſo­
phy. Now God is there ſaid, To have laid the Foundations of

the Earth, that it ſhould not be removed for ever. But here al­
ſo the Pſalmiſt is far from the Speculation of Phyſical Cauſes:
For he doth wholly acquieſce in the Greatneſſe of God,
who did all theſe things, and ſings an Hymne to God the
Maker of them, in which he runneth over the World in order,
as it appeared to his eyes. And if you well conſider this
Pſalme, it is a Paraphraſe upon the ſix dayes work of the Crea­
tion: For as in it the three firſt dayes were ſpent in the Separa­
tion of Regions; the firſt of Light from the exteriour Dark­
neſs; the ſecond, of the Waters from the Waters, by the inter­
poſition of the Firm ament; the third, of the Sea from Land;
when alſo the Earth was cloathed with Herbage and Plants:
And the three laſt dayes were ſpent in the filling the Re­
gions thus diſtinguiſhed; the fourth, of Heaven; the
fifth, of the Seas and Aire; the fixth, of the Earth: So
here in this Pſalme there are ſo many diſtinct parts pro­
portionable to the Analogy of the ſix dayes Works. For
in Verſe 2. he cloaths and covereth the Creator with Light
(the firſt of Creatures, and work of the firſt day) as with a
Garment. The ſecond part beginneth at Verſe 3. and treats of
the Waters above the Heavens, the extent of Heaven and of Me­
teors (which the Pſalmiſt ſeemeth to intend by the Waters a­
bove) as namely of Clouds, Winds, Whirl-winds, Lightnings.
The third part begins at Verſe 6. and doth celebrate the Earth
as the foundation of all thoſe things which he here conſidereth.
For he referreth all things to the Earth, and to thoſe Animals
which inhabit it, for that in the judgment of Sight the two prin­
cipal parts of the World are Heaven and Earth. He therefore
here obſerveth that the Earth after ſo many Ages hath not falte­
red, tired, or decayed; when as notwithſtanding no man hath
yet diſcovered upon what it is founded. He goeth not about to
teach men what they do not know, but putteth them in minde
of what they neglect, to wit, the Greatneſſe and Power of God
in creating ſo huge a Maſs ſo firm and ſtedfaſt. If an Aſtrono­
mer ſhould teach that the Earth is placed among the Planets, he
1overthroweth not what the Pſalmiſt here ſaith, nor doth he con­
tradict Common Experience; for it is true notwithſtanding,
that the Earth, the Structure of God its Architect, doth not de­
cay (as our Buildings are wont to do) by age, or conſume by
wormes, nor ſway and leane to this or that ſide; that the Seats
and Neſts of Living Creatures are not moleſted; that the
Mountains and Shores ſtand immoveable againſt the violence of
the Winds and Waves, as they were at the beginning. But the
Pſalmiſt addeth a moſt Elegant Hypotheſis of the Separation of
the Waters from the Continent or Main-land, and adorns it
with the production of Fountains, and the benefits that Springs
and Rocks exhibit to Birds and Beaſts. Nor doth he omit the
apparelling the Earths Surface, mentioned by Moſes amongſt the
works of the third Day, but more ſublimely deſcribeth it in his
Caſe in expreſſions infuſed from Divine Inſpiration; and flouri­
ſheth out the commemoration of the many commodities which
redound from that Exornation for the Nouriſhment and Com­

fort of Man, and ^{*} Covert of Beaſts. The fourth part begins
at Verſe 20. celebrating the fourth dayes work, viz. The Sun
and Moon, but chiefly the commodiouſneſſe of thoſe things,
which in their Seaſons befall to all Living Creatures and to Man;
this being the ſubject matter of his Diſcourſe: So that it plain­
ly appeareth he acted not the part of an Aſtronomer. For if he
had, he would not then have omitted to mention the five Planets,
than whoſe moiton nothing is more admirable, nothing more ex­
cellent, nothing that can more evidently ſet forth the Wiſdome
of the Creator amongſt the Learned. The fifth part begins,
Verſe 25. with the fifth Dayes work. And it ſtores the Seas with
Fiſhes, and covers them with Ships. The ſixth part is more ob­
ſcurely hinted at, Verſe 28. and alludeth to the Land-Creatures
that were created the ſixth day. And laſtly, he declareth the
goodneſſe of God in general, who daily createth and preſerveth
all things? So that whatever he ſaid of the World is in relation
to Living Creatures; He ſpeaks of nothing but what is granted
on all hands; for that it was his intent to extol things known,
and not to dive into hidden matters, but to invite men to con­
template the Benefits that redouud unto them from the works of
each of theſe dayes.
Pſal. 104. v. 5.
* Shelter.
And I do alſo beſeech my Reader, not forgetting the Divine
Goodneſſe conferred on Mankind; the conſideration of which
the Pſalmiſt doth chiefly urge, that when he returneth from the
Temple, and enters into the School of Aſtronomy, he would
with me praiſe and admire the Wiſdome and Greatneſſe of the
Creator, which I diſcover to him by a more narrow explication
of the Worlds Form, the Diſquiſition of Cauſes, and Detection
1of the Errours of Sight: And ſo he will not onely extoll the
Bounty of God in the preſervation of Living Creatures of all
kindes, and eſtabliſhment of the Earth; but even in its Motion
alſo, which is ſo ſtrange, ſo admirable, he will acknowledge the
Wiſdome of the Creator. But he who is ſo ſtupid as not to
comprehend the Science of Aſtronomy, or ſo weak and ſcrupu­
lous as to think it an offence of Piety to adhere to Copernicus,
him I adviſe, that leaving the Study of Aſtronomy, and cenſuring
the opinions of Philoſophers at pleaſure, he betake himſelf to
his own concerns, and that deſiſting from further purſuit of theſe
intricate Studies, he keep at home and manure his own Ground;
and with thoſe Eyes wherewith alone he ſeeth, being eleva­
ted towards this to be admired Heaven, let him pour forth his
whole heart in thanks and praiſes to God the Creator; and aſ­
ſure himſelf that he ſhall therein perform as much Worſhip to
God, as the Aſtronomer, on whom God hath beſtowed this Gift,
that though he ſeeth more clearly with the Eye of his Under­
ſtanding; yet whatever he hath attained to, he is both able and
willing to extoll his God above it.
And thus much concerning the Authority of Sacred Scripture.
Now as touching the opinions of the Saints about theſe Natural
Points. I anſwer in one word, That in Theology the weight of
Authority, but in Philoſophy the weight of Reaſon is to be con­
ſidered. Therefore Sacred was Lactantius, who denyed the
Earths rotundity; Sacred was Auguſtine, who granted the Earth
to be round, but denyed the Antipodes; Sacred is the ^{*}Liturgy of

our Moderns, who admit the ſmallneſſe of the Earth, but deny
its Motion: But to me more ſacred than all theſe is Truth, who
with reſpect to the Doctors of the Church, do demonſtrate
from Philoſophy that the Earth is both round, circumhabited by
Antipodes, of a moſt contemptible ſmalneſſe, and in a word,
that it is ranked amongſt the Planets.
1
* Officium
AN
ABSTRACT
OF
Some paſſages in the Commentaries of
Didacus à Stunica,
OF
SALAMANCA
Upon JOB:
The Toledo Edition, Printed by JOHN RODERICK,
Anno 1584, in Quarto, Pag. 205. & ſeqque on
theſe Words, Chap. 9. Verſe 6.
Who ſhaketh the Earth out of her place, and the Pil­
lars thereof Tremble.
The Sacred Pen-man here ſets down another ef­
fect whereby God ſheweth his Ahnighty Po­
wer, joyned with infinite Wiſdom. Which
place, though it muſt be confeſſed very diffi­
cult to underſtand, might be greatly cleared
by the Opinion of the Pythagorians, who
hold the Earth to be moved of its own Na­
ture, and that the Motion of the Stars can no other way be aſcer­
tained, they being ſo extreamly different in tardity and velocity.
Of which judgement was Philolaus, and Heraclides Ponticus, as
Plutarch relateth in his Book De Placitis Philoſophorum: Who
were followed by Numa Pompilius, and, which I more regard,
The Divine Plato in his old age; inſomuch that he affirmed that
it was moſt abſurd to think otherwiſe, as the ſame Plutarch tells
us in his ^{*} Numa. And Hypocrates in his Book De Flatibus,

calleth the Air τησγησὀχἠμα, i. e. The Earths Chariot. But in this
1our Age, Copernicus doth demonſtrate the courſes of the Pla­
nets to be according to this Opinion. Nor is it to be doubted
but that the Planets Places may be more exactly and certainly
aſſigned by his Doctrine, than by Ptolomies Great Almogeſt of
Syſteme, or the Opinions of any others. For its manifeſt, that
Ptolomy could never deſcribe either the Motion of the Equi­
noxes, or aſſign the certain and poſitive beginning of the Year:
the which he ingeniouſly confeſſeth in Lih. 3. De Almageſt. Mag­
num. Ch. 2. and which he leaveth to be diſcovered in after times
by thoſe Aſtronomers, who coming into the World much later
than he, might be able to invent ſome way to make more accurate
obſervations. And although the ^{*} Alphonſines & Thebith Ben Core

have attempted to explain them; yet it appeareth that they have
done as much as nothing. For the Poſitions of the Alphonſines
diſagree amongſt themſelves, as Ricius proveth. And although
the Reaſon of Thebith be more acute, and that thereby he de­
termined the certain beginning of the year, (being that which
Ptolomy ſought for) yet it is now clear, that the Progreſſions of
the Equinoxes are much longer than he conceived they could be.
Moreover, the Sun is found to be much nearer to us than it was

held to be in times paſt, by above fourty thouſand ^{*} Stadia, or
furlongs. The Cauſe and Reaſon of whoſe Motion, neither
Ptolomy nor any other Aſtrologers could ever comprehend: And
yet the Reaſons of theſe things are moſt plainly explained and
demonſtrated by Copernicus from the Motion of the Earth, with
which he ſheweth that all the other Phœnomena of the Univerſe
do more aptly accord. Which opinion of his is not in the leaſt
contradicted by what Solomon ſaith in ^{*} Eccleſiaſtes: But the

Earth abideth for ever. For that Text ſignifieth no more but
this, That although the ſucceſſion of Ages, and generations of
Men on Earth, be various; yet the Earth it ſelf is ſtill one and
the ſame, and continueth without any ſenſible alteration; For
the words run thus: One Generation paſſeth away, and another
Generation cometh; but the Earth abideth for ever. So that it
hath no coherence with its Context, (as Philoſophers ſhew) if it

be expounded to ſpeak of the Earths immobility. And al­
though in this Chapter Eccleſiaſtes, and in many others, Holy
Writ aſcribes Motion to the Sun, which Copernicus will have to
ſtand fixed in the Centre of the Univerſe; yet it makes nothing
againſt his Poſition. For the Motion that belongs to the Earth,
is by way of ſpeech aſſigned to the Sun, even by Copernicus him­
ſelf, and thoſe who are his followers, ſo that the Revolution of
the Earth is often by them phraſed, The Revolution of the Sun.
To conclude, No place can be produced out of Holy Scripture,
which ſo clearly ſpeaks the Earths Immobility, as this doth its
1Mobility. Therefore this Text, of which we have ſpoken, is ea­
ſily reconciled to this Opinion. And to ſet forth the Wonder­
ful power and Wiſdome of God, who can indue and actuate the
Frame of the Whole Earth (it being of a monſtrous weight by
Nature) with Motion, this our Divine pen-man addeth; And
the pillars thereof tremble: As if he would teach us, from the
Doctrine laid down, that it is moved from its Foundations.
* In vita ejus.
* Followers of
that Learned
Kings Hypothe­
ſis.
* That is 5000
miles; eight of
theſe making an
Italian, or Engliſh
mile of a 1000.
paces, every pace
containing 5.
Feet.
* Chap. 1. v. 4.
The Motion of
the Earth, not a­
gainſt Scripture.
1
AN
EPISTLE
Of the Reverend Father
PAOLO ANTONIO FOSCARINI,
A CARMELITE;
Concerning
The PYTHAGORIAN and COPERNICAN Opinion
OF
The Mobility of the EARTH,
AND
Stability of the SVN;
AND
Of the New Syſteme or Conſtitution
OF THE
WORLD.
IN WHICH,
The Authorities of SACRED SCRIPTVRE,
and ASSERTIONS of DIVINES,
commonly alledged againſt this Opinion,
are Reconciled.
WRITTEN
To the moſt Reverend FATHER,
SEBASTIANO FANTONI,
General of the Order of CARMELITES.
Engliſhed from the Original,
BY
THOMAS SALVSBVRIE.
So quis indiget ſapientia, poſtulet
à Deo. Jacobi 1. verſu. 5.
Optavi, & datus eſt mihi ſenſus.
Sapientiæ 7. verſu. 7.
LONDON,
Printed by WILLIAM LEYBOURN, MDCLXI.
1
[Empty page]
1
To the Moſt
Reverend Father
SEBASTIANO FANTONI,
General of the Order of
CARMELITES.
In obedience to the command of the No­
ble Signore Vincenzo Carraffa, a Neapo­
litan, and Knight of S. John of Jeru­
ſalem, (a perſon, to ſpeak the truth, of
ſo great Merit, that in him Nobility of
Birth, Affability of Manners, Univerſal
knowledge of Arts and things, Piety
and Vertue do all contend for prehemi­
nence) I reſolved with my ſelf to un­
dertake the Defence of the Writings of the New, or rather Re­
newed, and from the Duſt of Oblivion (in which it hath long
lain hid) lately Revived Opinion, Of the Mobility of the Earth,
and Stability of the Sun, in times paſt found out firſt by Pytha­
goras, and at laſt reduced into Practice by Copernicus; who like­
wiſe hath deduced the Poſition of the Syſteme and Conſtitution
of the World and its parts from that Hypotheſis: on which
Subject I have formerly writ to You, Moſt Reverend Sir: But
in regard I am bound for Rome to preach there by your Com­
mand; and ſince this Speculation may ſeem more proper for a­
nother Treatiſe, to wit, a Volume of Coſmography, which I am
in hand with, and which I am daily buſie about, that it may
come forth in company with my Compendium of the Liberal Arts,
which I have already finiſhed, rather than now to diſcuſs it by it
ſelf, I thought to forbear, imparting what I have done for the
preſent; Yet I was deſirous to give, in the mean time, a brief ac­
count of this my Determination, and to ſhew You, Moſt Reve­
rend Father, (to whom I owe all my indeavours, and my very
ſelf) the Foundations on which this Opinion may be grounded,
leaſt, whilſt otherwiſe it is favoured with much probability, it be
found in reality to be extreamly repugnant (as at firſt ſight it
1ſeems) not onely to Phyſical Reaſons, and Common Principles
received on all hands (which cannot do ſo much harm) but alſo
(which would be of far worſe conſequence) to many Authori­
ties of ſacred Scripture: Upon which account many at their
firſt looking into it, explode it as the moſt fond Paradox and
Monſtrous Capriccio that ever was heard of. Which thing pro­
ceeds only from an antiquated and long confirmed Cuſtome,
which hath ſo hardened men in, and habituated them to Vul­
gar, Plauſible, and for that cauſe by all men (aſwell learned as
unlearned) Approved Opinions, that they cannot be removed
one ſtep from them: So great is the force of Cuſtome (which
not unfitly is ſtiled a ſecond Nature) prevailing over the whole
World, that touching things men are rather pleaſed with, de­
lighted in, and deſirous of thoſe, which, though evil and obnox­
ious, are by uſe made familiar to them, than ſuch, wherewith,
though better, they are not accuſtomed and acquainted. So in
like manner, and that chiefly, in Opinions, which when once they
are rooted in the Mind, men ſtart at, and reject all others
whatſoever; not only thoſe that are contrary to, but even all
that ever ſo little diſagree with or vary from theirs, as harſh to
the Ear, diſcoloured to the Eye, unpleaſant to the Smell, nauſe­
ous to the Taſt, rough to the Touch. And no wonder: For
Phyſical Truths are ordinarily judged and conſidered by men,
not according to their Eſſence, but according to the preſcript of
ſome one whoſe deſcription or definition of them gaines him
Authority amongſt the vulgar. Which authority nevertheleſs
(ſince 'tis no more than humane) ought not to be ſo eſteemed, as
that that which doth manifeſtly appear to the contrary, whether
from better Reaſons lately found out, or from Senſe it ſelf, ſhould
for its ſake be contemned and ſlighted; Nor is Poſterity ſo to be
confined, but that it may, and dares, not only proceed farther,
but alſo bring to light better and truer Experiments than thoſe
which have been delivered to us by the Ancients. For the Ge­
nius's of the Antients, as in Inventions they did not much ſur­
paſs the Wits of our times; ſo for the perfecting of Inventions
this Age of ours ſeems not only to equal, but far to excell former
Ages; Knowledge, whether in the Liberal or Mechanical Arts,
daily growing to a greater height. Which Aſſertion might be
eaſily proved, were it not that in ſo clear a caſe, there would be
more danger of obſcuring, than hopes of illuſtrating it with any
farther light.
But (that I may not wholly be ſilent in this point) have not the
ſeveral Experiments of Moderns, in many things, ſtopped the
mouth of Venerable Antiquity, and proved many of their great­
teſt and weightieſt Opinions, to be vain and falſe? The Doctrine
1of the Antipodes by many of the Antients of approved Wiſ­
dome and Learning was held a Paradox no leſs abſurd than this
Our Opinion of the Earths Motion may ſeem to be; as likewiſe
that of the Habitableneſſe of the Torrid Zone: Of theſe Opini­
ons, the firſt was accounted unpoſſible by many, but the latter
was abſolutely denyed by the unanimous conſent of all: But
later Authors (to the great felicity and perpetual Glory of
their Age) have, not ſo much by Authority, as by accurate
diligence and indefatigable ſtudy to finde out the truth, pro­
ved them both to be undoubtedly true. Thus I affirm that
the Antients were deceived, and that in too lightly challenging
Credid and Authority for their Inventions, they diſcovered too
much folly. Here for brevities ſake I paſs by many Dreams
lately detected, both of Ariſtotle and other of the antient Philo­
ſophers; who in all likelihood if they had dived into the Obſer­
vations of Modern Writers, and underſtood their Reaſons, would,
by changing their Judgements, have given them the precedency,
and would have ſubſcribed to their manifeſt Truth. Hereby we
ſee that we are not to have ſo high a reſpect for the Antiens, that
whatever they aſſert ſhould be taken upon truſt, and that Faith
ſhould be given to their ſayings, as if they were Oracles and
Truths ſent down from Heaven. But yet (which indeed is
chiefly to be regarded in theſe matters) if any thing be found out
that is repugnant to Divine Authority, or to the Sacred Leaves,
that were dictated by the Holy Ghoſt, and by His Inſpiration

expounded by the Holy Doctors of the Church, in this caſe not
onely Humane Reaſon, but even Senſe it ſelf is to ſubmitt:
which, though by all manner of weighty Conditions and circum­
ſtances it ſhould hold forth any thing contrary to Divine Autho­
rity, (which indeed is ſo plain, that there is no way left to evade
the right un erſtanding of it) yet is it to be rejected; and we
muſt conclude our ſelves deceived by it, and believe that that is
not true which Senſe and Reaſon repreſents unto us: For, however
we judge of things, we have, both in this and all other caſes, a
more certain knowledge, which proceeds from Divine Faith; as
S. Peter hath moſt excellently expreſt it: Who though with his
Senſes he ſaw, and perceived the Glory of our Lord in his
Transfiguration, and heard his words manifeſting his great Pow­
er, yet nevertheleſs all theſe things compared with the Light of
Faith, he adds: ^{*}We have alſo a more ſure word of Prophecy, &c.

Wherefore ſince this Opinion of Pythagoras and Copernicus hath
entred upon the Stage of the World in ſo ſtrange a Dreſs, and at
the firſt appearance (beſides the reſt) doth ſeem to oppoſe ſun­
dry Authorities of Sacred Scripture, it hath (this being granted)
been juſtly rejected of all men as a meer abſurdity.
1
Faith is more
certain, than ei­
ther Senſe or Rea­
ſon.
* 2 Pet. 1. 19.
But yet becauſe the common Syſteme of the World deviſed by
Ptolomy hath hitherto ſatisfied none of the Learned, hereupon a
ſuſpicion is riſen up amongſt all, even Ptolemy's followers them­
ſelves, that there muſt be ſome other Syſteme, which is more true
than this of Ptolemy; For although the Phœnomena of Celeſtial
Bodys may ſeem to be generally reſolved by this Hypotheſis, yet
they are found to be involved with many difficulties, and refer­
red to many devices; as namely of Orbes of ſundry Forms and
Figures, Epicicles, Equations, Differences, Excentricks, andinnu­
merable ſuch like fancies and Chymæra's which ſavour of the
Ens Rationis of Logicians, rather than of any Realem Eſſentiam.
Of which kinde is that of the Rapid Motion, than which I finde
not any thing that can be more weakly grounded, and more eaſi­
ly controverted and diſproved: And ſuch is that conceit of the
^{*} Heaven void of Stars, moving the inferior Heavens or Orbes:

All which are introduced upon occaſion of the variety of the
Motions of Celeſtial Bodyes, which ſeemed impoſſible, by any
other way, to be reduced to any certain and determinate Rule.
So that the Aſſertors of that common Opinion, freely confeſs,
that in deſcribing the Worlds Syſteme, they cannot as yet diſco­
ver, or teach the true Hypotheſis thereof: But that their endea­
vours are onely to finde out, amongſt many things, what is moſt
agreeable with truth, and may, upon better and more accomo­
date Reaſons, anſwer the Celeſtial Phœnomena.
* Or Primum
Mobile.
Since that, the Teleſcope (an Optick Invention) hath been found
out, by help of which, many remarkable things in the Heavens,
moſt worthy to be known, and till then unthought of, were diſ­
covered by manifeſt ſenſation; as for inſtance, That the Moon is
Mountainous; Venus and Saturn Tricorporeal; and Jupiter
Quadricorporeal: Likewiſe that in the Via Lactea, in the Ple­
iades, and in the Stars called Nobuloſœ there are many Stars, and
thoſe of the greateſt Magnitude which are by turns adjacent to
one another; and in the end it hath diſcovered to us, new fixed
Stars, new planets, and new Worlds. And by this ſame Inſtru­
ment it appears very probable, that Venus and Mercury do not
move properly about the Earth, but rather about the Sun; and
that the Moon alone moveth about the Earth. What therefore
can be inferred from hence, but that the Sun doth ſtand immo­
vable in the Centre, and that the Earth, with the other Celeſtial
Orbes, is circumvolved about it? Wherefore by this and many
other Reaſons it appears, That the Opinion of Pythagor as and
Copernicus doth not diſagree with Aſtronomical and Coſmogra­
phical Principles; yea, that it carryeth with it a great likelihood
and probability of Truth: Whereas amongſt the ſo many ſeve­
ral Opinions, that deviate from the common Syſteme, and deviſe
1others, ſuch as were thoſe of Plato, Calippus, Eudoxus; and ſince

them of Averroe, ^{*} Cardanus, Fracaſtorius, and others both Anti­
ent and Modern, there is not one found that is more facile, more
regularly ahd determinately, accommodated to the Phœnomena
and Motions of the Heavens, without Epicycles, Excentrix, Ho­
mocentricks Deferents, and the ſupputation of the Rapid Motion.
And this Hypotheſis hath been aſſerted for true, not onely by
Pythagoras, and, after him, by Copernicus, but by many famous
men, as namely, Heraclitus, and Ecphantus, Pythagoreans, all the
Diſciples of that Sect, Miceta of Syracuſe, Martianus Capella, and
many more. Amongſt whom, thoſe (as we have ſaid) that
have attempted the finding out of New Syſtemes (for they refu­
ſed both this of Pythagoras, and that of Ptolemy) are numberleſs:
who yet notwithſtanding allowed this Opinion of Pythagoras to
carry with it much probability, and indirectly confirmed it; inaſ­
much as that they rejected the common one as imperfect, defe­

ctive, and attended with many contradictions and difficulties.
Amongſt theſe may be numbered Father ^{*} Clavius, a moſt learn­
ed Jeſuite; who, although he refutes the Syſteme of Pythagoras,
yet acknowledgeth the Levity of the common Syſteme, and he
ingeniouſly confeſſeth, that for the removal of difficulties, in which
the common Syſteme will not ſerve the turn, Aſtronomers are
forced to enquire after another Syſteme, to the diſcovery of
which, he doth very earneſtly exhort them.
* Cardan de re­
rum variet. Lib. 1.
Cap. 1.
* P. Clavins in
ultima ſuor. Ope­
rum editione.
Now can there a better or more commodious Hypotheſis
be deviſed, than this of Copernicus,? For this Cauſe many Mo­
dern Authors are induced to approve of, and follow it: but
with much hæſitancy, and fear, in regard that it ſeemeth in their
Opinion ſo to contradict the Holy Scriptures, as that it cannot
poſſibly be reconciled to them. Which is the Reaſon that this
Opinion hath been long ſuppreſt, and is now entertained by men
in a modeſt manner, ad as it were with a veiled Face; according
to that advice of the Poet:
Judicium populi nunquam contempſeris unus,
Ne nullis place as, dum vis contemnere multos.
Upon conſideration of which, (out of my very great love to­
wards the Sciences, and my ardent defire to ſee the encreaſe and
perfection of them, and the Light of Truth freed from all Er­
rours and Obſcurities) I began to argue with my ſelf touching
this Point after this manner: This Opinion of the Pythagoreans
is either true, or falſe; If falſe, it ought not to be mentioned, and
deſerves not to be divulged: If true, it matters not, though it
contradict all, as well Philoſophers as Aſtronomers: And though
for its eſtabliſhment and reducement to uſe a new Philoſophy
1and Aſtronomy, (ſounded upon new Principles and Hypotheſe)
ſhould be conſtituted: For the Authority of Sacred Scripture
will not oppoſe it; neither doth one Truth contradict another.
If therefore the Opinion of Pythagoras be true, without doubt
God hath diſpoſed and dictated the words of of Holy Writ in
ſuch a manner, that they may admit an apt ſenſe and reconcilia­
tion with that Hypotheſis. Being moved by theſe Reaſons, and
the probability of the ſaid Opinion, I thought good to try whe­
ther Texts of Sacred Scripture might be expounded according to
Theological and Phyſical Principles, and might be reconciled to
it, ſo that (in regard that hitherto it hath been held probable) it
may in after times, coming without ſcruple to be acknowledged
for true, advance it ſelf, and appear in publick with an uncover­
ed Face, without any mans prohibition, and may lawfully and
freely hold a Sacred intelligence with Holy Truth, ſo earneſtly
coveted and commended by good Men. Which deſigne, having hi­

therto been undertaken by none that I know, wil, I am perſwaded,
be very acceptable to the Studious of theſe Learnings, eſpecially to
the moſt Learned Galilœo Galilœi, chief Mathematician to the
moſt Serene Grand Duke of Tuſcany, and John Kepler, chief
Mathematician to his Sacred and invincible Majeſty, the Empe­
rour, and to all that Illuſtrious, and much to be commended Ac­
cademy of the Lynceans; whom, if I miſtake not, are all of this
Opinion. Although I doubt not but they, and many other
Learned Men might eaſily have found out theſe or the like Re­
conciliations of Scriptural expreſſions; to whom nevertheleſs I
have thought fit (in reſpect of that profeſſion which I have under­
taken, upon the faith of my ſoul, and the propenſity that I have
towards Truth) to offer that of the Poet,
The Author
firſt Theologically
defendeth the
Earths Mobili­
ty, approved by
many of the Mo­
derns.
Nullius addictus jur are in verba Magiſtri.
And in teſtimony of my eſteem to them and all the Learned,
to communicate theſe my thoughts; confidently aſſuring my ſelf
that they will accept them, with a Candor equal to that where­
with I have written them.
Therefore to come to the buſineſs: All Authorities of Di­
vine Writ which ſeem to oppoſe this Opinion, are reducible to
ſix Claſſes: The firſt is of thoſe that affirm the Earth to ſtand
ſtill, and not to move: as Pſal. 92. He framed the round World
ſo ſure, that it cannot be moved: Alſo Pſal. 104. Who laid the
Foundations of the Earth, that it ſhould not be removed for ever:
And Eccleſiaſtes 1. But the Earth abideth for ever: And others
of the like ſenſe.
The ſecond is of thoſe which atteſt the Sun to move, and
1Revolve about the Earth; as Pſal. 19. (b) In them hath be ſet a

Tabernacle for the Sun, which cometh forth as a Bridegroom out
of his chamber, and rejoyceth as a Gyant to run his Courſe. It
cometh forth from the uttermoſt part of the Heaven, and runneth
about unto the end of it again; and there is nothing hid from the
heat thereof. And Eccleſiaſt. 1. The Sun riſeth, and the Sun go­
eth down, and haſteth to the place where be aroſe: it goeth towards
the South, and turneth about unto the North. Whereupon the
Suns Retrogradation is mentioned as a Miracle, Iſaiah 38. The
Sun returned ten degrees. And Eccleſiaſticus 48. In his time the
Sun went backward, and lengthened the life of the King. And
for this reaſon it is related for a Miracle, in the Book of Joſbuah,
that at the Prayers of that great Captain the Sun ſtood ſtill, its
motion being forbidden it, by him: Joſh.10. Sun ſtand thou
ſtill upon Gibeon. Now if the Sun ſhould ſtand ſtill, and the
Earth move about it, its ſtation at that time was no Miracle;
and if Joſhuah had intended, that the light of the day ſhould
have been prolonged by the Suns ſplendour, he would not have
ſaid, Sun ſtand thou ſtill, but rather Earth ſtand thou ſtill.
(b) Or In Sole
poſuit tabernacu­
lum ſuum, accor­
ding to the Tran­
ſlation our Au­
thor followeth.
The third Claſſis is of thoſe Authorities which ſay, that Hea­
ven is above, and the Earth beneath; of which ſort is that place
of Joel, chap. 2. cited by S. Peter, in Acts. 2. I will ſhew wonders
in Heaven above, and ſignes in the Earth beneath, with others of
the like purport. Hereupon Chriſt at his Incarnation is ſaid to
come down from Heaven; and after his Reſurrection to have aſ­
cended up into heaven. But if the Earth ſhould move about
the Sun, it would be, as one may ſay, in Heaven, and conſe­
quently would rather be above Heaven than beneath it. And
this is confirmed; For that the Opinion which placeth the Sun in
the Centre, doth likewiſe place Mercury above the Sun, and
Venus above Mercury; and the Earth above Venus, together
with the Moon, which revolves about the Earth, and therefore
the Earth, together with the Moon, is placed in the third Heaven.
If therefore in Spherical Bodies, as in the World, beneath ſigni­

fies no more than to be neer to the centre, and above, than to
approach the Circumference, it muſt needs follow, that for ma­
king good of Theological Poſitions concerning the Aſcenſion
and Deſcenſion of Chriſt, the Earth is to be placed in the cen­
tre, and the Sun, with the other Heavens in the Circumference;
and not according to Copernicus, whoſe Hypotheſis inverts this
Order: with which one cannot ſee how the true Aſcenſion and
Deſcenſion can be conſiſtent.
In Spberieall
Bodies, Deorſum
is the Centre, and
Surſum the Cir­
cumference.
The fourth Claſſis is of thoſe Authorities which make Hell to
be in the Centre of the World, which is the Common Opinion
of Divines, and confirmed by this Reaſon, That ſince Hell
1ken in its ſtrict denomination) ought to be in the loweſt part of
the World, and ſince that in a Sphere there is no part lower
then the Centre, Hell ſhall be, as it were, in the Centre of the
World, which being of a Spherical Figure, it muſt follow, that

Hell is either in the Sun (foraſmuch as it is ſuppoſed by this Hy­
potheſis to be in the Centre of the World) or elſe ſuppoſing
that Hell is in the Centre of the Earth, if the Earth ſhould move
about the Sun, it would neceſſarily enſue, that Hell, together
with the Earth, is in Heaven, and with it revolveth about the third
Heaven; than which nothing more abſurd can be ſaid or imagi­
ned.
Hell is in the
centre of the
Earth, not of the
World.
The fifth Claſſis, is of thoſe Authorities which alwayes op­

poſe Heaven to the Earth, and ſo again the Earth to Heaven; as
if there were the ſame relation betwixt them, with that of the
Centre to the Circumference, and of the Circumference to the
Centre. But if the Earth were in Heaven, it ſhould be on one
ſide thereof, and would not ſtand in the Middle, and conſequent­
ly there would be no ſuch relation betwixt them; which never­
theleſs do, not only in Sacred Writ, but even in Common Speech,
ever and every where anſwer to each other with a mutual Oppo­
fition. Whence that of Geneſ. 1. In the beginning God created
the Heaven and the Earth: and Pſal. 115. The Heaven, even
the Heavens are the Lords; but the Earth hath he given to the
Children of men: and our Saviour in that Prayer which he pre­
ſcribeth to us, Matth. 6. Thy will be done in Earth, as it is in
Heaven: and S. Paul, 1 Corinth. 15. The firſt man is of the
Earth, earthy; the ſecond man is of Heaven, heavenly: and
Coloſſ. 1. By him were all things created that are in Heaven, and
that are in Earth: and again, Having made peace through the
Blood of his Croſſe for all things, whether they be things in Earth
or things in Heaven: and Chap. 3. Set your affections on things
above, not on things on the Earth; with innumerable other ſuch
like places. Since therefore theſe two Bodies are alwayes mu­
tually oppoſed to each other, and Heaven, without all doubt,
referreth to the Circumference, it muſt of neceſſity follow, that
the Earth is to be adjudged the place of the Centre.
Heaven and
Earth are always
mutually oppoſed
to each other.
The ſixth and laſt Claſſis is of thoſe Authorities, which (being
rather of Fathers and Divines, than of the Sacred Scripture) ſay,
That the Sun, after the day of Judgment ſhall ſtand immoveable

in the Eaſt, and the Moon in the Weſt. Which Station, if the
Pythagorick Opinion hold true, ought rather to be aſcribed to
the Earth, than to the Sun; for if it be true, that the Earth doth
now move about the Sun, it is neceſſary that after the day of
Judgment it ſhould ſtand immoveable. And truth is, if it muſt
ſubſiſt without motion in one conſtant place, there is no reaſon
1why it ſhould rather ſtand in one ſite of that Place than in ano­
ther, or why it ſhould rather turn one part of it than another to
the Sun, if ſo be that every of its parts without diſtinction, which
is deſtitute of the Suns light, cannot chooſe but be diſmal, and
much worſe affected than that part which is illuminated. Hence
alſo would ariſe many other abſurdities beſides theſe.
After the day
of Judgment the
Earth ſhall ſtand
immoveable.
Theſe are the Claſſes, &c. from which great aſſaults are made
againſt the ſtructure of the Pythagorick Syſteme; yet by that
time I ſhall have firſt laid down ſix Maximes or Principles, as
impregnable Bulwarks erected againſt them, it will be eaſie to
batter them, and to defend the Hypotheſis of Pythagoras from
being attaqued by them. Which before I propound, I do pro­
feſs (with that Humility and Modeſty which becometh a Chri­
ſtian, and a perſon in Religious Orders) that I do with reverence
ſubmit what I am about to ſpeak to the Judgment of Holy
Church. Nor have I undertaken to write theſe things out of
any inducements of Temerity, or Ambition, but out of Charity
and a Deſire to be auxiliary to my neighbour in his inquiſition
after Truth. And there is nothing in all this Controverſie
maintained by me (that expect to be better inſtructed by thoſe
who profeſs theſe Studies) which I ſhall not retract, if any per­
ſons ſhall by ſolid Reaſons & reiterated Experiments, prove ſome
other Hypotheſis to be more probable; but yet, until ſuch time as
they ſhall decide the Point, I ſhall labour all I can for its ſupport.
My firſt and chiefeſt Maxime is this; When any thing is at­
tributed in Holy Writ, to God, or to a Creature, thats not be­
ſeeming to, or incommenſurate with them, it muſt of neceſſity
be received and expounded one, or more of the four following
wayes; Firſt, it may be ſaid to agree with them Metaphorically,
and Proportionally, or by Similitude. Secondly, According to
our manner of Conſidering, Apprehending, Conceiving, Vnderſtand­
ing, Knowing, &c. Thirdly, according to the Opinion of the
Vulgar, and the Common way of Speaking: to which Vulgar
Speech the Holy Ghoſt doth very often with much ſtudy acco­
modate it ſelf. Fourthly, In reſpect of our ſelves, and for that
he makes himſelf like unto us. Of each of theſe wayes there are
theſe examples: God doth not walk, ſince he is Infinite and Im­
moveable; He hath no Bodily Members, ſince he is a Pure Act;
and conſequently is void of all Paſſion of Minde; and yet in
Sacred Scripture, Gen. 3. verſ. 8. it is ſaid, He walked in the cool of
the day: and Job 22. verſ. 14. it is ſaid, He walketh in the ^{*} Cir­

cuit of Heaven: and in many other places coming, departing,
making haſt is aſcribed to God; and likewiſe Bodily parts, as
Eyes, Ears, Lips, Face, Voice, Countenance, Hands, Feet, Bow­
els, Garments, Arms; as alſo many Paſſions, ſuch as Anger,
1Sorrow, Repentance, and the like. What ſhall we ſay there­
fore? Without doubt ſuch like Attributes agree with God (to
uſe the Schoolmens words Metaphorically, Proportionally, and by
Similitude: And touching Paſſions, it may be ſaid, that God
condeſcendeth to repreſent himſelf after that manner: as for
inſtance, The Lord is angry; i.e. He revealeth himſelf as one that
is angry: He grieved; i. e. He revealeth himſelf, as one that
is ſorrowful: It repented him that he had made man; i.e. He ſee­
med as one that repented. And indeed all theſe things are Com­
parativè ad nos, and in reſpect of us. So God is ſaid to be in
Heaven, to move in time, to ſhew himſelf, to hide himſelf, to
obſerve and mark our ſteps; to ſeek us, to ſtand at the door,
to knock at the door; not that he can be contained in a bodily
place, nor that he is really moved, nor in time; nor that humane
manners or cuſtomes can agree with him, ſave only according to
our manner of Apprehenſion: This Conception of ours orderly
diſtinguiſheth theſe Attributes in him one from another, when,
notwithſtanding, they are one and the ſame with him: This Ap­
prehenſion of ours divideth alſo his actions into ſeveral times,
which, nevertheleſſe, for the moſt part, are produced in one and
the ſame inſtant: And this, to conclude, alwayes apprehendeth
thoſe things with ſome defect, which, notwithſtanding are in
God moſt perfect. For this reaſon doth the Sacred Scripture
expreſs it ſelf according to the Vulgar Opinion, whilſt it aſcribes
to the Earth Ends and Foundations, which yet it hath not; to
the Sea a Depth not to be fathomed; to Death (which is a Pri­
vation, and conſequently a Non entity) it appropriates Actions,
Motion, Paſſions, and other ſuch like Accidents, of all which it is
deprived, as alſo Epithites and Adjuncts, which really cannot
ſuit with it: Is not the bitterneſſe of Death paſt? 1 Sam. 15. 32.
Let death come upon them, Pſal 6. He hath prepared the Inſtru­
ments of Death, Pſal. 7. 14. Thou raiſeſt me from the gates of
Death, Pſal. 84. In the midſt of the ſhadow of Death, Pſal. 23.
Love is ſtrong as Death, Cant. 8. 9. The Firſt-Born of Death, Job
18. 13. Deſtruction and Death ſay, &c. Job 28. 22. And who knows
not that the whole Hiſtory of the rich Glutton doth conſiſt of

the like phraſes of Vulgar Speech? So Eccleſiaſticus, Chap. 27.
verſ. 11. The godly man abideth in wiſdome, as the Sun; but a
fool changeth as the Moon; and yet the Moon according to the
real truth of the matter no wayes changeth, but abides the ſame
for ever, as Aſtronomers demonſtrate, one half thereof remain­
ing alwayes lucid, and the other alwayes opacous. Nor at any
time doth this ſtate vary in it, unleſſe in reſpect of us, and ac­
cording to the opinion of the Vulgar. Hence it is cleer, that the
holy Scripture ſpeaks according to the common form of ſpeech
1ſed amongſt the unlearned, and according to the appearance of
things, and not according to their true Exiſtence. In like man­
ner Geneſ. 1. in the deſcription of the Creation of all things,
the Light is ſaid to be made firſt of all, and yet it followeth in
the Text, And the Evening and the Morning made the firſt day:
and a little after the ſeveral Acts of the Creation are diſtinguiſhed
and aſſigned to ſeveral days, and concerning each of them it is
ſaid in the Text, And the Evening and the Morning made the
ſecond day; and then the third day, the fourth day, &c. Hence
many doubts ariſe, all which I ſhall propound according to the
common Syſteme, that it may appear even from the Hypotheſis
of that Syſteme, that the ſacred Scripture ſometimes, for the a­
voyding of emergent difficulties, is to be underſtood in a vulgar
ſenſe and meaning, and in reſpect of us, and not according to
the nature of things. Which diſtinction even Ariſtotle himſelf

ſeemeth to have hinted, when he ſaith, ^{*} Some things are more
intelligible to us; others by nature, or ſecundum ſe.
* Circa Cardi­
nes Cœli.
Luke 16.
Alia ſunt notio­
ra nobis, alia, no­
tiora natura, vel
ſecundum ſe, A­
r ſt. lib. 1. Phyſ.
Firſt therefore; If the light were made before heaven, then
it rolled about without heaven to the making of the diſtinction
of Day and Night. Now this is contrary to the very doctrine
of theſe men, who affirm that no Cœleſtial Body can be moved
unleſſe per accidens, and by the motion of Heaven, and as a knot
in a board at the motion of the board. Again, if it be ſaid, that
the Light was created at the ſame time with Heaven, and began
to be moved with Heaven, another doubt ariſeth, that likewiſe
oppoſeth the foreſaid common Hypotheſis: For it being ſaid,
that Day and Night, Morning and Evening were made, that ſame
is either in reſpect of the Univerſe, or onely in reſpect of the
Earth and us. If ſo be that the Sun turning round (according to
the Hypotheſis of the Common Syſteme) doth not cauſe the
Night and Day, but only to opacous Bodies which are deſtitute
of all other light, but that of the Sun, whilſt in their half part
(which is their Hemiſphœre) and no more, (for that the Suns
light paſſeth over but one half of an opacous Body, unleſs a ve­
ry ſmall matter more in thoſe of leſſer bulk) they are illumina­
ted by the Suns aſpect, the other half remaining dark and tene­
broſe, by reaſon of a ſhadow proceeding from its own Body.
Therefore the diſtinction of dayes by the light of heaven, ac­
cording to the deſcription of them in the ſacred Scriptures, muſt
not be underſtood abſolutely, and ſecundum ſe, and Nature her
ſelf; but in reſpect of the Earth, and of us its inhabitants, and
conſequently ſecundum nos. 'Tis not therefore new, nor unu­
ſual in ſacred Scripture to ſpeak of things ſecundum nos, and on­
ly in reſpect of us, and ſecundum apparentiam; but not ſecundum
ſe, and reinaturam, or Abſolutely and Simply.
1
And if any one would underſtand theſe Days of ſacred Scri­
pture, not only ſecundum nos, but alſo ſecundum naturam, as
circulations of Cœleſtial Light returning to the ſelf ſame point
from whence it did at firſt proceed; ſo as that there needs no
reſpect to be had to Night or to ^{*} Darkneſſe, for which ſole rea­

ſon we are fain to imbrace the Interpretation of ſacred Scripture
ſecundum nos; In oppoſition to this we may thus argue: If the
ſacred Scripture be underſtood to ſpeak abſolutely, of iterated
and ſucceſſive circulations of light, and not reſpectu noſtri, as if
theſe words Evening and Morning had never been inſerted, which
in their natural acceptation denote the Suns habitude to us and to
the Earth: For that the Morning is that time when the Sun be­
gins to wax light, and to riſe above the Horizon in the Eaſt,
and become viſible in our Hemiſphœre, and Evening is the time
in which the Sun declines in the Weſt, and approacheth with its
light neerer to the other oppoſite Horizon and Hemiſphœre,
which is contiguous to this of ours. But the word Day is a Co­
relative to the word Night. From hence therefore it evidently
appeareth, that theſe three words Evening, Morning, and Day,
cannot be underſtood of a Circulation of Light ſecundum ſe,
and abſolutè, but only ſecundum nos, and reſpectu noſtri; and in
that ſenſe indeed the Morning and Evening do make the Night
and Day,
* Aut ad Umbram
In like manner, Gen. 1. 16. it is ſaid, God made two great Lights;
the greater Light to rule the Day, and the leſſer Light to rule the
Night, and the Stars. Where both in the Propoſition and in the
ſpecification of it, things are ſpoken which are very diſagreeing
with Cœleſtial Bodies. Therefore thoſe words are in that place
to be interpreted according to the foreſaid Rules; namely, ac­
cording to the third and fourth; ſo that they may be ſaid to be
underſtood according to the ſenſe of the vulgar, and the common
way of ſpeaking, which is all one, as if we ſhould ſay, ſecundum
apparentiam, and ſecundum nos, vel reſpectu noſtri. For firſt, it
is ſaid in the Propoſition, And God made two great Lights;
meaning by them the Sun and Moon, whereas according to the
truth of the matter theſe are not the Greater Lights; For al­
though the Sun may be reckoned amongſt the Greater, the Moon
may not be ſo, unleſs in reſpect of us. Becauſe amongſt
thoſe that are abſolutely the Greater, and a little leſſer than the

Sun (nay in a manner equal to it) and far bigger than the Moon,
we may with great reaſon enumerate Saturn, or ſome of the
Fixed Stars of the firſt Magnitude, ſuch as Canopus, (otherwiſe
called Arcanar) in the end of a River; or the Little Dog in
the mouth of the Great Dog; or the Foot of Orion, called Ri­
gel; or his Right ſhoulder, or any other of that Magnitude.
1Therefore the two great Lights are to be underſtood in reſpect of
us, and according to vulgar eſtimation, and not according to the
true and reall exiſtence of ſuch Bodies. Secondly, in the ſpeci­
fication of the Propoſition it is ſaid, The greater Light to rule the
Day; hereby denoting the Sun; in which the verbal ſenſe of
Scripture agreeth with the Truth of the Thing; For that the Sun
is the Greateſt of all Luminaries, and Globes. But that which
followeth immediately after, And the leſſer Light to rule the
Night, meaning the Moon, cannot be taken in the true and real
ſenſe of the words: For the Moon is not the leſſer Light, but
Mercury; which is not only much leſſer than the Moon, but alſo
than any other Star. And if, again, it be ſaid, That the Holy
Text doth not ſpeak of the Stars, but onely of the Luminaries,
for that preſently after they are mentioned apart, And the Stars;
and that what we ſay is true touching the compariſon of the Stars
amongſt themſelves, but not in reſpect of the Luminaries, name­
ly, the Sun and Moon: This reply doth diſcover a man to be
utterly ignorant in theſe Studies, and ſuch who having not the
leaſt ſmattering in them, doth conceive an abſurd and erroneous
Opinion of the Cœleſtial Bodies. For the Moon and Sun, con­
ſidered in themſelves, and as they appear to us, if they ſhould
be a far greater diſtance from us, than indeed they are, would be
no other, nor would appear to us otherwiſe than Stars, as the
reſt do in the Firmament. But Great Luminaries they neither

are, nor ſeem to be, ſave only in reſpect of us: And ſo, on
the other ſide, the Stars, as to themſelves, are no other than ſo
many Suns and ſo many Moons; yet are ſo far remote from us,
that by reaſon of their diſtance they appear thus ſmall, and dim
of light, as we behold them. For the greater and leſſer diſtance
of heavenly Bodies (cæteris paribus) doth augment and diminiſh
their appearance both as to Magnitude and Light. And there­
fore the words which follow in that place of Geneſis, And the
Stars (as diſtinguiſhing the Stars from the Sun and Moon) are
to be taken in no other acceptation than that which we have ſpo­
ken of, namely, according to the ſenſe of the Vulgar, and the
common manner of ſpeech. For indeed, according to the truth
of the matter, all Cœleſtial Bodies, being ſhining Globes, are of
a vaſt bigneſs, to which if we ſhould be ſo neer as we are to the
Moon, they would ſeem to us of as great, yea a greater magni­
tude than the Moon: As likewiſe on the contrary, if we were as
far diſtant from the Sun and Moon, as we are from them, both
Moon and Sun would ſhew but as ſtars to us. And yet the
ſplendor of the Sun would doubtleſs be greater intenſivè than
that of any other ſtar. For, although it ſhould be granted that
ſome ſtars (as thoſe of the Fixed that twinkle) do ſhine of
1ſelves, aud by their own nature, as the Sun, that derives not its
light from others (which yet remains undecided and doubtful)
and borrow not their light from the Sun; Nevertheleſs ſince the
brightneſs of none of the ſtars may be compared with the Suns
ſplendour, which was created by God firſt, and before all other
Luminaries, in the higheſt kind of Light, it would therefore
notwithſtanding follow, that none of thoſe ſtars, although pla­
ced in the ſame proximity to us with the Sun, and therefore ap­
pearing to us of the ſame Magnitude as the Sun, can beſtow up­
on us ſo much Light as we receive from the Sun: As on the
contrary, the Sun, at the ſame remoteneſſe from us as they are,
would indeed, as to its Magnitude, appear to us as one of thoſe
ſtars, but of a ſplendour much more intenſe than that of theirs.

So that, now, the Earth is nothing elſe but another Moon or ſtar,
and ſo would it appear to us, if we ſhould behold it from a con­
venient diſtance on high. And in it might be obſerved (in that
variety of Light and Darkneſs which the Sun produceth in it by
making Day and Night) the ſame difference of Aſpects that are
ſeen in the Moon, and ſuch as are obſerved in tricorporate Ve­
nus; in like manner alſo 'tis very probable that the ſame might
be diſcerned in other Planets, which ſhine by no light of their
own, but by one borrowed from the Sun. What ever there­
fore may touching theſe matters be delivered in the ſacred Leaves
or the common ſpeech of men, diſſenting from the real truth, it
ought (as we have ſaid before) abſolutely to be received and un­
derſtood ſecundum vulgi ſententiam, & communem loquendi &
concipiendi ſtylum.
Which are really
the great Lights
in Heaven.
The Sun, Moon,
and Stars are one
& the ſame thing.
The Earth is a­
nother Moon or
Star.
And ſo, to return to our purpoſe, if, all this conſidered, the
Pythagorian opinion be true, it will be eaſie, according to the
ſame Rule, to reconcile the authority of ſacred Scriptures with
it, however they ſeem to oppoſe it, and in particular thoſe of the
firſt and ſecond Claſſis, ſcilicet by my firſt Maxime: For that in
thoſe places the holy Records ſpeak according to our manner of
underſtanding, and according to that which appeareth in reſpect
of us; For thus it is with thoſe Bodies, in compariſon of us, and

as they are deſcribed by the vulgar and commune way of humane
Diſcourſe; So that the Earth appears as if it were ſtanding ſtill
and immoveable, and the Sun, as if it were circumambient about
her. And ſo the Holy Scripture is uſed in the Commune and
Vulgar way of ſpeaking; becauſe in reſpect of our ſight, the
Earth ſeems rather to ſtand fixed in the Centre, and the Sun to
circumvolve about it, than otherwiſe: as it happens to thoſe that
are putting off from the Banks of a River to whom the ſhose
ſeems to move backwards, and go from them: but they do not
perceive (which yet is the truth) that they themſelves go forwards.
1Which fallacy of our ſight is noted, and the Reaſon thereof aſ­
ſigned by the Opticks; upon wich, as being ſtrange to, and be­
ſides my purpoſe, I will not ſtay) and on this account is Æneas
brought in by Virgil, ſaying;
Why the Sunne
ſeemeth to us to
move, & not the
Earth.
Æneid. 3.
Provehimur portu, terræque urbeſque recedunt.
But it will not be amiſs to conſider why the ſacred Scripture
doth ſo ſtudiouſly comply with the opinions of the Vulgar, and
why it doth not rather accurately inſtruct men in the truth of the
matters, and the ſecrets of Nature. The Reaſon is, firſt, the be­
nignity of Divine Wiſdome, whereby it ſweetly accomodates it
ſelf to all things, in proportion to their Capacity and Nature.
Whence in Natural Sciences, it uſeth natural and neceſſary cau­
ſes, but in Liberal Arts it worketh liberally, upon Generous
Perſons after a ſublime and lofty manner; upon the Common
People, familiarly and humbly; upon the Skilful, learnedly;
upon the Simple, vulgarly; and ſo on every one, according to
his condition and quality. Secondly, becauſe it is not its In­
tention to fill our mindes in this life with vain and various curi­
oſities, which might occaſion our doubt and ſuſpenſe. For the

truth is, (a) He that increaſeth knowledge, increaſeth ſorrow.
Moreover it did not only permit, but even decree, thatth e
World ſhould be very much buſied in Controverſies and Diſpu­
tations, and that it ſhould be imployed about the uncertainty of

things; according to that ſaying of Eccleſiaſtes (b) He hath
ſet the World in their heart; ſo that no man can find out the work
that God maketh from the beginning unto the end. And touching
thoſe doubts, God will not permit that they ſhall be diſcovered

to us before the end of the World: (c) At which time he will
bring to light the hidden things of darkneſſe: But Gods onely
ſcope in the ſacred Scripture is to teach men thoſe things which
conduce to the attainment of Eternal Life; which having ob­

tained, (d) We ſhall ſee him face to face: (e) and ſhall be

like him, for we ſhall ſee him as he is. Then ſhall he clearly à
Priori make known unto us all thoſe Curioſities, and Dogmati­
cal Queſtions, which in this life, (f) in which we ſee through a

Glaſſe darkly, could be known by us but imperfectly and à poſte­
riori, and that not without much pains and ſtudy. For this
cauſe the Wiſdome of God, revealed to us in the ſacred Leaves,
is not ſtiled Wiſdome abſolutely, but (g) Saving Wiſdome;

Its onely end being to lead us to ſalvation. And S. Paul preach­
ing to the Corinthians, ſaith; (h) I determined to know nothing

among you, ſave Jeſus Chriſt, and him crucified: whereas not­
withſtanding he was thorowly inſtructed, and profoundly learned
1in all humane Sciences; but making no account of theſe things
he profeſſeth that it was his deſire to teach them no more but the
way to Heaven. Hence is that which God ſpeaketh to us by

Iſaiah, (i) Ego Dominus Deus, docens te utilia [I am the Lord
thy God which teacheth thee profitable things:] Where the Gloſ­
ſary addeth, non ſubtilia [not ſubtilties.] For God neither taught
us, Whether the Materia Prima of Heaven, and the Elements
be the ſame; nor Whether Cominual be compoſed of Indiviſi­
bles, or whether it be diviſible in infinitum; nor, whether the
Elements are formally mixt; nor how many the Cœleſtial
Spheres, and their Orbs are; Whether there be Epicycles or
Eccentricks; nor the Vertues of Plants and Stones; nor the Na­
ture of Animals; nor the Motion and Influence of the Planets;
nor the Order of the Univerſe; nor the Wonders of Minerals,
and univerſal Nature: but only [utilia:] things profitable, to
wit, his Holy Law ordained to the end, that we being put into
poſſeſſion of Bleſſedneſs, might at length be made capable of all
perfect knowledge, and the viſion of the whole Order and ad­
mirable Harmony, as alſo the Sympathy and Antipathy of the
Univerſe and its parts, in his Word, wherein all thoſe
things ſhall moſt clearly and diſtinctly, then, appear to us, which
mean while, in this life, he hath remitted (as far as its ability
reacheth) to humane ſearch and enquiry: But it was not his
purpoſe to determine any thing, directly or indirectly, touching
the truth of them. Becauſe as the knowledge thereof would lit­
tle or nothing profit Us, but might in ſome caſes prove prejudi­
cial; ſo the ignorance thereof can doubtleſs be no detriment,
but may in ſome caſes be very beneficial to us. And therefore
by his moſt admirable Wiſdome it comes to paſs, that though all
things in this World are dubious, uncertain, wavering, and per­
plexed; yet his Holy Faith alone is moſt certain; and although
the opinions about Philoſophical and Doctrinal points be divers,
there is in the Church but one Truth of Faith and Salvation.
Which Faith, as neceſsary to Salvation, is ſo ordered by Divine
Providence, that it might not only be indubitable, but alſo un­
ſhaken, ſure, immutable, and manifeſt to all men: the infallible
Rule of which he hath appointed the Holy Church, that is waſh­
ed with his precious Blood, and governed by his Holy Spirit, to
whom belongs our Sanctification, as being his work. This there­

fore is the Reaſon why God would have Speculative Queſtions,
which nothing conduce to our Salvation and Edification, and why
the Holy Ghoſt hath very often condeſcended to Vulgar Opini­
ons and Capacities, and hath diſcovered nothing that is ſingular
or hidden to us, beſides thoſe things that pertain to Salvation.
So that conſequently it is clear by what hath been ſaid, how and
1why nothing of certainty can be evinced from the foreſaid Au­
thorities to the determining of Controverſies of this Nature; as
alſo with what Reaſon from this firſt Axiome the Objections of
the firſt and ſecond Claſſe are eaſily anſwered, as alſo any other
Authority of ſacred Scripture produced againſt the Pythagorian
and Copernican Syſteme ſo long as by other proofs it is true.
(a) Eccleſ. c. 1. v.
ult.
(b) Chap. 3. v. 11.
(c) 1 Cor. c. 4. v. 5
(d) 1 Cor. c. 13. v.
12.
(e) 1 John c. 3. v.
2.
(f) 1 Cor. c. 13. v.
12.
(g) Eccleſiaſt. 15. 3
(h) 1 Cor. c. 2. v. 2
(i) Iſa. c. 48. v. 17.
1 Theſſ. 4.
And the Authorities of the ſecond Claſſe in particular by
this ſame Maxime, Of the ordinary manner of apprehending
things as they appear to us, and after the common way of ſpeak­
ing, may be thus reconciled and expounded; namely, Oftentimes
an Agent is commonly, and not improperly ſaid to move, (though
it have no motion) not becauſe it doth indeed move, but by ex­
trinſick denomination, becauſe receiving its influence and action at
the motion of the Subject; the Form and Quality infuſed to
the Subject by the ſaid Agent doth likewiſe move. As for ex­
ample, a Fire burning in a Chimney is an immoveable Agent,
before which a man oppreſt with cold ſits to warm himſelf who
being warmed on one ſide, turns the other to the Fire, that he
may be warmed on that ſide alſo, and ſo in like manner he holds
every part to the Fire ſucceſſively, till his whole body be warm­
ed. 'Tis clear, that although the Fire do not move, yet at the
Motion of the Subject, to wit the Man, who receiveth the heat
and action of the Fire, the Form and Quality of its Heat doth
move ſingulatim, & per partes, round about the mans body, and
alwayes ſeeketh out a new place: and ſo, though the Fire do
not move, yet by reaſon of its effect, it is ſaid to go round all
the parts of the Mans body, and to warm it, not indeed by a
true and real motion of the Fire it ſelf, ſince it is ſuppoſed (and
that not untruly) not to move, but by the motion to which the
Body is excited, out of a deſire of receiving the heat of the Fire
in each of its parts. The ſame may be applied to the Illumina­
tion impreſſed ſucceſſively on the parts of any Globe, which
moves Orbicularly at the aſpect of a ſhining immoveable
Light. And in the ſame manner may the Sun be ſaid to riſe and
ſet, and to move above the Earth, although in reality he doth
not move, nor ſuffer any mutation; that is to ſay, Inaſmuch as
his Light (which effect is the Form and Quality proceeding from
him, as the Agent, to the Earth as the Subject) doth ſenſibly
glide forwards, by reaſon of the Orbicular motion of the Earth;
and doth alwayes be take it ſelf to ſome new place of her ſurface;
upon which ground he is truly ſaid (ſecundum vnlgarem ſermo­
nem) to move above, and revolve about the Earth: Not that the
Sun doth move, (for by this Opinion we affirm the Earth to
move, that it may receive the Sun one while in one, another
while in another part of it) but that at the motion of the Earth
1her ſelf a contrary way, the Quality diffuſed into her, and im­
preſſed upon her by the Sun, namely the Light of the Day is
moved, which riſeth in one part of her, and ſets in another con­
trary to that, according to the nature and condition of her motion;
And for this reaſon the Sun it ſelf by conſequence is ſaid to riſe
and ſet, (which notwithſtanding ex Hypotheſi ſtands immovea­
ble) and that no otherwiſe then per donominationem extrinſecam,
as hath been ſaid.
After this manner the command of Joſhuah, Sun ſtand thou

ſtill, and the Miracle of the Suns ceſſation of Motion wrought
by him, may be ſo underſtood, as that not the Solar Body pro­
perly, but the Suns ſplendour upon the Earth ſtood ſtill; ſo that
not the Sun it ſelf, (being of it ſelf before that time immovea­
ble) but the Earth that receiveth its ſplendour, ſtayed her Mo­
tion; which, as ſhe inceſſantly purſuing her ordinary Motion to­

wards the Eaſt, ^{*} called up the Light of the Sun in the Weſt, ſo
ſtanding ſtill, the Suns light impreſt upon it likewiſe ſtood ſtill.

After the ſame manuer pioportionally is that Text of Iſaiah ex­
plained, touching the Suns going ten degrees back ward upon the
Dial of Ahaz. So (which may ſerve for another Example) the
Hand being moved about the flame of a burning Candle that
ſtands ſtill, the Light moveth on the Hand, that is to ſay, the
ſaid Hand is illuſtrated now in one part, anon in another, when
as the Candle it ſelf all the while removes not out of its place:
whereupon per denominationem extrinſecam, the ſaid Light may
be affirmed to riſe and ſet upon the Hand, namely, by the ſole
motion of the ſaid Hand, the Candle it ſelf never moving all the
while. And let this ſuffice for the explanation of my firſt Prin­
ciple or Maxime, which by reaſon of its difficulty and extraordi­
nary weight required ſome prolixity in the handling of it.
Joſhua c. 10.
ver. 12.
* expected.
Iſa. c. 38. v. 8.
My ſecond Maxime is this, Things both Spiritual and Cor­
poreal, Durable and Corruptible, Moveable and Immoveable,
have received from God a perpetual, unchangeable, and inviola­
ble Law, conſtituting the Eſſence and Nature of every one of
them: according to which Law all of them in their own Na­
ture perſiſting in a certain Order and Conſtancy, and obſerving
the ſame perpetual Courſe, may deſervedly be ſtiled moſt Stable
and Determinate. Thus Fortune (than which there is nothing
in the World more inconſtant or fickle) is ſaid to be conſtant
and unalterable in her continual volubility, viciſſitude, and in­
conſtancy, which was the occaſion of that Verſe,
Et ſemper conſtans in levitate ſua eſt.
And thus the motion of Heaven (which by the conſtan Law
1of Nature ought to be perpetual) may be ſaid to be immutable
and immoveable, and the Heavens themſelves to be immovea­
bly moved, and Terrene things to be immutably changed, be­
cauſe thoſe never ceaſe moving, nor theſe changing. By this Prin­
ciple or Maxime all difficulties belonging to the firſt Claſſis are
cleared, by which the Earth is ſaid to be ſtable and immoveable,
that is, by underſtanding this one thing, That the Earth, as to its
own Nature, though it include in it ſelf a local Motion, and that
threefold, according to the opinion of Copernicus (ſcilicet Diur­

nal, with which it revolveth about its own Centre; Annual,
by which it moveth through the twelve Signes of the Zodiack,
and the motion of Inclination, by which its Axis is alwayes op­
poſed to the ſame part of the World) as alſo other Species of
Mutation, ſuch as Generation and Corruption, Accretion and
Diminution, and Alteration of divers kinds; yet in all theſe ſhe
is ſtable & conſtant, never deviating from that Order which God
hath appointed her, but moveth continually, conſtantly and im­
mutably, according to the ſix before named Species of Motion.
Several Motions
of the Earth ac­
cording to Coper­
nicus.
My third Maxime ſhall be this; When a thing is moved ac­
cording to ſome part of it, and not according to its whole, it
cannot be ſaid to be ſimply & abſolutely moved, but only per acci­
dens, for that ſtability taken ſimply & abſolutly do rather accord
with the ſame. As for example, if a Barrel or other meaſure of
Water be taken out of the Sea, and transferred to another place,
the Sea may not therefore abſolutely & ſimply be ſaid to be remo­
ved from place to place; but only per accidens, and ſecundum
quid, that is, according to a part of it, but rather (to ſpeak ſim­
ply) we ſhould ſay that the Sea cannot be carried or moved out of
its proper place,, though as to its parts it be moved, and transfer­
red to & again. This Maxime is manifeſt of it ſelf, and by it may
the Authorities be explained which ſeem to make for the immo­
bility of the Earth in this manner; namely, The Earth per ſe &
abſolutè conſidered as to its Whole, is not mutable, ſeeing it is
neither generated nor corrupted neither increaſed nor diminiſhed;
neither is it altered ſecundum totum, but only ſecundum partes.

Now it plainly appears, that this is the genuine and true Senſe of
what is aſcribed to it out of Eccleſiaſtes, cap. 1. v. 4. One Generation
paſſeth away, and another Generation cometh, but the Earth abideth
for ever: as if he ſhould ſay; although the Earth, according to its
parts, doth generate and corrupt, and is liable to the viciſſitudes of
Generation and corruption, yet in reference to its Whole it never
generateth nor Corrupteth, but abideth immutable for ever:
Like as a Ship, which though it be mended one while in the Sail­
yard, another while in the Stern, and afterwards in other parts
it yet remains the ſame Ship as it was at firſt. But tis to be
1vertized, that that Scripture doth not ſpeak of a Local Motion,
but of Mutations of another nature; as in the very ſubſtance,
quantity or quality of the Earth it ſelf. But if it be ſaid, that
it is to be underſtood of a Local Motion, then it may be ex­
plained by the inſuing Maxime, that is to ſay, a reſpect being had
to the natural Place aſſigned it in the Univerſe, as ſhall be ſhewed
by and by.
The Earth Se-
cundum Totum is
Immutable,
though not Immo­
vable.
The fourth Axiome is this; That every Corporeal thing, mo­
veable or immoveable from its very firſt Creation, is alotted its
proper and natural place; and being drawn or removed from
thence, its motion is violent, and it hath a natural tendency to
move back thither again: alſo that nothing can be moved from
its natural place, ſecundum Totum; For moſt great and dreadſul
miſchiefs would follow from that perturbation of things in the
Univerſe. Therefore neither the whole Earth, nor the whole

Water, nor the whole Air can ſecundum totum be driuen or for­
ced out of their proper place, ſite, or Syſteme in the Univerſe,
in reſpect of the order and diſpoſition of other mundane Bodies.
And thus there is no Star (though Erratick) Orb or Sphere that
can deſert its natural place, although it may otherwiſe have ſome
kind of motion. Therefore all things, how moveable ſoever,
are notwithſtanding ſaid to be ſtable and immoveable in their
proper place, according to the foreſaid ſenſe, i.e. ſecundum to­
tum; For nothing hinders, but that ſecundum partes they may
ſome waymove; which motion ſhall not be natural, but violent.
Therefore the Earth, although it ſhould be moveable, yet it
might be ſaid to be immoveable, according to the precedent
Maxime, for that its neither moved in a right Motion nor out of
the Courſe aſſigned it in its Creation for the ſtanding Rule of its
motion; but keep within its own ſite, being placed in that
which is called the Grand Orb, above Venus, and beneath Mars,

and being in the middle betwixt theſe (which according to the
common opinion is the Suns place) it equally and continually
moveth about the Sun, and the two other intermediate Planets,
namely Venus and Mercury, and hath the Moon (which is another
Earth, but Ætherial, as Macrobius after ſome of the ancient Phi­

loſophers, will have it) about it ſelf. From whence, inaſmuch as
ſhe perſiſteth uniformly in her Courſe, and never at any time
departeth from it, ſhe may be ſaid to be ſtable and immoveable:
and in the ſame ſenſe Heaven likewiſe, with all the Elements,
may be ſaid to be immoveable.
The Earth can­
not Secundum To­
tum, remove out of
its Natural Place.
The Natural
Place of the Earth.
The Moon is an
Ætherial Body.
The fifth Maxime followeth, being little different from the
former. Amongſt the things created by God, ſome are of ſuch a
nature, that their parts may be ab invicem, or by turns, ſe­
parated from themſelves, and diſ-joyned from their Whole;
1others may not, at leaſt, taken collectively: now thoſe are pe­
riſhable, but theſe perpetual. The Earth therefore ſince it
is reckoned amongſt thoſe things that are permanent, as hath

been ſaid already, hath its parts, not diſſipable, nor ab invicem,
ſeparable from its Centre (whereby its true and proper place is
aſſigned it) and from its whole, taken collectively: becauſe ac­
cording to its whole it is always preſerved, compact, united, and
cohærent in it ſelf, nor can its parts be ſeperated from the Cen­
tre, or from one another, unleſs it may ſo fall out per accidens,
and violently in ſome of its parts; which afterwards, the obſtacle
being removed, return to their Natural Station ſpontaneouſly,
and without any impulſe. In this Senſe therefore the Earth is
ſaid to be Immoveable, and Immutable: yea even the Sea, Aire,
Heaven, and any other thing (although otherwiſe moveable) ſo
long as its parts are not diſſipable and ſeperable, may be ſaid to
be Immoveable, at leaſt taken collectively. This Principle
or Maxim differeth from the precedent only in that this referrs
to the parts in order to Place, and this, in order to the Whole.
The Earths Cen­
tre keepeth it in
its Natural Place.
From this Speculation another Secret is diſcovered. For hence

it is manifeſt wherein the proper and genuine formality of the
Gravity aad Levity of Bodyes conſiſteth; a point which is not ſo
clearly held forth, nor ſo undeniably explained by the Peripate­
tick Phyloſophy. Gravity therefore is nothing elſe according to
the Principles of this new Opinion, than a certain power and ap­
petite of the Parts to rejoyn with their Whole, and there to reſt
as in their proper place. Which Faculty or Diſpoſition is by
Divine Providence beſtowed not only on the Earth, and Ter­
rene Bodies, but, as is believed, on Cœleſtial Bodies alſo, name­

ly the Sun, Moon, and Starrs; all whoſe parts are by this Impul­
ſion connected, and conſerved together, cleaving cloſely to each
other, and on all ſides preſſing towards their Centre, until they
come to reſt there. From which Concourſe and Compreſſion a
Sphærical and Orbicular Figure of the Cæleſtial Orbes is produ­
ced, wherein by this occult Quality naturally incident to
each of them they of themſelves ſubſiſt, and are alwayes preſer­
ved. But Levity is the Extruſion and Excluſion of a more te­
nuoſe and thin Body from the Commerce of one more Solid and

denſe, that is Heterogeneal to it, by vertue of Heat. Where­
upon, as the Motion of Grave Bodies is Compreſſive, ſo the Mo­
tion of Light Bodies is Extenſive: For its the propperty of Heat
to dilate and rarify thoſe things to which it doth apply, conjoine
and communicate it ſelf. And for this reaſon we find Levity
and Gravity not only in reſpect of this our Tereſtrial Globe, and
the Bodies adjacent to it, but alſo in reſpect of thoſe Bodies
which are ſaid to be in the Heavens, in which thoſe parts which
1by reaſon of their proclivity make towards their Centre are
Grave, and thoſe that incline to the Circumference Light. And
ſo in the Sun, Moon, and Starrs, there are parts as well Grave as

Light. And conſequently Heaven it ſelf that ſo Noble Body,
and of a fifth Eſſence, ſhall not be conſtituted of a Matter diffe­
rent from that of the Elements, being free from all Mutation in
it's Subſtance, Quantity, and Quality: Nor ſo admirable and

excellent as Ariſtotle would make us to believe; nor yet a ſolid
Body, and impermeable; and much leſſe (as the generality of
men verily believe) of an impenetrable and moſt obdurate Den­
ſity: but in it (as this Opinion will have it) Comets may be ge­
nerated; and the Sun it ſelf, as tis probable, exhaling or attract­
ing ſundry vapours to the ſurface of its Body, may perhaps pro­
duce thoſe Spots which were obſerved to be ſo various, and irre­

gular in its Diſcus: of which Galilæus in a perticular ^{*} Treatiſe
hath moſt excellently and moſt accurately ſpoken; inſomuch,
that though it were not beſides my preſent purpoſe, yet it is con­
venient that I forbear to ſpeak any thing touching thoſe matters,
leaſt I ſhould ſeem to do that which he hath done before me: But
now if there be found in the Sacred Scriptures any Authority
contrary to theſe things, it may be ſalved by the foreſaid Argu­
ments Analogically applyed. And further more it may be ſaid,
that that Solidity is to be ſo underſtood, as that it admits of no
vacuum, cleft, or penetration from whence the leaſt vacuity might
proceed For the truth is, as that cannot be admitted in bodily
Creatures, ſo it is likewiſe repugnant to Heaven it ſelf, being
indeed a Body of its own Nature the moſt Rare of all o­

thers, and tenuoſe beyond all Humane Conception, and happly
hath the ſame proportion to the Aire, as the Aire to the
Water.
Gravity and Le­
vity of Bodies,
what it is.
All Cœleſtial Bo­
dies have Gravity
and Levety.
Compreſſive Ma­
tion, proper to
Gravity; the Ex­
tenſive, to Levity.
Heaven is not
compoſed of a fift
Eſſence differing
from the matter of
inferior Bodies.
Nor yet a Solid
or denſe Body but
Rare.
* Delle Macchie
ſolarj.
* Vnius Corporis
fimplicis, unus eſt
motus ſimplex, et
huic duæ ſpecies,
Rectus & Circu­
laris: Rectus du­
plex à medio, &
ad medium; pri­
mus levium, ut A­
eris & Ignis: ſe­
cundus gravium,
ut Aquæ & Ter­
ræ: Circularis,
quieſt circa medi­
um competit Cœlo,
quod neque eſt
grave, neque leve.
Ariſt. de Cœlo.
Lib. 1.
It is clear alſo from theſe Principles how falſe theſe words of
Ariſtotle are, that: Of one ſimple Body, there is one ſimple Motion;
and this is of two kindes, Right and Circular: the Right is two­
fold, from the medium, and to the medium; the firſt of Light Bo­
dyes, as the Aire and Fire: the ſecond of Grave Bodyes, as the
Water and Earth: the Circular, which is about the medium, be­
longeth to Heaven, which is neither Grave nor Light: For all this
Philoſophy is now forſaken, and of it ſelf grown into diſ-eſteem;
for though it be received for an unqueſtionable truth in this new
Opinion, that to a ſimple body appertains one only ſimple Moti­

on, yet it granteth no Motion but what is Circular, by which alone
aſimple body is conſerved in its naturall Place, and ſubſiſts in its
Unity, and is properly ſaid to move in loco [in a place:] whereby

it comes to paſs that a Body for this reaſon doth continue to move
in it ſelf, [or about its own axis;] and although it have a Motion,
1yet it abideth ſtill in the ſame place, as if it were perpetually im­
moveable. But right Motion, which is properly ad locum, [to a
place] can be aſcribed only to thoſe things which are out of their
naturall place, being far from union with one another, and from
unity with their whole, yea that are ſeperated and divided from
it: Which being that it is contrary to the Nature and forme of
the Univerſe, it neceſſarily followeth, that right Motion doth in

ſhort ſute with thoſe things which are deſtitute of that perfection,
that according to their proper Nature belongeth to them, and
which by this ſame right Motion they labour to obtaine, untill
they are redintigrated with their Whole, and with one another,
and reſtored to their Naturall place; in which at the length,
having obtained their perfection, they ſettle and remaine immove­
able. Therefore in right Motions there can be no Uniformity,

nor ſimplicity; for that they vary by reaſon of the uncertaine
Levity or Gravity of their reſpective Bodyes: for which cauſe
they do not perſevere in the ſame Velocity or Tardity to the end
which they had in the beginning. Hence we ſee that thoſe things
whoſe weight maketh them tend downwards, do deſcend at firſt
with a ſlow Motion; but afterwards, as they approach neerer
and neerer to the Centre, they precipitate more and more ſwiftly.
And on the otherſide, thoſe things which by reaſon of their light­
neſs are carryed upwards (as this our Terreſtriall fire, which is no­
thing elſe but a ſmoak that burneth, and is inkindled into a flame)
are no ſooner aſcended on high, but, in almoſt the ſelf-ſame mo­
ment, they fly and vaniſh out of fight; by reaſon of the rare­
faction and extenſion, that they as ſoon as they acquire, are freed
from thoſe bonds which violently and againſt their own Nature

kept them under, and deteined them here below. For which
reaſon, it is very apparent, that no Right Motion can be called
Simple, not only in regard that (as hath been ſaid) it is not
^{*} even and uniforme, but alſo becauſe it is mixt with the Circu­

lar, which lurketh in the Right by an occult conſent, ſcilicet by
reaſon of the Natural affection of the Parts to conforme unto
their Whole. For when the Whole moveth Circularly, it is re­
quiſite likewiſe that the Parts, to the end that they may be uni­
ted to their Whole, (howbeit per accidens they are ſometimes
moved with a Right Motion) do move (though not ſo appa­
rently) with a Circular Motion, as doth their Whole. And thus
at length we have evinced that Circular Motion only is Simple,

Uniform and ^{*} Æquable, and of the ſame tenor [or rate] for that

it is never deſtitute of its interne Cauſe: whereas on the contra­
ry, Right Motion, (which pertains to things both Heavy and
Light) hath a Cauſe that is imperfect and deficient, yea that ari­
ſeth from Defect it ſelf, and that tendeth to, and ſeeketh after
1nothing elſe but the end and termination of it ſelf: in regard
that Grave and Light Bodies, when once they have attained their
proper and Natural Place, do deſiſt from that Motion to which
they were incited by Levity and Gravity. Therefore: ſince Cir­

cular Motion is proper to the Whole, and Right Motion to the
Parts, theſe differences are not rightly referred to Motion, ſo as
to call one Motion Right, another Circular, as if they were not
conſiſtent with one another: For they may be both together, and

that Naturally, in the ſame Body; no leſſe than it is equally
Natural for a Man to participate of Senſe and Reaſon, ſeeing
that theſe differences are not directly oppoſite to one another.
Hereupon Reſt and Immobility only are oppoſed to Motion;
and not one Species of Motion to another. And for the other
differences à medio, ad medium, and circa medium, they are di­
ſtinguiſhed not really, but only formally, as the Point, Line and
Superficies, none of which can be without the other two, or
without a Body. Hence it appears, that in as much as this Phy­
loſophy differs from that of Ariſtotle, ſo in like manner doth this
New Coſmographical Syſtem vary from the Common one, that
hath been hitherto received. But this by the way, upon occaſion
of explaining the Fifth Maxim: For as to the truth or falſhood
of theſe foregoing Poſitions (although I conceive them very pro­
bable) I am reſolved to determine nothing at preſent, neither
ſhall I make any farther enquiry into them.
* Vide Coperni­
cum de Revolutio­
nibus Cœleſt.
Simple Motion
peculiar to only
Simple Bodies.
Right Motion
belongeth to Im­
perfect Bodies, and
that are out of
their natural Pla­
ces.
Right Motion
cannot be Simple.
Right Motion is
ever mixt with
the Circular.
* æquabilis.
* Even.
Circular Mo­
tion is truly Sim­
ple and Perpetual.
Circular Mo­
tion belongeth to
the Whole Body,
and the Right to
its parts.
Circular and
Right Motion co­
incedent, and may
conſiſt together in
the ſame Body.
The Sixth and Laſt Maxim is this. Every thing is Simply deno­
minated ſuch as it is in compariſon of all things, or of many
things which make the greater number of that kinde, but not in
reſpect of a few which make but the leſſer part of them. As,
for inſtance, a Veſſel ſhall not be called abſolutely Great be­
cauſe it is ſo whilſt it is compared with two or three others: but
it ſhall be ſaid to be great abſolutely, and will be ſo, if it ex­
ceed in magnitude all indivials, or the greater part of them. Nor
again ſhall a Man be ſaid to be abſolutely Big, becauſe he is big­
ger than a Pigmey; nor yet abſolutely Little, becauſe leſſe than
a Gyant: but he ſhall be termed abſolutely Big or Little in com­
pariſon of the ordinary Stature of the greater part of Men. Thus
the Earth cannot abſolutely be ſaid to be High or Low for that it
is found to be ſo in reſpect of ſome ſmall part of the Univerſe; nor
again ſhall it be abſolutely affirmed to be High, being compared
to the Centre of the World, or ſome few parts of the Univerſe,
more near to the ſaid Centre, as is the Sun, Mercury or Venus:

but it ſhall receive its abſolute denomination according as it ſhall
be found to be in compariſon of the greater number of the
Spheres and Bodies of the Univerſe. The Earth therefore, in
compariſon of the whole Circuit of the Eighth Sphære which
1cludeth all Corporeal Creatures, and in compariſon of Jupiter,
Mars, and Saturn together with the Moon, and much more in
compariſon of other Bodies, (if any ſuch there be) above the
Eighth Sphere and eſpecially the Empyrial Heaven, may be truly
ſaid to be in the loweſt place of the World, and almoſt in the
Centre of it; nor can it he ſaid to be above any of them, except
the Sun, Mercury and Venus: So that one may apply unto it the
name of an Infime and Low, but not a Supreme or Middle Body.
And ſo to come down from Heaven, eſpecially the Empyrian, to it
(as it is accepted in the Deſcent of Chriſt from Heaven to his Holy
Incarnation) and from it to go up to Heaven (as in Chriſts return

to Heaven in his Glorious Aſcention) is truly and properly to
Deſcend from the Circumference to the Centre, and to aſcend
from the parts which are neareſt to the Centre of the World
to its utmoſt Circumference. This Maxim therefore may eaſily
and according to truth explain Theologicall Propoſitions: and
this is ſo much the more confirmed, in that (as I have obſerved)
almoſt all Texts of Sacred Scripture which oppoſe the Earth to
Heaven, are moſt conveniently and aptly underſtood of the Em­
pyrial Heaven (being the Higheſt of all the Heavens, and Spiritual
in reſpect of its end) but not of the inferiour or intermediate Hea­
vens, which are a Corporeal, and were framed for the benefit of
Corporeal Creatures: and thus when in the Plural Number
Heavens are mentioned, then all the Heavens promiſcuouſly and
without diſtinction are to be underſtood, as well the Empyrian
it ſelf as the Inferiour Heavens. And this Expoſition indeed any
man (that doth but take notice of it) may find to be moſt true.
And ſo for this Reaſon the Third Heaveu into which St. Paul

was wrapt up, by this Maxim may be taken for the Empyrean:
if for the the Firſt Heaven we underſtand that immenſe Space of
Erratick and Moveable Bodies illuminated by the Sun, in which
are comprehended the Planets, as alſo the Earth moveable, and
the Sun immoveable, Who like a King upon his Auguſt Tribu­
nal, ſits with venerable Majeſty immoveable and conſtant in
Centre of all the Sphæres, and, with his Divine Beames, doth
bountifully exhilerate all Cœleſtial Bodies that ſtand in need of
his vital Light, for which they cravingly wander about him; and
doth liberally and on every ſide comfort and illuſtrate the Thea­
tre of the whole World, and all its parts, even the very leaſt, like
an immortal and perpetual Lamp of high and unſpeakable va­
lue. The Second Heaven ſhall be the Starry Heaven, common­
ly called the Eighth Sphære, or the Firmament, wherein are all
the Fixed Starrs, which according to this Opinion of Pythagoras,
is (like as the Sun and Centre) void of all Motion, the Centre
and utmoſt Circumference mutually agreeing with each other in
1Immobility. And the Third ſhall be the Empyrean Heaven, that
is the Seat of the Bleſſed. And in this manner we may come to
explain and underſtand that admirable Secret, and profound My­

ſtery ænigmatically revealed by Plato to Dionyſius of Syracuſe:

(a) All things are about the King of all things, Second things
about the ſecond, and Third things about the Third: For that
God being the Centre of Spiritual things, the Sun, of Cor­
poreal, Chriſt, of thoſe that are Mixt, or made up of both, things
do doubtleſſe depend of that of theſe three Centres that is moſt
correſpondent and proportionable to them, and the Centre is
ever adjudged to be the nobler and worthier place: and therefore
in Animals the Heart, in Vegitables the Pith or Kernell wherein
the Seed lyeth that conſerveth their perpetuity, and virtually in­
cludes the whole Plant, are in the Midſt, and in the Centre: and
thus much ſhall ſuffice to have hinted at, ſince there may another
occaſion offer it ſelf for a larger Explication of theſe things. By
this Maxim the Authorities and Arguments of the Third Fourth
and Fifth Claſſes are reſolved.
The Earth in
what ſenſe it may
abſolutely be ſaid
to be in the loweſt
part of the World.
Chriſt in his
Incarnation tru­
ly deſcended from
Heaven, and in
his Aſcenſion tru­
ly aſcended into
Heaven.
2 Cor. c. 12. v.
3. Whether in the
body or out of the
body, I cannot tell,
The Sun is King,
Heart and Lamp
of the World him­
ſelf being αυταρκης
abſolutely indepen­
dent.)
The Ænignsa of
Plato.
(a) Circa omni­
um Regem ſunt
omnia. & Secun­
da circa Secun­
dum, et Tertia
circa Tertium:
Vide Theodo. de
Græc. affect. curat.
lib. 2. Steuch. lib.
de Parennj. Phi­
loſo.
It may be added withall, that even the Sun, Mercury and Ve­
nus (that is to ſay in reſpect of the Earth) are to be thought
aboue, and not beneath the Earth it ſelf, although in reſpect of
the Univerſe, yea and alſo abſolutely, they are below. The rea­
ſon is, becauſe in reſpect of the Earth they alwayes appear above
its Surface: and although they do not environe it, yet by the
Motion of the ſaid Earth they behold one while one part, another
while another part of its Circumference. Since therefore thoſe
things which in a Sphærical Body are nearer to the Circumfe­
rence and more remote from the Cenrre are ſaid to be above, but
thoſe that are next adjoyning to the Centre are ſaid to be below;
it clearly followeth that whilſt the Sun, Mercury and Venus are
not only turned towards the Surface and Circumference of the
ſaid Earth, but are at a very great diſtance without it, ſucceſſively
turned about it, and every way have a view of it, and are very
far remote from its Centre, they may, in reſpect of the ſaid Earth,
be ſaid to be above it; as alſo on the other ſide, the Earth in
reſpect of them may be ſaid to be beneath: howbeit on the con­
trary, in reſpect of the Univerſe, the Earth in reality is much
higher than they. And thus is ſalved the Authority of Eccleſi-

aſtes in many places, expreſſing thoſe things that are, or are done
on the Eeath in theſe words, Which are done, or which are under

the Sun, And in the ſame manner thoſe words are reduced to their
true Senſe wherein it is ſaid, That we are under the Sun, and un­
der the Moon, whereupon Terrene things are expreſſed by the
name of Sublunary.
Eccleſ. c. 1. 2. 3.
and almoſt tho­
out.
* Quod fiunt, vel
ſunt ſub ſole.
The Sixth Claſſis threatneth a difficulty which is common as
1well to this of Copernicus, as to the Vulgar Opinion; ſo that they
are both alike concerned in the ſolution of it: But ſo far as it
oppoſeth that of Copernicus, its anſwer is eaſy from the Firſt
Maxim.
But that which is added in the Fourth Claſſe, That it follow­
eth from this Opinion, that Hell (for that it is included by the
Earth, as is commonly held) doth move circularly about the
Sun, and in Heaven, and that ſo Hell it ſelf will be found to be
in Heaven; diſcovers, in my judgment, nothing but Ignorance
and Calumny, that inſinuate the belief of their Arguments ra­
ther by a corrupt ſenſe of the Words, than by ſolid Reaſons
taken from the boſome of the Nature of things. For in this
place Heaven is no wiſe to be taken for Paradice, nor according
to the Senſe of Common Opinion, but (as hath been ſaid above)

according to the Copernican Hypotheſis, for the ſubtileſt and
Pureſt Aire, far more tenuous and rare than this of ours; where­
upon the Solid Bodies of the Stars, Moon, and Earth, in their
Circular and Ordinary Motions, do paſſe thorow it, (the Sphære
of Fire being by this Opinion taken away.) And as according
to the Common Opinion it was no abſurdity to ſay, That Hell
being demerged in the Centre of the Earth and of the World it
ſelf, hath Heaven and Paradice above and below it, yea and on
all ſides of it, and that it is in the middle of all the Cœleſtial
Bodies (as if it were poſited in a more unworthy place) ſo, nei­
ther in this will it be deemed an Error, if from the other Syſtem,
which differeth not much from the Vulgar one, thoſe or the like
things follow as do in that. For both in that of Copernicus, and
the Vulgar Hypotheſis, Hell is ſuppoſed to be placed amongſt the
very dreggs of the Elements, and in the Centre of the Earth it
ſelf, for the confinement and puniſhment of the damned. There­
fore we ought not for want of Reaſons to trifle away time in
vain and impertinent ſtrife about words, ſince their true Senſe
is clouded then with no obſcurity, and in regard that it is very
clear to any man indued with a refined Intellect, and that hath
but an indifferent judgment in the Liberal Arts, and eſpecially
in the Mathematicks, that the ſame, or not very different Gon­
ſequences do flow from both theſe Opinions.
Heaven accord­
ing to Copernicus
is the ſame with
the moſt tenuous
Æther; but dif­
ferent from Para­
dice, which ſar­
paſſeth all the
Heavens.
By theſe Maxims and their Interpretations it appears, that
the Pythagorick and Copernican Opinion is ſo probable, that its
poſſible it may exceed even the Ptolemaick in probability; and
ſince there may be deduced from it a moſt ordinate Syſteme, and
a mroe admirable and myſterious Hypotheſis of the World
than from that of Ptolomy: the Authorities of Sacred Scripture
and Theological Tenents in the mean while not oppoſing it, be­
ing opportunely and appoſitely (as I have ſhown how they may
1be) reconciled with it: And ſince that by it not only the Phœ­
nomena of all the Cœleſtial Bodies are moſt readily ſalved, but
alſo many Natural Reaſons are diſcovered, which could not o­
therwiſe, (but with extream difficulty) have been found out:
And ſince it, laſt of all, doth open a more eaſy way into Aſtro­
nomy and Phyloſophy, and rejecteth all thoſe ſuperfluous and
imaginary inventions produced by Aſtronomers to the end only,
that they might be able by them to render a reaſon of the ſo ma­
ny and ſo various Motions of the Cœleſtial Orbs.
And who knows, but that in that admirable compoſure of the
Candleſtick which was to be placed in the Tabernacle of God, he
might out of his extraordinary love to us have been pleaſed to
ſhaddow forth unto us the Syſteme of the Univerſe, and more

eſpecially of the Planets? (a) Thou ſhalt make a Candleſtick of

pure Gold, (ſaith the Text;) of beaten work ſhall it be made:
his Shaft, and his Branches, his Bowls, his Knops, and his
Flowers (b) ſhall be of the ſame. Here are five things deſcribed, the
Shaft of the Candleſtick in the midle, the Branches on the ſides,
the Bowls, the Knops and the Flowers. And ſince there can be no
more Shafts but one, the Branches are immediatly deſcribed in
theſe (c) words: Six Branches ſhall come out of the ſides of it:
three Branches out of the one ſide, and three Branches out of the
other ſide: Happly theſe fix Branches may point out to us ſix
(d) Heavens, which are moved about the Sun in this order; Saturn,
the ſloweſt and moſt remote of all, finiſheth his courſe about the

Sun thorrow all the twelve Signes of the Zodiack in thirty Years:

Jupiter, being nearer than he, in twelve Years: Mars, being yet

nearer than him, in two Years: The Earth, which is ſtill nearer
than he, doth perform the ſame Revolution, together with
the Orbe of the Moon, in the ſpace of a Year, that is in Twelve
Months: Venus, which is yet nearer than all theſe, in (e) 9 Months:
And laſt of all Mercury, whoſe vicinity to the Sun is the greateſt
of all, accompliſheth its whole converſion about the Sun in eighty
Dayes. After the deſcription of the ſix Branches, the ſacred
Text proceeds to the deſcription of the Bowls, the Knops, and
the Flowers, ſaying, (f) Three Bowls made like unto Almonds,
with a Knop and a Flower in one Branch; and three Bowls made
like Almonds in the other Branch, with a Knop and a Flower: this
ſhall be the work of the ſix Branches that come out of the Shaft.
And in the Candleſtick ſhall be four Bowls made like unto Al­
monds, with their Knops and their Flowers: there ſhall be a knop
under two branches of the ſame, and a Knop under two Branches
of the ſame, and a Knop under two Branches of the ſame; which
together are ſix Branches, proceeding from one Shaft. The truth

is, the ſhallowneſſe of my underſtanding cannot fathome the
1depth of all the Myſteries that are couched in this moſt wiſe
diſpoſure of things: nevertheleſſe being amazed, and tranſported
with admiration, I will ſay; Who knows but that thoſe three
Bowls like unto Almonds to be repreſented on each of the
Branches of the Candleſtick may ſignifie thoſe Globes which are
apter (as is this our Earth) for the receiving than emitting of Influ­
ences? Perhaps alſo they denote thoſe Globes of late diſcovered
by the help of the Optick Teleſcope, which participate with
Saturn, Jupiter, Venus, and poſſibly alſo with the other Planets?
Who knows likewiſe, but that there may be ſome occult propor­
tion between theſe Globes and thoſe Myſterious Knops and
Lilies inſinuated unto us in the ſacred Scriptures? But this
ſhall here ſuffice to bound humane Preſumption, and to teach us
to exſpect with an Harpocratick ſilence from Time, the Indice of
Truth, a diſcovery of theſe Myſteries: (g) Solomon made ten

Candleſticks by the ſame Patern of Moſes, which he placed, five
on one hand and five on another, in the Temple erected by him
in honour of the moſt High God; which very thing doth alſo,
without all queſtion, contain moſt abſtruſe ſigniſications. More­
over, that Apple of the Knowledg of Good and Evil prohibited
our firſt Parents by God is not without a Myſtery; which ſome
ſay was an Indian Figg. In which theſe things are to be obſerv­
ed: Firſt, That it is replete with many Kernels, every one of
which hath a particular Centre. Secondly, Though of it ſelf it
be hard and ſolid, yet about its Circumference it is of a more rare
and tenuouſe ſubſtance; herein reſembling the Earth, which
though in its Centre, and thoſe parts which are neareſt to it, it
be ſtony, Metallick, and compact, yet the nearer one approacheth
to the Circumference, its parts are ſeen to be the more rare and
tenuouſe: and withall it hath another body, more rare than its
own, namely the Water, above which there is yet another, more
ſubtil than all the reſt of inferiour Bodyes, that is to ſay,
the Aire,
(a) Exod. 25. 31.
(b) My Authour
following the vul­
gar Tranſlation,
which hath an E­
ligance in ſome
things beyond ours,
cites the words
thus, Facies Can­
delabrum ducti­
le de auro mun­
diſſimo, Haſtile
ejus, & Calamos,
& Sphærulas, ac
Lilia, ex ipſo pro­
cedentia.
(c) verſe 12.
(d) or Spheres.
(e) Though our
Authour ſpeaketh
here poſitively of
nine Months, &c.
Fathers are not a­
greed about the pe­
riod of this planet,
nor that of Mercu­
ry, as you may ſee
at large in Riccio­
lus, Almageſt. nov.
Tom. 1. part 1. l.
7. ſect. 3. cha. 11.
num. 11. page 627.
where he maketh
Venus to conſum­
mate her Revolu­
tion in neer 225
dayes, or 7 1/2 Mon.
and Mecury in a­
bout 88 dayes, or 3
Months: in which
he followeth Kepl.
in Epitome Aſtro­
nom. p. 760.
(f) verſ. 33, 34.
(g) 1 Kings c. 7.
v. 49. 2 Chron. c.
4. verſ. 7.
The ſame Repreſentation with that of the Indian Figg is held
forth to us by the Malum Punicum, or Pomegranate, with its
innumerable poly centrick Stones or Kernels, all which in the parts
more remote from their Centre, and nearer approaching towards
the Circumference, are of a ſubſtance ſo ſubtil and rare, that being
but lightly compreſſed, they in a manner wholly convert into a
moſt tenuoſe Liquor or juice: Of which fruit it pleaſed Divine
Wiſdom to make mention, and ordained that its Figure ſhould be
imbroidered and wrought with a needle in the ſacerdotal Garment
of Aaron: (h) Beneath (ſaith God) upon the hem of it thou

ſhalt make Pomegranates of blew, and of purple, and of ſcarlet,
round about the border thereof; and Bells of gold between them
1round about: a golden bell and a pomegranate, a golden bell and a
pomegranate, upon the hem of the Robe round about. And that this
was a Myſtical Repreſentation of the Worlds Effigies, is averred

by Solomon, ſaying; (i) For in the long (k) Garment that be
had on was the (l) whole World; and in the foure rows of the ſtones

was the Glory of the Fathers graven, and thy Majeſty in the Di-

adem of his Head.
(h) Exod. 28. 33,
34, & 39. v. 24,
25, 26.
(i) Sap. c. 18. v.
24.
(k) Exod. c. 28.
v. 6, 9. 17, 36.
(l) Or, totus Or­
bis Terrarum, as
the vulgar Tranſ­
lation hath it.
The ſame likewiſe is ſignified to us by the Grape, and in like
manner by all other Fruits; but eſpecially the Figg, Grape, and
Pomegranate: whence theſe three are almoſt alwayes placed to­
gether in the Sacred Scriptures. So Numb. 20. the People of Iſra­
el complain againſt Moſes and Aaron: (m) Wherefore have you

made us to come up out of Egypt, to bring us into this evil place,
where there can grow no Seed, neither is there either Figgs, or
Vines, or Pomegranates? Intimating that theſe kinds of Fruits
were preferred by them for their excellency before all others.
And in Joel (n) The Vine is dryed up, and the Figg-tree languiſh-

eth, the Pomegranate-trce, the Palm-tree alſo, and the Apple-tree,
even all the Trees of the field are withered; becauſe joy is wither­
ed away from the Sons of Men. Likewiſe in Haggai: (o) Is the

ſeed yet in the Bud? and hath as yet the Vine and the Fig-tree,
and the Pomegranate, and the Olive-tree brought forth? In like
manner in Deuteronomie the Land of Promiſe is commended to
be (p) A Land of Wheat, and Barly, and Vines in which grow,

Figg-trees, and Pomegranates, and Olive-trees, &c. And in the
Structure of the Temple undertaken by Solomon upon Divine In­

ſpiration the (q) Chapiters of the Pillars were adorned with ſeve­
ral rowes of Pomegranates: which particular is mentioned, not
in one but many places of Holy Writ. Yea and ſometimes acci­
dentally and occaſionally the Holy hath Ghoſt ænigmatically re­
preſented this moſt admirable and Moſt Wiſe Sructure of the
World, the Order of the Heavens, and the diſpoſure of Crea­
tures Spiritual and Corporeal by Emblems, Parables, and Figures,
leaſt they ſhould be as it were dazled and blinded, by the reful­
gent ſplendor of ſo excellent an Object. Hence we ſee, that in
theſe Doctrinal & Dubious Points we may diſcourſe in ſuch man­
ner by help of the Holy Scripture as is meet for the underſtanding
of the Prophets; which ſeeing they are very obſcure, they ſhall be
fully underſtood, and may be aptly applyed only then when they
ſhall be fulfilled, and not before: So alſo when once the true
Syſteme of the Univerſe is found out, then, and not till then, the
meaning of theſe Figures, and Ænigma's ſhall be made known
unto us: Thus before the coming of the Son of God had diſco­
vered unto us the Myſtery of the Holy Trinity, none were able
to comprehend or imagine what was concealed under thoſe
1words; (r) In Principio creavit Elohim Cœlum & Terram: for

that they did not ſee how the Noun Plural Elohim (which is as much
as to ſay Dij, [Gods] ſhould be joyned with the Verb Singular,
Creavit: But the Myſtery of the Unity of Eſſence and Trinity
of Perſons in God being revealed, it was preſently known, that
the Singular Number, Creavit, had reference to the Unity of Eſ­
ſence, (in regard that the Works of the Trinity ad extra are in­
diviſible) and the Plural, Elohim, to the Perſons. Who, I pray,
in elder times could have found out this Myſtery? And thus the
Name of God is thrice repeated in Pſal. 67. (s) God, even our

God ſhall bleſſe us, God ſhall bleſſe us, &c. Which at firſt might
ſeem a Pleonaſme, and ſuperfluous repetition; but afterwards it
was evident that David did there ſet out the Benedictions of ſe­
veral Perſons implyed, to wit, the Father, Son, and Holy Ghoſt.
Innumerable Examples of the like kind may be found in the Sa­
cred Leaves. Therefore, to conclude, I will ſay with ^{*}David,

Pſal. 92. Oh Lord how glorious are thy Works! thy thoughts
are very deep: an unwiſeman knoweth not, and a fool doth not
underſtand theſe things.
(m) Numb. c. >20.
v. 5.
(n) Joel c. 1. v. 12.
(o) Hagg. c. 2.
v. 19.
(p) Deut. c. 8. v. 8.
(q) 1 Kings c 7.
v. 20. & 2 Kings
c. 25. v. 17. &
2 Chro. c. 3. v. 15,
16. & c. 4. v. 12.
13. & Jerem. c.
52. v. 21, 22.
(r) Gen. c. 1. v. 1
(s) Pſal. 67. v. 6
7.
* Pſal. 92 v. 536.
Theſe are the particulars that I have thought fit to offer, as
a Divine, concerning the not-improbable Opinion of the Mobili­
ty of the Earth and Stability of the Sun: which I hope will be
acceptable to you, Reverend Sir, out of the love and diligence
wherewith you perſue Virtue and Learning. But (to the end
that you may alſo receive an account of my other Studies) I
hope very ſhortly to publiſh in Print my Second Tome ^{*}Of the In-

ſtitutions of all Learnings, which ſhall containe all the Liberall
Arts, as I have already ſignified in that Syntax, and Spicimen by
me heretofore put forth, and publiſhed under your Name. The
other five following Tomes by me promiſed (which ſhall treat of
Phyloſophy and Theology) are not altogether ſo forward, ne­
vertheleſs they will be ſpeedily finiſhed. In the mean time there
will come forth my Book Concerning ^{*} Oracles, now finiſhed, to­

gether with a Treatiſe ^{*} Of Artificial Divination. And for a

pledge thereof, I ſend you at this time annexed to this Epiſtle a
Tract ^{*} Concerning Natural Coſmological Divination, or of Natu­

ral Prognoſticks, and Preſages of the Changes oſ Weather, and
other things which fall within the compaſſe of Natue. God grant
you all Happineſſe.
* Inſtitutionum
omnium Doctri­
narum.
* De Oraculis.
* De Divinatio­
ne artificioſa.
* De Divinatio­
ne Naturali Coſ­
mologica.
Moſt Reverend Sir
NAPLES, from the Covent
of the Carmelites, Jan.
6. 1615.
Your Moſt Humble Servant
PAOLO ANTONIO FOSCARINI.
FINIS.
1
Imprimatur, P. ANT. GHIBERT, Vic. Gen.
JOANNES LONGUS Can. & Cur. Archiep.
Neap. THEOL. Vidit.
1
A
TABLE
Of the moſt Obſervable
PERSONS and MATTERS
Mentioned in the FIRST PART Of
The Firſt Tome.
AABSTACT.Things are exactly the ſame in Abstract, as in Concrete.185AIRE.The part of the Aire inferiour to the Higher Mountains doth follow the Motion of the Earth.124 The motion of the Aire apt to carry with it light things, but not heavy.124 The Aire alwayes touching us with the ſame part of it, cannot make us feel it.228 It is more reaſonable that the Aire be commoved by the rugged ſurface of the Earth, than by the Celeſtial Motion.400 It is demonſtrated, inverting the Argument, that the perpetual Motion of the Aire from Eaſt to Weſt, commeth from the Motion of Heaven.403ANIMALS.Animals, Vide, The Motion of Animals.The cauſe of the Wearineſſe that attends the Motion of Animals.244APOLLONIUS.Apollonius and Copernicus demonſtrate the Re­trogradations of Venus and Mercury.311Arguing, Arguments, & ArgumentationsSomein Arguing fix in their minds the Conclu­ſion believed by them, and then adapt their Reaſons to that.250One ſingle Experiment or ſound Demonſtrati­on, overthroweth all Arguments meerly pro­bable.105A pleaſant Example ſhewing the invalidity of ſome Phiſical Argumentations.363ARISTARCHUS.Reaſon and Diſcourſe in Ariſtarchus and Coper­nicus prevailed over manifeſt Senſe.301ARISTOTLE.Ariſtotle maketh the World perfect, becauſeit hath the Threefold Dimenſion.2Ariſt. his Demonſtrations to prove the Worlds Dimenſions to be three, and no more.2Ariſtotle his Definition of Nature either imper­fect or unſeaſonable.7Ariſtotle accomodates the Rules of Architecture to the Frame of the World, and not the Frame to the Rules.8Ariſtotle cannot equivocate, being the Inventer oſ Logick.23Ariſtotle his Paralogiſme in proving the Earth to be in the centre of the World.24Ariſt. Paralogiſme another way diſcovered.24Ariſtotle his Diſcourſe to prove the Incorrupti­bility of Heaven.26Ariſtotle proveth that Circular Motion hath no Contrary.26Ariſtotle defective in aſſigning the Cauſes, why the Elements are Generable and Corrup­tible.31Ariſiotle would change his opinion, did he ſee the Novelties of our Age.37
1Ariſt, preferres Senſe before Ratiocination.42Ariſtotle affirmeth the Heavens alterable, rather then otherwiſe, by his Doctrine.42Requifites to fit a man to Philoſophate well in the way of Ariſtotle.92Some of Ariſtotles Sectators impaire his Repu­tation, in going about to enhanſe it.93The ſervile Spirit of ſome of Ariſt. followers.95Too cloſe an adherence to Aristotle is blame­able.95Ariſtotle and Ptolomy argue againſt the Diurnal Motion aſcribed to the Earth.97A Propoſition that Ariſtotle filched from the Ancients, and ſomewhat altered.99Ariſtotle his Arguments for the Earths Quie­ſcence and Immobility.107Ariſtotle were he alive, would either refute his Adverſaries Arguments, or elſe would alter his Opinion.113Aristotles firſt Argument againſt the Earths Mo­tion, is defective in two things.121The Paralogiſme of Aristotle and Ptolomy in ſuppoſing that for known, which is in que­ſtion.121Ariſtotle admitteth that the Fire moveth direct­ly upwards by Nature, and round about, by Participation.122Ariſtotle and Ptolomy ſeem to confute the Earths Mobility againſt thoſe who think that it, ha­ving along time ſtood ſtill, began to move in the time of Pythagoras.168Aristotle his errour in affirming falling Grave Bodies to move according to the proportion of their gravities.199Ariſtotle his Demonſtrations to prove the Earth is finite, are all nullified, by denying it to be moveable.294Aristotle maketh that Point to be the Centre of the Univerſe, about which all the Celeſtial Spheres do revolve294A queſtion is put, if Ariſt. were forced to receive one of two Propoſitions, that make againſt his Doctrine, which he would admit.294Aristotle his Argument againſt the Ancients, who held that the Earth was a Planet.344Aristotle taxeth Plato of being over­ſtudious of Geometry.361Aristotle holdeth thoſe Effects to be miraculous, of which the Cauſes are unknown.384ASTRONOMERS.Aſtronomers confuted by Anti­Tycho.38The principal Scope of Aſtronomers is to give a reaſon of Appearances and Phænomena.308Actronomers all agree that the greater Magni­tudes of the Orbes is the cauſe of the tardity in their Converſions.331Aſtronomers perhaps have not known what Appearances ought to follow, upon the An­nual Motion of the Earth.338Actronomers having omitted to inſtance what al­terations thoſe are, that may be derived from the Annual Motion of the Earth, do thereby teſtifie that they never rightly un­derſtood the ſame.343ASTRONOMICAL.Aſtronomical Obſervations wreſted by Anti­Ty­cho to his own purpoſe.39Actronomical Inſtruments are very ſubject to errour.262ASTRONOMY.Aſtronomy reſtored by Copernicus upon the Suppoſitions of Ptolomy308Many things may remain as yet unobſerved in Aſtronomy415AUCUPATORIAN.An Aucupatorian Problem for ſhooting of Birds flying.157AXIOME, or Axiomes.In the Axiome, Fruſtra fit per plura, &c. the addi­tion of æquœ bene is ſuperfluous.106Three Axiomes that are ſuppoſed manifeſt.230Certain Axiomes commonly admitted by all Philoſophers.361BBODY and Bodies.Contraries that corrupt, reſide not in the ſame Body that corrupteth.30GRAVE BODY; If the Celeſtial Globe were perforated, a Grave Body deſcending by that Bore, would paſſe and aſcend as far beyond the Centre, as it did deſcend.203The motion of Grave Bodies, Vide Motion.The Accelleration of Grave Bodies that deſcend naturally, increaſeth from moment to moment.205We know no more who moveth Grave Bodiesdownwards, than who moveth the Stars round; nor know we any thing of theſe
1Courſes, more than the Names impoſed on them by our ſelves.210The great Maſſe of Grave Bodies being tranſ­ferred out of their Place, the ſeperated parts would follow that Maſſe.221PENSILE BODY; Every Penſile Body carried round in the Circumference of a Circle, ac­quireth of it ſelf a Motion in it ſelf contrary to the ſame.362CBLESTIAL BODIES neither heavy nor light according to Ariſtoile.23Celeſtial Bodies are Generable and Corruptible becauſe they are Ingenerable aud Incorrup­tible.29Amongſt Celeſt. Bodies there is no contrariety.29Celeſtial Bodies touch, but are not touched by the Elements.30Rarity and Denſity in Celectial Bodies, different from Rarity and Denſity in the Elements.30Celeſtial Bodies deſigned to ſerve the Earth, need no more but Motion and Light.45Celeſtial Bodies wantan interchangeable Opera­tion on each other.46Celeſtial Bodies alterable in their externe parts.46Perfect Sphericity why aſcribed to Celeſtial Bo­dies by Peripateticks.69All Celectial Bodies have Gravity and Levity.493ELEMENTARY BODIES; Their propenſi­on to follow the Earth, hath a limited Sphere of Activity.213LIGHT BODIES eaſier to be moved than heavy, but leſſe apt to conſerve the Motion.400LUMINOUS BODIES; Bodies naturally Lu­minous are different from thoſe that are by na­ture Obſcure.34The reaſon why Luminous Bodies appear ſo much the more enlarged, by how much they are leſſer.304Manifeſt Experience ſhews that the more Lumi­nous Bodies do much more irradiate than the leſſe Lucid.306SIMPLE BODYES have but one Simple Motion that agreeth with them.494SPHERICAL BODIES; In Spherical Bodies Deorſum is the Centre, and Surſum the Cir­ference.479BONES.The ends of the Bones are rotund, and why.232BUONARRUOTTI.Buonarruotti a Statuary of admirable ingenuity.86CCANON.A ſhameful Errour in the Argument taken from the Canon­Bullets falling from the Moons Concave.197An exact Computation of the fall of the Canon­Bullet from the Moons Concave, to the Centre of the Earth.198CELESTIALCeleſtial Subſtances that be Unalterable, and Elementary that be Alterable, neceſſary in the opinion of Ariſtotle.2CENTRE.The Sun more probably in the Centre of the U­niverſe, than the Earth.22Natural inclination of all the Globes of the World to go to their Centre.22Grave Bodies may more rationally be affirmed to tend towards the Centre of the Earth, than of the Univerſe.25CHYMISTS.Chymiſts interpret the Fables of Poets to be Se­crets for making of Gold.93CIRCLE, and Circular.It is not impoſſible with the Circumference of a ſmall Circle few times revolved, to meaſure and deſcribe a line bigger than any great Cir­cle whatſoever.222The Circular Line perfect, according to Ariſtotle,and the Right imperfect, and why.9CLARAMONTIUS.The Paralogiſme of Claramontius.241The Argument of Claramontius recoileth upon himſelf.245The Method obſerved by Claramontius in confu­ting Aſtronomers, and by Salviatus in re­futing him.253CLOUDS.Clouds no leſſe apt than the Moon to be illumi­nated by the Sun.73
1CONCLUSION and Concluſions.The certainty of the Concluſion helpeth by a reſo­lutive Method to finde the Demonſtration.37The Book of Concluſio s, frequently mentioned, was writ by Chriſtopher Scheiner a Jeſuit.195, & 323.CONTRARIES.Contraries that corrupt, reſide not in the ſame Body that corrupteth.30COPERNICAN.Anſwers to the three firſt Objections againſt the Copernican Syſtem.303The Copernican Syſtem difficul to be underſtood, but eaſie to be effected.354A plain Scheme repreſenting the Copernican Sy­cteme and its conſequences.354The proſcribing of the Copernican Doctrine, af­ter ſo long a Tolleration, and now that it is more than ever followed, ſtudied and con­firmed, would be an affront to Truth.444The Copern. Syſtem admirably agreeth with the Miracle of Joſhuah in the Literal Senſe.456If Divines would admit of the Copernican Sy­ſtem, they might ſoon find out Expoſitions for all Scriptures that ſeem to make againſt it.459The Copernican Syſtem rejected by many, out of a devout reſpect to Scripture Authorities.461The Copernican Syſtem more plainly aſſerted in Scripture than the Ptolomaick.469COPERNICANS.Copernicans are not moved through ignorance of the Arguments on the Adverſe part.110Copernicans were all firſt againſt that Opinion, but the Peripateticks were never on the other ſide.110Copernicans too freely admit certain Propoſiti­ons for true, which are doubtful.159He that will be a Copernican muſt deny his Sen­ſes.228A Great Mathematician made a Copernican, by looking into that Doctrine, with a purpoſe to confute it.443COPERNICUS.Copernicus eſteemeth the Earth a Globe, like to a Planet.1Objections of two Moderne Authours [Schei­ner and Claramontius] againſt Copernicus.195Copernicus his Opinion overthrows the Criteriumof Phyloſophers.223A groſle Errour in the Oppoſer of Copernicus,and wherein it appears.234, 235, & 236A ſubtle and withal ſimple Argument againſt Copernicus.234Copernicus his Opponent had but little ſtudied him, as appears by another groſſe Errour.235Its queſtioned whither he underſtood the third Motion aſſigned to the Earth by Copern.236Copernicus erroneouſly aſſignes the ſame Opera­tions to different Natures.238A declaration of the improbability of Copernicushis Opinion.301Reaſon and Diſcourſe in Copernicus and Ariſtar­chus prevailed over Senſe.301Copernicus ſpeaketh nothing of the ſmall Variati­on of Bigneſſe in Venus and Mars.302Copernicus perſwaded by Reaſons contrary to Senſible Experiments.306Copernicus reſtored Aſtronomy upon the Suppo­ſitions of Ptolomy.308What moved Copernicus to eſtabliſh his Sy­ſteme.308Its a great argument in favour of Copernicus, that he obviates the Stations and Retrogradati­ons of the Motions of the Planets.309Inſtances Ironically propounded by Scheiner againſt Copernicus.323Copernicus underſtood not ſome things for want of Inſtruments.338The grand difficulty in Copernicus his Doctrine, is that which concerns the Phænomena of the Sun and fixed Stars.343Copernicus the Reſtorer of the Pythagorean Hy­potheſis, and the Occaſion of it.429Copernicus founded not his Doctrine on Reaſons depending on Scripture, wherein he might have miſtaken their Senſe, but upon Natu­ral Concluſions and Aſtronomical and Ge­ometrical Demonſtrations.431CORRUPTIBLE, and Corruptibility.The perfection of Figure operates in Corruptible Bodies, but not in Eternal.69The Diſparagers of Corruptibility ought to be turned into Statua's.37Corruptibility admits of more and leſſe, ſo doth not Incorruptibility.69COUNCILS.The Councils refuſe to impoſe Natural Conclu­ſions as matters of Faith.450
1DDIAMONDS.Diamonds ground to divers ſides, and why.63DIDACUS. Didacus à Stunica reconcileth Texts of Scripture with the Copernican Hypotheſis.468DEFINITIONS.Definitions contain virtually all the Paſſions of the things defined.87EEARTH.The Earth Spherical by the Conſpiration of its parts to go to its Centre.21Itis eaſier to prove the Earth to move, than that Corruptibility is made by Contraries.27The Earth very Noble, by reaſon of the Mu­tations made therein.45The Earth unprofitable and full of Idleneſſe, its Alterations being taken away.45The Earth more Noble than Gold and Jewels.45The Celeſtial Bodies deſigned to ſerve the Earth,need no more but Motion and Light.45 The Generations and Mutations that are in the Earth, are all for the Good of Man.47From the Earth we ſee more than half the Lu­nar Globe.51Seven Reſemblances between the Earth and Moon.48 to 53The Earth unable to reflect the Suns Rays.54The Earth may reciprocally operate on Celeſti­al Bodies with its Light.80Affinity between the Earth and Moon, by rea­ſon of their Vicinity.81The Motions of the Earth imperceptible to its Inhabitants.97The Earth can have no other Motions than thoſe which to us appear commune to all the reſt of the Univerſe, the Earth excepted.97The Diurnal Motion ſeemeth commune to all the Univerſe, the Earth onely excepted.97Ariſtotle and Ptolomy argue againſt the EarthsDiurnal Motion.97The Diurnal Motion of the Earth. Vide Diur­nal Motion.Seven Arguments to prove the Diurnal Moti­on to belong to the Earth.99 to 103The Earth a pendent Body, and equilibrated in a fluid Medium, ſeems unable to reſiſt the Rapture of the Diurnal Motion.103Two kinds of Arguments againſt the EarthsMotion.108Arguments of Ariſtotle, Ptolomy, Tycho, and other perſons, againſt the Earths Motion.107 & 108The firſt Argument againſt the Earths Motion taken from Grave Bodies falling from on high to the Ground.108Which Argument is conſirmed by the Experi­ment of a Body let fall from the Round­top of a Ships Maſt.108The ſecond Argument taken from a Project ſhot very high.108The third Argument taken from the Shot of a Canon towards the Eaſt, and towards the Weſt.108This Argument is conſirmed by two Shots to­wards the North and South, and two others towards the Eaſt and Weſt.109The fourth Argument taken from the Clouds and from Birds.113A fifth Argument taken from the Aire which we feel beat upon us when we run an Horſe at full ſpeed.114A ſixth Argument taken from the whirling of Circular Bodies, which hath a faculty to extrude and diſſipate.114The Anſwer to Ariſtotles firſt Argument.115The Anſwer to the ſecond Argument.117The Anſwer to the third Argument.120 to 150An Inſtance of the Diurnal Motion of the Earth,taken from the Shot of a Piece of Ordinance perpendicularly, and the Anſwers to the ſame, ſhewing the Equivoke.153, 154The Anſwer to the Argument of the Shots of Canons made towards the North and South.158The Anſwer to the Argument taken from the Shots at point blank towards the Eaſt and Weſt.159The Anſwer to the Argument of the flying of Birds contrary to the Motion of the Earth.165An Experiment by which alone is ſhewn the Nullity of all the Arguments produced a­gainſt the Motion of the Earth.165The Stupidity of ſome that think the Earth be­gan to move, when Pythagoras began to af­firme that it did ſo.167A Geometrical Demonſtration to prove the Impoſſibility of Extruſion, by means of the Earths Vertigo, in Anſwer to the ſixth
1Argument.176Granting the Diurnal Vertigo of the Earth, and that by ſome ſudden Stop or Obſtacle it were Arreſted, Houſes, Mountains themſelves, and perhaps the whole Globe, would be ſhaken in pieces.190Other Arguments of two Modern Authours [Scheiner and. Claramontius] againſt the Copernican Hypotheſis of the Earths Mo­tion.195The firſt Objection of the Modern Authour [Scheiner] in his Book of Concluſions.195The Argument of [Claramontius] againſt the Earths Motion, taken from things falling per­pendicularly, another way anſwered.223The Earths Motion collected from the Stars.229Argumeuts againſt the Earths Motion, taken ex rerum natura.230A Simple Body as the Earth, cannot move with three ſeveral Motions.231The Earth cannot move with any of the Moti­ons aſſigned it by Copernicus.231Anſwers to the Arguments againſt the EarthsMotion, token ex rerum natnra.231Four Axiomes againſt the Motion of the Earth.230 to 232One onely Principle might cauſe a Plurality of Motions in the Earth.233The ſame Argument againſt the Plurality of Motions in the Earth, anſwered by Exam­ples of the like Motions in other Celeſtial Bodies.236A fourth Argument [of Claramontius] againſt the Copernican Hypotheſis of the EarthsMobility.239From the Earths obſcurity, and the ſplendor of the fixed Stars, it is argued that it is move­able, and they immoveable.239A fifth Argument [of Claramontius] againſt the Copernican Hypotheſis of the EarthsMobility.240Another difference between the Earth and Ce­leſtial Bodies, taken from Purity and im­purity.240It ſeems a Soleciſme, to affirme that the Earthis not in Heaven.241Granting to the Earth the Annual, it muſt of neceſſity alſo have the Diurnal Motion aſſi­gned to it.300Diſcourſes more than childiſh, that ſerve to keep Fools in the Opinion of the Earths Sta­bility.301The Difficulties removed that ariſe from the Earths moving about the Sun, not ſolitari­ly, but in conſort with the Moon.307The Axis of the Earth continueth alwayes pa­rallel to it ſelf, and deſcribeth a Cylindrai­cal Superficies, inclining to the Orb.344The Orb of the Earth never incllneth, but is immutably the ſame.345The Earth approacheth or recedeth from the fixed Stars of the Ecliptick the quantity of the Grand Orb.349If in the fixed Stars one ſhould diſcover any Mu­tation, the Motion of the Earth would be undeniable.351Neceſſary Propoſitions for the better concei­ving of the Conſequences of the Earths Mo­tion.354An admirable Accident depending on the not­inclining of the Earths Axis.358Four ſeveral Motions aſſigned to the Earth.362The third Motion aſcribed to the Earth, is ra­ther a reſting immoveable.363An admirable interne vertue [or faculty] of the Earths Globe, to behold alwayes the ſame part of Heaven.363Nature, as iu ſport, maketh the Ebbing and Flowing of the Sea to prove the Earths Mo­bility.379All Terrene Effects indifferently confirm the Motion or Reſt of the Earth, except the Eb­bing and Flowing of the Sea.380The Cavities of the Earth cannot approach or recede from the Centre of the ſame.387The Hypotheſis of the Earths Mobility taken in favour of the Ebbing and Flowing op­poſed.399The Anſwers to thoſe Objections made againſt the Earths Motion.399The Revolution of the Earth confirmed by a new Argument taken from the Aire.400The vaporous parts of the Earth partake of its Motions.400Another obſervation taken from the Ayr, in confirmation of the motion of the Earth.402A Reaſon of the continual Motion of the Air and Water may be given by making the Earth moveable, rather then by making it immoveable.405The Earths Mobility held by ſundry great Phi­loſophers amongſt the Antients.437 & 468The Fathers agree not in expounding the Texts of Scripture that are alledged againſt the Earths Mobility.450The Earth Mobility defended by many a­mongſt the Modern Writers.478The Earth ſhall ſtand ſtill after the Day of Judgement.480The Earth is another Moon or Star.486The Earths ſeveral Motions, according to Co­
1pernicus.491The Earth ſecundum totum is Immutable, though not Immoveable.491The Earths Natural Place.492The Earths Centre keepeth her in her Natural Place.493The Earth, in what Senſe it may abſolutely be ſaid to be in the loweſt part of the World.496EBBING and Ebbings.The firſt general Concluſion of the impoſſibi­lity of Ebbing and Flowing the Immobility of the Terreſtrial Globe being granted.380The Periods of Ebbings and Flowings, Diurnal, Monethly, and Annual.381Varieties that happen in the Diurnal Period of the Ebbings and Flowings.382The Cauſes of Ebbings and Flowings alledged by a Modern Phyloſopher.382The Cauſe of the Ebbing and Flowing aſeribed to the Moon by a certain Prelate.383The Cauſe of the Ebbing, &c. referred by Hye­ronimus Borrius and other Peripateticks, to the temperate heat of the Moon.383Anſwersto the Vanities alledged as Cauſes of the Ebbing and Flowing.383Its proved impoſſible that there ſhould natu­rally be any Ebbing and Flowing, the Earth being immoveable.386The moſt potent and primary Cauſe of the Eb­bing and Flowing.390Sundry accidents that happen in the Ebbingsand Flowings.391Reaſons renewed of the particular Accidents obſerved in the Ebbings and Flowings.393Second Cauſes why in ſeveral Seas and Lakes there are no Ebbings and Flowings.394The Reaſon why the Ebbings and Flowings for the moſt part, are every Six Hours.395The Cauſe why ſome Seas though very long, ſuffer no Ebbing and Flowing.395Ebbings and Flowings, why greateſt in the Ex­tremities of Gulphs, and leaſt in the middle parts.396A Diſcuſſion of ſome more Abſtruce Accidents obſerved in the Ebbing and Flowing.396The Ebbing and Flowing may depend on the Di­urnal Motion of Heaven.404The Ebbing and Flowing cannot depend on the Motion of Heaven.405The Cauſes of the Periods of the Ebbings and Flowings Monethly and Annual, at large aſſigned407The Monethly and Annual alterations of the Ebbings and Flowings, can depend on no­thing, ſave on the alteration of the Additions and Subtractions of the Diurnal Period from the Annual.408Three wayes of altering the proportion of the Additions of the Diurnal Revolutions, to the Annual Motion of the Ebbing and Flow­ing.409Ebbings and Flowings are petty things, in compariſon of the vaſtneſſe of the Seas, and the Velocity of the Motion of the Terreſtrial Globe.417EFFECT and Effects.Of anew Effect its neceſſary that the Cauſe be likewiſe new.370The Knowledge of the Effects contribute to the inveſtigation of the Cauſes.380True and Natural Effects follow without diffi­culty.387Alterations in the Effects argue alteration in the Cauſe.407ELEMENTS, and their Motions, Vide MOTION.ENCYCLOPEDIA.Subtilties fufficiently inſipid, ironically ſpoken, and taken from a certain Encyclopedia.153EXPERIMENTS.Senſible Experiments are to be preferred before Humane Argumentations.21, 33, 42.It is good to be very cautious in admitting Ex­periments for true, to thoſe that never tryed them.162Experiments and Arguments againſt the Earths Motion, ſeem ſo far concluding, as they lye under Equivokes162The Authority of Senſible Experiments and ne­ceſſary Demonſtrations in deciding of Phy­ſical Controverſies.436EYE.The Circle of the Pupil of the Eye contracteth and enlargeth.329How to finde the diſtance of the Rays Con­courſe from the Pupil of the Eye.329FFAITH.Faith more infallible than either Senſe of
1Reaſon.475FIRE.Fire moveth directly upwards by Nature, and round about by Participation, according to Ariſtotle.122It is improbable that the Element of Fire ſhould be carried round by the Concave of the Moon.405FIGURE and Figures.Figure is not the Cauſe of Incorruptibility, but of Longer Duration.66The perfection of Figure appeareth in Corrup­tible Bodies, but not in the Eternal.69If the Spherical Figure conferred Eternity, all things would be Eternal.69It is more difficult to finde Figures that touch in a part of their Surface, then in one ſole point.185The Circular Figure placed amongſt the Postu­lata of Mathematicians.186Irregular Figure and Formes difficult to be in­troduced.187Superficial figures increaſe in proportion dou­ble to their Lines.304FLFXURES.The neceſſity and uſe of Flexures in Animals, for varying of their Motions.232FOSCARINI.Foſcarini his Reconciling of Scripture Texts with the Copernican Hypotheſis.473GGENERABILITY.Generability and Corruptibility are onely a­mongſt Contraries, according to Ariſt.26Generability and Alterability are greater perfecti­ons in Mundane Bodies, then the Contrary Qualities.44GEOMETRICAL, and Geometry.Geometrical Demonſtrations of the Triple Di­menſion.4Geometrical Exactneſſe needleſſe in Phyſical Proofs.6Ariſtotle taxeth Plato for being too ſtudious of Geometry.334Peripatetick Phyloſophers condemne the Stu­dy of Geometry, and why.461GILBERT.The Magnetick Phyloſophy of Will. Gilbert.364The Method of Gilbert in his Philoſophy.367GLOBE.Our Globe would have been called Stone, inſtead of Earth, if that name had been given it in the beginning.367GOD.God and Nature do employ themſelves in caring for Men, as if they minded nothing elſe.333An Example of Gods care of Man­kind, taken from the Sun.333God hath given all things an inviolable Law to obſerve.4..GREAT.Great and Small, Immenſe, &c. are Relative Terms.334GRAVITY.Grave; Vide Body.Gravity and Levity, Rarity and Denſity, are contrary qualities.30Things Grave had being before the Common Centre of Gravity.221Gravity and Levity of Bodies defined.493GUN and Gunnery.The Reaſon why a Gun ſhould ſeem to carry farther towards the Weſt than towards the Eaſt.148The Revolution of the Earth ſuppoſed, the Ball in the Gun erected perpendicularly, doth not move by a perpendicular, but an incli­ned Line.155It is ingenuouſly demonſtrated, that, the Earths Motion ſuppoſed, the Shot of Great Gunsought to vary no more than in its Reſt.161The Experiment of a Running Chariot to find out the difference of Ranges in Gunnery.148A Computation in Gunnery, how much the Ranges of Great Shot ought to vary from the Mark, the Earths Motion being Granted.160
1HHEAVEN.Heaven an Habitation for the Immortal Gods.26Heavens Immutability evident to Senſe.26Heaven Immutable, becauſe there never was any Mutation ſeen in it.34One cannot (ſaith Ariſtotle) ſpeak confident­ly of Heaven, by reaſon of its great di­ſtance.42The ſubſtance of the Heavens impenetrable, ac­cording to Ariſtotle.54The Subſtance of Heaven Intangible.55 Many things may be in Heaven, that are Inviſi­ble to us.334There are more Documents in the Open Book of Heaven, than Vulgar Wits are able to Penetrate.444Heaven and Earth ever mutually oppoſed to each other.480Which are really the Greater Lights in Heaven,and which the leſſer.484Heaven is not compoſed of a fifth Eſſence, differ­ing from the Matter of inferiour Bodies.494Heaven is no Solid or Denſe Body, but Rare.494Chriſt at his Incarnatiou truly deſcended from Heaven, and at his Aſcenſion truly aſcended into Heaven.496Of the Firſt, Second and Third Heaven.497Heaven in the Senſe of Copernicus, is the ſame with the moſt tenuous Æther, but different from Paradice, which excells all the Hea­vens.499HELL.Hell is in the Centre of the Earth, not of the World.480HELIX.The Helix about the Cylinder may be ſaid to be a Simple Line.7HYPOTHESIS.The true Hypotheſis may diſpatch its Revoluti­ons in a ſhorter time in leſſer Circles, than in greater, the which is proved by two Examples.410IJEST.A Jeſt put upon one that offered to ſell a cer­tain Secret of holding Correſpondence at a Thouſand Miles diſtance.79A Jest of a certain Statuary.94IMPOSSIBILITY and Impoſſibilities.Nature attempts not Impoſſibilities.10To ſeek what would follow upon an Impoſſibi­lity is Folly.22INCORRUPTIBILITY.Incorruptibility eſteemed by the Vulgar, out of their fear of Death.45INFINITY.Of Infinity the Parts are not one greater than another, although they are comparatively unequal.105INSTRUMENT and Inſtruments.Inſtruments Aſtronomical very ſubject to Er­rour.262Copernicus underſtood not ſome things for want of Instruments.338A proof of the ſmall credit that is to be given to Aſtronomical Instruments in Minute Ob­ſervations.351Ptolomy did not confide in an Instruments made by Archimedes.352Inſtruments of Tycho made with great Ex­pence.352What Inſtruments are moſt apt for exact Obſer­vations.352INVENTORS.The Firſt Inventors and Obſervers of things ought to be admired.370JOSHUAH.The Miracle of Joſhuah in commanding the Sun to ſtand ſtill, contradicts the Ptolomaick Syſtem.456Joſhuahs Miracle admirably agreeth with the Pythagorick Syſteme.457
1IRON.Its proved that Iron conſiſts of parts more ſubtil, pure and compact than the Magner.370JUPITER.Jupiter and Saturn do encompaſſe the Earth, and the Sun.258Jupiter augments leſſe by Irradiation, than the Dog­Star.305KKEPLER.The Argument of Kepler in favour of Coper­nicus.242An Explanation of the true Senſe of Kepler, and his Defence.243The feigned Anſwer of Kepler couched in an Artificial Irony.244Kepler is, with reſpect, blamed.422Keplers reconciling of Scripture Texts whith the Copernican Hypotheſis.461KNOW, &c.The having a perfect Knowledge of nothing, maketh ſome beleeve they underſtand all things.84Gods manner of Knowing different from that of Man.87The great Felicity for which they are to be en­vied, who perſwade themſelves that they Know every thing.164Our Knowledge is a kind of Reminiſcence, ac­cording to Plato.169LLIGHT.Light reflected from the Earth into the Moon.52The Reflex Light of uneven Bodies is more uni­verſal than that of the ſmooth, and why.62The more rough Superficies make greater Re­flection of Light than the leſſe rough65Perpendicular Rays of Light illuminate more than the Oblique, and why.65The more Oblique Rays of Light illuminate leſſe, and why,65Light or Luminous Bodies appear the brighter in an Obſcure Ambient.74LINE.The Right Line and Circumference of an infi­nite Circle are the ſame thing.342LAWYERS.Contentious Lawyers that are retained in an ill Cauſe, keep cloſe to ſome expreſſion fallen from the adverſe party at unawares.324LOOKING­GLASSES.Flat Looking­Glaſſes caſt forth their Reflection to­wards but one place, but the Spherical eve­ry way.39LYNCEAN.The Lyncean Academick the firſt Diſcoverer of the Solar ſpots, and all the other Celeſtial Novelties.312The Hiſtory of his proceedings for a long time, about the Obſervation of the Solar Spots.312MMAGNET.Many properties in the Magnet.367The Magnet armed takes up more Iron, than when unarmed.369The true cauſe of the Multiplication of Vertue in the Magnet, by means of the Arming.370A ſenſible proof of the Impurity of the Mag­net.371The ſeveral Natural Motions of the Mag­net.374Philoſophers are forced to confeſſe that the Magnet is compounded of Celeſtial Subſtan­ces, and of Elementary.375The Error of thoſe who call the Magnet a mixt Body, and the Terreſtrial Globe, a ſimple Body.375An improbable Effect admired by Gilbertus in the Magnet.376MAGNETICK Philoſophy.The Magnetick Philoſophy of William Gilbert.364MAGNITUDE.The Magnitude of the Orbs and the Velocity of the Motions of Planets anſwer proporti­
1onably, as if deſcended from the ſame place.19Immenſe Magnitudes and Numbers are incom­prehenſible by our Underſtandings.332MARS.Mars neceſſarily includeth within its Orb the Earth, and alſo the Sun.298Mars at its Oppoſition to the Sun, ſeems ſixty times bigger than towards the Conjuncti­on.298Mars makes an hot aſſault upon the Coperni­can Syſteme.302MARSILIUS.Signor Cæſar Marſilius obſerveth the Meridian to be moveable.422MEDICEAN.The time of the Medicean Planets converſi­ons.101The Medicean Planets are as it were four Moons about Jupiter.307MEDITERRAN.Mediterranean Sea made by the Seperation of Abila and Calpen.35The Voyages in the Mediterran from Eaſt to Weſt are made in ſhorter times than from Weſt to Eaſt.403MERCURY.The Revolution of Mercury concluded to be about the Sun, within the Orb of Venus.298Mercury admitteth not of clear Obſervati­ons.307MOON.The Moon hath no Generation of things, like as we have, nor is it inhabited by Men.47In the Moon may be a Generation of things dif­ferent from ours.47There may be Subſtances in the Moon, very different from ours.48The firſt reſemblance between the Moon and Earth, which is that of Figure, is proved, by their manner of being illuminated by the Sun.48The ſecond reſemblance is the Moons being Opacous, as the Earth.48The third reſemblance is the Moons being Denſe and Mountainous as the Earth.49The fourth reſemblance is the Moons being di­ſtinguiſhed into two different parts for Cla­rity and Obſcurity, as the Terreſtrial Globe into Sea and Land.49The fifth reſemblance is Mutation of Figures in the Earth, like thoſe of the Moon, and made with the ſame Periods.49All the Earth ſeeth halfe onely of the Moon,and halfe onely of the Moon ſeeth all the Earth51Two Spots in the Moon, by which it is percei­ved that She hath reſpect to the Centre of the Earth in her Motion.52Light reflected from the Earth into the Moon.52The ſixth reſemblance is that the Earth and Moon interchangeably illuminate.53The ſeventh reſemblance is that the Earth and Moon interchangeably Ecclipſe.53The Secondary Clarity of the Moon eſteemed to be its Native Light.54The Surface of the Moon more ſleek then any Looking­Glaſſe.55The eminencies and Cavities in the Moon, are illu­ſions of its Opacous and Perſpicuous parts.55The Moons Surface is ſharp, as is largely pro­ved.57The Moon, if it it were ſleek like a Spherical Looking­Glaſſe, would be inviſible.60 & 62The apparent Unevenneſſes of the Moons Sur­face aptly repreſented by Mother of Pearl.70The apparent Unevenneſſes of the Moon cannot be imitated by way of more and leſſe Opa­city, and Perſpicuity71The various Aſpects of the Moon imitable by any Opacous matter.71Sundry Phænomena from whence the MoonsMontuoſity is argued.71The Moon appears brighter by night, than by day.72The Moon beheld in the day time, is like to a little Cloud.72Clouds are no leſſe apt than the Moon to be il­luminated by the Sun.73A Wall illuminated by the Sun, compared to the Moon, ſhines no leſſe than it.73The third reflection of a Wall illuminates more than the firſt of the Moon.74The Light of the Moon weaker than that of the Twy­light.74The ſecondary Light of the Moon cauſed by the Sun, according to ſome.76
1The ſecondary Light of the Moon appears in form of a Ring, i. e. bright in the extreme Circumference, and not in the midſt, and why.77The ſecondary Light of the Moon, how it is to be obſerved.78The Moons Diſcus in a Solar Eclipſe can be ſeen onely by Privation.78Solidity of the Moons Globe argued from its being Mountainous.81The ſecondary Light of the Moon clearer before the Conjunction than after.82The obſcurer parts of the Moon are Plains, and the more bright Mountains.83Long Ledges of Mountains about the Spots of the Moon.83There are not generated in the Moon things like to ours, but if there be any Producti­ons, they are very different.83The Moon not compoſed of Water and Earth.83Thoſe Aſpects of the Sun neceſſary for our Productions, are not ſo in the Moon.83Natural Dayes in the Moon are of a Moneth long.84To the Moon the Sun declineth with a difference of ten Degrees, and to the Earth of Forty ſeven Degrees.84There are no Rains in the Moon.84The Moon cannot ſeperate from the Earth.295The Moons Orbe environeth the Earth, but not the Sun.299The Moon much diſturbeth the Order of the other Planets.362The Moons Motion principally ſought in the Account of Eclipſes.416The Moon is an Æthereal Earth.492MOTION and Motions.Motion of Projects. Vide Projects.The Conditions and Attributes which differ the Celeſtial and Elementary Bodies depend on the Motions aſſigned them by Ariſtotle.25Peripateticks improperly aſſign thoſe Motions to the Elements for Natural with which they never were moved, and thoſe for Preternatu­ral with which they alwayes move.33Motion, as to the things that move thereby, is as if it never were, and ſo farre operates, as it relates to things deprived of Motion.98Motion cannot be made without its moveable Subject.104Motion and Reſt principal Accidents in Na­ture.112Two things neceſſary for the perpetuating of a Motion; an unlimited Space, and an incor­ruptible Moveable.117Diſparity in the Motions of a Stone falling from the Round Top of a Ship, and from the Top of a Tower.123The Motion of grave Pendula might be perpe­tuated, impediments being removed.203Whence the Motion of a Cadent Body is col­lected.224The Motion of the Eye argueth the Motion of the Body looked on.224Different Motions depending on the Fluctuati­on of the Ship.226Our Motion may be either interne, or externe, and yet we never perceive or feelit.229The Motion of a Boat inſenſible to thoſe that are within it, as to the Senſe of Feeling.229The Motion of a Boat ſenſible to Sight joyned with Reaſon.229A ſimple Body, as the Earth, cannot move with three ſeveral Motions.231Motion and Reſt are more different than Right Motion and Circular.237One may more rationally aſcribe to the Earth two intern Principles to the Right and Cir­cular Motion, than two to Motion and Reſt.237The diverſity of Motions helpeth us to know the Diverſity of Natures.237Bodies of the ſame kind, have Motions that agree in kinde.239The greatneſſe and ſmallneſſe of the Body make a difference in Motion and not in Reſt.243Every penſile and librated Body carried round in the Circumference of a Circle acquireth of it ſelf a Motion in it ſelf equal to the ſame.362Two ſorts of Motion in the containing Veſſel may make the containing Water to riſe and fall.387An Accident in the Earths Motion impoſſible to be imitated.392ABSOLUTE MOTION: Things ſaid to move according to certain of their parts, and not according to their whole, may not be ſaid to move with an Abſolute Motion, but per accidens.491ANIMAL MOTION: The Diverſity of the Motions of Animals, depend on their Flex­ures.232The Flexures in Animals are not made for vary­ing of their Motions.232The Motions of Animals are of oneſort.232The Motions of Animals are all Circular.233Secondary Motion of Animals dependent on the firſt.233
1Animals would not grow weary of their Mo­tion, proceeding as that which is aſſigned to the Terreſtrial Globe.244The Cauſe of the wearineſſe that attends the Motion of Animals.244The Motion of an Animal is rather to be called Violent than Natural.244ANNUAL MOTION: The Annual Motionof the Earth muſt cauſe a conſtant and ſtrong Winde.228The Errour oſ the Antagoniſt of Copernicus is manifeſt, in that he declareth that the Annual and Diurnal Motion belonging to the Earth, are both one way, and not contrary.235The Annual Motion of the Earth mixing with the Motions of the other Planets, produce extravagant Appearances.296Reſt, Annual Motion, and the Diurnal, ought to be diſtributed betwixt the Sun, Earth, and Firmament.300Granting to the Earth the Annual, it muſt of heceſſity have the Diurnal Motion aſſigned to it.300The ſole Annual Motion of the Earth, cauſeth great inequality in the Motions of the Pla­nets.310A Demonſtration of the inequalities of the three ſuperiour Planets dependent on the Annual Motion of the Earth.310The Annual Motion of the Earth moſt apt to render a reaſon of the Exorbitance of the five Planets.312Argument of Tycho againſt the Annual Moti­on, from the invariable Elevation of the Pole.338Upon the Annual Motion oſ the Earth, alterati­on may enſue in ſome Fixed Stars, not in the Pole.341The Parallogiſme of thoſe who believe that in the Annual Motion great alterations are to be made about the Elevation of the Fixed Stars, is confuted.341Enquiry is made what mutations, and in what Stars, are to be diſcovered by means of the Earths Annual Motion.342Aſtronomers having omitted to inſtance what alterations thoſe are that may be derived from the Annual Motion of the Earth, do thereby teſtifie that they never rightly un­derſtood the ſame.343The Anuual Motion made by the Centre of the Earth under the Ecliptick, and the Diurnal Motion made by the Earth about its own Centre.344Objections againſt the Earths Annual Motiontaken from the Fixed Stars placed in the E­cliptick.345An Indice or Obſervation in the Fixed Stars like to that which is ſeen in the Planets, is an Ar­gument of the Earths Annual Motion.347The Suns Annual Motion how it cometh to paſſe, according to Copernicus.355The Annual and Diurnal Motion are conſiſtent in the Earth.362Three wayes of altering the proportion of the Additions of the Diurnal Revolution to the Annual Motion.409The Earths Annual Motion thorow the Ecliptick unequal, by reaſon of the Moons Motion.413The Cauſes of the inequality of the Additions and Subſtractions of the Diurnal Converſi­on from the Annual Motion.418CIRCULAR MOTION: Circular and Right Motion are ſimple, as proceeding in ſimple Lines.6The Circular Motion is never acquired Natural­ly, unleſſe Right Motion precede it.18Circular Motion perpetually uniforme.18In the Circular Motion every point in the Cir­cumference is the beginning and end.20Circular Motion onely is Uniforme.20Circular Motion may be continued pcrpetu­ally.20Circular Motion onely and Reſt are apt to con­ſerve Order.20To the Circular Motion no other Motion is con­trary.26Circular Motions are not contrary, according to Ariſtotle.100The Motion of the Parts of the Earth returning to their Whole, may be Circular.237The Velocity in the Circular Motion encreaſeth according to the encreaſe of the Diameter of the Circle.242Circular Motion is truly ſimple and perpetu­al.495Circular Motion belongeth to the Whole Bo­dy, and the Right to its Parts.496Circular and Right Motion are coincident, and may conſiſt together in the ſame Body.496COMMON MOTION: A notable Inſtance of Sagredus, to ſhew the non­operating of Common Motion.151An Experiment that ſheweth how the Com­mon Motion is imperceptible.224The concurrence of the Elements in a Com­mon Motion imports no more than their con­currence in a Common Reſt.239Common Motion is as if it never were.223, 340COMPRESSIVE MOTION: Compreſſive Motion is proper to Gravity, Extenſive to Levity.493
1CONTRARY MOTIONS: An Experi­ment which plainly ſhews that two Con­trary Motions may agree in the ſame Move­able.363The parts of a Circle regularly moved about its own Centre, move in diverſe times with Contrary Motions.389DESCENDING MOTION: The Inclination of Grave Bodies to the Motion of Deſcent, is e­qual to their reſiſtance to the Motion of Aſcent.191The Spaces paſt in the Deſcending Motion of the ſalling Grave Body, are as the Squares|of their times.198The Motion of Deſcent belongs not to the Ter­reſtrial Globe, but to its parts.362DIVRNAL MOTION: The Diurnal Motionſeemeth Commune to all the Univerſe, the Earth onely excepted.97Diurnal Motion why it ſhould more probably belong to the Earth than to the Reſt of the Univerſe.98The firſt Diſcourſe to prove that the Diurnal Motion belongs to the Earth.99The Diurnal Motion cauſeth no Mutation among Celeſtial Bodies, but all changes have relati­on to the Earth.100A ſecond Confirmation that|the Diurnal Moti­on belongs to the Earth.100A third Confirmation that the Diurnal Motionbelongs to the Earth.101A fourth, fiſth, and ſixth Confirmation that the Diurnal Motion belongs to the Eatth.102Aſeventh Confirmation that the Diurnal Mo­tion belongs to the Earth.103If the Diurnal Motion ſhould alter, the Annual Period would ceaſe.409LOCAL MOTION: Local Motion of three kinds, Right, Circular, and Mixt.6An entire and new Science of our Academick [Galileo] concerning Local Motion.198MIXT MOTION: Of Mixt Motion we ſee not the part that is Circular, becauſe we pertake thereof.218Ariſtotle granteth a Mixt Motion to Mixt Bodies.375The Motion of Mixt Bodies ought to be ſuch as may reſult from the Compoſition of the Mo­tions of the ſimple Bodies compounding.375NATVRAL MOTION: Accelleration of the Natural Motion of Graves is made according to the Odd Numbers beginning at Uni­ty.198Natural Motion changeth into that which is Preter­Natural and Violent.212PROGRESSIVE MOTION: The Progreſſive Motion may make the Water in a Veſſel to run to and fro.387RIGHT MOTION: Sometimes Simple, and ſometimes Mixt, according to Ariſtotle.8Right Motion impoſſible in the World exactly Ordinate.10Right Motion Naturally Infinite.10Right Motion Naturally Impoſſible.10Right Motion might poſſibly have been in the Firſt Chaos.11Right Motion is uſeful to reduce into Order things out of Order.11Right Motion cannot naturally be Perpetual.20Right Motion aſſigned to Natural Bodies, to re­duce them to perfect Order, when removed from their Places.20Right Motion of Grave Bodies manifeſt to Senſe.22Right Motion with more reaſon aſcribed to the Parts, than to the whole Elements.33Right Motion cannot be Eternal, and conſe­quently cannot be Natural to the Earth.117Right Motion ſeemeth to be wholly excluded in Nature.147With two Right Motions one cannot compoſe Circular Motions.375Right Motion belongeth to imperfect Bodies, and that are out of their Natural Places.495Right Motion is not Simple.495Right Motion is ever mixt with the Circular.495SIMPLE MOTION peculiar onely to Simple Bodies.494TERRESTRIAL MOTION collected from the Stars.229The Parts of the Terreſtrial Globe accelerate and retard in their Motion.388One ſingle Terreſtrial Motion ſufficeth not to produce the Ebbing and Flowing.421UNEVEN MOTION may make the Water in a Veſſel to Run to and fro.387The Mixture of the two Motions Annual and Diurnal, cauſeth the unevenneſſe in the Motion of the parts of the Terreſtrial Globe.390MOVE.Its queſtionable whether deſcending Bodies Move in a Right Line.21Ariſtotles Argument to prove that Grave Bodies Move with an inclination to arrive at the Centre.22Grave Bodies Move towards the Centre of the Centre of the Earth per Accidens.22Things forſaking the place which was natural ro them by Creation, are ſaid to Move violently,
1and naturally tend to return back to the ſame.492MOVEABLE, &c.A Moveable being in the ſtate of Reſt ſhall not move unleſſe it have an inclination to ſome particular Place.11The Moveable accellerates its Motion in going towards the Place whither it hath an inclina­tion.11The Moveable departing from Reſt goeth thorow all the Degrees of Tardity.11The Moveable doth not accelerate ſave only as it approacheth near to its terme of Reſt.12To introduce in a Moveable a certain Degree of Velocity, Nature made it to move in a Right Line.12The Moveable departing from Reſt paſſeth through all the Degrees of Velocity without ſtaying in any.13The Grave Moveable deſcending, acquireth Impetus ſufficient to re­carry it to the like height.13The Impetus of Moveables equally approaching to the Centre are equal.14Upon an Horizontal Plane the Moveable lyeth ſtill.14A ſingle Moveable hath but one only Natural Motion, and all the reſt are by participa­tion.103A Line deſcribed by a Moveable in its Natural Deſcent, the Motion of the Earth about its own Centre being preſuppoſed, would pro­bably be the Circumference of a Circle.145A Moveable falling from the top of a Tower moveth in the Circumference of a Circle.146A Moveable falling from a Tower moveth neither more nor leſſe, then if it had ſtaid alwayes there.146A Moveable falling from a Tower moveth with an Uniforme not an Accelerate Motion.146The Cadent Moveable, if it fall with a Degree of Velocity acquired in a like time with an Uniform Motion, it ſhall paſſe a ſpace double to that paſſed with the Accelerate Mo­tion.202Admirable Problems of Moveables deſcending by the Quadrant of a Circle, and thoſe deſcending by all the Chords of the whole Circle.412MUNDANE.Mundane Bodies were moved in the beginning in a Right Line, and afterwards circularly, according to Plato.11NNATURAL.That which is Violent cannot be Eternall, and that which is Eternal cannot be Natural.116NATURE, and Natures.Nature attempts not things impoſſible to be effected.10Nature never doth that by many things which may be done by a few.99Nature firſt made things as ſhe pleaſed, and afterwards capacitated Mans underſtanding for conceiving of them.238From Common Accidents one cannot know different Natures.238Natures Order is to make the leſſer Orbes to Cir­culate in ſhorter times, and the bigger in longer.243That which to us is hard to be underſtood, is with Nature caſie to be effected.403Nature keeping within the bounds aſſigned her, little careth that her Methods of opperating fall within the reach of Humane Capacity.433Natures Actions no leſs admirably diſcover God to us than Scripture Dictions.434NERVES.The Original of the Nerves according to Ariſto­tle, and according to Phyſitians.91The ridieulous Anſwer of a Phyloſopher deter­mining the Original of the Nerves.91OOBJECTS.Objects, the more Vigorous they are in Light, the more they do ſeem to encreaſe.305That Remote Objects appear ſo ſmall is the Defect of the Eye, as is demonſtrated.337In Objects far Remote and Luminous, a ſmall acceſſion or receſſion is imperceptible.350OPINIONS.It's all one, whether Opinions are new to Men, or Men new to Opinions.77ORBE, and Orbes.The greater Orbes make their Converſions in
1greater times.101 & 331It's more rational, that the Orbe containing and the Parts contained do move all about one Centre, than about divers.295PPASSIONS.Infinite Paſſions are perhaps but one onely.87PENDULUM, and Pendula.Pendula might have a perpetual Motion, impedi­ments being removed.203The Pendulum hanging at a longer thread maketh its Vibrations more ſeldome than the Pendu­lum hanging at a ſhorter.206The Vibrations of the ſame Pendulum are made with the ſame frequency, whether they be ſmall or great.206The cauſe which impedeth the Pendulum, and reduceth it to reſt.206The thread or Chain to which the Pendulum is faſtened maketh an Arch, and doth not ſtretch it ſelf ſtraight out in its Vibrations.207Two particular notable Accidents in the Pendulaand their Vibrations.411PERIPATETICK, &c.Peripatetick Phyloſophy unchangeable.42A brave reſolution of a certain PeripatetickPhiloſopher to prove the Right Line to be the ſhorteſt of all Lines.182The Paralogiſme of the ſaid Peripatetick who proveth Ignotum per ignotius.183The Diſcourſes of Peripateticks full of Errors and Contradictions.376The Peripateticks perſecuted Galileo out of envy to his happy Diſcoveries in Phyloſophy.427The Peripateticks in defect of Reaſons repair to Scripture for Arguments againſt their Adverſaries.429PHYLOSOPHERS.It is not juſt, that thoſe who never. Phyloſophate, ſhould uſurp the title of Phyloſophers.96PHYLOSOPHY.The Diſputes and Contradictions of Phyloſophersmay conduce to the benefit of Phyloſophy.25A cunning way to gather Phyloſophy out of any Book whatſoever.92PLANETS.The approximation and receſſion of the three ſuperiour Planets importeth double the Suns diſtance.299The difference of the Tlanets apparent Magni­tude leſſe in Saturn than in Jupiter, and leſſe in Jupiter than in Mars, and why.299The Station, Direction, and Retrogradation of the Planets is known in relation to the fixed Stars.347The particular Structures of the Orbes of the Planets not yet well reſolved.416The Planets places may more certainly be aſſigred by this Doctrine, than by that of Ptolomies great Almageſt.469PLATO.Plato held, that Humane underſtanding pertook of Divinity, becauſe it underſtood Num­bers.3Plato his Ænigma, and the Interpretation of it.498POLE.The invariable Elevation of the Pole urged as an Argument againſt the Annual Motion.338An Example to prove that the Altitude of the Pole ought not to vary by means of the Earths Annual Motion.340POWER.Of an infinite Power one would think a greater part ſhould rather be imployed than a leſſer.105PRINCIPLES.By denying Principles in Sciences, any Paradox may be maintained.28Contrary Principles cannot naturally reſide in the ſame Subject.211PROJECT, &c.The Project, according to Ariſtotle, is not mo­ved by virtue impreſſed, but by the Me­dium.130Operation of the Medium in continuing the Motion of the Project.131Many Experiments and Reaſons againſt the Motions of Projects aſſigned by Ariſtotle.132The Medium doth impede and not conferre the
1Motion of Projests.134An admirable accident in the Motion of Pro­jects.135Sundry curious Problems touching the Motion of Projects.137Projects continue their Motion by a Right Line that follows the direction of the Motion made together with the Projicient, whilſt they were conjoyned therewith.154The Motion impreſſed by the Projicient is onely in a Right Line.170The Project moveth by the Tangent of the Cir­cle of the Motion preceeding in the inſtant of Seperation.172A Grave Project aſſoon as it is ſeperated from the Projicient, beginneth to decline.173The Cauſe of the Projection encreaſeth not ac­cording to the Proportion of Velocity en­creaſed by making the Wheel bigger.189The Virtue which carrieth Grave Projects up­wards, is no leſſe Natural to them than the Gravity which moveth them down­wards.211PTOLOMY, &c.Inconveniences that are in the Syſtem of Pto­lomy.309Ptolomies Syſtem full of defects.476The Learned both of elder and later times diſ­ſatisfied with the Ptolomaick Syſtem.477PYTHAGORAS, &c.Pythagorick Miſtery of Numbers fabulous.3Pythagoras offered an Hecatombe for a Geo­metrical Demonſtration which he found.38Pythagoras and many other Ancients enumera­ted, that held the Earths Mobility.437 & 468RRAYS.Shining Objects ſeem fringed and environed with adventitious Rays.304RIST.Reſt. Vide Motion.Reſt the Infinite degree of Tardity.11RBTROGRADATIONS.Retrogradations more frequent in Saturn, leſſe fre quent in Jupiter, and yet leſſe in Mars, and why.311The Retrogradations of Venus and Mercury demonſtrated by Apollonius and Coper­nicus.311SSATURN.Saturn for its ſlowneſſe, and Mercury for its late appearing, were amongſt thoſe that were laſt obſerved.416SCARCITY.Scarcity and Plenty enhanſe and debaſe the price of all things.43SCHEINER.Chriſtopher Scheiner the Jefuit his Book of Con­cluſions confuted.78 & 195, & ſeque & 323A Canon Bullet would ſpend more than ſix dayes in falling from the Concave of the Moon to the Center of the Earth, according to Scheiner.195Chriſtopher Scheiner his Book entituled Apelles poſt Tabulam cenſured, and diſproved.313The Objections of Scheiner by way of Interro­gation.336Anſwers to the Interrogations of Schtiner.336Queſtions put to Scheiner, by which the weak­neſle of his is made appear.336SCIENCES.In Natural Sciences the Art of Oratory is of no uſe.40In Natural Sciences it is not neceſſary to ſeek Mathematical evidence.206SCRIPTURE, &c.The Caution we are to uſe in determining the Senſe of Scripture in difficult points of Phy­loſophy.427Scripture ſtudiouſly condeſcendeth to the ap­prehenſion of the Vulgar.432In dicuſſing of Natural Queſtions, we ought not to begin at Scripture, but at Senſible Experiments and Neceſſary Demonſtra­tions.433The intent of Scripture is by its Authority to recommend thoſe Truths to our beliefe, which being un­intelligible, could no other wayes be rendered credible.434
1Scripture Authority to be preferred, even in Na­tural Controverſies to ſuch Sciences as are not confined to a Demonſtrative Me­thod.434The Pen­men of Scripture, though read in A­ſtronomy, intentionally forbear to teach us anything of the Nature of the Stars.435The Spirit had no intent at the Writing of the Scripture, to teach us whether the Earth mo­veth or ſtandeth ſtill, as nothing concerning our Salvation.436Inconveniencies that ariſe from licentious u­ſurping of Scripture, to ſtuffe out Books that treat of Nat. Arguments.438The Literal Senſe of Scripture joyned with the univerſal conſent of the Fathers, is to be re­ceived without farther diſpute444A Text of Scripture ought no leſſe diligently to be reconciled with a Demonſtrated Pro­poſition in Philoſophy, than with another Text of Scripture ſounding to a contrary Senſe.446Demonſtrated Truth ought to aſſiſt the Com­mentator in finding the true Senſe of Scrip­ture.446It was neceſſary by way of condeſcenſion to Vulgar Capacities, that the Scripture ſhould ſpeak of the Reſt and Motion of the Sun and Earth in the ſame manner that it doth.447Not onely the Incapacity of the Vulgar, but the Current Opinion of thoſe times, made the Sacred Writers of the Scripture to ac­commodate themſelves to Popular Eſteem more than Truth.447The Scripture had much more reaſon to affirm the Sun Moveable, and the Earth Immove­able, than otherwiſe.448Circumſpection of the Fathers about impoſing poſitive Senſes on Doubtful Texts of Scrip­ture.451Tis Cowardice makes the Anti­Copernican fly to Scripture Authorities, thinking thereby to affright their Adverſaries.455Scripture ſpeaks in Vulgar and Common Points after the manner of Men.462The intent of Scripture is to be obſerved in Pla­ces that ſeem to affirme the Earths Stabi­lity.464Scripture Authorities that ſeem to affirm the Mo­tion of the Sun and Stability of the Earth, divided into ſix Claſſes.478Six Maximes to be obſerved in Expounding Dark Texts of Scripture.481Scripture Texts ſpeaking of things inconveni­ent to be underſtood in their Literal Senſe, are to be interpreted one of the four wayes named.81Why the Sacred Scripture accommodates it ſelf to the Senſe of the Vulgar.487SEA.The Seas Surface would ſhew at a diſtance more obſcure than the Land.49The Seas Reflection of Light much weaker than that of the Earth.81The Iſles are tokens of the unevenneſſe of the Bottoms of Seas.383SELEUCUS.Opinion of Seleucus the Mathematician cen­ſured.422SENSE.He who denieth Senſe, deſerves to be deprived of it.21Senſe ſheweth that things Grave move ad Me­dium, and the Light to the Concave.21It is not probable that God who gave us our Senſes, would have us lay them aſide, and look for other Proofs for ſuch Natural Points as Senſe ſets before our Eyes.434Senſe and Reaſon leſſe certain than Faith.475SILVER.Silver burniſhed appears much more obſcure than the unburniſhed, and why.64SIMPLICIUS.Simplicius his Declamation.43SOCRATES.The Anſwer of the Oracle true in judging So­crates the Wiſeſt of his time.85SORITES.The Forked Sylogiſme called Sοπειτες29SPEAKING.We cannot abſtract our manner of Speakingfrom our Senſe of Seeing.461SPHERE.The Motion of 24 hours aſcribed to the Higheſt
1Sphere, diſorders the Period of the Inferi­our.102The Sphere although Material, toucheth the Material Plane but in one point onely.182The Definition of the Sphere.182A Demonſtration that the Sphere toucheth the Plane but in one point.183Why the Sphere in abſtract toucheth the Plane onely in one point, and not the Material in Concrete.184Contact in a Single Point is not peculiar to the perfect Sphere onely, but belongeth to all Curved Figures.185In a Moveable Sphere it ſeemeth more reaſona­ble that its Centre be ſtable, than any of its parts.300SPHERE of Activity.The Sphere of Activity greater in Celeſtial Bo­dies than in Elimentary.59STARRY SPHERE.Wearineſſe more to be feared in the Starry Spherethan in the Terreſtrial Globe.245By the proportion of Jupiter and of Mars, the Starry Sphere is found to be yet more re­mote.331Vanity of thoſe mens diſcourſe, who argue the Starry Sphere to be too vaſt in the Coper­nican Hypotheſis.335The whole Starry Sphere beheld from a great di­ſtance, might appear as ſmall as one ſingle Star.335SPHERICAL.The Spherical Figure is eaſier to be made than any other.186Spherical Figures of ſundry Magnitudes, may be made with one ſole Inſtrument.187SPIRIT.The Spirit had no intent to teach us whether the Earth moveth or ſtandeth ſtill, as no­thing concerning our Salvation.436SOLAR SPOTS.Spots generate and diſſolve in the face of the Sun.38Sundry Opinions touching the Solar Spots.39An Argument that neceſſarily proveth the So­lar Spots to generate and diſſolve.40A concluſive Demonſtration to prove that the Spots are contiguous to the Body of the Sun.41The Motion of the Spots towards the Circum­cumference of the Sun appears ſlow.41The Figure of the Spots towards the Circumfe­rence of the Suns Diſcus, appear narrow, and why.41The Solar Spots are not Spherical, but flat, like thin plates.41The Hiſtory of the proceedings of the Acade­mian for a long time about the Obſervation of the Solas Spots.312A conceit that ſuddenly came into the mind of our Academian concerning the great conſe­quence that followeth upon the Motion of the Solar Spots.314Extravagant Mutations to be obſerved in the Motions of the Solar Spots foreſeen by the Academick, in caſe the Earth had the Annu­al Motion.314The firſt Accident to be obſerved in the Moti­on of the Solar Spots, and conſequently all the reſt, explained.315The events being obſerved were anſwerable to the Predictions touching theſe Spots.318Though the Annual Motion aſſigned to the Earth, anſwereth to the Phænomena of the Solar Spots, yet doth it not follow by conver­ſion, that from the Phænomena of the Spotsone may inferre the Annual Motion to be­long to the Earth.319The Pure Peripatetick Philoſophers will laugh at the Spots and their Phænomena, as the Illuſions of the Chriſtals in the Tele­ſcope.319The Solar Spots of Galileo.494STAR and Stars.The Stars infinitely ſurpaſſe the reſt of Heaven in Denſity.30It is no leſſe impoſſible for a Star to corrupt, than the whole Terreſtrial Globe.37New Stars diſcovered in Heaven.38The ſmall Body of a Star fringed about with Rays, appeareth very much bigger than plain, naked, and in its native Clarity.61An eaſie Experiment that ſheweth the encreaſe in the Stars, by means of the Adventitious Rays.305A Star of the Sixth Magnitude ſuppoſed by Ty­cho and Scheiner an hundred and ſix Millions of times bigger than needs.326A common errour of all Aſtronomers touching the Magnitude of the Stars.326
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1 a falſe one, none.112. 245TRUTH, and Truths.Untruths cannot be Demonſtrated as Truthsare.112The Truth ſometimes gains ſtrength by Con­tradiction.181Truth hath not ſo little light as not to be diſco­vered amongſt the Umbrages of Fal­ſhoods.384TYCHO.The Argument of Tycho grounded upon a falſe Hypotheſis.324Tycho and his Followers never attempted to ſee whether there were any Phænomena in the Firmament for or againſt the Annual Mo­tion.337Tycho and others argue againſt the Annual Mo­tion, from the invariable Elevation of the Pole.338VVELOCITY.Vniform Velocity ſutable with Circular Mo­tion.12Nature doth not immediately conferre a de­terminate degree of Velocity, although She could.12The Velocity by the inclining plane equal to the Velocity by the Perpendicular, and the Mo­tion by the Perpendicular ſwifter than by the inclining plane.14Velocities are ſaid to be equal, when the Spa­ces paſſed are proportionate to their times.15The greater Velocity exactly compenſates the greater Gravity.192VENUS.The Mutation of Figure in Venus argueth its Motion to be about the Sun.295Veuus very great towards the Veſpertine Con­junction, and very ſmall towards the Ma­cutine.297Venus neceſſarily proved to move about the Sun.298The Phænomena of Venus appear contrary to the Syſtem of Copernicus.302Another Difficulty raiſed by Venus againſt Co­pernicus.302Venus according to Copernicus either lucid in it ſelf, or a tranſparent ſubſtance.302The Reaſon why Venus and Mars do not ap­pear to vary Magnitude ſo much as is re­quiſite.303A ſecond Reaſon of the ſmall apparent encreale of Venus.306Venus renders the Errour of Aſtronomers in de­termining the Magnitude of Stars inex­cuſeable.327VESSEL.Of the Motion of Water in a Veſſel. Vide Water.UNDERSTAND, &c.Man Underſtandeth very much intenſive, but little extenſive.86Humane Uuderſtanding operates by Ratioci­nation.87UNIVERSE.The Conſtitution of the Uuiverſe is one of the Nobleſt Problems a Man can ſtudy.187The Centre of the Univerſe according to Ari­ſtotle is that Polnt about which the Cele­ſtial Spheres do revolve.294Which ought to be accounted the Sphere of the Univerſe.299It is a great raſhneſſe to cenſure that to be ſu­perfluous in the Univerſe which we do not perceive to be made for us.334VURSTITIUS.Chriſtianus Vurſtitius read certain Lectures touching the Opinion of Copernicus, and what happened thereupon.110WWATER.He that had not heard of the Element of Water,could never fancie to himſelf Ships and Fi­ſhes.47An Experiment to prove the Reflection of Wa­ter lefs bright than that of the Land.81The Motion of the Water in Ebbing and Flow­ing, not interrupted by Reſt.251The vain Argumentation of ſome, to prove the Element of Water to be of a Spherical Superficies.377
1The Progreſſive and uneven Motion makes the Water in a Veſſel to run to and fro.387The Several Motions in the conteining Veſſel, may make the conteined Water to riſe and fall.387The Water raiſed in one end of the Veſſel re­turneth it ſelf to Æquilibrium.391In the ſhorter Veſſels the Undulations of Wa­ters are more frequent.391The greater profundity maketh the Undulati­ons of Water the more frequent.391Why in narrow places the Courſe of the Wa­ters is ſwifter than in larger.396The cauſe why in ſome narrow Chanels, we ſee the Sea­Waters run alwayes one way.398The Water more apt to conſerve an Impetus conceived than the Air.400The Motion of the Water dependeth on the Motion of Heaven.404WEIGHTS.Its queſtionable whether Deſcending Weightsmove in a Right Line.21WEST.The Courſe to the West India's eaſie, the re­turn difficult.402WINDE.Conſtant Gales of Winde within the Tropicks blow towards the Weſt.402Windes from the Land, make rough the Seas.402WISDOME Divine.Divine Wiſdome infinitely infinite.85The Diſcourſes which Humane Reaſon makes in time, the Divine Wiſdom reſolveth in a Moment, that is hath them alwayes pre­ſent.87WIT.The Wit of Man admirably acute.87The Puſilanimity of Popular Wits.364Poctick Wits of two kinds.384WORLD.World. Vide Univerſe.The Worlds parts are according to Ariſtotle two, Celeſtial and Elementary, contrary to each other.6The World ſuppoſed by the Anthour [Galileo] to be perfectly Ordinate.10The Senſible World.96It hath not been hitherto proved by any whe­ther the World be finite or infinite.293If the Centre of the World be the ſame with that about which the Planets move, the Sun and not the Earth is placed in it.295WRITING.Some Write what they underſtand not, and therefore underſtand not what they Write.63The Invention of Writing Stupendious above all others.88YYEAR.The Years beginning and ending, which Ptolomy and his Followers could never poſitively aſ­ſign, is exactly determined by the Coper­nican Hypotheſis.469
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The ERRATA of the firſt PART of the firſt TOME.
line 31. for where leave, read why omit. p 3, l 32, only for. p 5, l 8, Dimenſions of a Superficies, ibid. l 15, for line r. thread, l ult.
for on all ſides, r. every way. p 6, l 41, by neceſſary. p 9, l 15, for Medium, r. Way. l 40. for ſome r. ſave, marg and the. p 10, l 1. farther be
l 28. intigrall, l 44, prefixed. p 11, 19, oppoſitely might have. l 10, conſtituted Bodie. l 11, ſo are. l 15, would only enſue. p 12, l 28,
doth, p 14, l 25. inclined plane. l 16. p 34, for by r. through. p 17, l 20, beyond T, p 19, l 3, dele of. l 6, for of aſſigning, r. that he
aſſigned. l 9, for and with the &c. r. and given them the intended inclinations of moving thence towards the Centre. l 15, for Orbes,
r. Globes, l 38, for truly r. exactly. p 21, l 36, for another, r. one. p 22, l 19, that contra, l 20. for than contend with you, r. than as being.
convinced by the ſtrength of your Reaſons. p 23, 18. for to diſcover, r. to be ſhowne, l 17, ſuppoſing. l 22, for follow, r. hit upon. l 52, as
you well underſtand. p 24, l 17, for thither r. there. l 33, r. Earth aſcend and deſcend. p 25, l 7, for quality r. power. l ult. part. p 26,
l 9. contraries; But of contraries the motions are contrary, l 32, for beſides r. in caſe. p 27, l 2, for repeat, r. go over. l 3. for reaſſume, r.
repeat. p 29, l ult. for ſay r. mean. l 18, reſide. l 39, for may. r. can. p 32, l 1, for others, r. one. l 15, for the beſt we can whether, r. whats to
be done with it in caſe that. l 37, for they muſt grant us, r. let it be granted, p 32, l 5, what. l 12, unalterable. p 37, l 28, for confront r.
preferre. l 37, for bethink, r. think, p 41. l 39, for obſerve them to be hid, r. observe that he hath concealed from you thoſe that are
diſſolved. p 42, l 17. which experience and ſenſe. l 17, unalterable. p 43, l 15, for more r. leſſe. p 44. l 4, Globes? p 46, l 18, r. liquifie,
for them r. it, p 49. l 11, for thing r. thinke. p 50, l 19. and p 51, l 3, Superficies p 53, l 14, Truths. p 54, l 38, be ſolid. p 55, l 15,
ult. l 36, of the. l 40, omit ſo. p 57, l 44, maketh, p 59, l 1, for that r. the. p 61, l 5, thoſe. p 62, l 6, diſperſe. p 64, l 13, evene. l 26,
change. l 37, for of, r. in. l 42, acquieſſe. p 65. l 20, happeneth. p 67, l 13, Solutions, l 15, viſive. p 69, l 18, wood?. l 31, wayes,. p 70, l 7,
concluſion is very good for, l 10, ſhould we, l 11, would alter. l 12, for or, r. and, l 22, Propoſitions, l 29, Protubrances, l 41, for their, r. its.
p. 71, l 5, by one dele;. l 12, of the Moon, l 37, for in youes, &c. r. with your Opacity and Perſpicuity. p 72, l 20, what time do.
for p 74. r. 73. l 26, yea and more. p 76, l 18, Vitellio. p 81, l 6, dele more. p 81, l 25, of a fluid matter, l 29, for ſentence r. Centre. for on
r. one. p 85, l 39, for make raiſins, r. make the kernels, p 86, l 29 intenſivè, p 87, l 17, the which, neither,. p. 88. l. 8. Raffaelio, or a Tiziano?
p 90. l 20. for receſſe r. remote. p 91. l 11, curioſity. p 94. l 41. reputation. p 101, l 18, altercations. p 107, l 29, ſtar. p 104, l 32,
naturally. p 107, l 26, accidens. p 111, l 24, ſelfe, l 18, third teime, p. 113, l 21, Guns. p 111, l 3, tranſported, l. 7, we paſſe. p 116, l 15,
otherwiſe r. any wayes. p 118, Marg. rendred, p 128, 35, aſcending?. p 130, l 42, as being the. p 131, l 19, occaſion, l 30, ſeparated.
3, l 11, pendula. p 134, ll 20, arows? p 135, l 12, time to prove it,. p 137, l 2, and 6, for ball, r. bowl. p 142, l 17, dele very. p 143, l 3,
l, l 4, liberty. p 144, l 8, find out. p 145, l 21, dele;. p 147, l 9, dele that. p 148, l 7, which ſo far exceeds their flight, l 33, is the. l ult.
moment of. p 149, l 44, Tycho. p 153, l 21, for that is r. or. p 154. 3. dele of. p 157, l 7, for to the, r. by the. p 161, l 15, fifteen ſeconds:
Marg in its reſt. p 162, l 13, for motion r. Immobility. p. 163, l 30, like. p 164, l 22, ſeeing. l 31, for as great as, r no greater than. 166,
l 24, poope, l 40, Aufractions. p 175, l 26, ſpeak. p 177, l 13, contraſt. p 184, l 15, for becauſe it cannot, r. why may it not?. p 185, l 6, 7, is
Marg Sphere. p 188. l 19 freind. p 190, l 28. for give leave, r. permit. p 191, l 17, for on, r. one. l 31. ſee you. p 193, l 21, Vertigo?
p 197, l 1, ſubject. p 200, l 36, dele that, p 201, l 21, pace, l 35, will profeſſe, with. p 203, l 6, dele ſo, l 31, diminiſheth, l 33, degrees. p
104, l 14, dele and. p 206, l 19, and 44. Pendula, p 212, l 14, dele it. p 216, l ult. propieres. p 219, 10, for to theſe that, r. ſeeing that to theſe.
p 220, l 12, what. p 221, l 2, than an. l 222, 6, us take. p 224, 37, for that to r. that for. 225, 25, invented it, 227, 9, that the 229, l 6, dele
either. l 18, dele and wee, l 45, for From, r. By. p 230, l 14, in the. p. 232. l 41. augre, p 233, l 22, inarticulate. p 234, l 20, for were of, r.
were with. p 233, l 6, the error, l 14, revolve. p 240, l 40, virtue; amongſt. l 41, for Mars, &c. r. Mars. l 44, more ſuiting. p 224, l 44,
r.contrary. p 245, l 10, interfere. p 250, l 44, dele being. p 252, l 26, mainteined. p 254, l 7, it was, l 43, uphold. p 258, l 8, ſelfe. p 259, l 9,
being p 260, l 35, calculations. p 61, l 16, interfering. l 15. if not. p 264, l 11, ſame that you do, line 18, rather than. p 266, l 8, I make. p 267,
l 24 Buſchins. p 266, l 16, r. 40 min. pr. p 272, l 20, r. B G, is 42657. p 272. l 29, of the ^{*} 67^{d} 36. p 274, l 32, every. p 275. l 25, halfe ſo
p 277, l 18, and 37, r. B.D. Chord. p 281, l 30. r. 540. ­­­­­540 00. p. 285, l. 8. r. been the, l 38, ſay of: l 39, circà. p 286, l 24, than: BP, PB.
being bigger than P D. p 287, l 4, ſee, l 33, 582 ­­­­100000. p 288, l 21, r. 276, quep 289 l 32, ſpake. p, 290, for p. 274. r. 290. l 12. they kept.
p 291, l 8, uncertain, l 37, Braces, l 42, breadth. p 292, l 6. dele the other ar. p 244. l 23, Peripateticks ­­­­­, p 295. l 1. figure, and morning­
p 297, l 11, oppoſition, marg r. veſpertine conjunction. p 298. l 23, argument and. p 301, l 1, your, l 30, are yet p. 304, l 9, and allured, marg
 enlarged ſoe. p 305, l 27, we leave. p 306, l 25, it ought. p 307, for 330, r. 307. l 10, digreſſions, l 16, diſcus. l 32, years, together, with, l 34,
Jovial, l 41, alwayes all lucid. p 308, for 394, r. 308. p 309, for 395, r. 309. l in it. l 34, ſole and ſingle p 310, l 11, CD. DE. EF. p 312. l 19,
shaking off, l 19, matters that. p 314, l 8, & 10, Ecliptick. in 316, l 5, nor, l FG: whereupon p 319, l 7, circuition,
l 31, that he hath. p 220, l 31, extreme Terminator. p 124. l 30, Solar Globe, p 322. l 40. thoſe Phyſical and. p 324, l 20, ſaith that, l 29
Copernicus ſaith. p 329, l 39, this ſecond. marg. to be the ſame. p. 332, l 24, below it. p 333, l 17, ſtar, that. p 335, l 24, ſtar now, marg. called
small in. p 338, l 41, Into this l 24, now, no not for an. l 28, follow thereupon, l 31, point equidiſtant. p 341, l 10, out
till l 18, yet the force (which. p 342, l 25, Orbe; ſo, p 343, l 21, be ſeen, l 33, Latitudes and, l 38, ours, l 91, greater varieth. p 344, l 39, and,
that. p 345. l 23. Cancer and Capricorn, p 347, l 1, feinedly, l 30, Stars are. p 349, l 35, [in Fig. 9.]. p 350, l 42, knew. p 355. l 12, Weſt to
ſt. p 356, l 15, G N. p 360, l 38, circle l K. p 382, l 30, the propenſion. marg. librated body. p 363, l 3, Experiment, l 7, baſon ſhall. p 364, l 2 of William, l 17, them as, l 38, that, think. p 366, l 14, and 39, ſtived. p 367, l. that this, p 370, l 3, do that for natural, l 12, appli­
cation of a perſon to. p 372, l ult. thoſe. p 373, l 17, than if, l 39, Launes, Woods, l 43, whither, p 374, l 16, dele ſelfe. p 375, l 28. ſtreight
motion is peculiar, l 39, and an. p 376, l 5, (For, l 6, together, l 12, granted ought, p 380, l 1, dele hath. l 5, a mutual, l 6, Indices, l 45, admit.
p 381, l 36, which with, ibid. dele with. p 382, l 3, place), l 13, extremities. p 384, l 3. write of, l 29, SALU. p 385, l 18, more, in l 13, againſt
the l 24, ſwagg, l 37, reply, p 386, l 16, as if it. p. 387, l 33, Water, conteined. p 389, l 43, at the. p 290 l 22, that the diurnall litle. p 391,
11, grow even, it, l 13, Æquilibrium, but. p 392, l 35, unitedly, equally. p 394, l 16, velocity, when. p 396, l 11, Sardigna p 397, l 38, returns.
p399, l 30, is free. p 401, l 10, pound you, l 13, and argument. p 402, l 25, alledged that, l 37, interruptions for. p 405, l 19, contact, l 37,
at in a Sea only which, l penult. ordinate. p 205, l 38, concern. p 407, l 3, for ſpeculation and the, l 8, light, with, l 23, at thoſe, l 28,
showwings, conſiſteth, l 42, from the, l penult, ſubſtractions that, l ult. maketh to or from. p 48, l 4, proportion in, l 14, leſſer, ſo as that, p
409, l 12, ſwift, p 411, l 24 circles marg, pendula, p 412, l 27, ſubtend, p 413, l 14, projected, l 24, conſume, l 93, is, contracted, l 34, of in the
p 441, l 3, differs, l 5, Moon about, l 21, Orb, by. p 415, l 4, do either with. p 416, l 8, ran, l 11, Excentricks, l 13, apparitions, how, l 33,
cliptick divided, l 44, on account. p 417, l 43, on which. p 418, l 4, inequalities. p 419, l 12, dele therefore. p 430, l 33, Anomalies,
l 45, tracts. p 421,, l 4, Weſtern. p 423, l 41, dele in. p 425, l 16, GALILEO GALILEI p 428, l 32, theſe. p 430, l 27, from its. p 431, marg.
parum, ibid. marg. de iis. p 432, l 39, corporeal. p 433, l 26, dele in, l 37, appearance and. p 435, marg. Cœli eſſe, l 27, Spirit of God who
pake by them. p 430, l 34, tatling p 440, l 40, propoſe. p 443, l 2, interfere. p 445, l 34, dele with. p 448, l 14, but. p 449, l 27, make reflection.
p 450, marg. & Sanctœ, l 42, ſtood ſtill,. p 451, l 37, her curſes. p 453, marg. l 13, evoluerit. p 454, l 29, Lap. Your. marg. l 6, prœſumptores,
ſatis, l 14, auctoritate non tenentur, ad deſcendendum id, quod leviſſima temeritate, &. p 451, l 27, or at leaſt the. p 456, l 47, in marg In
Epist ad Polycarpum. p 463, l 17, Stabil try. p 454, l ult. riſe, p 468, l 25, motion. p 467, l 26, Sacred, is the Inquiſition. p 469,
l 4, Almageſt. p 471, l 28, Si quis. p 475, l 12, Credit. l 19, Antlents. p 476, l 9, Deferents, l 33, and in a word. p 477, l 10, Nicetas. p 478, l 1,
Hypotheſes), l 5, dece of, l 19, Galileo Galilei, l 21, Invinſible, l 23, who. p 481, l 26, or thats incommenſurate, l 33, vulgar mode of, p 482
l 7, grieveth. p 485, l 18, ſuch that having, p 487, l 3, ſtay: and. p 488, l 41, Edification, leſt undecided in Holy Scripture. p 491, l 15,
Alterations. p 492, l 30, keeps, marg Æthereal Earth. p 493, l 17, that that. p 495, l 27, frees them. p 500, marg Authors are not agreed,
p 582, l 30, Holy Ghoſt hath.
1
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1
MATHEMATICAL
COLLECTIONS
AND
TRANSLATIONS:
THE SECOND
TOME.
THE SECOND PART,
Containing,
D. BENEDICTUS CASTELLUS, his DISCOURSE
of the MENSURATION of RUN­
NING WATERS.
His Geometrical DEMONSTRATIONS of
the Meaſure of RUNNING WATERS.
I. His LETTERS and CONSIDERATIONS
touching the Draining of FENNS, Diverſions of
RIVERS, &c.
V. D. CORSINUS, His RELATION of the ſtate of the
Inundations, &c. in the Territories of BOLOGNA,
and FERRARA.
By THOMAS SALUSBURY, Eſque
LONDON,
Printed by WILLIAM LEYBOURNE, MDCLXI.
1
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1
OF THE
MENSURATION
OF
RUNNING WATERS.
An Excellent Piece
Written in ITALIAN
BY
DON BENEDETTO CASTELLI,
Abbot of St. BENEDETTO ALOYSIO,
and Profeſſour of the Mathematicks to
Pope URBAN VIII. in ROME.
Engliſhed from the Third and beſt Edition, with
the addition of a Second Book not before extant:
By THOMAS SALUSBURY.
LONDON,
Printed by WILLIAM LEYBOURN, 1661.
1
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1
THE
AUTHOURS EPISTLE
TO
Pope VRBAN VIII.
I lay at the Feet of your Ho­
lineſſe theſe my Conſide­
rations concerning the
MENSURATION OF
RUNNING WATERS:
Wherein if I ſhall have ſucceeded, being a
matter ſo difficult and unhandled by Wri­
ters both Ancient Modern, the diſcovery of
any thing of truth hath been the Effect of
Your Holineſſes Command; and if through
inability I have miſſed the Mark, the ſame
1Command will ſerve me for an Excuſe with
Men of better Judgment, and more eſpeci­
ally with Your Holineſſe, to whom I humbly
proſtrate my ſelf, and kiſſe Your Sacred
Feet.
From ROME.
Your Holineſſes
Moſt humble Servant
BENEDETTO.
A Monk of Caſſino.
1
AN
ACCOUNT
OF THE
Authour and Work.
DON BENEDETTO CASTELLI,
the famous Authour of theſe enſuing
Diſcourſes of the Menſuration of
Running Waters, is deſcended from
the Worſhipful FAMILY of the
GASTELLII, and took his
firſt breath near to the lake THR A­
SIMENVS, (where Hanibal gave
a fatal overthrow to the Roman
Legions) in that ſweet and fertile part
of happy ITALY, called the Territory
of PERUGIA, a branch of the Dukedome of TUSCANY, which
at preſent ſubmitteth to the Juriſdiction of the Church, as being a
part of St. PETER'S Patrimony. His Parents, who were more
zealous of the good of his Soul than obſervant of the Propenſion of
his Genius, dedicated him (according to the Devotion of that Coun­
try) to the Service of the Church; and entered him into the Flou­
riſhing Order of Black-Friers, called from the place Moncks
of Monte Caſino, and from the Founder Benedictines. Na­
ture, that She might conſummate the Profuſion of her Fa­
vours upon him, ſent him into the World in an Age that was ſo
ennobled and illuminated with Eminent Scholars in all Kinds of
Literature, that hardly any Century ſince the Creation can boaſt
the like.
1
§. In particular, the SCIENCES MATHEMATI­
CAL had then got that Fame and Eſteem in the Learned World,
that all men of Spirit or Quality became either Students in, or
Patrons of thoſe Sublime Knowledges. On this occaſion the Curi­
oſity of our AUTHOUR being awakened, his Active Wit
could not endure to be any longer confined to the Slaviſh Tuition
of Hermetical Pedagogues; but in concurrence with the Genius
of the Age, he alſo betook himſelf to thoſe moſt Generous and
Liberal Studies. His helps in this his deſign were ſo many, and
ſo extraordinary, that had his Inclination been weaker, or his
Apprehenſion leſſer, he could hardly have failed attaining more
than a Common Eminency in theſe Sciences. For beſides the De­
luge of Learned and Vſeful Books, which the Preſſe at that
time ſent forth from all parts of EUROPE, he had the good
Fortune to fall into the Acquaintance, and under the Inſtruction
of the moſt Demonſtrative and moſt Familiar Man in the World,
the Famous GALILEO: whoſe ſucceſſe being no leſſe upon
this his Pupil than upon the reſt of thoſe Illuſtrious and Ingeni­
ous Perſons that reſorted from all parts to ſit under his Admi­
rable Lectures, he in a ſhort time attained to that Name in the
Mathematicks, that he was invited to ROME, Complemen­
ted, and Preferred by his then Holineſſe the Eighth URBAN,
upon his very firſt Acceſſion to the Papacy, which was in the
Year 1623.
§. This Pope being moved with a Paternal Providence for the
Concerns of his Subjects in that part of ITALY about BO­
LOGNA, FERRARA, and COMMACHIO, ly­
ing between the Rivers of PO and RENO, which is part of
Lo Stato della Chieſa, or the Church Patrimony, appoints this
our CASTELLI in the Year 1625, to accompany the Right
Honourable Monſignore GORSINI (a moſt obſervant and
intelligent perſon in theſe affaires, and at that time Superinten­
dent of the General Draines, and Preſident of ROMAGNA)
in the Grand Viſitation which he was then ordered to make con­
cerning the diſorders occaſioned by the Waters of thoſe parts.
§. CASTELLI, having now an Opportunity to employ,
yea more, to improve ſuch Notions as he had imbued from the
Lectures of his Excellent MASTER, falls to his work with
all induſtry: and in the time that his Occaſions detained him in
ROMAGNA he perfected the Firſt Book of this his Diſ­
courſe concerning the Menſuration of Running Waters. He con­
feſſeth that he had ſome years before applyed himſelf to this part
of Practical Geometry, and from ſeveral Obſervations collected
part of that Doctrine which at this time he put into Method, and
which had procured him the Repute of ſo much Skill that he began
1to be Courted by ſundry Princes, and great Prelates. In particu­
lar about the beginning of the Year 1623. and before his Invita­
tion to ROME he was employed by Prince Ferdinando I, Grand
Duke of TUSCANY, to remedy the Diſorders which at that
time happened in the Valley of PISA in the Meadows that lye
upon the Banks of Serchio and Fiume Morto: and in the pre­
ſence of the Grand Duke, Grand Dutcheſſe Mother, the Commiſ­
ſioners of Sewers, and ſundry other Perſons in a few hours he
made ſo great a progreſſe in that affair, as gave his Moſt Serene
Highneſſe high ſatisfaction, and gained himſelf much Honour.
§. No ſooner had he in his fore-mentioned Voiage to RO­
MAGNA (which was but few Moneths after, in the ſame
Year) committed his Conceptions to paper, but he communicated
them to certain of his Friends. In which number we finde Signo­
re Ciampoli Secretary of the Popes Private Affaires; whom in
the beginning of the Firſt Book he gratefully acknowledgeth to
have been contributary, in his Purſe, towards defraying the
charge of Experiments, and in his Perſon, towards the debating
and compleating of Arguments upon this Subject. Some few years
after the Importunity of Friends, and the Zeal he had for the
Publique Good prevailed with him to preſent the World with his
Firſt Diſcourſe, accompanied with a Treatiſe of the Geometrical
Demonſtrations of his whole Doctrine. What Reception it found
with the Judicious muſt needs be imagined by any one that hath
obſerved how Novelty and Facility in conjunction with Verity
make a Charm of irreſiſtable Operation.
§. New it was, for that no man before him had ever attemp­
ted to Demonſtrate all the three Dimenſions, to wit, the Length,
Breadth and Profundity, of this Fluid and Current Ele­
ment. And he detecteth ſuch groſſe Errours in thoſe few that
had untertook to write upon the Subject (of which he inſtan­
ceth in Frontinus and Fontana, as thoſe that include the rest)
and delivereth ſuch ſingular and unheard-of Paradoxes (for ſo
they ſound in Vulgar Eares) as cannot but procure unſpeakable
delight to his Reader.
§. Eafie it is likewiſe and True; and that upon ſo Familiar
Experiments and Manifeſt Demonſtrations, that I have oft que­
ſtioned with my ſelf which merited the greater wonder, he, for
diſcovering, or all men that handled the Argument before him
for not diſcovering a Doctrine of ſuch ſtrange Facility and Infal­
libility. But yet as if our Authour deſigned to oblige the whole
World to him by ſo excellent a Preſent, he ſelects a Subject that
he knew would be carreſſed by all perſons of Nobler Souls, upon
the accounts afore-named, and by all Mankind in General, as
gratifying them in their much adored Idol Utility. And to ren-
1der his Art the more profitable, he reduceth the lofty, and eaſie-to­
be-miſtaken Speculations of the Theory, into certain and facile
Directions for Practice; teaching us how to prevent and repaire
the Breaches of Seas, and Inundations of Rivers; to draine
and recover Fenns and Marches; to divert, conveigh and di­
ſtribute Waters for the Flowing and Stercoration of Grounds,
ſtrengthening of Fortifications, ſerving of Aquaducts, preſer­
ving of Health (by cleanſing Streets, and ſcowring Sewers) and
maintaining of Commerſe (by defending Bridges, cleering Ri­
vers, and opening Ports and Channels) with innumerable other
Benefits of the like nature. And, that I may omit no circumſtance
that may recommend my Authour, the Fortune of this his Trea­
tiſe hath been ſuch, that as if he intended a Plus ultra by it,
or as if all men deſpaired to out-do it, or laſtly, as if CA­
STELLI hath been ſo great a Maſter that none have preſu­
med to take Pencil in hand for the finiſhing of what he Pour­
foild, this ſmall Tract like the Arabian Phœnix (of which it is
ſaid Unica ſemper Avis) did for ſeveral years together continue
ſingle in the World, till that to verifie it to be truly Phœnician,
it renewed its Age by undergoing a ſecond Impreſſion. And as if
this did not make out the Immortal vertue of it, it hath had
Anno 1660 a third Circulation, and riſen in this laſt Edition as
it were from the Vrne of its Authour; and that ſo improved by
the Addition of a ſecond part, that it promiſeth to perpetuate
his Merits to all Poſterity. To be brief, the meer Fame of this
Work reſounded the Honourable Name of CASTELLI in­
to all the Corners of Italy, I may ſay of Europe; inſomuch,
that, in hopes to reap great benefit by his Art, the reſpective
Grandees of the adjacent Countries courted his Judgment and
Advice about their Draining of Fenns, Diverſion of Rivers,
Evacuation of Ports, Preventing of Inundations, &c. So that
every Summer he made one or more of theſe Journies or Viſitati­
ons. Particularly, the Senate of Venice conſulted him about their
Lake; to whom he delivered his Opinion in May 1641. and up­
on farther thoughts he preſented them with another Paper of Con­
ſiderations the 20 December following. Prince LEOPOLDO
of TUSCANY likewiſe requeſted his Advice in the begin­
ning of the enſuing year 1642, which occaſioned his Letter to
Father Franceſco di San Giuſeppe, bearing date February 1,
To which Signore Bartolotti oppoſing, he writes a ſecond Let­
ter, directed to one of the Commiſſioners of Sewers, vindicating
his former, and refuting Bartolotti, both which I here give
you.
§. The Preferments which his Merits recommended him unto,
were firſt to be Abbot of Caſſino, from which he was removed
1Anno 1640, or thereabouts, unto the Abbey of Santo Benedet­
to Aloyſio; and much about the ſame time preferred to the Dig­
nity of Chief Mathematician to his grand Patron Pope URBAN
VIII. and Publique Profeſſour of Mathematicks in the Vni­
verſity of ROME.
§. Here a Stop was put to the Carier of his Fortunes, and be­
ing fuller of Honour than of Years, was by Death, the Importu­
nate Intrerupter of Generous Deſigns, prevented in doing that
farther Good which the World had good reaſon to promiſe it ſelf
from ſo Profound and Induſtrious a Perſonage, leaving many
Friends and Diſciples of all Degrees and Qualities to lament
his loſſe, and honour his Memory.
§. His ſingular Virtues and Abilities had gained him the
Friendſhip of very many; as to inſtance in ſome, he had con­
racted ſtrict Amity with Monſignore Maffei Barberino a Floren­
tine, Præfect of the Publique Wayes, and afterwards Pope with
the Name of URBAN VIII. as was ſaid before; with the
above-named Monſignore Corſini Superintendant of the General
Draines: with Monſignore Piccolomini Arch-Biſhop of Siena:
with Cardinal Serra: with Cardinal Caponi, who hath ſtudied
much and writ well upon this Subject; and with Cardinal Gae­
tano who frequently conſulted with him in his deſign of Drain­
ing the Fenns of ROMAGNA. Moreover Prince LEO­
POLDO, and his Brother the Grand Duke had very great
kindneſſe for him; which ſpeaks no ſmall attractions in him,
conſidering him as a favourite of the Family of Barberini, be­
tween whom and the Houſe of Medeci there is an inveterate
Fewd. Amongſt perſons of a lower Quality he acknowledgeth
Signore Ciampoli the Popes Secretary, Sig. Ferrante Ceſarini,
Sig. Giovanni Baſadonna Senator of Venice; and I find menti­
oned Sig. Lana, Sig. Albano, Padre Serafino, Pad. Franceſco
de San. Giuſeppe, and many others.
§. The Works in which he will ſurvive to all ſucceeding Ages
are firſt His ſolid and ſober Confutation of the Arguments of
Signore Lodovico dell Columbo, and Signore Vincentio di
Gratia againſt the Tract of Galileo Delle coſe che ſtanno ſopra
Aqua, wherein he vindicates bis ſaid Maſter with a Gratitude
that Tutors very rarely reap from the pains they take in Culti­
vating their Pupils. This Apology was firſt Printed Anno 1615.
and was a ſecond time publiſhed, as alſo thoſe of his Antago­
niſts, amongſt the Works of GALILEO, ſet forth by the
Learned Viviani 1656. He hath likewiſe writ ſeveral other
curious Pieces, as I am informed by the moſt Courteous Carolo
Manoleſſi of Bologna; amongſt others an excellent Treatiſe
concerning Colours, which he putteth me in hopes to ſee printed
1very ſpeedily. And laſt of all theſe Diſcourſes and Reflections
upon the Menſuration of Running Waters, with the addition of
a Second Book, three Epiſtles, and four Conſiderations upon
the ſame Argument, which conduce much to Illuſtrate his Do­
ctrine and Facilitate the Practice of it; and which with a Rela­
tion of Monſignore Corſini, make the ſecond part of my Firſt
Tome.
§. I might here ſally forth into the Citation of ſundry Au­
thours of Good Account, that have tranſmitted his Character
to Poſterity, but ſhall confine my ſelf to onely two; the one is
of his Maſter, the other of his Scholar; than whom there can­
not be two more competent Judges of his Accompliſhments. To
begin with his Maſter, the Quick-ſighted, and truly Lyncean
GALILEO, who ſpeaking of his Abilities in Aſtronomy ſaith

(a) Che la felicità del ſuo ingegno non la fà biſognoſa dell' o­
pera ſuo. And again, ſubmitting a certain Demonſtration,
which he intended to divulge, to the Judgment of this our Abbot, he

writes to him in this manner: (b) Queſto lo comunico a V. S.
per lettera prima che ad alcun altro, con attenderne principal­
mente il parer ſuo, e doppo quello de' noſtri Amici diſcoſti,
conpenſiero d' inviarne poi altre Copie ad altri Amici d' Italia,
e di Francia, quando io ne venga da lei conſigliato: e qui pre­
gandola a farci parte d' alcuna delle ſue peregrine ſpeculationi;
con ſinceriſſimo affetto, &c. And the moſt acute Mathematician
Signore Evangeliſta Terricelli, late Profeſſour to the Grand
Duke in immediate Succeſſion after GALILEO, maketh this

Honourable and Grateful Mention of him, and his Book: (c) O­
mitto magnum illum nutantis Maris motum; Prætereo etiam
omnem Fluminum, Aquarumque Currentium tum menſurum,
tum uſum, quarum omnis doctrina reperta primum fuit ab
Abbate BENEDICTO CASTELLIO Preceptore
meo. Scripſit ille Scientiam ſuam, & illam non ſolum demonſtra­
tione, verum etiam opere confirmavit, maxima cum Princi­
pum & populorum utilitatate, majore cum admiratione Phylo­
ſophorum. Extat illius Liber, vere aureus.
(a)Nella continu­
atione dell Nun­
tio ſiderio.
(b) Lettera al P.
Abbate D. B. Ca­
ſtelli D'Arcetro;
li. 3. Decemb.
1639.
(c) De Motu A­
quarum. Lib. 2.
Prop. 37. p. 191.
§. I have onely two particulars more to offer the Engliſh Rea­
der: The one concerns the Book, and it is this, That after the
general Aprobation it hath had in Italy, I cannot but think it
deſerveth the ſame Civil Entertainment with us, in regard that
it cometh with no leſſe Novelty, Facility, Verity, and Utility to
us than to thoſe whom the Authour favoured with the Original.
Our Rivers and Sewers through Publique Diſtractions and Pri­
vate Incroachments are in great diſorder, as thoſe Channels for
iuſtance which formerly were Navigable unto the very Walls of
1York and Salisbury, &c: Our Ports are choaked and obſtructed
by Shelfes and Setlements: Our Fenns do in a great part lie waſte
and unimproved: Now all theſe may be (and, as I find by the
Confeſſion of ſome whoſe Practiſes upon the Copy of the Firſt
Book onely of our Authour hath got them both Money and Repu­
tation, in part have been) remedied by the Ways and Means he
here ſets down. The truth is the Argument hath been paſt over
with an Vniverſal Silence; ſo that to this day I have not ſeen
any thing that hath been written Demonſtratively and with Ma­
thematical Certainty concerning the ſame, ſave onely what this
Learned Prelate hath delivered of his Own Invention in theſe
Treatiſes: who yet hath ſo fully and plainly handled the Whole
Doctrine, that I may affirm his Work to be every way abſolute. It
muſt be confeſt the Demonſtration of the Second Propoſition of the
Second Book did not well pleaſe the Authour, and had he lived
he would have ſupplyed that defect, but being prevented by
Death, the Reader muſt content himſelf with the Mechanical
Proof that he giveth you of the truth of ſo Excellent a Con­
cluſion.
§. The other particular that I am to offer is, that out of my de­
ſire to contribute what lyeth in me to the compleating of this Piece
for Engliſh Practice, I have exeeded my promiſe not onely in gi­
ving you the Second and following Books which were not extant at
the time of tendring my Overtures, but alſo in that I have added
a Map or Plat of all the Rivers, Lakes, Fenns, &c. mentioned
thorow out the Work. And if I have not kept touch in point of
Time, let it be conſidered that I am the Tranſlator and not the
Printer. To conclude, according to your acceptance of theſe my
endeavours, you may expect ſome other Tracts of no leſſe Profit
and Delight. Farewell.
T. S.
1
ERRATA of the ſecond PART of the firſt TOME.
In PREFACE, I cad Ferdinando II. ibid. l' Aqua.
PAGE 2. LINE 26, for muſt read much. P. 3. l. 22, r. and let. l. 25. r. water, from l. 41.
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25, r. meaſured it,. r. neceſſarily. P. 23. l. 19. r. for help. for Page 31. r. P. 32. P. 24.
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p. 31. l. 32. r. Soe. p. 41. l. 20. r. to the line. p. 48. l. 19. r. us the ^{*}. id. Figure falſe p. 52.
l. 30, and 31. for Theorem r. Propoſition. p. 53. l. 29. r. again. p. 57. l. 19, r. ſame if.
l. 44. r. bodily. p. 58. l. 9, r. gathering. l. 40. omit;. p. 60. l. 2. omit, if. p. 65. l. 1. r. tide
dele;. p. 66. l. 35. r. Stoppage of. p. 68. l. 12, for Lords the r. Lords. l. ult. for they
r. it. p. 69. l. 14. r. to one. id. carried dele to. p. 71. l. 20, r. and that. l. 25, r. Braces; it. l.
29. r. Braces. l. 44, r. the Brent. p. 72. l. 23. r. Serene Highneſſe. p. 73. l. 24, r. deliberation:.
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85. l. 9, 10. dele a free drame. p. 88. l. 5. r. Palmes. p. 89. l. 8. r. Princes. p. 92. l. 3. r. Diſ­
courſes. p. 93. l. 31. r. Tautologie. p. 94. l. 9. r. miracle;. p. 97. l. 13. r, weighty. p. 101.
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r. p. 114. p. 114. l. 35. r. of 200, l. 41. r. cloſed. p. 115. l. 29. r. conſtant;.
1
OF THE
MENSURATION
OF
Running Waters.
LIB. I.
What, and of how great moment the confi­
deration of Motion is in natural things,
is ſo manifeſt, that the Prince of Peri­
pateticks pronounced that in his Schools
now much uſed Sentence: Ignorato mo­
tu, ignoratur natura. Thence it is that
true Philoſophers have ſo travailed in the
contemplation of the Celeſtial motions,
and in the ſpeculation of the motions of
Animals, that they have arrived to a wonderful height and ſub­
limity of underſtanding. Under the ſame Science of Motion
is comprehended all that which is written by Mechanitians con­
cerning Engines moving of themſelves, Machins moving by the
force of Air, and thoſe which ſerve to move weights and im­
menſe magnitudes with ſmall force. There appertaineth to the
Science of Motion all that which hath been written of the
alteration not onely of Bodies, but of our Minds alſo; and
in ſum, this ample matter of Motion is ſo extended and di­
lated, that there are few things which fall under mans no­
tice, which are not conjoyned with Motion, or at leaſt de­
pending thereupon, or to the knowledge thereof directed;
and of almoſt every of them, there hath been written and
compoſed by ſublime wits, learned Treatiſes and Inſtructions.
1And becauſe that in the years paſt I had occaſion by Order of
our Lord Pope Vrban 8. to apply my thoughts to the motion of
the Waters of Rivers, (a matter difficult, moſt important, and
little handled by others) having concerning the ſame obſerved
ſome particulars not well obſerved, or conſidered till now, but of
great moment both in publick and private affairs; I have thought
good to publiſh them, to the end that ingenious ſpirits might
have occaſion to diſcuſſe more exactly then hitherto hath been
done, ſo neceſſary and profitable a matter, and to ſupply alſo my
defects in this ſhort and difficult Tractate. Difficult I ſay, for
the truth is, theſe knowledges, though of things next our ſenſes,
are ſometimes more abſtruce and hidden, then the knowledge of
things more remote; and much better, and with greater exquiſit­
neſs are known the motions of the Planets, and Periods of the
Stars, than thoſe of Rivers and Seas: As that ſingular light of
Philoſophie of our times, and my Maſter Signore Galileo Galilei
wiſely obſerveth in his Book concerning the Solar ſpots. And
to proceed with a due order in Sciences, I will take ſome ſuppo­
ſitions and cognitions ſufficiently clear; from which I will after­
wards proceed to the deducing of the principal concluſions. But
to the end that what I have written at the end of this diſcourſe in
a demonſtrative and Geometrical method, may alſo be under­
ſtood of thoſe which never have applyed their thoughts to the
ſtudy of Geometry; I have endeavoured to explain my conceit
by an example, and with the conſideration of the natural things
themſelves, muſt after the ſame order in which I began to doubt
in this matter; and have placed this particular Treatiſe here in
the beginning, adverting nevertheleſs, that he who deſires more
full and abſolute ſolidity of Reaſons, may overpaſs this prefatory
diſcourſe, and onely conſider what is treated of in the demonſtra­
tions placed towards the end, and return afterwards to the conſi­
deration of the things collected in the Corollaries and Appendices;
which demonſtrations notwithſtanding, may be pretermitted by
him that hath not ſeen at leaſt the firſt ſix Books of the Elements
of Euclid; ſo that he diligently obſerveth that which fol­
loweth.
I ſay therefore, that having in times paſt, on divers occaſi­
ons heard ſpeak of the meaſures of the waters of Rivers, and
Fountains, ſaying, ſuch a River is two or three thouſand feet of
water; ſuch a ſpring-water is twenty, thirty, or forty inches, &c.
Although in ſuch manner I have found all to treat thereof in
word and writing, without variety, and as we are wont to ſay,
conſtanti ſermone, yea even Artiſts and Ingeneers, as if it were
a thing that admitted not of any doubt, yet howſoever I re­
mained ſtill infolded in ſuch an obſcurity, that I well knew I un­
1derſtood nothing at all, of that which others pretended full and
clearly to underſtand. And my doubt aroſe from my frequent
obſervation of many Trenches and Channels, which carry
water to turn Mills, in which Trenches, and Channels, the
water being meaſured, was found pretty deep; but if afterwards
the ſame water was meaſured in the fall it made to turn the
Wheel of the Mill, it was much leſſe, not amounting often to the
tenth part, nor ſometimes to the twentieth, inſomuch, that the
ſame running water came to be one while more, another while leſs
in meaſure, in divers parts of its Channel; and for that reaſon this
vulgar manner of meaſuring running Waters, as indeterminate and
uncertain, was by me juſtly ſuſpected, the meaſure being to be de­
terminate, and the ſame. And here I freely confeſſe that I had fin­
gular help to reſolve this difficulty from the excellent & accurate
way of diſcourſing, as in allother matters, ſo alſo in this, of the
Right Honourable and Truly Noble Signior Ciampoli, Secretary
of the Popes ſecret affairs. Who moreover, not ſparing ſor the coſts
of the ſame, generouſly gave me occaſion a few years paſt to try by
exact experiments that which paſt concerning this particular. And
to explain all more clearly with an example; we ſuppoſe a Veſſel
filled with Water, as for inſtance a Butt, which is kept full, though
ſtill water runneth out, and the Water run out by two Taps equal
of bigneſſe, one put in the bottom of the Veſſel, and the other in
the upper part; it is manifeſt that in the time wherein from the
upper part ſhall iſſue a determinate meaſure of water ſrom
the inferiour part there ſhall iſſue four, five, and many more of
the ſame meaſures, according to the difference of the height of
the Taps, and the diſtance of the upper Tap from the Superfici­
es and level of the water of the Veſſel: and all this will alwayes
follow, though, as hath been ſaid, the Taps be equal, and the
water in diſcharging keep the ſaid Taps alwayes full. Where firſt
we note, that, although the meaſure of the Taps be equal, never­
theleſſe there iſſueth from them in equal times unequal quantities
of water, And if we ſhould more attentively conſider this buſi­
neſſe, we ſhould find, that the water by the lower Tap, run­
neth and paſſeth with much greater velocity, then it doth by the
upper, whatever is the reaſon. If therefore we would have
ſuch a quantity of Water diſcharge from the upper tap, as
would diſcharge from the neather in the ſame time, it is plain, that
either the upper Taps muſt be multiplyed in ſuch ſort, that ſo
many more Taps in number be placed above than below, as the
neather tap ſhall be more ſwift than the upper, or the upper Tap
made ſo much bigger than the nether, by how much that be­
neath ſhall be more ſwift than that above; and ſo then in equal
times, the ſame quantity of Water ſhall diſcharge from the upper,
as doth from the neather part.
1
I will declare my ſelf by another example. If we ſhould ima­
gine, that two cords or lines of equal thickneſs, be drawn through
two holes of equal bore; but ſo that the firſt paſs with quadruple
velocity to the ſecond: It is manifeſt, that if in a determinate
time, we ſhall by the firſt bore have drawn four Ells of the line,
in the ſame time, by the ſecond hole we ſhall have drawn but one
Ell of cord onely; and if by the firſt there paſſe twelve Ells, then
through the ſecond there ſhall paſſe onely three Ells; and in
ſhort the quantity of cord ſhall have the ſame proportion to the
cord, that the volocity hath to the velocity. And therefore we
deſiring to compenſate the tardity of the ſecond cord, and main­
taining the ſame tardity to draw through the ſecond hole as much
cord as through the firſt, it will be neceſſary to draw through the
ſecond bore four ends of cord; ſo that the thickneſs of all the
cords by the ſecond hole, have the ſame proportion to the thick­
neſs of the cord which paſſeth onely by the firſt, as the velocity
of the cord by the firſt hole hath reciprocally to the velocity of
the codrs by the ſecond hole. And thus its clear, that when
there is drawn through two holes equal quantity of cords in
equal time, but with unequal velocity, it will be neceſſary, that
the thickneſs of all the four cords ſhall have the ſame reciprocal
proportion to the thickneſs of the ſwifter cord, that the velo­
city of the ſwifter cord hath to the velocity of the ſlower. The
which is verified likewiſe in the fluid Element of Water.
And to the end that this principal fundamental be well under­
ſtood, I will alſo note a certain obſervation made my me in the
Art of Wyer-drawing, or ſpinning Gold, Silver, Braſs, and Iron,
and it is this; That ſuch Artificers deſiring more and more to
diſgroſſe and ſubtillize the ſaid Metals, having would about a
Rocket or Barrel, the thread of the Metal, they place the Roc­
ket in a frame upon a ſtedfaſt Axis, in ſuch ſort that the Rocket
may turn about in it ſelf; then making one end of the thread to
paſſe by force through a Plate of Steel pierced with divers holes,
greater and leſſer, as need requireth, faſtning the ſame end of the
thread to another Rocket, they wind up the thread, which paſ­
ſing through a bore leſs than the thickneſſe of the thread, is of
force conſtrained to diſgroſſe and ſubtillize. Now that which is
intenſly to be obſerved in this buſineſs, is this, That the parts of
the thread before the hole, are of ſuch a thickneſſe, but the parts
of the ſame thread after it is paſſed the hole, are of a leſſer thick­
neſſe: and yet nevertheleſſe the maſſe and weight of the thread
which is drawn forth, is ever equal to the maſſe and weight of the
thread which is winded up. But if we ſhould well conſider the mat­
ter, we ſhould finde, that the thicker the thread before the hole is,
than the thread paſſed the hole, the greater reciprocally is the
1velocity of the parts of the thread paſſed the hole, than the volo­
city of the parts before the hole: Inſomuch that if verbi gratia
the thickneſſe of the thread before the hole, were double to the
thickneſſe after the hole, in ſuch caſe the velocity of the parts of
the thread paſſed the hole, ſhould be double to the velocity of the
parts of the thread before the hole; and thus the thickneſſe
compenſates the velocity, and the velocity compenſates the thick­
neſſe. So that the ſame occurreth in the ſolid Metals of Gold,
Silver, Braſs, Iron, &c. that eveneth alſo in the fluid Element of
Water, and other liquids, namely, That the velocity beareth the
ſame proportion to the velocity, that the thickneſſe of the Me­
tal, or Water, hath to the thickneſſe.
And therefore granting this diſcourſe, we may ſay, that as of­
ten as two Taps with different velocity diſcharge equal quanti­
ties of Water in equal times, it will be neceſſary that the Tap
leſſe ſwift be ſo much greater, and larger, than the Tap more
ſwift, by how much the ſwifter ſuperates in velocity the ſlower;
and to pronounce the Propoſition in more proper terms, we ſay;
That if two Taps of unequal velocity, diſcharge in equal times
equal quantities of Water, the greatneſſe of the firſt ſhall be to
the greatneſſe of the ſecond, in reciprocal proportion, as the ve­
locity of the ſecond to the velocity of the firſt. As for example,
if the firſt Tap ſhall be ten times ſwifter than the ſecond Tap, it
will be neceſſary, that the ſecond be ten times bigger and larger
than the firſt; and in ſuch caſe the Taps ſhall diſcharge equall
quantities of water in equal times; and this is the principal and
moſt important point, which ought to be kept alwayes in minde,
for that on it well underſtood depend many things profitable,
and worthy of our knowledge.
Now applying all that hath been ſaid neerer to our purpoſe, I
conſider, that it being moſt true, that in divers parts of the ſame
River or Current of running water, there doth always paſſe equal
quantity of Water in equal time (which thing is alſo demon­
ſtrated in out firſt Propoſition) and it being alſo true, that in di­
vers parts the ſame River may have various and different veloci­
ty; it follows of neceſſary conſequence, that where the River
hath leſſe velocity, it ſhall be of greater meaſure, and in thoſe
parts, in which it hath greater velocity, it ſhall be of leſſe mea­
ſure; and in ſum, the velocity of ſeveral parts of the ſaid River,
ſhall have eternally reciprocall and like proportion with
their meaſures. This principle and fundamental well eſtabliſh­
ed, that the ſame Current of Water changeth meaſure, accor­
ding to its varying of velocity; that is, leſſening the meaſure,
when the velocity encreaſeth, and encreaſing the meaſure, when
the velocity decreaſeth; I paſſe to the conſideration of many
1particular accidents in this admirable matter, and all depending
on this ſole Propoſition, the ſenſe of which I have oft repeated,
that it might be well underſtood.
COROLLARIE I.
And firſt, we hence conclude, that the ſame Streams of a
Torrent, namely, thoſe ſtreams which carry equal quantity of
Water in equal times, make not the ſame depths or meaſures in
the River, in which they enter, unleſſe when in the entrance in­
to the River they acquire; or to ſay better, keep the ſame velo­
city; becauſe if the velocicities acquired in the River ſhall be
different, alſo the meaſures ſhall be diverſe; and conſequently
the depths, as is demonſtrated.
COROLLARIE II.
And becauſe ſucceſſively, as the River is more and more full,
it is conſtituted ordinarily in greater & greater velocity: hence
it is that the ſame ſtreams of the Torrent, that enter into the Ri­
ver, make leſſe and leſſe depths, as the River grows more and
more full; ſince that alſo the Waters of the Torrent being en­
tered into the River, go acquiring greater and greater velocities,
and therefore diminiſh in meaſure and height.
COROLLARIE III.
We obſerve alſo, that while the main River is ſhallow, if there
fall but a gentle rain, it ſuddenly much increaſeth and riſeth;
but when the River is already ſwelled, though there fall again a­
nother new violent ſhower, yet it increaſeth not at the ſame rate
as before, proportionably to the rain which fell: which thing
we may affirm particularly to depend on this, that in the firſt
caſe, while the River is low, it is found alſo very ſlow, and there­
fore the little water which entereth into it, paſſeth and runs with
little velocity, and conſequently occupieth a great meaſure:
But when the River is once augmented, by new water being alſo
made more ſwift, it cauſeth the great Flood of water which fal­
leth, to bear a leſſe meaſure, and not to make ſuch a depth.
COROLLARIE IV.
From the things demonſtrated is manifeſt alſo, that whilſt a
Torrent entereth into a River, at the time of Ebbe, then the
Torrent moveth with ſuch a certain velocity, what ever it be,
1paſſing by its extreameſt parts, wherewith it communicateth with
the River; in which parts, the Torrent being meaſured, ſhall
have ſuch a certain meaſure: but the River ſwelling and riſing,
alſo thoſe parts of the Torrent augment in greatneſſe and mea­
ſure, though the Torrent, in that inſtant, diſ-imbogue no more
water than it did before: ſo that the River being ſwelled, we
are to conſider two mouths of the ſame Torrent, one leſſe be­
fore the riſing, the other greater after the riſing, which mouths
diſcharge equal quantities of water in equal times; therefore the
velocity by the leſſer mouth ſhall be greater than the velocity by
the greater mouth; and thus the Torrent ſhall be retarded from
its ordinary courſe.
COROLLARIE V.
From which operation of Nature proceedeth another effect
worthy of conſideration; and it is, that the courſe of the water
retarding, as hath been ſaid in thoſe ultimate parts of the Tor­
rent, if it ſhall happen that the Torrent grow torbid and mud­
dy, and its ſtreame be retarded in ſuch a degree, that it is not
able to carry away thoſe minute grains of Earth, which com­
poſe the muddineſſe; in this caſe the Torrent ſhall clear away
the mud, and carry away the Sand at the bottome of its own
Chanel, in the extream parts of its mouth, which raiſed and
voided Sand, ſhall again afterwards be carried away, when the
River abating, the Torrent ſhall return to move with its primitive
velocity.
COROLLARIE VI.
Whilſt it is demonſtrated, that the ſame water hath different
meaſures in its Chanel or courſe, according as it varieth in
velocity; ſo that the meaſure of the water is alwayes greater, where
the velocity is leſſer; and on the contrary, the meaſure leſſer,
where the velocity is greater: from hence we may moſt ele­
gantly render the reaſon of the uſual Proverb, Take heed of the
ſtill waters: For that if we conſider the ſelf ſame water of a
River in thoſe parts, wherein it is leſs ſwift, and thence called ſtill
or ſmooth water, it ſhall be, of neceſſity, of greater meaſure
than in thoſe parts, in which it is more ſwift, and therefore ordi­
narily ſhall be alſo more deep and dangerous for paſſengers;
whence it is well ſaid, Take heed of the ſtill Waters; and this
ſaying hath been ſince applied to things moral.
1
COROLLARIE VII.
Likewiſe, from the things demonſtrated may be concluded,
that the windes, which ſtop a River, and blowing againſt the
Current, retard its courſe and ordinary velocity ſhall neceſſarily
amplifie the meaſure of the ſame River, and conſequently ſhall
be, in great part, cauſes; or we may ſay, potent con-cauſes of
making the extraordinary inundations which Rivers uſe to make.
And its moſt certain, that as often as a ſtrong and continual wind
ſhall blow againſt the Current of a River, and ſhall reduce the
water of the River to ſuch tardity of motion, that in the time
wherein before it run five miles, it now moveth but one, ſuch a
River will increaſe to five times the meaſure, though there ſhould
not be added any other quantity of water; which thing indeed
hath in it ſomething of ſtrange, but it is moſt certain, for that
look what proportion the waters velocity before the winde, hath
to the velocity after the winde, and ſuch reciprocally is the mea­
ſure of the ſame water after the winde, to the meaſure before
the winde; and becauſe it hath been ſuppoſed in our caſe that the
velocity is diminiſhed to a fifth part, therefore the meaſure ſhall
be increaſed five times more than that, which it was before.
COROLLARIE VIII.
We have alſo probable the cauſe of the inundations of Tyber,
which befel at Rome, in the time of Alexander the Sixth, & of
Clement the Seventh; which innundations came in a ſerene time,
and without great thaws of the Snows; which therefore much
puzzled the wits of thoſe times. But we may with much pro­
bability affirm, That the River roſe to ſuch a height and excreſ­
cence, by the retardation of the Waters dependant on the
boiſtrous and conſtant Winds, that blew in thoſe times, as is no­
red in the memorials.
COROLLARIE. IX.
It being moſt manifeſt, that by the great abundance of Water
the Torrents may increaſe, and of themſelves alone exorbitantly
ſwell the River; and having demonſtrated that alſo without new
Water, but onely by the notable retardment the River riſeth and
increaſeth in meaſure, in proportion as the velocity decreaſeth:
hence it is apparent, that each of theſe cauſes being able of it ſelf,
and ſeparate from the other to ſwell the River; when it ſhall
happen that both theſe two cauſes conſpire the augmentation of
1the River, in ſuch a caſe there muſt follow very great and irre­
pable innundations.
COROLLARIE X.
From what hath been demonſtrated, we may with facility re­
ſolve the doubt which hath troubled, and ſtill poſeth the moſt
diligent, but incautelous obſervers of Rivers, who meaſuring
the Streams and Torrents which fall into another River; as thoſe
for inſtance, which enter into the Po, or thoſe which fall into Ti­
ber; and having ſummed the total of theſe meaſures, and con­
ferring the meaſures of the Rivers and Brooks, which fall into
Tiber, with the meaſure of Tiber, and the meaſures of thoſe which
diſimbogue into Po, with the meaſure of Po, they find them not
equal, as, it ſeems to them, they ought to be, and this is becauſe
they have not well noted the moſt important point of the varia­
tion of velocity, and how that it is the moſt potent cauſe of won­
derfully altering the meaſures of running Waters; but we moſt
facilly reſolving the doubt, may ſay that theſe Waters diminiſh
the meaſure, being once entered the principal Channel, becauſe
they increaſe in velocity.
COROLLARIE XI.
Through the ignorance of the force of the velocity of the Wa­
ter, in altering its meaſure, & augmenting it when the velocity
diminiſheth; and diminiſhing it when the velocity augmenteth:
The Architect Giovanni Fontana, endeavoured to meaſure, and
and to cauſe to be meaſured by his Nephew, all the Brooks and
Rivers which diſcharged their Waters into Tiber, at the time of
the Innundation; which happened at Rome in the year 1598,
and publiſhed a ſmall Treatiſe thereof, wherein he ſummeth up
the meaſures of the extraordinary Water which fell into Tiber,
and made account that it was about five hundred Ells more than
ordinary; and in the end of that Treatiſe concludeth, that to re­
move the Innundation wholly from Rome, it would be neceſſary
to make two other Channels, equal to that at preſent, and that
leſſe would not ſuffice; and finding afterwards that the whole
Stream paſſed under the Bridge Quattro-Capi, (the Arch where­
of is of a far leſs meaſure then five hundred Ells) concludeth,
that under the ſaid Bridge paſt a hundred fifty one Ells of Water
compreſſed, (I have ſet down the preciſe term of compreſt Wa­
ter, written by Fontana) wherein I finde many errors.
The firſt of which is to think that the meaſures of theſe Wa­
ters compreſſed in the Channels of thoſe Brooks and Rivers,
1ſhould maintain themſelves the ſame in Tiber, which by his leave,
is moſt falſe, when ever thoſe waters reduced into Tiber, retain
not the ſame velocity which they had in the place in which Fon­
tana and his Nephew meaſured them: And all this is manifeſt
from the things which we have above explained; for, if the Wa­
ters reduced into Tiber increaſe in velocity, they decreaſe in mea­
ſure; and if they decreaſe in velocity, they increaſe in mea­
ſure.
Secondly, I conſider that the meaſures of thoſe Brooks and
Rivers, which enter into Tiber at the time of Innundation, are
not between themſelves really the ſame, when their velocities are
not equal, though they have the ſame names of Ells and Feet;
for that its poſſible that a diſinboguement of ten Ells requadrated
(to ſpeak in the phraſe of Fontana) of one of thoſe Brooks,
might diſcharge into Tiber at the time of Innundation, four, ten,
and twenty times leſs Water, than another mouth equal to the
firſt in greatneſs, as would occur when the firſt mouth were four,
ten, or twenty times leſs ſwift than the ſecond. Whereupon,
whilſt Fontana ſummes up the Ells and Feet of the meaſures of
thoſe Brooks and Rivers into a total aggregate, he commits the
ſame error with him, which would add into one ſumme diverſe
moneys of diverſe values, and diverſe places, but that had the
ſame name; as if one ſhould ſay ten Crowns of Roman money,
four Crowns of Gold, thirteen Crowns of Florence, five Growns
of Venice, and eight Crowns of Mantua, ſhould make the ſame
ſumme with forty Crowns of Gold, or forty Crowns of Mantua.
Thirdly, It might happen that ſome River or Current in the
parts nearer Rome, in the time of its flowing, did not ſend forth
more Water than ordinary; and however, its a thing very clear,
that whilſt the ſtream came from the ſuperior parts, that ſame
Brook or River would be augmented in meaſure, as hath been
noted in the fourth Corollary; in ſuch ſort, that Fontana might
have inculcated, and noted that ſame River or Current as con­
curring to the Innundation, although it were therein altogether
unconcerned.
Moreover, in the fourth place we muſt note, That it might
ſo fall out, that ſuch a River not onely was unintereſſed in the
Innundation, though augmented in meaſure, but it might I ſay
happen, that it was inſtrumental to the aſſwaging the Innunda­
tion, by augmenting in the meaſure of its own Channel; which
matter is ſufficiently evident; for if it be ſuppoſed that the Ri­
ver in the time of flood, had not had of it ſelf, and from its pro­
per ſprings more Water than ordinary, its a thing certain, that
the Water of Tiber riſing and increaſing; alſo that River, to le­
vel it ſelf with the Water of Tiber, would have retained ſome of
1its Waters in its own Chanel, without diſcharging them into Ty­
ber, or elſe would have ingorged and ſwallowed (if I may ſo ſay)
ſome of the water of Tyber; and in this caſe, at the time of In­
undation, leſſe abundance of water would have come to Rome,
and yet nevertheleſſe the meaſure of that River would have been
increaſed.
Fifthly, Fontana deceiveth himſelf, when he concludeth, that
to remove the Inundation from Rome, it would be neceſſary to
make two other Chanels of Rivers, that were as large as that,
which is the preſent one, and that leſs would not ſuffice, which,
I ſay, is a fallacy: and to convince him eaſily of his errour, it
ſufficeth to ſay, that all the Streams being paſſed under the Bridge
Quattro-Capi, as he himſelf atteſts, a Channel would ſuffice on­
ly of the capacity of the ſaid Bridge, provided that the water
there might run with the ſame velocity, as it did under the Bridge
at the time of Inundation; and on the contrary, twenty Cur­
rents of capacity equal to the preſent one, would not ſuffice, if
the water ſhould run with twenty times leſs velocity, than it made
at the time of the Inundation.
Sixthly, to me it ſeemeth a great weakneſſe to ſay, that there
ſhould paſſe under the Bridge Quattro-Capi, an hundred fifty one
ells of water compreſſed; for that I do not underſtand that wa­
ter is like Cotton or Wool, which matters may be preſt and trod,
as it happeneth alſo to the air, which receiveth compreſſion in
ſuch ſort, that after that in ſome certain place a quantity of air
ſhall be reduced to its natural conſtitution; and having taken up
all the ſaid place, yet nevertheleſſe compreſſing the firſt Air
with force and violence, it is reduced into far leſs room, and will
admit four or ſix times as much air, as before, as is experimen­
tally ^{*} ſeen in the Wind-Gun, invented in our dayes by M. Vin,

cenzo Vincenti of Vrbin, which property of the Air of admit­
ting condenſation, is alſo ſeen in the portable Fountains of the
ſame M. Vincenzo: which Fountains ſpirt the Water on high,
by force of the Air compreſſed, which whilſt it ſeeks to reduce
its ſelf to its natural conſtitution, in the dilation cauſeth that vi­
olence. But the water can never, for any thing I know, crowd,
or preſs ſo, as that if before the compreſſion it held or poſſeſt a
place, being in its natural conſtitution, I believe not, I ſay, that it
is poſſible, by preſſing and crowding to make it poſſeſs leſs room,
for if it were poſſible to compreſs the Water, and make it to oc­
cupy a leſs place, it would thence follow, that two Veſſels of e­
qual meaſure, but of unequal height, ſhould be of unequal capa­
city, and that ſhould hold more water which was higher; alſo a
Cylinder, or other Veſſel more high than broad, would containe
more water erected, than being laid along; for that being erect­
1ed, the water put therein would be more preſſed and crowded.
* And as is at
large demonſtrated
by that moſt excel­
lent and lonour­
able perſonage Mr.
Botle in the indu­
ſtrious experiment
of his Pneumatical
Engine.
And therefore, in our caſe, according to our principles we will
ſay, that the water of that Stream paſseth all under the ſaid
Bridge Quattro-Capi, for that being there moſt ſwift, it ought of
conſequence to be leſs in meaſure.
And here one may ſee, into how many errours a man may run
through ignorance of a true and real Principle, which once known
and well underſtood, takes away all miſts of doubting, and ea­
ſily reſolveth all difficulties.
COROLLARIE. XII.
Through the ſame inadvertency of not regarding the variation
of velocity in the ſame Current, therea re committed by Ingi­
neers and Learned men, errours of very great moment (and I
could thereof produce examples, but for good reaſons I paſs
them over in ſilence) when they think, and propoſe, by deriving
new Channels from great Rivers, to diminiſh the meaſure of the
water in the River, and to diminiſh it proportionally, according
to the meaſure of the Water which they make to paſs through
the Channel, as making v.g a Channel fifty foot broad, in which
the derived water is to run waſte, ten foot deep, they think they
have diminiſhed the meaſure of the Water in the River five hun­
dred feet, which thing doth not indeed ſo fall out; and the rea­
ſon is plain; for that the Chanel being derived, the reſt of the
main River, diminiſheth in velocity, and therefore retains a grea­
ter meaſure than it had at firſt before the derivation of the Cha­
nel; and moreover, if the Chanel being derived, it ſhall not
conſerve the ſame velocity which it had at firſt in the main Ri­
ver, but ſhall diminiſh it, it will be neceſſary, that it hath a grea­
ter meaſure than it had before in the River; and therefore
to accompt aright, there ſhall not be ſo much water derived into
the Channel, as ſhall diminiſh the River, according to the quanti­
ty of the water in the Channel, as is pretended.
COROLLARIE XIII.
This ſame conſideration giveth me occaſion to diſcover a moſt
ordinary errour, obſerved by me in the buſineſſe of the wa­
ter of Ferara, when I was in thoſe parts, in ſervice of the moſt
Reverend and Illuſtrious Monfignor Corſini; the ſublime wit of
whom hath been a very great help to me in theſe contemplations;
its very true, I have been much perplexed, whether I ſhould
commit this particular to paper, or paſſe it over in ſilence, for
that I have ever doubted, that the opinion ſo common and
1moreover confirmed with a moſt manifeſt experiment, may not
onely make this my conjecture to be eſteemed far from true,
but alſo to diſcredit with the World the reſt of this my Treatiſe:
Nevertheleſſe I have at laſt reſolved not to be wanting to my
ſelf, and to truth in a matter of it ſelf, and for other conſe­
quences moſt important; nor doth it ſeem to me requiſite in
difficult matters, ſuch as theſe we have in hand, to refigne our
ſelves to the common opinion, ſince it would be very ſtrange if
the multitude in ſuch matters ſhould hit on the truth, nor ought
that to be held difficult, in which even the vulgar do know the
truth and right; beſides that I hope morever to prove all in ſuch
ſort, that perſons of ſolid judgment, ſhall reſt fully perſwaded,
ſo that they but keep in mind the principal ground and foundation
of all this Treatiſe; and though that which I will propoſe, be a par­
ticular, as I have ſaid, pertaining onely to the intereſts of Ferara;
yet nevertheleſſe from this particular Doctrine well underſtood,
good judgement may be made of other the like caſes in general.
I ſay then, for greater perſpecuity, and better underſtanding
of the whole, That about thirteen miles above Ferara, near to
Stellata, the main of Po, branching it ſelf into two parts, with one
of its Arms it cometh cloſe to Ferara, retaining the name of the
Po of Ferara; and here again it divideth it ſelf into two other
branches, and that which continueth on the right hand, is called
the Po of Argenta, and of Primaro; and that on the left the Po
of Volana. But for that the bed of the Po of Ferara being here­
tofore augmented and raiſed, it followeth that it reſteth wholly
deprived of the Water of the great Po, except in the time of its
greater ſwelling; for in that caſe, this Po of Ferara being re­
ſtrained with a Bank near to Bondeno, would come alſo in the
overflowings of the main Po, to be free from its Waters: But the
Lords of Ferara are wont at ſuch time as the Po threateneth to
break out, to cut the bank; by which cutting, there diſ­
gorgeth ſuch a Torrent of Water, that it is obſerved, that the
main Po in the ſpace of ſome few hours abateth near a foot, and
all perſons that I have ſpoken with hitherto, moved by this ex­
periment, think that it is of great profit and benefit to keep ready
this Vent, and to make uſe of it in the time of its fullneſſe. And
indeed, the thing conſidered ſimply, and at the firſt appearance,
it ſeemeth that none can think otherwiſe; the rather, for that
many examining the matter narrowly, meaſure that body of
Water which runneth by the Channel, or Bed of the Po of Fera­
ra, and make account, that the body of the Water of the great
Po, is diminiſhed the quantity of the body of the Water which
runneth by the Po of Ferara. But if we well remember what
hath been ſaid in the beginning of the Treatiſe, and how much
1the variety of the velocities of the ſaid Water importeth, and the
knowledge of them is neceſſary to conclude the true quantity of
the running Water, we ſhall finde it manifeſt, that the benefit of
this Vent is far leſſe than it is generally thought: And mereover,
we ſhall finde, if I deceive not my ſelf, that there follow from
thence ſo many miſchiefs, that I could greatly incline to believe,
that it were more to the purpoſe wholly to ſtop it up, than to
maintain it open: yet I am not ſo wedded to my opinion, but
that I am ready to change my judgement upon ſtrength of better
reaſons; eſpecially of one that ſhall have firſt well underſtood
the beginning of this my diſcourſe, which I frequently inculcate,
becauſe its abſolutely impoſſible without this advertiſement to
treat of theſe matters, and not commit very great errours.
I propoſe therefore to conſideration, that although it be true,
that whilſt the water of the main Po is at its greateſt height, the
Bank and Dam then cut of the Po of Ferara, and the ſuperior
waters having a very great fall into the Channel of Ferara, they
precipitate into the ſame with great violence and velocity, and
with the ſame in the beginning, or little leſſe, they run towards
the Po of Volana, and of Argenta on the ſea coaſts; yet after the
ſpace of ſome few hours, the Po of Ferara being full, and the ſu­
perior Waters not finding ſo great a diclivity there, as they had
at the beginning of the cutting, they fall not into the ſame with
the former velocity, but with far leſſe, and thereby a great deal
leſſe Water begins to iſſue from the great Po; and if we dili­
gently compare the velocity at the firſt cutting, with the velocity
of the Water after the cutting made, and when the Po of Ferara
ſhall be full of Water, we ſhall finde perhaps that to be fifteen or
twenty times greater than this, and conſequently the Water
which iſſues from the great Po, that firſt impetuoſity being paſt,
ſhall be onely the fifteenth or twentieth part of that which iſſued
at the beginning; and therefore the Waters of the main Po will
return in a ſmall time almoſt to the firſt height. And here I will
pray thoſe who reſt not wholly ſatisfied with what hath been ſaid,
that for the love of truth, and the common good, they would
pleaſe to make diligent obſervation whether in the time of great
Floods, the ſaid Bank or Dam at Bondeno is cut, and that in few
hours the main Po diminiſheth, as hath been ſaid about a foot in
its height; that they would obſerve I ſay, whether, a day or two
being paſt, the Waters of the main Po return almoſt to their firſt
height; for if this ſhould follow, it would be very clear, that the
benefit which reſulteth from this diverſion or Vent, is not ſo great
as is univerſally preſumed; I ſay, it is not ſo great as is
preſumed; becauſe, though it be granted for true, that
the Waters of the main Po, abate at the beginning of
1the Vent, yet this benefit happens to be but temporary and for a
few hours: If the riſing of Po, and the dangers of breaking forth
were of ſhort duration, as it ordinarily befalleth in the overflow­
ings of Torrents, in ſuch a caſe the profit of the Vent would be
of ſome eſteem: But becauſe the ſwellings of Po continue for
thirty, or ſometimes for forty dayes, therefore the gain which
reſults from the Vent proveth to be inconſiderable. It remain­
eth now to conſider the notable harms which follow the ſaid
Sluice or Vent, that ſo reflection being made, and the profit and
the detriment compared, one may rightly judge, and chooſe that
which ſhall be moſt convenient. The firſt prejudice therefore
which ariſeth from this Vent or Sluice, is; That the Channels of
Ferara, Primaro, and Volana filling with Water, all thoſe parts
from Bondeno to the Sea ſide are allarmed and endangered
thereby. Secondly, The Waters of the Po of Primaro having
free ingreſſe into the upper Valleys, they fill them to the great
damage of the Fields adjacent, and obſtruct the courſe of the
ordinary Trenches in the ſame Valleys; inſomuch that all the
care, coſt, and labour about the draining, and freeing the upper
Valleys from Water, would alſo become vain and ineffectual.
Thirdly, I conſider that theſe Waters of the Po of Ferara being
paſſed downwards towards the Sea, at the time that the main Po
was in its greater excreſcences and heights, it is manifeſt by expe­
rience, that when the great Po diminiſheth, then theſe Waters
paſſed by the Po of Ferara begin to retard in their courſe, and
finally come to turn the current upwards towards Stellata, reſting
firſt iu the intermediate time, almoſt fixed and ſtanding, and
therefore depoſing the muddineſſe, they fill up the Channel of
the River or Current of Ferara. Fourthly and laſtly, There
followeth from this ſame diverſion another notable damage, and
it is like to that which followeth the breaches made by Rivers;
near to which breaches in the lower parts, namely below the
breach, there is begot in the Channel of the River, a certain ridge
or ſhelf, that is, the bottom of the River is raiſed, as if ſufficiently
manifeſt by experience; and thus juſt in the ſame manner cutting
the Bank at Bondeno, there is at it were a breach made, from which
followeth the riſing in the lower parts of the main Po, being paſt
the mouth of Pamaro; which thing, how pernitious it is, let any one
judge that underſtandeth theſe matters. And therefore both for
the ſmall benefit, and ſo many harms that enſue from maintain­
ing this diverſion, I ſhould think it were more ſound advice to
keep that Bank alwaies whole at Bondeno, or in any other conve­
nient place, and not to permit that the Water of the Grand Po
ſhould ever come near to Ferara.
1
COROLLARIE XIV.
* Arteſia.
In the Grand Rivers, which fall into the Sea, as here in Italy
Po, Adige,^{*} and Arno, which are armed with Banks againſt their
excreſcencies, its obſerved that far from the Sea, they need
Banks of a notable height; which height goeth afterwards by
degrees diminiſhing, the more it approacheth to the Sea-coaſts:
in ſuch ſort, that the Po, diſtant from the Sea about fifty or ſixty
miles at Ferara, ſhall have Banks that be above twenty feet
higher than the ordinary Water marks; but ten or twelve miles
from the Sea, the Banks are not twelve feet higher than the ſaid
ordinary Water-marks, though the breadth of the River be the
ſame, ſo that the excreſcence of the ſame Innundation happens
to be far greater in meaſure remote from the Sea, then near; and
yet it ſhould ſeem, that the ſame quantity of Water paſſing by
every piace, the River ſhould need to have the ſame altitude of
Banks in all places: But we by our Principles and fundamentals
may be able to render the reaſon of that effect, and ſay; That
that exceſſe of quantity of Water, above the ordinary Water,
goeth alwaies acquiring greater velocity; the nearer it approach­
eth the Sea, and therefore decreaſeth in meaſure, and conſequenly
in height. And this perhaps might have been the cauſe in great
part, why the Tyber in the Innundation Anno 1578. iſſued not
forth of its Channel below Rome towards the Sea.
COROLLARIE XV.
From the ſame Doctrine may be rendred a moſt manifeſt rea­
ſon why the falling Waters go leſſening in their deſcent, ſo
that the ſame falling Water, meaſured at the beginning of
its fall, is greater, and bigger, and afterwards by degrees leſſeneth
in meaſure the more it is remote from the beginning of the fall.
Which dependeth on no other, than on the acquiſition, which
it ſucceſſively makes of greater velocity; it being a moſt fami­
liar concluſion among Philoſophers, that grave bodies falling,
the more they remove from the beginning of their motion, the
more they acquire of ſwiftneſſe; and therefore the Water, as a
grave body, falling, gradually velocitates, and therefore de­
creaſeth in meaſure, and leſſeneth.
COROLLARIE XVI.
And on the contrary, the ſpirtings of a Fountain of Water,
which ſpring on high, work a contrary effect; namely
1in the beginning they are ſmall, and afterwards become greater
and bigge; and the reaſon is moſt manifeſt, becauſe in the be­
ginning they are very ſwift, and afterwards gradually relent
their impetuoſity, and motion, ſo that in the beginning of the
excurſion that they make, they ought to be ſmall, and after­
wards to grow bigger, as in the effect is ſeen.
APPENDIX. I.
Into the errour of not conſidering how much the different
velocities of the ſame running water in ſeveral places of
its current, are able to change the meaſure of the ſame
water, and to make it greater, or leſſe, I think, if I be not
deceived, that Ginlio Frontino a noble antient Writer, may
have faln in the Second Book which he writ, of the Aqueducts
of the City of Rome: Whilſt finding the meaſure of the Water
^{*}Commentaries leſſe than it was in erogatione 1263. Quinaries, he

thought that ſo much difference might proceed from the negligence
of the Meaſures; and when afterwards with his own induſtry he
meaſured the ſame water at the beginnings of the Aqueducts,
finding it neer 10000. Quinaries bigger than it was in Commenta­
riis he judged, that the overplus was imbeziled by Miniſters and
Partakers; which in part might be ſo, for it is but too true, that
the publique is almoſt alwayes defrauded; yet nevertheleſſe, I
verily believe withal, that beſides the frauds of theſe Officers,
the velocities of the water in the place wherein Frontino meaſu­
red, it might be different from thoſe velocities, which are
found in other places before meaſured by others; and there­
fore the meaſures of the waters might, yea ought necſſarily to
be diffcrent, it having been by us demonſtrated, that the mea­
ſures of the ſame running water have reciprocal proportion to
their velocities. Which Frontino not well conſidering, and find­
ing the water in Commentariis 12755. Quinaries in erogati­
one 14018, and in his own meaſure ad capita ductuum, at the
head of the fountain 22755. Quinaries, or thereabouts, he
thought, that in all theſe places there paſt different quantities of
water; namely, greater at the fountain head then that which was
in Erogatione, and this he judged greater than that which was
in Commentariis.
+ Commentarius
beareth many ſen­
ſes, but in this
place ſignifieth a
certain Regiſter of
the quantities of
the Waters in the
ſeveral publique A­
qu ducts of Rome;
which word I find
frequently uſed in
the Law-books of
antient Civilians:
Andby errogation
we are to under­
ſtand the diſtribu­
tion or delivering
out of thoſe ſtores
of Water.
APPENDIX II.
Alike miſtake chanced lately in the Aqueduct of Acqua­
Paola, which Water ſhould be 2000 Inches, and ſo many
effectively ought to be allowed; and it hath been given in
1ſo to be by the Signors of Bracciano to the Apoſtolick-Chamber;
and there was a meaſure thereof made at the beginning of the
Aqueduct; which meaſure proved afterwards much leſſe and
ſhort, conſidered and taken in Rome, and thence followed diſ­
contents and great diſorders, and all becauſe this property of
Running-Waters, of increaſing in meaſure, where the velocity
decreaſed; and of diminiſhing in meaſure, where the velocity
augmented, was not lookt into.
APPENDIX III.
Alike errour, in my judgement, hath beeen committed by
all thoſe learned men, which to prevent the diverſion of
the Reno of Bologna into Po by the Channels, through
which it at preſent runneth, judged, that the Reno being in its
greater excreſcence about 2000 feet, and the Po being near
1000 feet broad, they judged, I ſay, that letting the Reno into
Po, it would have raiſed the Water of Po two feet; from which
riſe, they concluded afterwards moſt exorbitant diſorders, either
of extraordinary Inundations, or elſe of immenſe and intolera­
ble expences to the people in raiſing the Banks of Po and Reno,
and with ſuch like weakneſſes, often vainly diſturbed the minds
of the perſons concerned: But now from the things demonſtra­
ted, it is manifeſt, That the meaſure of the Reno in Reno, would
be different from the meaſure of Reno in Po; in caſe that the
velocity of the Reno in Po, ſhould differ from the velocity
of Reno in Reno, as is more exactly determined in the fourth Pro­
poſition.
APPENDIX IV.
No leſs likewiſe are thoſe Ingeneers and Artiſts deceived,
that have affirmed, That letting the Reno into Po, there
would be no riſe at all in the Water of Po: For the truth
is, That letting Reno into Po, there would alwaies be a riſing; but
ſometimes greater, ſometimes leſſe, as the Po ſhall have a ſwifter
or ſlower Current; ſo that if the Po ſhall be conſtituted in a great
velocity, the riſe will be very ſmall; and if the ſaid Po ſhall be
ſlow in its courſe, then the riſe will be notable.
APPENDIX V.
And here it will not be beſides the purpoſe to advertiſe, That
the meaſures, partments, and diſtributions of the Waters
of Fountains, cannot be made exactly, unleſs there be con­
1fidered, beſides the meaſure, the velocity alſo of the Water;
which particular not being thorowly obſerved, is the cauſe of
continual miſcariages in ſuch like affairs.
APPENDIX VI.
Like conſideration ought to be had with the greater diligence,
for that an errour therein is more prejudicial; I ſay, ought to
be had by thoſe which part and divide Waters; for the
watering of fields, as is done in the Territories of Breſcia, Ber­
gama, Crema, Pavia, Lodigiano, Cremona, and other places:
For if they have not regard to the moſt important point of the
variation of the velocity of the Water, but onely to the bare
Vulgar meaſure, there will alwaies very great diſorders and pre­
judices enſue to the perſons concerned.
APPENDIX VII.
It ſeemeth that one may obſerve, that whilſt the Water run­
neth along a Channel, Current, or Conduit, its velocity is
retarded, withheld, and impeded by its touching the Bank or
ſide of the ſaid Channel or Current; which, as immoveable, not
following the motion of the Water, interrupteth its velocity:
From which particular, being true, as I believe it to be moſt
true, and from our conſiderations, we have an occaſion of diſ­
covering a very nice miſtake, into which thoſe commonly fall
who divide the Waters of Fountains. Which diviſion is wont
to be, by what I have ſeen here in Rome, performed two wayes;
The firſt of which is with the meaſures of like figures, as Cir­
cles, or Squares, having cut through a Plate of metal ſeveral
Circles or Squares, one of half an inch, another of one inch,
another of two, of three, of four, &c. with which they after­
wards adjuſt the Cocks to diſpence the Waters. The other
manner of dividing the Waters of Fountains, is with rectangle
paralellograms, of the ſame height, but of different Baſes, in ſuch
ſort likewiſe, that one paralellogram be of half an inch, another
of one, two, three, &c. In which manner of meaſuring and
dividing the Water, it ſhould ſeem that the Cocks being placed
in one and the ſame plain, equidiſtant from the level, or ſuperior
ſuperficies of the water of the Well; and the ſaid meaſures be­
ing moſt exactly made, the Water ought conſequently alſo to
be equally divided, and parted according to the proportion of
the meaſures. But if we well conſider every particular, we ſhall
finde, that the Cocks, as they ſucceſſively are greater, diſcharge
alwaies more Water than the juſt quantity, in compariſon of
1the leſſer; that is, to ſpeak more properly, The Water which
paſſeth through the greater Cock, hath alwaies a greater pro­
portion to that which paſſeth through the leſſer, than the greater
Cock hath to the leſſer. All which I will declare by an exam­
ple.
Let there be ſuppoſed for more plainneſs two Squares; (the
ſame may be underſtood of Circles, and other like Figures) The
firſt Square is, as we will ſuppoſe, quadruple to the other, and
theſe Squares are the mouths of two Cocks.; one of four inches,
the other of one: Now its manifeſt by what hath been ſaid, that
the Water which paſſeth by the leſs Cock, findeth its velocity
impeded in the circumference of the Cock; which impediment
34[Figure 34]
is meaſured by the ſaid circumfe­
rence. Now it is to be conſider­
ed, that if we would have the Wa­
ter which paſſeth through the
greater Cock, to be onely qua­
druple to that which paſſeth
through the leſſe, in equal ſpaces of time, it would be neceſſary,
that not onely the capacity and the meaſure of the greater Cock
be quadruple to the leſſer Cock, but that alſo the impediment be
quadrupled. Now in our caſe it is true, That the belly and
mouth of the Cock is quadrupled, and yet the impediment is not
quadrupled, but is onely doubled; ſeeing that the circumference
of the greater Square, is onely double to the circumference of
the leſier Square; for the greater circumference containeth eight
of thoſe parts, of which the leſſer containeth but four, as is ma­
nifeſt by the deſcribed Figure; and for that cauſe there ſhall
paſs by the greater Cock, above four times as much Water, as
ſhall paſs by the leſſer Cock.
The like errour occurreth alſo in the other manner of meaſu­
ring the Water of a Fountain, as may eaſily be collected from
what hath been ſaid and obſerved above.
APPENDIX VIII.
The ſame contemplation diſcovereth the errour of thoſe
Architects, who being to erect a Bridge of ſundry Arches
over a River, conſider the ordinary breadth of the River;
which being v. g. fourty fathom, and the Bridge being to conſiſt
of four Arches, it ſufficeth them, that the breadth of all the four
Arches taken together, be fourty fathom; not conſidering that
in the ordinary Channel of the River, the Water hath onely
two impediments which retard its velocity; namely, the touching
and gliding along the two ſides or ſhores of the River: but
1the ſame water in paſſing under the Bridge, in our caſe meeteth
with eight of the ſame impediments, bearing, and thruſting upon
two ſides of each Arch (to omit the impediment of the bottom,
for that it is the ſame in the River, and under the Bridge) from
which inadvertency ſometimes follow very great diſorders, as
quotidian practice ſhews us.
APPENDIX IX.
It is alſo worthy to conſider the great and admirable benefit
that thoſe fields receive, which are wont to drink up the Rain­
water with difficulty, through the height of the water in the
principal Ditches; in which caſe the careful Husbandman cutteth
away the reeds and ruſhes in the Ditches, through which the
waters paſs; whereupon may be preſently ſeen, ſo ſoon as the
reeds and ruſhes are cut, a notable Ebb in the level of the water
in the Ditches; inſomuch that ſometimes it is obſerved, that the
water is abated after the ſaid cutting a third and more, of what it
was before the cutting. The which effect ſeemingly might de­
pend on this, That, before thoſe weeds took up room in the
Ditch, and for that cauſe the water kept a higher level, and the
ſaid Plants being afterwards cut and removed, the water came to
abate, poſſeſſing the place that before was occupied by the
weeds: Which opinion, though probable, and at firſt ſight ſa­
tisfactory, is nevertheleſs inſufficient to give the total reaſon of
that notable abatement which hath been ſpoken of: But it is ne­
ceſſary to have recourſe to our confideration of the velocity in
the courſe of the water, the chiefeſt and true cauſe of the vari­
ation of the meaſure of the ſame Running-Water; for, that
multitudes of reeds, weeds, and plants diſperſed through the cur­
rent of the Ditch, do chance notably to retard the courſe of the
water, and therefore the meaſure of the water increaſeth; and
thoſe impediments removed, the ſame water gaineth velocity,
and therefore decreaſeth in meaſure, and conſequently in
height.
And perhaps this point well underſtood, may be of great
profit to the fields adjacent to the Pontine Fens, and I doubt not
but if the River Ninfa, and the other principal Brooks of thoſe
Territories were kept well cleanſed from weeds, their waters
would be at a lower level, and conſequently the drains of the
fields would run into them more readily; it being alwayes to be
held for undoubted, that the meaſure of the water before the
cleanſing, hath the ſame proportion to the meaſure after clean­
ſing, that the velocity after the cleanſing hath to the velocity
before the cleanſing: An dbecauſe thoſe weeds being cleanſed
1away, the courſe ef the water notably increaſeth, it is therefore
neceſſary that the ſaid water abate in meaſure, and become
lower.
APPENDIX. X.
We having above obſerved ſome errors that are commit­
ted in diſtributing the waters of Fountains, and thoſe
that ſerve to water fields; it ſeemeth now fit, by way of
a cloſe to this diſcourſe, to advertiſe by what means theſe divi­
ſions may be made juſtly and without error. I therefore think
that one might two ſeveral wayes exquiſitly divide the water of
Fountains; The firſt would be by diligently examining, Firſt,
how much water the whole Fountain diſchargeth in a determi­
nate time, as for inſtance: How many Barrels, or Tuns it carri­
eth in a ſet time; and in caſe you are afterwards to diſtribute
the water, diſtribute it at the rate of ſomany Barrels or Tuns, in
that ſame time; and in this caſe the participants would have
their punctual ſhares: Nor could it ever happen to ſend out more
water, than is reckoned to be in the principal Fountain; as befel
Giulio Frontino, and as alſo it frequently happeneth in the Mo­
dern Aqueducts, to the publick and private detriment.
The other way of dividing the ſame waters of a Fountain, is
alſo ſufficiently exact and eaſie, and may be, by having one one­
ly ſize for the Cock or Pipe, as ſuppoſe of an inch, or of half an
inch; and when the caſe requireth to diſpence two, three, and
more inches, take ſo many Cocks of the ſaid meaſure as do eva­
cuate the water, which is to be emitted; and if we are to make
uſe onely of one greater Cock, we being to place one to diſ­
charge for example four inches; and having the former ſole mea­
ſure of an inch, we muſt make a Cock that is bigger, its true, than
the Cock of one inch; but not ſimply in a quadruple propor­
tion, for that it would diſcharge more than juſt ſo much water,
as hath been ſaid above; but we ought to examine diligently
how much water the little Cock emitteth in an hour; and then
enlarge, and contract the greater Cock, ſo, that it may diſ­
charge four times as much water as the leſſer in the ſame time;
and by this means we ſhall avoid the diſorder hinted in the
ſeventh Appendix. It would be neceſſary nevertheleſs, to ac­
commodate the Cocks of the Ciſtern ſo, that the level of the
water in the Ciſtern may alwayes reſt at one determinate mark
above the Cock, otherwiſe the Cocks will emit ſometimes
greater, and ſometimes leſſe abundance of water: And becauſe
it may be that the ſame water of the Fountain may be ſometimes
more abundant, ſometimes leſs; in ſuch caſe it will be neceſſary
1to adjuſt the Ciſtern ſo, that the exceſs above the ordinary wa­
ter, diſcharge into the publick Fountains, that ſo the particular
participants may have alwayes the ſame abundance of
water.
APPENDIX XI.
Much more difficult is the diviſion of the waters which
ſerve to water the fields, it not being poſſible to obſerve
ſo commodiouſly, what quantity of water the whole
Ditch ſends forth in one determinate time, as may be done in
Fountains: Yet nevertheleſs, if the ſecond propoſition by us a
little below demonſtrated, be well underſtood, there may be
thence taken a very ſafe and juſt way to diſtribute ſuch waters.
The Propoſition therefore by us demonſtrated is this: If there
be two Sections, (namely two mouths of Rivers) the quantity of
the water which paſſeth by the firſt, hath a proportion to that
which paſſeth by the ſecond, compounded of the proportions of
the firſt Section to the ſecond, and of the velocity through
the firſt, to the velocity through the ſecond: As I will declare
for example by help of practice, that I may be underſtood by
all, in a matter ſo important. Let the two mouths of the
Rivers be A, and B, and let
35[Figure 35]
the mouth A be in meaſure
and content thirty two feet,
and the mouth B, eight feet.
Here you muſt take notice,
that it is not alwayes true, that
the Water which paſſeth by A,
hath the ſame proportion to that which paſſeth by B, that the
mouth A hath to the mouth B; but onely when the velocityes
by each of thoſe paſſages are equal: But if the velocityes ſhall
be unequal, it may be that the ſaid mouths may emit equal
quantity of Water in equal times, though their meaſure be un­
equal; and it may be alſo, that the bigger doth diſcharge a great­
er quantity of Water: And laſtly, it may be, that the leſs mouth
diſchargeth more Water than the greater; and all this is mani­
feſt by the things noted in the beginning of this diſcourſe, and
by the ſaid ſecond Propoſition. Now to examine the propor­
tion of the Water that paſſeth by one Ditch, to that which paſ­
ſeth by another, that this being known, the ſame Waters and
mouths of Ditches may be then adjuſted; we are to keep ac­
count not onely of the greatneſs of the mouths or paſſages of the
Water, but of the velocity alſo; which we will do, by firſt find­
ing two numbers that have the ſame proportion between them­
1ſelves, as have the mouths, which are the numbers 32 and 8
in our example: Then this
36[Figure 36]
being done, let the velocity
of the Water by the paſſa­
ges A and B, be examined
(which may be done keeping
account what ſpace a piece
of Wood, or other body that
ſwimmeth, is carried by the ſtream in one determinate time; as
for inſtance in 50 pulſes) and then work by the golden Rule, as
the velocity by A, is to the velocity by B, ſo is the number 8, to
another number, which is 4. It is clear by what is demonſtra­
ted in the ſaid ſecond Propoſition, that the quantity of water,
which paſſeth by the mouth A, ſhall have the ſame proportion of
that which paſſeth by the mouth B, that 8 hath to 1. Such pro­
portion being compoſed of the proportions of 32 to 8, and of 8 to
4; namely, tothe greatneſs of the mouth A, to the greatneſs of the
mouth B, and of the velocity in A, to the velocity in B. This being
done, we muſt then contract the mouth which diſchargeth more
then its juſt quantity of water, or enlarge the other which diſchar­
geth leſs, as ſhal be moſt commodious in practice, which to him that
hath underſtood this little that hath been delivered, will be very
afie.
APPENDIX XII.
Theſe opperations about Water, as I have hitherto on ſun­
dry occaſions obſerved, are involved in ſo many difficul­
ties, and ſuch a multiplicity of moſt extravagant accidents,
that it is no marvel if continually many, and very important er­
rours be therein committed by many, and even by Ingeneers
themſelves, and Learned-men; and becauſe many times they
concern not onely the publique, but private intereſts: Hence it
is, that it not onely belongeth to Artiſts to treat thereof, but very
oft even the vulgar themſelves pretend to give their judgement
therein: And I have been troubled many times with a neceſſity
of treating, not onely with thoſe, which either by practice, or
particular ſtudy, underſtood ſomewhat in theſe matters; but alſo
with people wholly void of thoſe notions, which are neceſſary for
one that would on good grounds diſcourſe about this particular;
and thus many times have met with more difficulty in the thick
skulls of men, than in precipitous Torrents, and vaſt Fennes.
And in particular, I had occafion ſome years paſt to go ſee the
Gave or Emiſſary of the Lake of Perugia, made many years agon
by Braccio Fortobraccio, but for that it was with great ruines by
Time decayed, and rendred unuſeful, it was repaired with in­
1duſtry truly heroicall and admirable, by Monſignor Maffei Bar­
herino, then Prefect for the Wayes, and now Pope. And being
neceſſitated, that I might be able to walk in the Cave, and for
other cauſes, I let down the Sluices of the ſaid Cave, at the mouth
of the Lake: No ſooner were they ſtopt, but a great many of the
people of the Towns and Villages coaſting upon the Lake
flocking thither, began to make grievous complaints, that if thoſe
Sluices were kept ſhut, not onely the Lake would want its due
Vent, but alſo the parts adjacent to the Lake would be over
flown to their very great detriment. And becauſe at firſt appea­
rance their motion ſeemed very reaſonable, I found my ſelf hard
put to it, ſeeing no way to perſwade ſuch a multitude, that the
prejudice which they pretended I ſhould do them by keeping
the Sluices ſhut for two dayes, was abſolutely inſenſible; and that
by keeping them open, the Lake did not ebb in the ſame time ſo
much as the thickneſs of a ſheet of Paper: And therefore I was
neceſſitated to make uſe of the authority I had, and ſo followed
my buſineſs as cauſe required, without any regard to that Rab­
ble tumultuouſly aſſembled. Now when I am not working with
Mattock or Spade, but with the Pen and Diſcourſe, I intend to
demonſtrate clearly to thoſe that are capable of reaſon, and that
have well underſtood the ground of this my Treatiſe, that the
fear was altogether vain which thoſe people conceited. And
therefore I ſay, that the Emiſſary or Sluice of the Lake of Peru­
gia, ſtanding in the ſame mannner as at preſent, and the water
paſſing thorow it with the ſame velocity as now; to examine
how much the Lake may abate in two days ſpace, we ought to
conſider, what proportion the ſuperficies of the whole Lake hath
to the meaſure of the Section of the Emiſſary, and afterwards to
infer, that the velocity of the water by the Emiſſary or Sluice,
ſhall have the ſame proportion to the abatement of the Lake,
and to prove thorowly and clearly this diſcourſe, I intend to
demonſtrate the following Propoſition.
Suppoſe a Veſſel of any bigneſſe, and that it hath an Emiſſary
or Cock, by which it diſchargeth its water. And look what pro­
portion the ſuperſicies of the
veſſel hath to the meaſure of
37[Figure 37]
the ſection of the cock, ſuch pro­
portion ſhall the velocity of the
Water in the Cock have to the
abatement of the Lake Let the
Veſſel be A B C D, H I L B, through which the Water runneth,
the ſuperficies of the Water in the Veſſel A D, and the ſection
of the Cock H L: and let the Water in the Veſſel
be ſuppoſed to have falne in one determinate time from A to F.
1I ſay that the proportion of the ſuperficies of the Veſſel A D is
in proportion to the meaſure of the ſection of the Emiſſary
H L, as the velocity of the Emiſſary or Cock to the line A F;
which is manifeſt, for that the Water in the Veſsel moving by
the line A F; as far as F, and the whole maſs of Water A G
diſcharging it ſelf, and in the ſame time the ſame quantity of
Water being diſcharged by the ſection of the Emiſſary H L; it
is neceſſary by what I have demonſtrated in the third Propoſition,
and alſo explained in the beginning of this Treatiſe, that the ve­
locity by the Emiſſary or Cock be in proportion to the velocity
of the abatement, as the ſuperficies of the Veſſel to the mea­
ſure of the ſection of the Emiſſary, which was to be demon­
ſtrated.
That which hath been demonſtrated in the Veſſel, falls out ex­
actly alſo in our Lake of Perugia, and its Emiſsary; and becauſe
the immenſity of the ſuperficies of the Lake is in proportion to
the ſuperficies of the Emiſsary or Sluice, as many millions to
one, as may be eaſily calculated; it is manifeſt, that ſuch abate­
ment ſhall be imperceptible, and almoſt nothing, in two dayes
ſpace, nay in four or ſix: and all this will be true, when we
ſuppoſe that for that time there entreth no other Water into the
Lake from Ditches or Rivolets, which falling into the Lake would
render ſuch abatement yet leſs.
Now we ſee, that it's neceſsary to examine ſuch abatements
and riſings, with excellent reaſons, or at leaſt, with accurate ex­
periments, before we reſolve and conclude any thing; and how
farre the vulgar are diſtant from a right judgment in ſuch
matters.
APPENDIX XIII.
For greater confirmation of all this which I have ſaid, I
will inſtance in another like caſe, which alſo I met with here­
tofore, wherein, for that the buſineſs was not rightly un­
derſtood, many diſorders, vaſt expences, and conſiderable miſ­
chiefs have followed. There was heretofore an Emiſsary or
Sluice made to drain the Waters, which from Rains, Springs, and
Rivolets fall into a Lake; to the end, the ſhores adjoyning on
the Lake, ſhould be free from the overflowing of the Waters;
but becauſe perhaps the enterprize was not well managed and
carried on, it fell out, that the Fields adjacent to the ſaid Chanel
could not drain, but continued under water; to which diſorders
a preſent remedy hath been uſed, namely, in a time convenient
to ſtop up the Sluice, by meanes of certain Floodgates kept on
purpoſe for that end; and thus abating the Level of the Water
1in the Emiſſary, in the ſpace of three or four dayes, the Fields
have been haply drained. But on the other part, the proprietors
bordering on the Lake oppoſed this, grievouſly complaining, that
whilſt the Floodgates are ſhut, and the courſe of the Water of
the Sluice hindered, the Lake overflowes the Lands adjacent, by
meanes of the Rivers that fell into it, to their very great damage;
and ſo continuing their ſuits, they got more of vexation than ſa­
tisfaction. Now, being asked my opinion herein, I judged it
requiſite (ſince the point in controverſie was about the riſing
and falling of the Lake) that the ſaid abatement, when the
Floodgates are open, and increaſe when they are ſhut ſhould be
exactly meaſured, and told them, that it might be eaſily done at
a time when no extraordinary Waters fell into the Lake, neither
of Rain, or otherwiſe; and the Lake was undiſturbed by winds
that might drive the Water to any ſide, by planting neer to an
Iſlet, which is about the middle of the Lake, a thick poſt, on
which ſhould be made the marks of the Lakes riſing and falling
for two or three dayes. I would not, at that time, pawn, or re­
ſolutely declare, my judgment, in regard I might be, by divers
accidents miſled. But this I told them, that (by what I have
demonſtrated, and particularly that which I have ſaid above
touching the Lake of Perugia) I inclined greatly to think,
that theſe riſings and fallings would prove imperceptible, and
inconſiderable; and therefore, that in caſe experience ſhould
make good my reaſon, it would be to no purpoſe for them to
continue diſputing and wrangling, which cauſeth, (according
to the Proverb) A great deal of cry, but produceth not much
Wool.
Laſtly, it importing very much to know what a Rain conti­
nued for many dayes can do in raiſing theſe Lakes, I will here in­
ſert the Copy of a Letter, which I writ formerly to Signior Ga­
lilæo Galilæi, chief Philoſopher to the Grand Duke of Tuſcany,
wherein I have delivered one of my conceits in this buſineſſe, and
it may be, by this Letter, I may, more ſtrongly, confirm what I
have ſaid above.
1
The Copy of a Letter to Signore GALILÆO
GALILÆI, Chief Philoſopher to the moſt Serene
Great Duke of TVSCANY.
Worthy and moſt Excellent SIR,
In ſatisfaction of my promiſe, in my former Letters of
repreſenting unto you ſome of my Conſiderations
made upon the Lake Thraſimeno, I ſay, That in times
paſt, being in Perugia, where we held our General
Convention, having underſtood that the Lake Thraſimeno, by
the great drought of many Moneths was much abated, It came
into my head, to go privately and ſee this novelty, both for my
particular ſatisfaction, as alſo that might I be able to relate the
whole to my Patrons, upon the certitude of my own ſight of the
place. And ſo being come to the Emiſſary of the Lake, I found
that the Level of the Lakes ſurface was ebbed about five Ro­
man Palmes of its wonted watermark, inſomuch that it was lower
than the tranſome of the mouth of the Emiſſary, by the length
of ----------------------------this deſcribed line, and there­
fore no Water iſſued out of the Lake, to the great prejudice of
all the places and villages circumjacent, in regard that the Wa­
ter which uſed to run from the ſaid Lake turned 22 Mills, which
not going, neceſſitated the inhabitants of thoſe parts to go a
dayes journey and more, to grinde upon the Tiber. Being retur­
ned to Perugia, there followed a Rain, not very great, but con­
ſtant, and even, which laſted for the ſpace of eight hours, or
thereabouts; and it came into my thoughts to examine, being
in Perugia, how much the Lake was increaſed and railed by this
Rain, ſuppoſing (as it was probable enough) that the Rain had
been univerſal over all the Lake; and like to that which fell in
Perugia, and to this purpoſe I took a Glaſſe formed like a Cy­
linder, about a palme high, and half a palme broad; and having
put in water ſnfficient to cover the bottome of the Glaſſe, I no­
ted diligently the mark of the height of the Water in the Glaſſe,
and afterwards expoſed it to the open weather, to receive the
Raine-water, which fell into it; and I let it ſtand for the
ſpace of an hour; and having obſerved that in that time the Wa­
ter was riſen in the Veſſel the height of the following line---,
I conſidered that if I had expoſed to the ſame rain ſuch other veſ­
ſels equal to that, the Water would have riſen in them all accor­
ding to that meaſure: And thereupon concluded, that alſo in all
1the whole extent of the Lake, it was neceſſary the Water ſhould
be raiſed in the ſpace of an hour the ſame meaſure. Yet here I
conſidered two difficulties that might diſtutb and altar ſuch an
effect, or at leaſt render it inobſerveable, which afterwards well
weighed, and reſolved, left me (as I will tell you anon) in the
concluſion the more confirmed; that the Lake ought to be in­
creaſed in the ſpace of eight hours, that the rain laſted eight
times that meaſure. And whilſt I again expoſed the Glaſs to re­
peat the experiment, there came unto me an Ingeneer to talk
with me touching certain affairs of our Monaſtary of Perugia, and
diſcourſing with him, I ſhewed him the Glaſs out at my Cham­
ber-window, expoſed in a Court-yard; and communicated to
him my fancy, relacing unto him all that I had done. But I
ſoon perceived that this brave fellow conceited me to be but of
a dull brain, for he ſmilling ſaid unto me; Sir, you deceive
your ſelf: I am of opinion that the Lake will not be increaſ­
ed by this rain, ſo much as the thickneſſe of a ^{*} Julio.

Hearing him pronounce this his opinion with freeneſs and
confidence, I urged him to give me ſome reaſon for what he
ſaid, aſſuring him, that I would change my judgement, when I
ſaw the ſtrength of his Arguments: To which he anſwered, that
he had been very converſant about the Lake, and was every day
upon it, and was well aſſured that it was not at all increaſed. And
importuning him further, that he would give me ſome reaſon
for his ſo thinking, he propoſed to my conſideration the great
drought paſſed, and that that ſame rain was nothing for the
great parching: To which I anſwered, I believe Sir that the ſur­
face of the Lake, on which the rain had fallen was moiſtned; and
therefore ſaw not how its drought, which was nothing at all,
could have drunk up any part of the rain. For all this he per­
ſiſting in his conceit, without yielding in the leaſt to my allega­
tion; he granted in the end (I believe in civility to me) that
my reaſon was plauſible and good, but that in practiſe it could
not hold. At laſt to clear up all, I made one be called, and
ſent him to the mouth of the Emiſſary of the Lake, with order
to bring me an exact account, how he found the water of the
Lake, in reſpect of the Tranſome of the Sluice. Now here,
Signore Galilo, I would not have you think that I had brought
the matter in hand to concern me in my honour; but believe me
(and there are witneſſes of the ſame ſtill living) that my meſſen­
ger returning in the evening to Perugia, he brought me word,
that the water of the Lake began to run through the Cave; and
that it was riſen almoſt a fingers breadth above the Tranſome:
Inſomuch, that adding this meaſure, to that of the lowneſs of
the ſurface of the Lake, beneath the Tranſome before the rain,
1it was manifeſt that the riſing of the Lake cauſed by the rain, was
to a hair thoſe four fingers breadth that I had judged it to be.
Two dayes after I had another bout with the Ingeneer, and re­
lated to him the whole buſineſs, to which he knew not what to
anſwer.
* A Coyn of Pope
Julius worth ſix
pence.
Now the two difficulties which I thought of, able to impede
my concluſion, were theſe following: Firſt, I conſidered that
it might be, that the Wind blowing from the ſide where the
Sluice ſtood, to the Lake-ward; the mole and maſs of the Wa­
ter of the Lake might be driven to the contrary ſhore; on which
the Water riſing, it might be fallen at the mouth of the Emiſſa­
ry, and ſo the obſervation might be much obſcured. But this
difficulty wholly vaniſhed by reaſon of the Aires great tranqui­
lity; which it kept at that time, for no Wind was ſtirring on any
ſide, neither whilſt it rained, nor afterwards.
The ſecond difficulty which put the riſing in doubt, was, That
having obſerved in Florence, and elſewhere, thoſe Ponds into
which the rain-water, falling from the houſe, is conveyed
through the Common-ſhores: And that they are not thereby
ever filled, but that they ſwallow all that abundance of water,
that runs into them by thoſe conveyances which ſerve them with
water; inſomuch that thoſe conveyances which in time of
drought maintain the Pond, when there comes new abundance
of water into the Pond, they drink it up, and ſwallow it: A like
effect might alſo fall out in the Lake, in which there being many
veins (as it is very likely) that maintain and feed the Lake; theſe
veins might imbibe the new addition of the Rain-water, and ſo
by that means annuall the riſing; or elſe diminiſh it in ſuch ſort, as
to render it inobſervable. But this difficulty was eaſily reſolved
by conſidering my Treatiſe of the meaſure of Running-Waters;
foraſmuch as having demonſtrated, that the abatement of a Lake
beareth the reciprocal proportion to the velocity of the Emiſſa­
ry, which the meaſure of the Section of the Emiſſary of the Lake,
hath to the meaſure of the ſurface of the Lake: making the
calculation and account, though in groſs; by ſuppoſing that its
veins were ſufficiently large, and that the velocity in them were
notable in drinking up the water of the Lake; yet I found never­
theleſs, that many weeks and moneths would be ſpent in drink­
ing up the new-come abundance of water by the rain, ſo that
I reſted ſure, that the riſing would enſue, as in effect it did.
And becauſe many of accurate judgement, have again cauſed
me to queſtion this riſing, ſetting before me, that the Earth be­
ing parched by the great drought, that had ſo long continued, it
might be, that that Bank of Earth which environed the brink of
the Lake, being dry, and imbibing great abundance of Water
1from the increaſing Lake, would not ſuffer it to increaſe in
height: I ſay therefore, that if we would rightly conſider this
doubt here propoſed, we ſhould, in the very conſideration of it,
ſee it reſolved; for, it being ſuppoſed that that liſt or border of
Banks which was to be occupied by the increaſe of the Lake, be
a Brace in breadth quite round the Lake, and that by reaſon of
its dryneſs it ſucks in water, and that by that means this propor­
tion of water co-operates not in raiſing of the Lake: It is abſo­
lutely neceſſary on the other hand, that we conſider, That the
Circuit of the water of the Lake being thirty miles, as its com­
monly held, that is to ſay, Ninety thouſand Braces of Florence
in compaſs; and therefore admitting for true, that each Brace of
this Bank drink two quarts of water, and that for the ſpieading
it require three quarts more, we ſhall finde, that the whole agre­
gate of this portion of water, which is not imployed in the raiſing
of the Lake, will be four hundred and fifty thouſand Quarts of
water; and ſuppoſing that the Lake be ſixty ſquare miles, three
thouſand Braces long, we ſhall finde, that to diſpence the water
poſſeſt by the Bank about the Lake, above the total ſurface of
the Lake, it ought to be ſpread ſo thin, that one ſole quart of
water may over-ſpread ten thouſand ſquare Braces of ſurface:
ſuch a thinneſs, as muſt much exceed that of a leaf of beaten
Gold, and alſo leſs than that skin of water which covers the Bub­
bles of it: and ſuch would that be, which thoſe men would have
ſubſtracted from the riſing of the Lake: But again, in the ſpace
of a quarter of an hour at the beginning of the rain, all that
Bank is ſoaked by the ſaid rain, ſo that we need not for the
moiſtning of it, imploy a drop of that water which falleth into
the Lake. Beſides we have not brought to account that abun­
dance of water which runs in time of rain into the Lake, from
the ſteepneſs of the adjacent Hills and Mountains; which would
be enough to ſupply all our occaſions: So that, neither ought
we for this reaſon to queſtion our pretended riſing. And this
is what hath fallen in my way touching the conſideration of the
Thraſimenian Lake.
After which, perhaps ſomewhat raſhly, wandring beyond my
bounds, I proceeded to another contemplation, which I will re­
late to you, hoping that you will receive it, as collected with
theſe cautions requiſite in ſuch like affairs; wherein we ought
not too poſitively to affirm any thing of our own heads for cer­
tain, but ought to ſubmit all to the ſound and ſecure delibera­
tion of the Holy Mother-Church, as I do this of mine, and all
others; moſt ready to change my judgement, and conform my
ſelf alwaies to the deliberations of my Superiors. Continu­
1ing therefore my above-ſaid conceit about the riſing of the wa­
ter in the glaſs tried before, it came into my minde, that the
forementioned rain having been very gentle, it might well be,
that if there ſhould have faln a Rain fifty, an hundred, or a thou­
ſand times greater than this, and much more intenſe (which
would inſue as oft as thoſe falling drops were four, ſive or ten
times bigger than thoſe of the above-mentioned rain, keeping
the ſame number) in ſuch a caſe its manifeſt, that in the ſpace
of an hour the Water would riſe in our Glaſs, two, three, and
perhaps more Yards or Braces; and conſequently, if ſuch a
Raine ſhould fall upon a Lake, that the ſaid Lake would
riſe, according to the ſame rate: And likewiſe, if ſuch a
Rain were univerſall, over the whole Terreſtriall Globe, it
would neceſſarily, in the ſpace of an hour, make a ri­
ſing of two, or three braces round about the ſaid Globe,
And becauſe we have from Sacred Records, that in the
time of the Deluge, it rained fourty dayes and fourty nights;
namely, for the ſpace of 960 houres; its clear, that if the ſaid
Rain had been ten times bigger than ours at Perugia, the riſing
of the Waters above the Terreſtrial Globe would reach and paſs
a mile higher than the tops of the Hills and Mountains that are
upon the ſuperficies of the Earth; and they alſo would concur
to increaſe the riſe. And therefore I conclude, that the riſe of
the Waters of the Deluge have a rational congruity with natural
Diſcourſes, of which I know very well that the eternal truths of
the Divine leaves have no need; but however I think ſo clear an
agreement is worthy of our conſideration, which gives us occa­
ſion to adore and admire the greatneſſe of God in his mighty
Works, in that we are ſometimes able, in ſome ſort, to meaſure
them by the ſhort Standard of our Reaſon.
Many Leſſons alſo may be deduced from the ſame Doctrine,
which I paſſe by, for that every man of himſelf may eaſily know
them, having once ſtabliſhed this Maxime; That it is not poſſi­
ble to pronounce any thing, of a certainty, touching the quantity
of Running Waters, by conſidering only the ſingle vulgar mea­
ſure of the Water wichout the velocity; and ſo on the contrary,
he that computes only the velocity, without the meaſure, ſhall
commit very great errours; for treating of the meaſure of Run­
ning Waters, it is neceſſary, the water being a body, in handling
its quantity, to conſider in it all the three dimenſions of breadth,
depth, and length: the two firſt dimenſions are obſerved by all
in the common manner, and ordinary way of meaſuring Running
Waters; but the third dimenſion of length is omitted; and hap­
ly ſuch an overſight is committed, by reaſon the length of Run­
1ning Water is reputed in ſome ſenſe infinite, in that it never cea­
ſeth to move away, and as infinite is judged incomprehenſible;
and ſuch as that there is no exact knowledge to be had thereof;
& ſo there comes to be no account made thereof; but if we ſhould
make ſtrict reflection upon our conſideration of the velocity of
Water, we ſhould find, that keeping account of the ſame, there
is a reckoning alſo made of the length; foraſmuch as whilſt we
ſay, the Water of ſuch a Spring runs with the velocity of paſſing
a thouſand or two thouſand paces an hour: this in ſubſtance is
no other than if we had ſaid, ſuch a Fountain diſchargeth in an
hour a Water of a thouſand or two thouſand paces long. So
that, albeit the total length of Running water be incomprehen­
ſible, as being infinite, yet nevertheleſſe its rendered intelligible
by parts in its velocity. And ſo much ſufficeth to have hinted
about this matter, hoping to impart on ſome other occaſion other
more accurate Obſervations in this affair.
LAVS DEO.
38[Figure 38]
1
GEOMETRICAL
DEMONSTRATIONS
OF THE
MEASURE
OF
Running Waters.
BY
D. BENEDETTO CASTELLI,
Abbot of CASSINA, and Mathematician to
P. VRBAN. VIII.
DEDICATED
To the moſt Illuſtrious, and moſt Excellent Prince
DON THADDEO BARBERINI,
PRINCE OF
PALESTRINA,
AND
GENERAL of the HOLY CHURCH.
LONDON,
Printed Anno Domini, MDCLXI.
1
OF THE
MENSURATION
OF
Running Waters.
SUPPOSITION I.
Let it be ſuppoſed, that the banks of the Rivers of which
we ſpeak be erected perpendicular to the plane of the up­
per ſuperficies of the River.
SUPPOSITION II.
We ſuppoſe that the plane of the bottome of the River, of
which we ſpeak is at right angles with the banks.
SUPPOSITION III.
It is to be ſuppoſed, that we ſpeak of Rivers, when they are at
ebbe, in that ſtate of ſhallowneſſe, or at flowing in that ſtate
of deepneſſe, and not in their tranſition from the ebbe to the
flowing, or fr m the flowing to the ebbe.
Declaration of Termes.
FIRST.
If a River ſhall be cut by a Plane at right angles to the ſurface
of the water of the River, and to the banks of the River,
that ſame dividing Plane we call the Section of the River; and
this Section, by the Suppoſitions above, ſhall be a right angled
Parallelogram.
SECOND.
We call thoſe Sections equally Swift, by which the water runs
with equal velocity; and more ſwift and leſs ſwift that
Section of another, by which the water runs with greater or leſſe
velocity.
1
AXIOME I.
Sections equal, and equally ſwift, diſcharge equal quantities
of Water in equal times.
AXIOME II.
Sections equally ſwift, and that diſcharge equal quantity of
Water, in equal time, ſhall be equal.
AXIOME III.
Sections equal, and that diſcharge equal quantities of Water
in equal times, ſhall be equally ſwift.
AXIOME IV.
When Sections are unequal, but equally ſwift, the quanti­
ty of the Water that paſſeth through the firſt Section,
ſhall have the ſame proportion to the quantity that paſ­
ſeth through the Second, that the firſt Section hath to the ſecond
Section. Which is manifeſt, becauſe the velocity being the
ſame, the difference of the Water that paſſeth ſhall be according
to the difference of the Sections.
AXIOME V.
If the Sections ſhall be equal, and of unequal velocity, the
quantity of the Water that paſſeth through the firſt, ſhall
have the ſame proportion to that which paſſeth through the
ſecond, that the velocity of the firſt Section, ſhall have to the
velocity of the ſecond Section. Which alſo is manifeſt, becauſe
the Sections being equal, the difference of the Water which
paſſeth, dependeth on the velocity.
PETITION.
A Section of a River being given, we may ſuppoſe another
equal to the given, of different breadth, heigth, and ve­
locity.
1
PROPOSITION I.
The Sections of the ſame River diſcharge equal quan­
tities of Water in equal times, although the Secti­
ons themſelves he unequal.
Let the two Sections be A and B, in the River C, running
from A, towards B; I ſay, that they diſcharge equal quan­
tity of Water in equal times; for if greater quantity of Wa­
ter ſhould paſs through A, than paſſeth through B, it would
39[Figure 39]
follow that the Water in the intermediate ſpace of the River C,
would increaſe continually, which is manifeſtly falſe, but if
more Water ſhould iſſue through the Section B, than entreth at
the Section A, the Water in the intermediate ſpace C, would
grow continually leſs, and alwaies ebb, which is likewiſe falſe;
therefore the quantity of Water that paſſeth through the Secti­
on B, is equal to the quantity of Water which paſſeth through
the Section A, and therefore the Sections of the ſame River diſ­
charge, &c. Which w s to be demonſtrated.
PROPOSITION II.
In two Sections of Rivers, the quantity of the Water
which paſſeth by one Section, is to that which paſ­
ſeth by the ſecond, in a Proportion compounded of
the proportions of the firſt Section to the ſecond, and
of the velocitie through the first, to the velocitie
of the ſecond.
I Et A, and B be two Sections of a River; I ſay, that the
quantity of Water which paſſeth through A, is to that which
paſſeth through B, in a proportion compounded of the pro­
portions of the firſt Section A, to the Section B; and of the velo­
city through A, to the velocity through B: Let a Section be
1ſuppoſed equal to the Section A, in magnitude; but of velocity
equal to the Section B, and let it be G, and as the Section A is
40[Figure 40]
to the Section B, ſo let the line F be to the line D; and as the
velocity A, is to the velocity by B, ſo let the line D be to the
line R: Therefore the Water which paſſeth thorow A, ſhall be
to that which paſſeth through G (in regard the Sections A and
G are of equal bigneſs, but of unequal velocity) as the velocity
through A, to the velocity through G; But as the velocity
through A, is to the velocity through G, ſo is the velocity through
A, to the velocity through B; namely, as the line D, to the
line R: therefore the quantity of the Water which paſſe the
through A, ſhall be to the quantity which paſſeth through G, as
the line D is to the line R; but the quantity which paſſeth
through G, is to that which paſſeth through B, (in regard the
Sections G, and B, are equally ſwift) as the Section G to the Se­
ction B; that is, as the Section A, to the Section B; that is, as
the line F, to the line D: Therefore by the equal and perturbed
proportionality, the quantity of the Water which paſſeth through
A, hath the ſame proportion to that which paſſeth through B,
that the line F hath to the line R; but F to R, hath a proportion
compounded of the proportions of F to D, and of D to R; that
is, of the Section A to the Section B; and of the velocity through
A, to the velocity through B. Therefore alſo the quantity of
Water which paſſeth through the Section A, ſhall have a propor­
tion to that which paſſeth through the Section B, compounded of
the proportions of the Section A, to the Section B; and of
the velocity through A, to the velocity through B: And
therefore in two Sections of Rivers, the quantity of Water which
paſſeth by the firſt, &c. which was to be demonſtrated.
COROLLARIE.
The ſame followeth, though the quantity of the Water which
paſſeth through the Section A, be equal to the quantity of
Water which paſſeth through the Section B, as is manifeſt by the
ſame demonſtration.
1
PROPOSITION III.
In two Sections unequal, through which paſs equal
quantities of Water in equal times, the Sections
have to one another, reciprocal proportion to their
velocitie.
Let the two unequal Sections, by which paſs equal quantities
of Water in equal times be A, the greater; and B, the leſſer:
I ſay, that the Section A, ſhall have the ſame Proportion
to the Section B, that reciprocally the velocity through B, hath to
the velocity through A; for ſuppoſing that as the Water that
paſſeth through A, is to that which paſſeth through B, ſo is the
41[Figure 41]
line E to the line F: therefore the quantity of water which paſ­
ſeth through A, being equal to that which paſſeth through B,
the line E ſhall alſo be equal to the line F: Suppoſing moreover,
That as the Section A, is to the Section B, ſo is the line F, to the
line G; and becauſe the quantity of water which paſſeth
through the Section A, is to that which paſſeth through the
Section B, in a proportion compoſed of the proportions of the
Section A, to the Section B, and of the velocity through A, to the
velocity through B; therefore the line E, ſhall be the line to F, in
a proportion compounded of the ſame proportions; namely, of
the proportion of the Section A, to the Section B, and of the ve­
locity through A, to the velocity through B; but the line E, hath
to the line G, the proportion of the Section A, to the Section B,
therefore the proportion remaining of the line G, to the line F,
ſhall be the proportion of the velocity through A, to the velocity
through B; therefore alſo the line G, ſhall be to the line E, as
the velocity by A, to the velocity by B: And converſly, the ve­
locity through B, ſhall be to the velocity through A, as the line
E, to the line G; that is to ſay, as the Section A, to the Section B,
and therefore in two Sections, &c. which was to be demonſtrated.
1
COROLLARIE.
Hence it is manifeſt, that Sections of the ſame River (which
are no other than the vulgar meaſures of the River) have
betwixt themſelves reciprocal proportions to their veloci­
ties; for in the firſt Propoſition we have demonſtrated that the
Sections of the ſame River, diſcharge equal quantities of Water
in equal times; therefore, by what hath now been demonſtrated
the Sections of the ſame River ſhall have reciprocal proportion
to their velocities; And therefore the ſame running water chan­
geth meaſure, when it changeth velocity; namely, increaſeth the
meaſure, when it decreaſeth the velocity, and decreaſeth the
meaſure, when it increaſeth the velocity.
On which principally depends all that which hath been ſaid
above in the Diſcourſe, and obſerved in the Corollaries and Ap­
pendixes; and therefore is worthy to be well underſtood and
heeded.
PROPOSITION IV.
If a River fall into another River, the height of the
firſt in its own Chanel ſhall be to the height that it
ſhall make in the ſecond Chanel, in a proportion
compounded of the proportions of the breadth of
the Chanel of the ſecond, to the breadth of the
Chanel of the firſt, and of the velocitie acquired in
the Chanel of the ſecond, to that which it had in
its proper and first Chanel.
Let the River A B, whoſe height is A C, and breadth C B,
that is, whoſe Section is A C B; let it enter, I ſay, into a­
nother River as broad as the line E F, and let it therein make
the riſe or height D E, that is to ſay, let it have its Section in
the River whereinto it falls D E F; I ſay, that the height A C
hath to the height D E the proportion compounded of the pro­
portions of the breadth E F, to the breadth C B, and of the ve­
locity through D F, to the velocity through A B. Let us ſup­
poſe the Section G, equal in velocity to the Section A B, and in
breadth equal to E F, which carrieth a quantity of Water e­
qual to that which the Section A B carrieth, in equal times,
and conſequently, equal to that which D F carrieth. Moreover,
as the breadth E F is to the breadth C B, ſo let the line H be to
1the line I; and as the velocity of D F is to the velocity of A B,
ſo let the line I be to the line L; becauſe therefore the two
Sections A B and G are equally ſwift, and diſcharge equal quan­
tity of Water in equal times, they ſhall be equal Sections; and
42[Figure 42]
therefore the height of A B to the height of G, ſhall be as the
breadth of G, to the breadth of A B, that is, as E F to C B,
that is, as the line H to the line I: but becauſe the Water which
paſſeth through G, is equal to that which paſſeth through D E F,
therefore the Section G, to the Section D E F, ſhall have the re­
ciprocal proportion of the velocity through D E F, to the velo­
city through G; but alſo the height of G, is to the height D E,
as the Section G, to the Section D E F: Therefore the height of
G, is to the height D E, as the velocity through D E F, is to the
velocity through G; that is, as the velocity through D E F, is to
the velocity through A B; That is, finally, as the line I, to the
line L; Therefore, by equal proportion, the height of A B, that
is, A C, ſhall be to the height D E; as H to L, that is, com­
pounded of the proportions of the breadth E F, to the breadth
C B, and of the velocity through D F, to the velocity through
A B: So that if a River fall into another River, &c. which was
to be demonſtrated.
1
PROPOSITION V.
If a River diſcharge a certain quantitie of Water
in a certain time; and after that there come into it
a Flood, the quantity of Water which is diſchar­
ged in as much time at the Flood, is to that which
was diſcharged before, whilſt the River was low,
in a proportion compounded of the proportions of
the velocity of the Flood, to the velocity of the first
Water, and of the height of the Flood, to the
height of the first Water.
Suppoſe a River, which whilſt it is low, runs by the Section
AF; and after a Flood cometh into the ſame, and runneth
through the Section D F, I ſay, that the quantity of the Wa­
ter which is diſcharged through D F, is to that which is diſcharged
43[Figure 43]
through A F, in a proportion compounded of the proportions of
the velocity through D F, to the velocity through A F, and of
the height D B, to the height A B; As the velocity through DF
is to the velocity through A F, ſo let the line R, to the line S;
and as the height D B is to the height A B, ſo let the line S, to
the line T; and let us ſuppoſe a Section L M N, equal to D F
in height and breadth; that is L M equal to D B, and M N equal
to B F; but let it be in velocity equal to the Section A F, there­
fore the quantity of Water which runneth through D F, ſhall be
to that which runneth through LN, as the velocity through DF,
is to the velocity through L N, that is, to the velocity through
A F; and the line R being to the line S, as the velocity through
D F, to the velocity through A F; therefore the quantity which
runneth through D F, to that which runneth through L N, ſhall
have the proportion of R to S; but the quantity which runneth
through L N, to that which runneth through A F, (the Sections
1being equally ſwift) ſhall be in proportion as the Section L N, to
the Section A F; that is, as D B, to A B; that is as the line S, to
the line T: Therefore by equal proportion, the quantity of the
water which runneth through D F, ſhall be in proportion to that
which runneth through A F, as R is to T; that is, compounded of
the proportions of the height D B, to the height A B, and of the
velocity through D F, to the velocity through A F; and therefore
if a River diſcharge a certain quantity, &c. which was to be de­
monſtrated.
ANNOTATION.
The ſame might have been demonſtrated by the ſecond
Propoſition above demonſtrated, as is manifeſt.
PROPOSITION VI.
If two equal ſtreams of the ſame Torrent, fall into a
River at divers times, the heights made in the Ri­
ver by the Torrent, ſhall have between them­
ſelves the reciprocal proportion of the velocities
acquired in the River.
Let A and B, be two equal ſtreams of the ſame Torrent,
which falling into a River at divers times, make the heights
C D, and F G; that is the ſtream A, maketh the height
C D, and the ſtream B, maketh the height F G; that is, Let
their Sections in the River, into which they are fallen, be C E,
and FH; I ſay, that the height C D, ſhall be to the height F G,
in reciprocal proportion, as the velocity through F H, to the ve­
locity through C E; for the quantity of water which paſſeth
through A, being equal to the quantity which paſſeth through B,
in equal times; alſo the quantity which paſſeth through C E, ſhall
44[Figure 44]
be equal to that which paſſeth through F H: And therefore the
proportion that the Section C E, hath to the Section F H; ſhall
be the ſame that the velocity through F H, hath to the velocity
through C E; But the Section C E, is to the Section F H, as
C D, to F G, by reaſon they are of the ſame breadth: Therefore
C D, ſhall be to F G, in reciprocal proportion, as the velocity
through F H, is to the velocity through C E, and therefore if two
equal ſtreams of the ſame Torrent, &c. which was to be de­
monſtrated.
1
OF THE
MENSURATION
OF
Running Waters.
Lib. II.
Having, in the cloſe of my Treatiſe of the
Menſuration of Running Waters promiſed
to declare upon another occaſion other par­
ticulars more obſcure, and of very great
concern upon the ſame argumement: I now
do perform my promiſe on the occaſion
that I had the paſt year 1641. to propound
my thoughts touching the ſtate of the Lake
of Venice, a buſineſs certainly moſt important, as being the
concernment of that moſt noble and moſt admirable City; and
indeed of all Italy, yea of all Europe, Aſia, & Africa; & one may
truly ſay of all the whole World. And being to proceed according
to the method neceſſary in Sciences, I wil propoſe, in the firſt place
certain Definitions of thoſe Terms whereof we are to make uſe
in our Diſcourſe: and then, laying down certain Principles we
will demonſtrate ſome Problemes and Theoremes neceſſary for
the underſtanding of thoſe things which we are to deliver; and
moreover, recounting ſundry caſes that have happened, we will
prove by practice, of what utility this contemplation of the
Meaſure of Running Waters is in the more important affairs both
Publique and Private.
DEFINITION I.
Two Rivers are ſaid to move with equal velocity, when in e­
qual times they paſſe ſpaces of equal length.
DEFINITION II.
Rivers are ſaid to move with like velocity, when their propor­
tional parts do move alike, that is, the upper parts alike to
the upper, and the lower to the lower; ſo that if the upper
part of one River ſhall be more ſwift than the upper part of ano­
ther; then alſo the lower part of the former ſhall be more ſwift
than the part correſpondent to it in the ſecond, proportionally.
1
DEFINITON III.
To meaſure a River, or running Water, is in our ſenſe to finde
out how many determinate meaſures, or weights of Water
in a given time paſſeth through the River, or Channel of the
Water that is to be meaſured.
DEFINITION IV.
If a Machine be made either of Brick, or of Stone, or of
Wood, ſo compoſed that two ſides of the ſaid Machine be
placed at right angles upon the ends of a third ſide, that is
ſuppoſed to be placed in the bottom of a River, parallel to the
Horizon, in ſuch a manner, that all the water which runneth
through the ſaid River, paſſeth thorow the ſaid Machine: And
if all the water coming to be diverted
45[Figure 45]
that runneth through the ſaid River, the
upper ſuperficies of that third ſide placed
in the bottom do remain uncovered
and dry, and that the dead water be not
above it; This ſame Machine ſhall be

called by us ^{*} REGULATOR: And that third ſide of the
Machine which ſtandeth Horizontally is called the bottom of
the Regulator; and the other two ſides, are called the banks of
the Regulator; as is ſeen in this firſt Figure: A B C D, ſhall be
the Regulator; B C the bottom; and the other two ſides A B,
and C D are its banks.
* Or Sluice.
DEFINITION V.
By the quick height, we mean the Perpendicular from the upper
ſuperficies of the River, unto the upper ſuperficies of the bot­
tom of the Regulator; as in the foregoing Figure the line. G H.
DEFINITION VI.
If the water of a River be ſuppoſed to be marked by three
ſides of a Regulator, that Rightangled Parallelogram compre­
hended between the banks of the Regulator, and the bottom,
and the ſuperficies of the Water is called a Section of the
River.
1
ANNOTATION.
Here it is to be noted, that the River it ſelf may have ſundry
and divers heights, in ſeveral parts of its Chanel, by reaſon of
the various velocities of the water, and its meaſures; as hath
been demonſtrated in the firſt book.
SUPPOSITION I.
It is ſuppoſed, that the Rivers equal in breadth, and quick
height, that have the ſame inclination of bed or bottom, ought
alſo to have equal velocities, the accidental impediments being
removed that are diſperſed throughout the courſe of the water,
and abſtracting alſo from the external windes, which may velo­
citate, and retard the courſe of the water of the River.
SUPPOSITION II.
Let us ſuppoſe alſo, that if there be two Rivers that are in
their beds of equal length, and of the ſame inclination, but of
quick heights unequal, they ought to move with like velocity,
according to the ſenſe explained in the ſecond definition.
SUPPOSITION III.
Becauſe it will often be requiſite to meaſure the time exactly
in the following Problems, we take that to be an excellent
way to meaſure the time, which was ſhewed me many years ſince
by Signore Galilæo Galilæi, which is as followeth.
A ſtring is to be taken three Roman feet long, to the end of
which a Bullet of Lead is to be hanged, of about two or three
ounces; and holding it by the other end, the Plummet is to be
removed from its perpendicularity a Palm, more or leſs, and then
let go, which will make many ſwings to and again, paſſing and
repaſſing the Perpendicular, before that it ſtay in the ſame: Now
it being required to meaſure the time that is ſpent in any what­
ſoever operation, thoſe vibrations are to be numbred, that are
made whilſt the work laſteth; and they ſhall be ſo many ſecond
minutes of an hour, if ſo be, that the ſtring be three Roman feet
long, but in ſhorter ſtrings, the vibrations are more frequent, and
in longer, leſs frequent; and all this ſtill followeth, whether the
Plummet be little or much removed from its Perpendicularity, or
whether the weight of the Lead be greater or leſſer.
Theſe things being pre-ſuppoſed, we will lay down ſome fa­
1miliar Problems, from which we ſhall paſs to the Notions and
queſtions more ſubtil and curious; which will alſo prove profi­
table, and not to be ſleighted in this buſineſs of Waters.
PROPOSITION I. PROBLEME I.
Achanel of Running-Water being given, the breadth
of which paſsing through a Regulator, is three
Palms; and the height one Palm, little more or
leſs, to meaſure what water paſſeth through the
Regulator in a time given.
Firſt, we are to dam up the Chanel; ſo that there paſs not any
water below the Dam; then we muſt place in the ſide of the
Chanel, in the parts above the Regulator three, or four, or five
Bent-pipes, or Syphons, according to the quantity of the water
that runneth along the Chanel; in ſuch ſort, as that they may
drink up, or draw out of the Chanel all the water that the Cha­
nel beareth (and then ſhall we know that the Syphons drink up
all the water, when we ſee that the water at the Dam doth nei­
ther riſe higher, nor abate, but alwaies keepeth in the ſame Le­
vel.) Theſe things being prepared, taking the Inſtrument to
meaſure the time, we will examine the quantity of the water that
iſſueth by one of thoſe Syphons in the ſpace of twenty vibrations,
and the like will we do one by one with the other Syphons; and
then collecting the whole ſumme, we will ſay, that ſo much is
the water that paſſeth and runneth thorow the Regulator or
Chanel (the Dam being taken away) in the ſpace of twenty ſe­
cond minutes of an hour; and calculating, we may eaſily reduce
it to hours, dayes, months, and years: And it hath fallen to my
turn to meaſure this way the waters of Mills and Fountains, and I
have been well aſſured of its exactneſs, by often repeating the
ſame work.
CONSIDERATION.
And this method muſt be made uſe of in meaſuring the waters,
that we are to bring into Conducts, and carry into Cities
and Caſtles, for Fountains; and that we may be able afterwards
to divide and ſhare them to particular perſons juſtly; which will
prevent infinite ſuits and controverſies that every day happen in
theſe matters..
1
PROPOSITION II. THEOREM I.
If a River moving with ſuch a certain velocitie
through its Regulator, ſhall have a given quick
height, and afterwards by new water ſhall increaſe
to be double, it ſhall alſo increaſe double in ve­
locitie.
Let the quick height of a River in the Regulator A B C D,
be the perpendicular F B, and afterwards, by new water that
is added to the River, let the water be ſuppoſed to be raiſ­
ed to G, ſo that G B may be double to E B. I ſay, that all the
water G C ſhall be double in velocity to
46[Figure 46]
that of E C: For the water G F, having
for its bed the bottom E F, equally in­
clined as the bed B C, and its quick
height G E being equal to the quick
height E C, and having the ſame breadth
B C, it ſhall have of it ſelf a velocity e­
qual to the velocity of the firſt water
F C: but becauſe, beſides its own moti­
on, which is imparted to it by the motion of the water E C, it
hath alſo over and above its own motion, the motion of E C. And
becauſe the two waters G C, and E C, are alike in velocity, by
the third Suppoſition; therefore the whole water G C ſhall be
double in velocity to the water E C; which was that which we
were to demonſtrate.
This demonſtration is not here inſerted, as perfect, the Authour ha­
ving by ſeveral letters to his friends confeſſed himſelf unſatisfi­
ed therewith; and that he intended not to publiſh the Theorem
without a more ſolid demonſtration, which he was in hope to light
upon. But being overtaken by Death, he could not give the
finiſhing touch either to this, or to the rest of the ſecond Book. In
conſideration of which, it ſeemed good to the Publiſher of the
ſame, rather to omit it, than to do any thing contrary to the mind of
the Authour. And this he hints, by way of advertiſement, to
thoſe that have Manuſcript Copies of this Book, with the ſaid de­
monſtration. For this time let the Reader content himſelf with
the knowledge of ſo ingenious and profitable a Concluſion; of the
truth of which he may, with ſmall expence and much pleaſure, be
aſſured by means of the experiment to be made in the ſame man­
ner, with that which is laid down in the ſecond Corollary of
1the fourth Theorem of this, with its Table, and the uſe there­
of annexed.
COROLLARIE
Hence it followeth, that when a River increaſeth in quick
height by the addition of new water, it alſo increaſeth in ve­
locity; ſo that the velocity hath the ſame proportion to the velo­
city that the quick height hath to the quick height; as may be
demonſtrated in the ſame manner.
PROPOS. III. PROBLEME II.
Achanel of Water being given whoſe breadth exceeds not
twenty Palms, or thereabouts, and whoſe quick beight
is leſs than five Palms, to meaſure the quantity of the
Water that runneth thorow the Chanel in a time
given.
Place in the Chanel a Regulator, and obſerve the quick
height in the ſaid Regulator; then let the water be turned
away from the Chanel by a Chanellet of three or four Palms
in breadth, or thereabouts: And that being done, meaſure the
quantity of the water which paſſeth thorow the ſaid Chanellet,
as hath been taught in the ſecond Propoſition; and at the ſame
time obſerve exactly how much the quick height ſhall be abated
in the greater Chanel, by means of the diverſion of the Chancl­
let; and all theſe particulars being performed, multiply the quick
height of the greater Chanel into it ſelf, and likewiſe multiply
into it ſelf the leſſer height of the ſaid bigger Chanel, and the
leſſer ſquare being taken, from the greater, the remainder ſhall
have the ſame proportion to the whole greater ſquare, as the wa­
ter of the Chanellet diverted, hath to the water of the bigger
Chanel: And becauſe the water of the Chanellet is known by
the Method laid down in the firſt Theorem, and the terms of the
Theorem being alſo known, the quantity of the water which run­
neth thorow the bigger Chanel, ſhall be alſo known by the Gol­
den Rule, which was that that was deſired to be known. We
will explain the whole buſineſs by an example.
Let a Chanel be, for example, 15 Palms broad, its quick height
before its diverſion by the Chanellet ſhall be ſuppoſed to be 24
inches; but after the diverſion, let the quick height of the Chanel
be onely 22 inches. Therefore the greater height to the leſſer,
is as the number 11. to 12. But the ſquare of 11. is 121, and the
ſquare of 12. is 144, the difference between the ſaid leſſer
1ſquare and the greater is 23. Therefore the diverted water, is
to the whole water, as 23. to 144: which is well near as 1 to
6 6/23: and that is the proportion that the quantity of the water
which runneth through the Chanellet ſhall have, to all the water
that runneth thorow the great Chanel. Now if we ſhould finde
by the Rule mentioned above in the firſt Propoſition, that the
quantity of the water that runneth through the Chanellet, is
v. g. an hundred Barrels, in the ſpace of 15 ſecond minutes of
an hour, it is manifeſt, that the water which runneth through the
great Chanel in the ſaid time of 35 min. ſec. ſhall be about 600
Barrels.
The ſame operation performed another way.
And becauſe very often in applying the Theory to Practice
it happeneth, that all the neceſſary particulars in the The­
ory cannot ſo eaſily be put in execution; therefore we will
here add another way of performing the ſame Problem, if it ſhould
chance to happen that the Chanellet could not commodiouſly be
diverted from the great Chanel, but that it were eaſier for the
water of another ſmaller Chanel to be brought into the greater
Chanel; which water of the ſmaller Chanel might be eaſily mea­
ſured, as hath been ſhewen in the firſt Probleme; or in caſe that
there did fall into a greater Chanel, a leſſer Chanel that might
be diverted and meaſured. Therefore I ſay in the firſt caſe, If
we would meaſure the quantity of the water that runneth in a
certain time thorow the greater Chanel, into which another leſſer
Chanel that is meaſurable may be brought, we muſt firſt exactly
meaſure the Chanellet, and then obſerve the quick height of the
greater Chanel, before the introduction of the leſſer; and having
brought in the ſaid Chanellet, we muſt agnin find the propor­
tion that the water of the Chanellet hath to all the water of the
great Ghanel; for theſe terms of the proportion being known, as
alſo the quantity of the water of the Chanellet, we ſhall alſo
come to know the quantity of the water that runneth thorow
the great Chanel. It is likewiſe manifeſt, that we ſhall obtain
our intent, if the caſe were that there entered into the great
Chanel, another leſſer Chanel that was meaſurable, and that
might be diverted.
CONSIDERATION.
It would be neceſſary to make uſe of this Doctrine in the di­
ſtribution of the waters that are imploy'd to overflow the fields,
as is uſed in the Breſciau, Cremoneſe, Bergamaſe, Lodigian, Mila-
1neſe territories, and many other places, where very great ſuits
and differences ariſe, which not being to be determined with in­
telligible reaſons, come oftentimes to be decided, by force of
armes; and inſtead of flowing their Grounds with Waters, they
cruelly flow them with the ſhedding of humane blood, impiouſly
inverting the courſe of Peace and Juſtice, ſowing ſuch diſorders
and feuds, as that they are ſometimes accompanied with the ru­
ine of whole Cities, or elſe unprofitably charge them with vain,
and ſometimes prejudicial expences.
PROPOS. IV. THEOR. II.
If a River increaſe in quick height, the quantitie of
Water which the River diſchargeth after the in­
creaſe, hath the Proportion compounded of the
Proportions of the Quick height to the Quick
height, and of the velocity to the velocity.
Let there be a River, which whilſt it is low, runneth thorow
the Regulator D F, with the Quick height A B, and after­
wards let a Flood come; and then let it run with the height
D B, I ſay, that the quantity of the Water that is diſcharged
through D F, to that which diſchargeth through A F, hath the
proportion compounded of the proportions of the velocity
through D F to the velocity through A F, and of the height
D B to the height A B. As the velocity through D F is to the
velocity through A F, ſo let the line R be to the line S; and as
the height D B is to the height A B; ſo let the line S be to the
47[Figure 47]
line T. And let a Section be ſuppoſed L M N equal to the
Section D F in height and length, but let it be in velocity equal
to the Section AF. Therefore the quantity of the Water that run­
neth through D F to that which runneth through L N, ſhall be
1as the velocity through D F, to the velocity of L N, that is, to
the velocity through L N, that is, to the velocity through A F.
therefore the quantity of Water which runneth through D F,
to that which paſſeth through L N, ſhall have the proportion
that R hath to S; but the quantity of the Water that runneth
through L N, to that which runneth through A F; (the Sections
being equally ſwift) ſhall have the proportion that the Section
L N hath to the Section A F, that is, that the height B D hath to
the height B A, that is, that S hath to T. Therefore, by equal
proportion, the quantity of the Water which runneth by D F,
to that which runneth by A F, ſhall have the proportion of R to
T, that is, ſhall be compounded of the proportions of the height
D B, to the height A B; and of the velocity through D F, to
the velocity through A F. And therefore if a River increaſe in
quick height, the quantity of the Water that runneth after the
increaſe, to that which runneth before the increaſe, hath the
proportion compounded, &c. Which was to be demonſtrated.
COROLLARIE I.
Hence it followeth, that we having ſhewn, that the quantity of
the Water which runneth, whilſt the River is high, to that
which ran, whilſt it was low, hath the proportion compounded
of the velocity to the velocity, and of the height to the height.
And it having been demonſtrated, that the velocity to the velo­
city is as the height to the height; it followeth, I ſay, that the
quantity of the Water that runneth, whilſt the River is high, to
that which runneth, whilſt it is low, hath duplicate proportion of
the height to the height, that is, the proportion that the ſquares
of the heights have.
COROLLARIE II.
Vpon which things dependeth the reaſon of that which I have
ſaid, in my ſecond Conſideration, that if by the diverſion of
5/9 of the Water that entereth by the Rivers into the Moor or
Fen, the Water be abated ſuch a meaſure, that ſame ſhall be
only one third of its whole height; but moreover diverting the 4/9, it
ſhall abate two other thirds, a moſt principal point; and ſuch,
that its not having been well underſtood, hath cauſed very great
diſorders, and there would now, more than ever, follow extream
dammage, if one ſhould put in execution the diverſion of the Sile
and other Rivers; and it is manifeſt, that in the ſame manner,
wherewith it hath been demonſtrated, that the quantity of the
Water increaſing quadruple, the height would increaſe onely
1double, and the quantity increaſing nonuple, the height increa­
ſeth triple; ſo that, by adding to units all the odde numbers, ac­
cording to their Series, the heights increaſe according to the na­
tural progreſſion of all the numbers, from units. As for exam­
ple, there paſſing thorow a Regulator ſuch a certain quantity of
Water in one time; adding three of thoſe meaſures, the quick
height is two of thoſe parts, which at firſt was one; and con­
tinuing to adde five of thoſe ſaid meaſures, the height is three of
thoſe parts which at firſt were one; and thus adding ſeven, and
then nine, and then 11. and then 13, &c. the heights ſhall be 4.
then 5, then 6. then 7, &c. And for the greater facility of the
Work, we have deſcribed the following Table, of which we will
declare the uſe: The Table is divided into three Series or Pro­
greſſions of Numbers: the firſt Series containeth all the Num­
bers in the Natural Progreſſion, beginning at a Unit, and is called
the Series of the Heights; the ſecond containeth all the odde
numbers, beginning at an unit, and is called the Series of the
Additions: the third containeth all the ſquare numbers, begin­
ning at an unit, and is called the Series of Quantity.
Heights.1234567891011Additions.13579111315171921Quantities.149162536496481100121
The uſe of the afore-mentioned Table.
Firſt, if we ſuppoſe the whole quick height of a River of Run­
ning Water to be divided into any number of equal parts, at
pleaſure, and would abate the ſame one fift, by means of a divi­
ſron; let there be found in the Table in the Series of heights the
number 5. the denominator of the part which the River is to a­
bate, and take the number that is immediately under it in the
row of Additions, which is 9. which let be ſubſtracted from the
number 25. placed underneath the ſame in the row of Quanti­
ties, the remainder 16. ſignifieth that of the 25. parts of Water
that ran in the River, whilſt it was 5 meaſures high, there do
onely run 16. parts; ſo that to make it abate 1/5 it is neceſſary to
take 9/25 from the Water that the whole River did carry; ſo that
with ſubſtracting ſomewhat more than one third of the Water of
the River, it is abated but only one fift.
2. And thus, in the ſecond place, if on the contrary, one would
know how much water is to be added to the ſaid River to make
it increaſe one fift more in height, ſo as that it may run in the
1Regulator 6. of thoſe parts high; of which it ran before but 5. let
6 be found in the row of heights, and let the number 11. ſtand­
ing under the ſame be taken and added to the number 25.
that is placed under the number 9. in the Additions, and 5. in
the heights, and you ſhall have 36; which is the quantity of the
water that runneth with the height of the River, when it is high
6 of thoſe parts, whereof it was before but 5.
3. But if it ſhould be deſired, to know how much water it is
requiſite to add to make the River riſe ſo, as that it may run in
height 8. of thoſe parts of which before it ran but 5; one
ought to take the ſum of the number of the Series of Additions
ſtanding under 8. 7. and 6, which are 15. 13. and 11. that is, 39.
and this ſhall be the ſumme that muſt be added to 25: So that
to make the River to run 8. of thoſe parts in height, of which it
before did run 5, it will be neceſſary to add 39. of thoſe parts,
of which the River before was 25.
4. Likewiſe the ſame Table giveth the quantity of water
that runneth from time to time through a River, that increaſeth
by the addition of new water to the ſame in one of its heights, the
quantity of its water be known. As for example: If we knew that
the River in one minute of an hour diſchargeth 2500. of thoſe mea­
ſures of water, and runneth in height 5. parts in the Regulator, and
afterwards ſhould ſee that it runneth 8 Palms high, finding in the
row of quantity the number placed under 8. which is 64. we would
ſay that the River heightned, carrieth of water 64. of thoſe parts
whereof it carried before but 25; and becauſe before it carried
2500. meaſures, by the Golden Rule we will ſay, that the River
carrieth 6400. of thoſe meaſures, of which before it carried 2500.
In this progreſs of Nature, is one thing really curious, and that
at firſt ſight ſeemeth to be ſomewhat Paradoxal, that we pro­
ceeding ordinately in the diverſions and additions, with additi­
ons and diverſions ſo unequal, the abatings do notwithſtanding
alwaies prove equal, and ſo do the riſings: And who would ever
think that a River in height, v. g. 10. Palms, running and carry­
ing an hundred meaſures in a minute of an hour, is to abate but
one Palm, onely by the diverſion of 19. of thoſe meaſures; and
then again, that the buiſineſs cometh to that paſs, that it abateth
likewiſe a Palm by the diverſion of three onely of thoſe meaſures,
nay, by the diverſion of but one meaſure? and yet it is moſt
certain: And this truth meets with ſo manifeſt proofs in experi­
ence, that it is very admirable! And for the full ſatisfaction of
thoſe, who not being able to comprehend ſubtil demonſtrati­
ons, desire to be clearly inform'd by the matters of fact, and to
ſee with their bobily eyes, and touch with their hands, what their
underſtanding and reaſon cannot reach unto: I will hear add
another very eaſie way to reduce all to an experiment, the
1which may be made in little, in great, or in very great; of
which I make uſe frequently, to the admiration of ſuch as ſee it.
I prepared an hundred Siphons, or, if you will, bowed Pipes,
all equal; and placed them at the brim of a Veſſel, wherein the
water is kept at one and the ſame level (whether all the Syphons
work, or but a certain number of them) the mouths by which
the water iſſueth being all placed in the ſame level, parallel to
the Horizon; but lower in level than the water in the Veſſel; and
gathered all the water falling from the Syphons into another
Veſſel ſtanding lower than the former, I made it to run away
thorow a Chanel, in ſuch manner inclined, that wanting water
from the Syphons, the ſaid Chanel remained quite dry.
And this done, I meaſured the quick height of the Chanel
with care, and afterwards divided it exactly into 10 equal parts,
and cauſing 19. of thoſe Syphons to be taken away, ſo that the
Chanel did not run water, ſave onely with 81 of thoſe Syphons,
I again obſerved the quick height of the water in the ſame ſite
obſerved before, and found that its height was diminiſhed pre­
ciſely the tenth part of all its firſt height; and thus continuing to
take away 17. other Syphons, the height was likewiſe diminiſh­
ed 1/1. of all its firſt quick height; and trying to take away 15.
Syphons, then 13, then 11, then 9, then 7, then 5, and then 3.
alwaies in theſe diverſions, made in order as hath been ſaid, there
enſued ſtill an abatement of 1/1. of the whole height.
And here was one thing worthy of obſervation, that the water
encreaſing in [or through] the Chanel, its quick height was diffe­
rent in different ſites of the Chanel, that is ſtill leſſer, the more
one approached to the Out-let; notwithſtanding which the abate­
ment followed in all places proportionably, that is in all its ſites
the firſt part of the height of that ſite diminiſhed: And more­
over the water iſſued from the Chanel, and dilated into a broader
courſe, from which likewiſe having divers Out-lets and Mouths;
yet nevertheleſs in that breadth alſo the quick heights ſucceſſive­
ly varied and altered in the ſame proportions. Nor did I here
deſiſt my obſervation, but the water being diminiſhed, that iſſu­
ed from the Syphons, and there being but one of them left that
diſcharged water; I obſerved the quick height that it made in the
above-ſaid ſites, (the which was likewiſe 1/1. of all the firſt height)
there being added to the water of that Syphon, the water of
three other Syphons; ſo that all the water was of 4 Syphons,
and conſequently quadruple to the firſt Syphon; but the quick
height was onely double, and adding five Siphons, the quick
height became triple, and with adding ſeven Syphons, the height
increaſed quadruple; and ſo by adding of 9. it increaſed quin­
tuple, and by adding of 11. it increaſed ſextuple, and by ad­
1ding of 13. it increaſed ſeptuple, and by adding of 15. octuple,
and by adding of 17. nonuple, and laſtly by adding 19. Syphons;
ſo that all the water was centuple to the water of one Syphon,
yet nevertheleſs the quick height of all this water was onely de­
cuple to the firſt height conjoyned by the water that iſſued from
one onely Syphon.
For the more clear underſtanding of all which, I have made
the following Figure; in which we have the mouth A, that
maintaineth the water of the Veſſel B C in the ſame level; though
it continually run; to the brim of the Veſſel are put 25. Sy­
phons (and there may be many more) divided into 5 Claſſes,
D E F G H, and the firſt D, are of one onely Syphon; the ſecond
E, of three Syphons; the third F, of five; the fourth G, of 7; the
fifth H, of 9; and one may ſuppoſe the ſixth of 11, the ſeventh
of 13 Syphons, and ſo of the other Claſſes, all containing in con­
ſequent odd numbers ſucceſſively (we are content to repreſent in
the Figure no more but the five forenamed Claſſes to avoid con­
fuſion) the gathered water D E F G H, which runneth thorow
the Chanel I K L, and falleth into the out-let M N O P; and ſo
much ſufficeth for the explanation of this experiment.
48[Figure 48]
1
PROPOS. V. PROB. III.
Any River of any bigneſs, if being given to examine the
quantity of the Water that runneth thorow the River
in a time aſſigned.
By what we have ſaid already in the two preceding Pro­
blems, we may alſo reſolve this that we have now before
us; and it is done, by diverting in the firſt place from the
great River a good big meaſurable Chanel, as is taught in the
ſecond Probleme, and obſerving the abatement of the River,
cauſed by the diverſion of the Chanel; and finding the proporti­
on that the Water of the Chanel hath to that of the River, then
let the Water of the Chanel be meaſured by the ſecond Pro­
bleme, and work as above, and you ſhall have your deſire.
CONSIDERATION. I.
And although it ſeemeth as if it might prove difficult, and
almoſt impoſſible to make uſe of the Regulator number, if
one be about to meaſure the water of ſome great River,
and conſequently would be impoſſible, or at leaſt very difficult
to reduce the Theory of the firſt Probleme into practice: Yet ne­
vertheleſs, I could ſay that ſuch great conceits of meaſuring the
water of a great River, are not to come into the minds of any
but great Perſonages, and potent Princes; of whom it is expected
for their extraordinary concerns, that they will make theſe kinde
of enquiries; as if here in Italy it ſhould be of the Rivers Tyber,
Velino, Chiana, Arno, Serchio, Adice, in which it ſeemeth real­
ly difficult to apply the Regulator, to finde exactly the quick
height of the River: But becauſe in ſuch like caſes ſometimes
it would turn to account to be at ſome charge, to come to the
exact and true knowledge of the quantity of water which that
River carrieth, by knowledge whereof, other greater diſ­
burſments might afterwards be avoided, that would oft times be
made in vain; and prevent the diſguſts, which ſometimes happen
amongſt Princes: Upon this ground I think it will be well to
ſhew alſo the way how to make uſe of the Regulator in theſe
great Rivers; in which if we will but open our eyes, we ſhall meet
with good ones, and thoſe made without great coſt or labour,
which will ſerve our turn.
For upon ſuch like Rivers there are Wears, or Lockes made,
1to cauſe the Waters to riſe, and to turn them for the ſervice of
Mills, or the like. Now in theſe Caſes it is ſufficient, that one
erect upon the two extreames of the Weare two Pilaſters either
of Wood or Brick, which with the bottome of the Weare do
compoſe our Regulator, wherewith we may make our deſired
operation, yea the Chanel it ſelf diverted ſhall ſerve, without
making any other diverſion or union. And in brief, if the bu­
fineſſes be but managed by a judicious perſon, there may wayes
and helps be made uſe of, according to occaſion, of which it
would be too tedious to ſpeak, and therefore this little that hath
been hinted ſhall ſuſſice.
CONSIDERATION II.
From what hath been declared, if it ſhall be well under­
ſtood, may be deduced many benefits and conveniences,
not onely in dividing of Running Waters for infinite uſes
that they are put to in turning of Corne-Mills, Paper-Mills,
Gins, Powder-Mills, Rice-Mills, Iron Mills, Oil-Mills, Saw­
ing-Mills, Mirtle-Mills, Felling-Mills, Fulling-Mills, Silk-Mills,
and ſuch other Machines; but alſo in ordering Navigable Cha­
nels, diverting Rivers and Chanels of Waters, or terminating
and limiting the ſizes of Pipes for Fountains: In all which af­
fairs there are great errours committed, to the loſſe of much
expence, the Chanels and Pipes that are made, ſometimes not
being ſufficient to carry the deſigned Waters, and ſometimes they
are made bigger than is neceſſary; which diſorders ſhall be
avoided, if the Engineer be adviſed of the things aboveſaid: and
in caſe that to theſe Notions there be added the knowledge of
Philoſophy and Mathematicks, agreeable to the ſublime Diſco­
veries of Signore Galilæo, and the further improvement thereof
by Signore Evangeliſta Torricelli, Mathematician to the Grand
Duke of Tuſcany, who hath ſubtilly and admirably handled this
whole buſineſſe of Motion, one ſhall then come to the know­
ledge of particular notions of great curioſity in the Theoricks,
and of extraordinary benefit in the Practicks that daily occur in
theſe buſineſſes.
And to ſhew, in effect, of what utility theſe Notions are, I
have thought fit to inſert, in this place, the Conſiderations by
me made upon the Lake of Venice, and to repreſent,
at large, by the experience of the laſt year 1641. the moſt Se­
rene Erizzo, then Duke of the ſaid Republique. Being
therefore at Venice, in the year aforeſaid, I was requeſted by the
moſt Illuſtrious and moſt Excellent Signore Giovanni Baſa-
1donna, a Senatour of great worth and merit, that I would inge­
nuouſly deliver my opinion touching the ſtate of the Lake
of Venice; and after I had diſcourſed with his Honour ſeve­
ral times, in the end I had order to ſet down the whole
buſineſſe in writing, who having afterwards read it privately,
the ſaid Signore imparted the ſame, with like privacy, to the
moſt Serene PRINCE, and I received order to repreſent the
ſame to the full Colledge, as accordingly I did in the Moneth
of May, the ſame year, and it was as followeth.
49[Figure 49]
1
CONSIDER ATIONS
Concerning the
LAKE
OF
VENICE.
BY
D. BENEDETTO CASTELLI,
Abbot of S. Benedetto Aloyſio, Mathematician to
Pope VR BAN VIII. and Profeſſor in
ROME.
CONSIDERATION I.
Though the principal cauſe be but one
onely, that in my judgment threatneth
irreparable ruine to the Lake of
Venice, in the preſent ſtate in which it
now ſtands; Yet nevertheleſſe, I think
that two Heads may be conſidered.
And this Conſideration may peradven­
ture ſerve us for to facilitate and explain
the opportune remedies, though not to
render the ſtate of things abſolutely unchangeable and eternal:
an enterprize impoſſible, and eſpecially in that which having had
ſome beginning, ought likewiſe neceſſarily to have its end; or
at leaſt to prevent the danger for many hundreds of years; and
poſſibly it may, in the mean time, by the mutation it ſelf be
brought into a better condition.
I ſay therefore, that the preſent diſorder may be conſidered
under two Heads; One is the very notable diſcovery of Land
that is obſerved at the time of low Water, the which, beſides
the obſtructing of Navigation in the Lake and alſo in the
Chanels, doth likewiſe threaten another miſchief and diſorder
1worthy of very particular conſideration, which is, That the Sun
drying up that mudde, eſpecially in the times of hot Summers,
doth raiſe thence the putrified and pernicious vapours, fogs, and
exhalations that infect the Air, and may render the City unha­
bitable.
The ſecond Head is the great Stoppage that daily is grow­
ing in the Ports, eſpecially of Venice, at Malamoco; concerning
which matters I will hint certain general points, and then
will proceed to the more particular and important affairs.
And firſt, I ſay, that I hold it altogether impoſſible to effect
any thing, though never ſo profitable, which doth not bring with
it ſome miſchief; and therefore the good and the hurt ought to
be very well weighed, and then the leſſe harmful part to be im­
braced.
Secondly, I propoſe to conſideration, that the ſo notable diſ­
covery of Earth & Mud, hath not been long obſerved, as I under­
ſtand, from old perſons that can remember paſſages for fifty
years paſt; which thing being true, as to me it ſeemeth moſt
true, it ſhould appear that it could not but be good to reduce
matters to that paſſe that they were at formerly, (laying aſide
all affection or paſſion that ſelf-flattering minds have entertained
for their own conceits) or at leaſt it ſhall be neceſſary ſpeedily to
conſult the whole.
Thirdly, I hold that it is neceſſary to weigh, whether from the
foreſaid diſcovery of Land, it followeth, that onely the Earth ri­
ſeth, as it is commonly thought by all, without diſpute; or whe­
ther the Waters are abated and faln away; or elſe whether it
proceedeth from both the one and other cauſe. And here it would
be ſeaſonable to enquire, what ſhare the ſaid cauſes may have,
each conſidered apart in the foreſaid effect. For, in the firſt
caſe, if the Earth have been raiſed, it would be neceſſary to
conſider of taking it down, and removing it: But if the Wa­
ters have failed or abated, I believe that it would be extreamly ne­
ceſſary to reſtore and raiſe them: And if both theſe reaſons have
conſpired in this effect, it will be neceſſary to remedy them each
apart. And I do, for my part, think, that the ſo notable appea­
rance of Shelves at the time of low Water, proceeds principally
from the decreaſe and abatement of the Waters, which may
confidently be affirmed to need no other proof, in regard that the
Brent hath been actually diverted which did formerly diſcharge
its Water into the Lake.
As to the other point of the great Stoppage of Ports, I hold,
that all proceedeth from the violence of the Sea, which being
ſometimes diſturbed by windes, eſpecially at the time of the wa­
ters flowing, doth continually raiſe from its bottome immenſe
1heaps of ſand, carrying them by the tide; and force of the waves
into the Lake; it not having on its part any ſttength of current
that may raiſe and carry them away, they ſink to the bottom, and
ſo they choke up the Ports. And that this effect happeneth in
this manner, we have moſt frequent experiences thereof along the
Sea-coaſts: And I have obſerved in Tuſcany on the Roman­
ſhores, and in the Kingdom of of Naples, that when a river fal­
leth into the Sea, there is alwaies ſeen in the Sea it ſelf, at the place
of the rivets out-let, the reſemblance, as it were, of an half-Moon,
or a great ſhelf of ſettled ſand under water, much higher then the
reſt of the ſhore, and it is called in Tuſcany, il Cavallo; and here
in Venice, lo Scanto: the which cometh to be cut by the current
of the river, one while on the right ſide, another while on the
left, and ſometimes in the midſt, according as the Wind fits. And
a like effect I have obſerved in certain little Rillets of water,
along the Lake of Bolſena; with no other difference, ſave that of
ſmall and great.
Now whoſo well conſidereth this effect, plainly ſeeth that it
proceeds from no other, than from the contrariety of the ſtream
of the River, to the impetus of the Sea waves; ſeeing that
great abundance of ſand which the Sea continually throws upon
the ſhore, cometh to be driven into the Sea by the ſtream of the
river; and in that place where thoſe two impediments meet
with equal force, the ſand ſetleth under water, and thereupon is
made that ſame Shelf or Cavallo; the which if the river carry
water, and that any conſiderable ſtore, it ſhall be thereby cut
and broken; one while in one place, and another while in ano­
ther; as hath been ſaid, according as the Wind blows: And
through that Chanel it is that Veſſels fall down into the Sea, and
again make to the river, as into a Port. But if the Water of
the river ſhall not be continual or ſhall be weak, in that caſe the
force of the Sea-Wind ſhall drive ſuch a quantity of ſand into
the mouth of the Port, and of the river, as ſhall wholly choak it
up. And hereupon there are ſeen along the Sea-ſide, very many
Lakes and Meers, which at certain times of the year abound with
waters, and the Lakes bear down that encloſure, and run into
the Sea.
Now it is neceſſary to make the like reflections on our Ports
of Venice, Malamocco, Bondolo, and Chiozza; which in a certain
ſenſe are no other than Creeks, mouths, and openings of the ſhore
that parts the Lake from the main Sea; and therefore I hold that
if the Waters in the Lake were plentiful, they would have
ſtrength to ſcowr the mouths of the Ports thorowly, & with great
force; but the Water in the Lake failing, the Sea will with­
out any oppoſal, bring ſuch a drift of ſand into the Ports; that if
1it doth not wholly choke them up, it ſhall render them at leaſt
unprofitable, and impoſſible for Barks and great Veſſels.
Many other conſiderations might be propounded concerning
theſe two heads of the ſtoppage of the Ports, and of the appea­
rance of the Ouze and Mud in the Lakes, but ſo much ſhall ſuf­
fice us to have hinted, to make way for diſcourſing of the opera­
tions about the oportune remedies.
Yet before that I propound my opinion, I ſay, That I know
very well that my propoſal, at firſt ſight, will ſeem abſurd and in­
convenient; and therefore, as ſuch, will perhaps be rejected by
the moſt: and ſo much the rather, for that it will prove directly
contrary to what hath hitherto been, and as I hear, is intended to
be done. And I am not ſo wedded to my opinions, but that I
do conſider what others may judge thereof: But be it as it will,
I am obliged to ſpeak my thoughts freely, and that being done,
I will leawe it to wiſer men than my ſelf; when they ſhall have
well conſidered my reaſons, to judge and deliberate of the quid
agendum: And if the ſentence ſhall go againſt me, I appeal to the
moſt equitable and inexorable Tribunal of Nature, who not
caring in the leaſt to pleaſe either one party or another, will be
alwaies a punctual and inviolable executrix of her eternal De­
crees, againſt which neither humane deliberations, nor our vain
deſires; ſhall ever have power to rebell. I added by word of
mouth that which followeth.
Though your Highneſs intereſt your ſelf in this Noble Col­
ledge, and cauſe it to be confirmed in the ^{*} Senate by univerſal

Vote, that the Winds do not blow, that the Sea doth not fluctuate,
that the Rivers do not run; yet ſhall the Winds be alwaies deaf,
the Sea ſhall be conſtant in its inconſtancy, and the Rivers moſt
obſtinate: And theſe ſhall be my Judges, and to their determi­
nation I refer my ſelf.
* In Pregadi, a
particular Coun­
cil, the Senators of
which have great
Authority.
By what hath been ſaid, in my opinion, that is made very clear
and manifeſt, which in the beginning of this diſcourſe I glanced
at; namely, That the whole diſorder, although it be divided into
two heads, into the diſcovery of the Mud, and of the ſtoppage
Ports, yet nevertheleſs, by the application of one onely remedy,
and that in my eſteem very eaſie, the whole ſhall be removed:
And this it is; That there be reſtored into the Lake as much
Water as can be poſſible, and in particular from the upper parts
of Venice, taking care that the Water be as free from Mud as is
poſſible. And that this is the true and real remedy of the prece­
dent diſorders, is manifeſt: For in the paſſage that this Water
ſhall make thorow the Lakes, it ſhall of it ſelf by degrees clear
the Chanels in ſundry parts of them, according to the currents
that it ſhall ſucceſſively acquire, and in this manner being diſ­
1perſed thorow the Lake, it ſhall maintain the waters in the ſame,
and in the Chanels much higher, as I ſhall prove hereafter; a
thing that will make Navigation commodious; and that, which
moreover is of great moment in our buſineſſe; thoſe Shelves
of Mud which now diſcover themſelves at the time of Low­
Waters ſhall be alwayes covered, ſo that the putrefaction of
the Air ſhall alſo be remedied.
And laſtly, this abundance of Water being alwayes to diſ­
charge it ſelf into the Sea by the Ports, I do not doubt, but that
their bottomes will be ſcoured. And that theſe effects muſt fol­
low, Nature her ſelf ſeemeth to perſwade, there remaining onely
one great doubt, whether that abundance of Water that ſhall be
brought into the Lake may be really ſufficient to make the Wa­
ters riſe ſo much as to keep the Shelves covered, and to facilitate
Navigation, which ought to be at leaſt half a ^{*} Brace, or there­

abouts. And indeed it ſeemeth at firſt ſight to be impoſſible,
that the ſole Water of the ^{*} Brent let into the Lake, and diſ­

perſed over the ſame, can occaſion ſo notable an height of water;
and the more to confirm the difficulties, one might ſay, reducing
the reaſon to calculation, that in caſe the Brent were 40. Bra­
ces broad, and two and an half high, and the breadth of the
Lake were 20000. Braces, it would ſeem neceſſary that the
height of the water of the Brent dilated and diſtended thorow
the Lake would be but onely 1/200 of a Brace in height, which is
imperceptible, and would be of no avail to our purpoſe; nay
more, it being very certain that the Brent runneth very muddy
and foul, this would occaſion very great miſchief, filling and
contracting the Lake, and for that reaſon this remedy ought, as
pernicious, to be totally excluded and condemned.
* A Venice Brace
is 11/16 of our yard.
* A River of
that name.
I here confeſſe that I am ſurprized at the forme of the Argu­
ment, as if I were in a certain manner convinced, that I dare not
adventure to ſay more, or open my mouth in this matter; but
the ſtrength it ſelf of the Argument, as being founded upon
the means of Geometrical and Arithmetical Calculation, hath
opened me the way to diſcover a very crafty fraud that is couch­
ed in the ſame Argument, which fraud I will make out to any
one that hath but any inſight in Geometry and Arithmetick.
And as it is impoſſible, that ſuch an argument ſhould be produced
by any but ſuch as have taſted of theſe, in ſuch affairs, moſt pro­
fitable, and moſt neceſſary Sciences; ſo do not I pretend to make
my ſelf underſtood, ſave onely by ſuch, to whom I will evince
ſo clearly, as that more it cannot be deſired, the errour and fraud
wherein thoſe Ancients and Moderns have been, and alwayes
are intangled, that have in any way yet handled this matter of
conſidering the Meaſure and Quantity of the Waters that move.
1And ſo great is the eſteem that I have for that which I am now
about to ſay touching this particular, that I am content that all
the reſt of my Diſcourſe be rejected; provided, that that be per­
fectly underſtood, which I am hereafter to propoſe, I holding
and knowing it to be a main Principle, upon which all that is
founded that can be ſaid either well or handſomely on this parti­
cular. The other Diſcourſes may have an appearance of being
probable, but this hits the mark as full as can be deſired, arriving
at the higheſt degree of certainty.
I have, ſeventeen years ſince, as I repreſented to the moſt Se­
rene Prince, and to the Right Honourable the Preſident of the
Lords the Commiſſioners of the ^{*}Sewers, written a Treatiſe of the

Meaſure of the waters that move, in which I Geometrically de­
monſtrate and declare this buſineſſe, and they who ſhall have
well underſtood the ground of my Diſcourſe, will reſt fully ſa­
tisfied with that which I am now about to propoſe: But that all
may become rhe more eaſie, I will more briefly explicate and
declare ſo much thereof as I have demonſtrated in the Diſcourſe,
which will ſuffice for our purpoſe: And if that ſhould not be
enough, we have alwayes the experiment of a very eaſie and
cheap way to clear up the whole buſineſſe. And moreover I
will take the boldneſſe to affirm, that in caſe there ſhould not for
the preſent any deliberation be made concerning this affair, ac­
cording to my opinion; yet nevertheleſſe it will be, at ſome
time or other; or if it be not, things will grow worſe and
worſe.
* I. Savii dell'
Acque, a particu­
lar Council that
take care of the
Lakes and other
Aquatick affairs.
For more clear underſtanding, therefore, it ought to be known,
that it being required, as it is generally uſed, to meaſure the wa­
ters of a River, its breadth and its depth is taken, and theſe two
dimenſions being multiplied together, the product is affirmed to
be the quantity of that River: As for example, if a River ſhall
be 100. feet broad, and 20. feet high, it will be ſaid, that that
River is 2000 feet of Water, and ſo if a Ditch ſhall be 15. feet
broad, and 5. feet high, this ſame Ditch will be affirmed to be
75. feet of Water: And this manner of meaſuring Running
Water hath been uſed by the Ancients, and by Moderns, with
no other difference, ſave onely that ſome have made uſe of the
Foot, others of the Palme, others of the Brace, and others of
other meaſures.
Now becauſe that in obſerving theſe Waters that move, I fre­
quently found, that the ſame Water of the ſame River was in
ſome ſites of its Chanel pretty big, and in others much leſſe,
not arriving in ſome places to the twentieth, nor to the hundreth
part of that which it is ſeen to be in other places; therefore this
vulgar way of meaſuring the Waters that move, for that they did
1not give me a certain and ſtable meaſure and quantity of Water,
began deſervedly to be ſuſpected by me, as difficult and defective,
being alwayes various, and the meaſure, on the contrary, being
to be alwayes determinate, and the ſame; it is therefore written,
that Pondus & Pondus, Menſura & Menſura, utrumque abomi­
nabile eſt apud Deum, Exod. I conſidered that in the Terri­
tory of Breſcia, my native Countrey, and in other places, where
Waters are divided to overflow the Grounds, by the like way of
meaſuring them, there were committed grievous and moſt impor­
tant errours, to the great prejudice of the Publique and of Pri­
vate perſons, neither they that ſell, nor they that buy under­
ſtanding the true quantity of that which is ſold and bought: In
regard that the ſame ſquare meaſure, as is accuſtomed in thoſe
parts, aſſigned one particular perſon, carried to ſometimes above
twice or thrice as much water, as did the ſame ſquare meaſure aſ­
ſigned to another. Which thing proveth to be the ſame incon­
venience, as if the meaſure wherewith Wine and Oil is bought
and ſold, ſhould hold twice or thrice as much Wine or Oil at one
time as at another. Now this Conſideration invited my minde
and curioſity to the finding out of the true meaſure of Running
Waters. And in the end, by occaſion of a moſt important bu­
ſineſſe that I was imployed in ſome years ſince, with great in­
tenſeneſſe of minde, and with the ſure direction of Geometry, I
have diſcovered the miſtake, which was, that we being upon the
buſineſſe of taking the meaſure of the Waters that move, do make
uſe of two dimenſions onely, namely, breadth and depth, keep­
ing no account of the length. And yet the Water being, though
running, a Body, it is neceſſary in forming a conceit of its quan­
tity, in relation to another, to keep account of all the three Di­
menſions, that is of length, breadth, and depth.
Here an objection hath been put to me, in behalf of the ordi­
nary way of meaſuring Running Waters, in oppoſition to what
I have above conſidered and propoſed: and I was told, Its true,
that in meaſuring a Body that ſtands ſtill, one ought to take all
the three Dimenſions; but in meaſuring a Body that continually
moveth, as the Water, the caſe is not the ſame: For the length
is not to be had, the length of the water that moveth being infi­
nite, as never finiſhing its running; and conſequently is incom­
prehenſible by humane underſtanding, and therefore with reaſon,
nay upon neceſſity it cometh to be omitted.
In anſwer to this, I ſay, that in the aboveſaid Diſcourſe, two
things are to be conſidered diſtinctly; Firſt, whether it be poſſible
to frame any conceit of the quantity of the Body of the Water
with two Dimenſions onely. And ſecondly, whether this length
be to be found. As to the firſt, I am very certain that no man, let
1him be never ſo great a Wit, can never promiſe to frame a con­
ceit of the quantity of the Body of Water, without the third
Dimenſion of length: and hereupon I return to affirm, that the
vulgar Rule of meaſuring Running water is vain and erroneous.
This point being agreed on, I come to the ſecond, which is, Whe­
ther the third Dimenſion of length may be meaſured. And I ſay,
that if one would know the whole length of the water of a
Fountain or River, thereby to come to know the quantity of all
the Water, it would prove an impoſſible enterprize, nay the
knowing of it would not be uſeful. But if one would know how
much water a Fountain, or a River carrieth in a determinate time
of an hour, of a day, or of a moneth, &c. I ſay, that it is a very
poſſible and profitable enquiry, by reaſon of the innumerable
benefits that may be derived thence, it much importing to know
how much Water a Chanel carrieth in a time given; and I have
demonſtrated the ſame above in the beginning of this Book; and
of this we ſtand in need in the buſineſſe of the Lake, that ſo we
may be able to determine how much ſhall be the height of the
Brent, when it is ſpread all over the Lake: For the three dimen­
ſions of a Body being given, the Body is known; and the quan­
tity of a Body being given, if you have but two dimenſions, the
third ſhall be known. And thus diving farther and farther into
this Conſideration, I found that the Velocity of the courſe of the
water may be an hundred times greater or leſſer in one part of
its Chanel than in another. And therefore although there ſhould
be two mouths of Waters equal in bigneſſe; yet nevertheleſs it
might come to paſſe, that one might diſcharge an hundred or a
thouſand times more water than another: and this would be, if
the water in one of the mouths ſhould run with an hundred or a
thouſand times greater velocity, than the other; for that it
would be the ſame as to ſay, that the ſwifter was an hundred or
a thouſand times longer, than the ſlower: and in this manner I
diſcovered that to keep account of the velocity, was the keeping
account of the Length.
And therefore it is manifeſt, that when two Mouths diſcharge
the ſame quantity of Wa r in an equal velocity, it is neceſſary
that the leſs ſwift Mouth be ſo much bigger than the more ſwift;
as the more ſwift exceedeth in velocity the leſs ſwift; as for
example.
In caſe two Rivers ſhould carry equal quantity of water in
equal times, but that one of them ſhould be four times more
ſwift than the other, the more ſlow ſhould of neceſſity be four
times more large. And becauſe the ſame River in any part
thereof alwaies diſchargeth the ſame quantity of Water in equal
times (as is demonſtrated in the firſt Propoſition of the firſt
1
Book^{*} of the meaſure of Running Watets;) but yet doth not
run thorowout with the ſame velocity: Hence it is, that the vul­
gar meaſures of the ſaid River, in divers parts of its Chanel, are
alwaies divers; inſomuch, that if a River paſſing through its cha­
nel had ſuch velocity, that it ran 100 Braces in the 1/60 of an hour­
and afterwards the ſaid River ſhould be reduced to ſo much tardi,
ty of motion, as that in the ſame time it ſhould not run more than
one Brace, it would be neceſſary that that ſame River ſhould be­
come 100. times bigger in that place where it was retarded; I
mean, 100. times bigger than it was in the place where it was
ſwifter. And let it be kept well in mind, that this point rightly
underſtood, will clear the underſtanding to diſcover very many
accidents worthy to be known. But for this time let it ſuffice,
that we have onely declared that which makes for our purpoſe,
referring apprehenſive and ſtudious Wits to the peruſal of my
aforenamed Treatiſe; for therein he ſhall finde profit and delight
both together.
* He here intends
the Demonſtrati­
ons following, at
the end of the firſt
Book
Now applying all to our principal intent, I ſay, That by what
hath been declared it is manifeſt, that if the Brent were 40. Bra­
ces broad, and 2 1/2 high, in ſome one part of its Chanel, that after­
wards the ſame Water of the Brent falling into the Lake, andpaſ­
ſing thorow the ſame to the Sea, it ſhould loſe ſo much of its ve­
locity, that it ſhould run but one Brace, in the time wherein
whilſt it was in its Chanel at the place aforeſaid, it ran 100. Bra­
ces. It would be abſolutely neceſſary, that increaſing in mea­
ſure, it ſhould become an hundred times ^{*} thicker; and therefore

if we ſhould ſuppoſe that the Lake were 20000. Braces, the
Brent that already hath been ſuppoſed in its Chanel 100. Braces,
being brought into the Lake, ſhould be 100. times 100. Brates;
that is, ſhall be 10000. Braces in thickneſs, and conſequently ſhall
be in height half a Brace; that is, 100/200 of a Brace, and not 1/2. of a
Brace, as was concluded in the Argument.
* Deeper.
Now one may ſee into what a groſs errour of 99. in 100. one
may fall through the not well underſtanding the true quantity
of Running Water, which being well underſtood, doth open a
direct way to our judging aright in this moſt conſiderable affair.
And therefore admitting that wich hath been demonſtrated,
I fay, that I would (if it did concern me) greatly encline to con­
ſult upon the returning of the Brent again into the Lake: For it
being moſt evident, that the Brent in the Chanel of its mouth, is
much ſwifter than the Brent being brought into the Lake, it will
certainly follow thereupon, that the thickneſs of the Water of
Brent in the Lake, ſhall be ſo much greater than that of Brent in
Brent, by how much the Bront in Brent is ſwifter than thh Brent
in the Lake.
1
1. From which operation doth follow in the firſt place, that
the Lake being filled and increaſed by tbeſe Waters, ſhall be
more Navigable, and paſſible, than at preſent we ſee it to be.
2. By the current of theſe Waters, the Chanels will be ſcour­
ed, and will be kept clean from time to time.
3. There will not appear at the times of low-waters ſo many
Shelves, and ſuch heaps of Mud, as do now appear.
4. The Ayr will become more wholeſom, for that it ſhall not
be ſo infected by putrid vapours exhaled by the Sun, ſo long as
the Miery Ouze ſhall be covered by the Waters.
5. Laſtly, in the current of theſe advantagious Waters,, which
muſt iſſue out of the Lake into the Sea, beſides thoſe of the Tyde,
the Ports will be kept ſcoured, and clear: And this is as much as
I ſhall offer for the preſent, touching this weighty buiſineſs; al­
waies ſubmitting my ſelf to ſounder judgements.
Of the above-ſaid Writing I preſented a Copy at Venice, at a
full Colledge, in which I read it all, and it was hearkned to with
very great attention; and at laſt I preſented it to the Duke, and
left ſome Copies thereof with ſundry Senators, and went my way,
promiſing with all intenſeneſs to apply my pains with reiterated
ſtudies in the publick ſervice; and if any other things ſhould come
into my minde, I promiſed to declare them ſincerely, and ſo took
leave of His ſerenity, and that Noble Council. When I was
returned to Rome, this buſineſs night and day continually run­
ning in my mind, I hapned to think of another admirable and
moſt important conceit, which with effectual reaſons, confirmed
by exact operations, I with the Divine aſſiſtance, made clear and
manifeſt; and though the thing at firſt ſight ſeemed to me a moſt
extravagant Paradox, yet notwithſtanding, having ſatisfied my
ſelf of the whole buſineſs, I ſent it in writing to the moſt Illuſtri­
ous and moſt Noble Signore Gio. Baſadonna; who after he had
well conſidered my Paper, carried it to the Council; and after
that thoſe Lords had for many months maturely conſidered
thereon, they in the end reſolved to ſuſpend the execution of the
diverſion which they had before conſulted to make of the River
Sile, and of four other Rivers, which alſo fall into the Lake; a
thing by me blamed in this ſecond Paper, as moſt prejudicial,
and harmful. The writing ſpake as followeth.
1
CONSIDERATIONS
Concerning the
LAKE
OF
VENICE.
CONSIDERATION II.
If the diſcourſing well about the truth of
things, Moſt Serene Prince, were as the
carrying of Burdens, in which we ſee
that an hundred Horſes carry a greater
weight than one Horſe onely; it would
ſeem that one might make more account
of the opinion of many men, than of
one alone; But becauſe that diſcourſing
more reſembleth running, than carrying
Burdens, in which we ſee that one Barb alone runneth faſter
than an hundred heavy-heel'd Jades; therefore I have ever more
eſteemed one Concluſion well managed, and well conſidered by
one underſtanding man, although alone, than the common and
Vulgar opinions; eſpecially, when they concern abſtruce and
arduous points: Nay in ſuch caſes the opinions moulded and
framed by the moſt ignorant and ſtupid Vulgar, have been ever
ſuſpected by me as falſe, for that it would be a great wonder if
in difficult matters a common capacity ſhould hit upon that
which is handſom, good, and true. Hence I have, and do hold
in very great veneration the ſumme of the Government of the
moſt Serene, and eternal Republick of Venice; which although,
as being in nature a Common-wealth, it ought to be governed by
the greater part; yet nevertheleſs, in arduous affairs, it is alwaies
directed by the Grave Judgement of few, and not judged blindly
1by the Plebeian Rout. Tis true, that he that propoundeth Pro­
poſitions far above the reach of common capacity, runneth a
great hazard of being very often condemned without further Pro­
ceſs, or knowledge of the Cauſe; but yet for all that, the truth
is not to be deſerted in moſt weighty affairs, but ought rather to
be explained in due place and time with all poſſible perſpicuity;
that ſo being well underſtood, and conſidered, it may come after­
wards for the Common good to be embraced.
This which I ſpeak in general, hath often been my fortune in
very many particulars, not onely when I have kept within the
bounds of meer ſpeculation, but alſo when I have chanced to de­
ſcend to Practice, and to Operations: and your Highneſs know­
eth very well what befel me the laſt Summer 1641. when in obe­
dience to your Soveraign Command, I did in full Colledge repre­
ſent my thoughts touching the ſtate of the Lake of Venice; for
there not being ſuch wanting, who without ſo much as vouch­
ſafing to underſtand me, but having onely had an inkling, and
bad apprehenſion of my opinion, fell furiouſly upon me, and by
violent means both with the Pen and Preſs, full of Gall, did abuſe
me in reward of the readineſs that I had expreſt to obey and
ſerve them: But I was above meaſure encouraged and pleaſed, to
ſee that thoſe few who vouchſafed to hear me, were all either
thorowly perſwaded that my opinion was well grounded, or at
leaſt ſuſpended their prudent verdict to more mature deliberati­
on. And though at the firſt bout I chanced to propoſe a thing
that was totally contrary to the moſt received and antiquated
opinion, and to the reſolutions and conſultations taken above an
hundred years ago: Moved by theſe things, and to ſatisfie alſo
to the promiſe that I had made of tendering unto them what
ſhould farther offer it ſelf unto me touching the ſame buſineſs; I
have reſolved to preſent to the Throne of your Highneſs, another
Conſideration of no leſs importance, which perhaps at firſt ſight
will appear a ſtranger Paradox; but yet brought to the Teſt and
Touch-ſtone of experience, it ſhall prove moſt clear and evident.
If it ſhall be accounted of, ſo that it ſucceedeth to the benefit of
your Highneſs, I ſhall have obtained my defire and intent: And
if not, I ſhall have ſatisfied my ſelf, and ſhall not have been
wanting to the Obligation of your moſt faithful Servant, and na­
tive ſubject.
That which I propounded in the Mouths paſs, touching the
moſt important buſineſs of the Lake, though it did onely expreſ­
ly concern the point of the diverſion of the Mouth of the Lake,
already made and put in execution; yet it may be underſtood
and applyed alſo to the diverſion under debate, to be made of
the other five Rivers, and of the Sile in particular.
1
Now touching this, I had the fortune to offer an admirable
accident that we meet with when we come to the effect, which
I verily believe will be an utter ruine to the Lake of Ve­
nice.
I ſay therefore, that by diverting theſe five Rivers that re­
main, although their water that they diſcharge for the preſent in­
to the Lake is not all taken together 4/5 parts of what the Brent
alone did carry, yet nevertheleſſe the abatement of the water of
the Lake which ſhall enſue upon this laſt diverſion of four parts,
which was the whole water, ſhall prove double to that which hath
happened by the diverſion of Brent onely, although that the
Brent alone carried five parts of that water, of which the Rivers
that are to be diverted carry four: A wonder really great, and
altogether unlikely; for the reducing all this Propoſition to be
underſtood, is as if we ſhould ſay, that there being given us
three Rivers, of which the firſt diſchargeth five parts, the ſecond
three, and the third one, and that from the diverſion of the
firſt, there did follow ſuch a certain abatement or fall; from
the taking away of the ſecond there ought to follow alſo ſo
much more abatement; And laſtly, from the withdrawing of
the third the water ought to fall ſo much more, which is wholly
impoſſible: And yet it is moſt certain, and beſides the demon­
ſtration that perſwades me to it, which I ſhall explain in due
time, I can ſet before your eyes ſuch an experiment as is not to
be denied by any one, although obſtinate: and I will make it
plainly ſeen and felt, that by taking away only four parts of the
five, which ſhall have been taken away, the abatement proveth
double to the abatement enſuing upon the diverting firſt of the
five onely; which thing being true, as moſt certainly it is, it
will give us to underſtand how pernicious this diverſion of five
Rivers is like to prove, if it ſhall be put in execution.
By this little that I have hinted, and the much that I could
ſay, let your Highneſſe gather with what circumſpection this bu­
ſineſſe ought to be managed, and with how great skill he ought
to be furniſhed who would behave himſelf well in theſe difficult
affairs.
I have not at this time explained the demonſtration, nor have
I ſo much as propounded the way to make the Experiment, that
I am able to make in confirmation of what I have ſaid, that ſo
by ſome one or others miſ-apprehending the Demonſtration,
and maiming the Experiment, the truth may not happen to ſhine
with leſſe clarity than it doth, when all miſts of difficulty are re­
moved: and if ſo be, no account ſhould be made of the Reaſons
by me alledged, and that men ſhould ſhut their eyes againſt the
Experiments that without coſt or charge may be made, I do de­
1clare and proteſt that there ſhall follow very great dammages
to the Fields of the main Land, and extraordinary ſummes
ſhall be expended to no purpoſe. The Lake undoubtedly will
become almoſt dry, and will prove impaſſible for Navigation,
with a manifeſt danger of corrupting the Air: And in the laſt
place there will unavoidably enſue the choaking and ſtoppage of
the Ports of Venice.
Upon the 20th. of December, 1641. I imparted this my ſecond
Conſideration to the moſt Excellent Signore Baſadonna, preſen­
ting him with a Copy thereof amongſt other Writings, which I
have thought good to inſert, although they ſeem not to belong
directly to our buſineſſe of the Lake.
The way to examine the MUD and SAND
that entereth and remaineth in the
LAKE of VENICE.
To the moſt Excellent
SIGNORE GIO. BASADONNA.
Two very conſiderable Objections have been made a­
gainſt my opinion concerning the Lake of Venice: One
was that, of which I have ſpoken at large in my firſt
Conſideration, namely, that the Brents having been taken out of
the Lake, cannot have been the occaſion of the notable fall of
the Waters in the Lake, as I pretend, and conſequently, that
the turning Brent into the Lake would be no conſiderable reme­
dy, in regard that the water of Brent, and the great expanſion
of the Lake over which the water of Brent is to diffuſe and
ſpread being conſidered, it is found that the riſe proveth in­
ſenſible.
The ſecond Objection was, that the Brent is very muddy, and
therefore if it ſhould fall muddy into the Lake, the Sand would
ſink and fill up the ſame.
Touching the firſt Query, enough hath been ſaid in my firſt
Conſideration, where I have plainly diſcovered the deceipt of the
Argument, and ſhewn its fallacy; It remaineth now to examine
1the ſecond: to which in the firſt place I ſay, that one of the firſt
things that I propoſed in this affair was, that I held it impoſſible
to do any act, though never ſo beneficial, that was not alſo ac­
companied by ſome inconvenience and miſchief; and therefore
we are to conſider well the profit, and the loſſe and prejudice;
and they both being weighed, we ſhall be able to chooſe the leſ­
ſer evil: Secondly, I admit it to be moſt true, that Brent is at ſome
times muddy, but it is alſo true, that for the greater part of the
year it is not muddy. Thirdly, I do not ſee nor underſtand
what ſtrength this objection hath, being taken ſo at large, and in
general; and methinks that it is not enough to ſay, that the
Brent runneth muddy, and to aſſert that it depoſeth its Muddi­
neſſe in the Lake, but we ought moreover to proceed to particu­
lars, and ſhew how much this Mud is, and in what time this
choaking up of the Ports may be effected. For the Reaſons are
but too apparent and particular, that conclude the ruine of the
Lake, and that in a very ſhort time, (for mention is made of
dayes) the Waters diverſion being made, and moreover we
have the circumſtance of an Experiment, the ſtate of things be­
ing obſerved to have grown worſe ſince the ſaid diverſion. And
I have demonſtrated, that in caſe the Diverſion of the Sile and
the other Rivers ſhould be put in execution, the Lake would in a
few dayes become almoſt dry; and the Ports would be loſt, with
other miſchievous conſequences. But on the other ſide, al­
though that we did grant the choaking of them, we may very
probably ſay, that it will not happen, ſave onely in the ſucceſſion
of many and many Centuries of years. Nor can I think it pru­
dent counſel to take a reſolution and imbrace a Deſigne now, to
obtain a benefit very uncertain, and more than that, which only
ſhall concern thoſe who are to come very many Ages after us,
and thereby bring a certain inconvenience upon our ſelves, and
upon our children that are now alive and preſent.
Let it be alledged therefore, (although I hold it falſe) that by
the diverſions of the Rivers the Lake may be kept in good con­
dition for ſeveral years to come.
But I ſay confidently, and hope to demonſtrate it; That the
Diverſions will bring the Lake, even in our dayes, to be almoſt
dry, and at leaſt will leave ſo little water in it, that it ſhall ceaſe
to be Navigable, and the Ports ſhall moſt infallibly be choaked
up. I will therefore ſay upon experience, in anſwer to this Ob­
jection, that it is very neceſſary firſt well to diſcourſe, and ratio­
nally to particularize and aſcertain the beſt that may be this
point of the quantity of this ſinking Mud or Sand.
Now I fear I ſhall make my ſelf ridiculous to thoſe, who mea­
ſuring the things of Nature with the ſhallowneſſe of their brains
1do think that it is abſolutely impoſſible to make this enquiry, and
will ſay unto me, Quis menſus eſt pugillo aquas, & terram palmo
ponderavit? Yet nevertheleſs I will propound a way whereby,
at leaſt in groſs, one may find out the ſame.
Take a Veſſel of Cylindrical Figure, holding two barrels of
water, or thereabouts; and then fill it with the water of Brent,
at its Mouth or Fall into the Lake; but in the Lake at the time
that the Brent runneth muddy, and after it hath begun to run
muddy for eight or ten hours, to give the mud time to go as far
as S. Nicolo, to iſſue into the Sea; and at the ſame time take
another Veſſel, like, and equal to the firſt, and fill it with the wa­
ter of the Lake towards S. Nicolo, (but take notice that this ope­
ration ought to be made at the time when the waters go out,
and when the Sea is calm) and then, when the waters ſhall have
ſetled in the aforeſaid Veſſels, take out the clear water, and con­
ſider the quantity of Sand that remains behind, and let it be ſet
down, or kept in mind: And I am eaſily induced to think, that
that ſhall be a greater quantity of Sand which ſhall be left in the
firſt Veſſel, than that left in the ſecond Veſſel. Afterwards
when the Brent ſhall come to be clear, let both the operations be
repeated, and obſerve the quantity of Sand in the aforeſaid Veſ­
ſels; for if the Sand in the firſt Veſſel ſhould be moſt, it would
be a ſign, that in the revolution of a year the Brent would depoſe
Sand in the Lake: And in this manner one may calculate to a
ſmall matter what proportion the Sand that entreth into the Lake,
hath to that which remains: And by that proportion one may
judge how expedient it ſhall be for publick benefit. And if at
ſeveral times of the year you carefully repeat the ſame operati­
ons, or rather obſervations, you would come to a more exact
knowledge in this buſineſs: And it would be good to make the
ſaid operations at thoſe times, when the Lake is diſturbed by
ſtrong high Winds, and made muddy by its own Mud, raiſed by
the commotion of the Waters.
This notion would give us great light, if the ſame obſervations
ſhould be made towards the Mouth of Lio, at ſuch time as the
waters flow and ebb, in calm ſeaſons; for ſo one ſhould come to
know whether the waters of the Lake are more thick at the going
out, than at the entrance. I have propounded the foregoing
way of meaſuring Sands and Mud, to ſhew that we are not ſo
generally, and inconſiderately to pronounce any ſentence, but
proceed to ſtricter inquiries, and then deliberate what ſhall be
moſt expedient to be done. Others may propoſe more exqui­
ſite examinations, but this ſhall ſerve me for the preſent.
I will add onely, that if any one had greater curioſity (it would
be profitable to have it) in inveſtigating more exactly the quan­
1tity of the Water that entereth into the Lake, by the means that
I have ſhewen in the beginning of this Book: When he ſhall
have found the proportion of the quantity of water to the quan­
tity of Sand or Mud, he ſhall come to know how much Sand the
Brent ſhall leave in the Lake in the ſpace of a year. But to
perform theſe things, there are required perſons of diſcretion, and
fidelity, and that are imployed by publick Order; for there
would thence reſult eminent benefit and profit.
Here are wanting LETTERS from ſeveral perſons.
To the Reverend Father, Franceſco di
S. GIUSEPPE.
In execution of the command that you laid upon me in your
former Letters, by order from the moſt Serene, my Lord,
Prince Leopold; that I ſhould ſpeak my judgment concern­
ing the diſimboguement of the River called Fiume morto, whe­
ther it ought to be let into the Sea, or into Serchio; I ſay, that
I chanced 18. years ſince to be preſent, when the ſaid Mouth was
opened into the Sea, and that of Serchio ſtopt; which work was
done to remedy the great Innundation that was made in all that
Country, and Plain of Piſa, that lyeth between the River Arno,
and the Mountains of S. Giuliano, and the River Serchio; which
Plain continued long under water, inſomuch that not onely in the
Winter, but alſo for a great part of the Summer, thoſe fields
were overflowed; and when that the Mouth of Fiume morto was
effectually opened into the Sea, the place was preſently freed from
the waters. and drained, to the great ſatisfaction of the Owners
of thoſe Grounds. And here I judge it worth your notice, that
for the generality of thoſe that poſſeſs eſtates in thoſe parts, they
deſired that the Mouth of Fiume morto might ſtand open to the
Sea, and thoſe who would have it open into Serchio, are perſons
that have no other concernment there, ſave the hopes of gaining
by having the diſpoſe of Commiſſions, and the like, &c,
But for the more plain underſtanding of that which is to be
ſaid, it muſt be known, That the reſolution of opening the ſaid
Mouth into Serchio, was taken in the time of the Great Duke
Ferdinando the firſt, upon the ſame motives that are at this time
again propoſed, as your Letters tell me, Since that, it manifeſt­
ly appearing, that Fiume morto had, and hath its Mouth open to
the Sea, the Plain hathbeen kept dry; and it being alſo true, that
1the fury of the South, and South-Weſt-Winds carryed ſuch
abundance of ſand into the Mouth, or Out-let of Fiume morto,
that it wholly ſtopt it up: eſpecially when the waters on Piſa
ſide were low and ſhallow, And they think, that turning the
Lake of Fiume morto into Serchio, and the Serchio maintaining
continually its own Mouth with the force of its waters open to the
Sea, and conſequently alſo Fiume morto, they would have had the
Out-let clear and open; and in this manner they think, that the
Plain of Piſa would have been freed from the waters. The bu­
ſineſs paſſeth for current, at firſt ſight; but experience proveth
the contrary, and Reaſon confirmeth the ſame: For the height
of the water of thoſe Plains, was regulated by the height of the
waters in the Mouth of Fiume morto; that is, The waters at the
Mouth being high, the waters alſo do riſe in the fields; and when
the waters at the Mouth are low, the waters of the fields do like­
wiſe abate: Nor is it enough to ſay, That the Out-let or Vent
of Fiume morto is continual, but it muſt be very low: Now if
Fiume morto did determine in Serchio, it is manifeſt that it
would determine high; for Serchio terminating in the Sea, when
ever it more and more aboundeth with water, and riſeth, it is ne­
ceſlary that alſo Fiume morto hath its level higher, and conſe­
quently ſhall keep the waters in the Plains higher. Nay, it hath
happened ſometimes (and I ſpeak it upon my own ſight) that
Fiume morto hath reverſed its courſe upwards towards Piſa;
which caſe will ever happen, whenſoever the Piſan waters chance
to be lower than the level of thoſe of Serchio; for in that caſe
the waters of Serchio return back upon the Plains thorow Fiume
morto in ſuch ſort, that the Muddineſſes, and the Serchio have
been obſerved to be carried by this return as farr as the Walls of
Piſa; and then before ſuch time as ſo great waters can be aſ­
ſwaged, which come in with great fury, and go out by little and
little, there do paſs very many days, and moneths, nay ſome­
times one being never able to find the waters of Serchio,
when at the ſhalloweſt, ſo low as the Sea in level; (which is the
loweſt place of the waters) it thence doth follow, that the wa­
ters of Fiume morto ſhould never at any time of the year, ſo long
as they determine in Serchio, be ſo low, as they come to be when
the ſame Fiume morto determineth in the Sea. Tis true indeed,
that the Mouth of Fiume morto, opened into the Sea, is ſubject to
the inconvenience of being ſtopt up by the force of Winds: But
in this caſe, it is neceſſary to take ſome pains in opening it; which
may eaſily be done, by cutting that Sand a little which ſtayeth
in the Mouth, after that the Wind is laid; and it is enough if you
make a Trench little more than two Palms in breadth; for the
water once beginning to run into it, it will in a few hours carry
1that Sand away with it, and there will enſue a deep and broad
Trench that will drain away all the water of the Plains in very lit­
tle time. And I have found by practice, that there having been
a great quantity of Sand driven back, by the fury of the South­
Weſt-Wind, into the Mouth of Fiume morto, I having cauſed the
little gutter to be made in the Morning, ſomewhat before Noon,
a Mouth hath been opened of 40. Braces wide, and notably deep,
inſomuch that the water, which before had incommoded all the
Champian ran away in leſs than three dayes, and left the Coun­
try free and dry, to the admiration of all men. There was pre­
ſent upon the place, at this buſineſs, on the ſame day that I
opened the Mouth, the moſt Serene great Duke, the moſt Serene
Arch-Dutcheſs Mother, all the Commiſſioners of Sewers, with
many other Perſons and Peaſants of thoſe parts; and they all ſaw
very well, that it was never poſſible that a little Bark of eight
Oars, which was come from Legorn to wait upon the great
Duke, ſhould ever be able to maſter the Current, and to make
up into Fiume morto; and his Highneſs, who came with an intent
to cauſe the ſaid Mouth towards the Sea to be ſtopt; and that
into Serchio to be opened, changed his judgement, giving order
that it ſhould be left open towards the Sea, as it was done. And
if at this day it ſhall return into Serchio, I am very certain that it
will be neceſſary to open it again into the Sea. And there was
alſo charge and order given to a perſon appointed for the pur­
poſe, that he ſhould take care to open the ſaid Mouth, as hath
been ſaid upon occaſion. And thus things have ſucceeded very
well unto this very time. But from the middle of October, until
this firſt of February, there having continued high South, and
South-Weſt-Winds, with frequent and abundant Rains; it is no
wonder that ſome innundation hath happened; but yet I will
affirm, that greater miſchiefs would have followed, if the Mouth
had been opened into Serchio. This which I have hitherto ſaid,
is very clear and intelligible to all ſuch as have but competent in­
ſight, and indifferent skill in theſe affairs. But that which I am
now about to propoſe farther, will, I am very certain, be under­
ſtood by your ſelf, but it will ſeem ſtrange and unlikely to many
others. The point is, that I ſay, That by raiſing the level of
Fiume morto, one half Brace, onely at its Mouth, (it will peni­
penitrate into Serchio farther than it would into the Sea) it ſhall
cauſe the waters to riſe three, or perhaps more Braces upon the
fields towards Piſa, and ſtill more by degrees as they ſhall recede
farther from the Sea-ſide; and thus there will follow very great
Innundations, and conſiderable miſchiefs. And to know that
this is true, you are to take notice of an accident, which I give
warning of in my diſcourſe of the Meaſure of Running Waters:
1where alſo I give the reaſon thereof, ^{*} Coroll. 14. The ac­
cident is this, That there coming a Land-Flood, for example,
into Arno, which maketh it to riſe above its ordinary Mouth
wthin Piſa, or a little above or below the City ſix or ſeven Bra­
ces; this ſame height becometh alwaies leſſer and leſſer, the more
we approach towards the Sea-ſide; inſomuch, that near to the
Sea the ſaid River ſhall be raiſed hardly half a Brace: Whence
it followeth of neceſſary conſequence, that ſhould I again be at
the Sea-ſide, and knowing nothing of what hapneth, ſhould ſee
the River Arno raiſed by the acceſſion of a Land-flood, one third
of a Brace; I could certainly infer, that the ſame River was raiſed
in Piſa thoſe ſame ſix or ſeven Braces. And that which I ſay of
Arno, is true of all Rivers that fall into the Sea. Which thing
being true, it is neceſſary to make great account of every ſmall
riſing, that Fiume morto maketh towards the Sea-ſide by fal­
ling into Serchio. For although the riſing of Fiume morto, by
being to diſgorge its Waters into Serchio, towards the Sea, were
onely a quarter of a Brace; we might very well be ſure, that fart
from the Sea, about Piſa, and upon thoſe fields the riſe ſhall be
much greater, and ſhall become two or three Braces: And be­
cauſe the Countrey lyeth low, that ſame riſe will cauſe a conti­
nual Innundation of the Plains, like as it did before; I cauſed the
Mouth to be opened into the Sea. And therefore I conclude
that the Mouth of Fiume morto, ought by no means to be opened
into Serchio; but ought to be continued into the Sea, uſing all
diligence to keep it open after the manner aforeſaid, ſo ſoon as
ever the Wind ſhall be laid. And if they ſhall do otherwiſe, I
confidently affirm, that there will daily follow greater damages;
not onely in the Plains, but alſo in the wholeſomneſs of the
Air; as hath been ſeen in times paſt. And again, It ought with
all care to be procured, that no waters do by any means run or
fall from the Trench of Libra, into the Plain of Piſa, for theſe
Waters being to diſcharge into Fiume morto, they maintain it
much higher than is imagined, according to that which I have de­
monſtrated in my conſideration upon the ſtate of the Lake of
Venice. I have ſaid but little, but I ſpeak to you, who under­
ſtandeth much, and I ſubmit all to the moſt refined judgment of
our moſt Serene Prince Leopold, whoſe hands I beſeech you in all
humility to kiſs in my name, and implore the continuance of his
Princely favour to me; and ſo deſiring your prayers to God for
me, I take my leave.
Rome 1. Feb.
1642.
Your moſt affectionate Servant,
D. BENEDETTO CASTELLI.
1
The anſwer to a Letter written by BAR­
TOLOTTI, touching the
difficultyes obſerved.
The former part of the Letter is omitted, and the diſcourſe
beginneth at the firſt Head.
And firſt I ſay, Whereas I ſuppoſe that the level of the Ser­
chio is higher than that of Fiume morto; this is moſt true,
at ſuch time as the waters of Fiume morto are diſcharged in­
to the Sea; but I did never ſay that things could never be brought
to that paſs, as that the level of Fiume morto ſhould be higher than
Serchio: and ſo I grant that it will follow, that the waters of
Fiume morto ſhall go into Serchio, and its very poſſible, that the
Drain of Fiume morto into Serchio may be continuate; and I far­
ther grant, that its poſſible, that the Serchio doth never diſgorge
thorow Fiume morto towards Piſa; Nay, I will yet farther grant
that it might have happened, that Fiume morto might have had
ſuch a fall into Serchio, as would have ſufficed to have turned
Mills: But then I add withall, that the Plains of Piſa, and the
City it ſelf muſt be a meer Lake.
2. Signore Bartololti ſaith confidently, that when the Sea ſwel­
leth by the South-Weſt, or other Winds, the level of Serchio in
the place marked A in the Platt, diſtant about 200. Braces, riſeth
very little: But that Fiume morto in D, and in E, many miles
more up into Land riſeth very much, and that certain Fiſhermen
confirm this, and ſhew him the ſignes of the riſing of the Water.
I grant it to be very true, and I have ſeen it with my own eyes:
But this cometh to paſs, when the Mouth of Fiume morto is ſtopt
up by the Sea; as I ſhall ſhew by and by. And this riſing near
the Sea-ſide, is of no conſiderable prejudice to the fields. And
this is as much as I find to be true in the aſſertion of Signore Bar­
tolotti, (without his confirming it by any other proof; as indeed
it needs none) That the level of Fiume morto riſeth in E, and ma­
ny miles farther upwards it riſeth much; nor did I ever affirm the
contrary.
3. Concerning the difficulty of opening the Mouth of Fiume
morto into the Sea, that which Il Caſtellano ſaith is moſt certain;
namely, That at the entrance upon the opening of the Mouth, it
is neceſſary to make a deep Trench: But I ſay, that at that time
it is difficult to open it, unleſs upon great occaſions; for that the
1difficulty proceedeth from the waters of Fiume morto being low,
and the fields drained.
4. As to the particular of the Cauſes that you tell me men
preſs ſo much unto the moſt Serene Grand Duke, and to the
Prince, I have not much to ſay, becauſe it is not my profeſſion;
nor have I conſidered of the ſame: Yet I believe, that when the
Prince and his Highneſſe ſee the benefit of his People and Sub­
jects in one ſcale of the Ballance, and the accomodation of
Huntſmen in the other, his Highneſſe will incline to the profit
of his ſubjects; ſuch have I alwayes found his Clemency and
Nobleneſſe of minde. But if I were to put in my vote upon
this buſineſſe, I would ſay, that the points of Spears, and the
mouths of Guns, the yelping of Dogs, the wilyneſſe of Huntſ­
men, who run thorow and narrowly ſearch all thoſe Woods,
Thickets and Heathes, are the true deſtroyers of Bucks and
Boares, and not a little Salt-water, which ſetleth at laſt in ſome
low places, and ſpreadeth not very far. Yet nevertheleſſe, I will
not enter upon any ſuch point, but confine my ſelf ſolely to the
buſineſſe before me.
5. That Experiment of joyning together the water of Fiume
morto, and that of Serchio by a little trench to ſee what advan­
tage the Level E hath upon the Level I, doth not give me full
ſatisfaction, taken ſo particularly, for it may come to paſſe, that
ſometimes E may be higher, and ſometimes A lower, and I do
not queſtion but that when Serchio is low, and Fiume morto full
of Water, the level of Fiume morto will be higher than that of
Serchio. But Serchio being full, and Fiume morto ſcant of Wa­
ter, the contrary will follow, if the Mouth ſhall be opened to
the Sea. And here it ſhould ſeem to me, that it ought to be
conſidered, that there is as much advantage from E to the Sea
through the little Trench opened anew into Serchio, as from E to
the Sea by the Mouth of Fiume morto. But the difficulty (which
is that we are to regard in our caſe) is, that the courſe of the
Waters thorow the Trench is three times longer than the courſe
of the Mouth of Fiums morto, as appeareth by the Draught or
Plat which you ſent me, which I know to be very exactly drawn,
for that the ſituation of thoſe places are freſh in my memory.
Here I muſt give notice, that the waters of Fiume morto determi­
ning thorow the Trench in Serchio (the waters of which Fiume
morto are, for certain, never ſo low as the Sea) their pendency or
declivity ſhall, for two cauſes, be leſſe than the pendency of thoſe
waters through the Mouth towards the Sea, that is, becauſe of
the length of the line through the Trench, and becauſe of the
height of their entrance into Serchio, a thing which is of very
great import in diſcharging the waters which come ſuddenly, as
1he ſhall plainly ſee, who ſhall have underſtood my Book of the
Meaſure of Running Waters And this was the Reaſon why all
the Countrey did grow dry upon the opening of the Mouth into
the Sea. And here I propoſe to conſideration that which the Pea­
ſants about Piſa relate, namely, That the Water in the Fields
doth no conſiderable harm by continuing there five or ſix, yea, or
eight dayes. And therefore the work of the Countrey is to o­
pen the Mouth of Fiume morto, in ſuch manner, that the Water
being come, they may have the Trench free and ready, when that
the Water cometh it may have a free drain, and may not ſtay
there above eight or nine dayes, for then the overflowings be­
come hurtful. It is to be deſired alſo, that if any Propoſition is
produced touching theſe affairs, it might be propounded the moſt
diſtinctly that may be poſſible, and not conſiſt in generals, eſpe­
cially when the Diſpute is of the riſings, of velocity, of tardity,
of much and little water; things that are all to be ſpecified by
meaſures.
6. Your Letter ſaith, in the next place, that Signore Barto­
lotti confeſſeth, that if the Mouth of the Fiume morto might al­
wayes be kept open, it would be better to let it continue as it is:
the which, that I may not yield to him in courteſie, I confeſſe,
for the keeping it ſtopt on all ſides would be a thing moſt per­
nicious. But admitting of his confeſſion I again reply, that Fi­
ume morto ought not to be let into Serchio, but immediately in­
to the Sea; becauſe although ſometimes the Mouth to Sea­
wards be ſtopt up, yet for all that, the raiſing of the Bank above
the Plains (which is all the buſineſſe of importance) ſhall be ever
leſſer, if we make uſe of the Mouth leading to the Sea, than u­
ſing that of Serchio.
7. I will not omit to mention a kinde of ſcruple that I have
concerning the poſition of Sign. Bartolotti, that is, where he ſaith
that the two Mouths A and D are equal to the like Mouths into
the Sea; Now it ſeems to me, that the Mouth A of Fiume morto
into Serchio is abſolutely within Serchio, nor can it be made low­
er, and is regulated by the height of Serchio: But the Mouth
of Fiume morto terminates, and ought to be underſtood to ter­
minate in the Sea it ſelf, the loweſt place. And this I believe
was very well peroeived by Sig. Bartolotti, but I cannot tell why
he paſt it over without declaring it: and we ſee not that the
Mouth D falleth far from the Sea, which Mouth ought to be let
into the Sea it ſelf, and ſo the advantage of the Mouth into the
Sea more clearly appeareth.
8. That which Sig. Bartolotti addeth, that when it is high
Waters, at ſuch time as the Waters are out, and when Winds
choak up Fiume morto, they not only retard it, but return the
1courſe of the Waters upwards very leaſurely, perſwadeth me
more readily to believe that Sig. Bartolotti knoweth very well,
that the Mouth of Fiume morto let into Serchio is hurtful: for
by this he acknowledgeth that the Mouth towards the Sea doth
in ſuch ſort drain the Countrey of the Waters, as that they be­
come very low; and therefore upon every little impetus the wa­
ters turn their courſe: And from the motions, being exceeding
ſlow, is inferred, that the abundance of Sea-water that com­
eth into Fiume morto, is ſo much as is believed, and as Sig. Bat­
tolotti affirmeth.
9. After that Sig. Bartolotti hath ſaid what he promiſeth a­
bove, namely, that when the Windes blowing ſtrongly do ſtop
up Fiume morto, and not onely retard but turn the courſe up­
wards, the time being Rainy, and the Mouth of Fiume morto ſhut
up, the Waves of the Sea paſſe over the Bank of Fiume morto; at
that time, ſaith Signore Bartolotti, the Champain ſhall know the
benefit of Fiume morto diſcharged into Serchio, and the mouth A
ſhall ſtand alwayes open; and Fiume morto may alwayes con­
ſtantly run out, as alſo the Rains and Rain-waters, although the
hurtful Tempeſt ſhould laſt many dayes, &c. And I reply, that
all the Art conſiſts in this; for the benefit of thoſe Fields doth
not depend on, or conſiſt in ſaying, that Fiume morto is alwayes
open, and Fiume morto draineth continually; But all the buſi­
neſſe of profit lyeth and conſiſteth in maintaining the Waters
low in thoſe Plaines, and thoſe Ditches, which ſhall never be ef­
fected whilſt the World ſtands, if you let Fiume morto into Ser­
chio; but yet it may, by opening the mouth into the Sea: and
ſo much reaſon and nature proveth, and (which importeth) Ex­
perience confirmeth.
10. In the tenth place I come to conſider the anſwer that
was made to another Propoſition in the Letter which I writ to
Father Franceſco, which prudently of it ſelf alone might ſerve
to clear this whole buſineſſe. I ſaid in my Letter, That great
account is to be made of every ſmall riſing and ebbing of the
Waters neer to the Sea in Fiume morto, for that theſe riſings and
fallings, although that they be ſmall neer to the Sea-ſide, yet ne­
vertheleſſe, they operate and are accompanied by notable riſings
and fallings within Land, and far from the Sea-ſide, and I have
declared by an example of Arno, in which a Land-flood falling,
that made it increaſe above its ordinary height within Piſa ſix or
ſeven Braces, that this height of the ſame Flood becometh ſtill
leſſer, the neerer we approach to the Sea-coaſts. Nor ſhall the
ſaid River be raiſed hardly half a Brace; whereupon it neceſſ­
rily followeth, that if I ſhould return to the Sea-ſide, and not
knowing any think of that which happeneth at Piſa, and ſeeing
1the River Arno raiſed by a Land-flood half a Brace, I might con­
fidently affirm the ſaid River to be raiſed in Piſa thoſe ſix or ſe­
ven Braces, &c. From ſuch like accidents I conclude in the ſame
Letter, that it is neceſſary to make great account of every little
riſe that Fiume morto ſhall make towards the Sea. Now cometh
Bartolotti (and perhaps becauſe I knew not how to expreſs my
ſelf better, underſtandeth not my Propoſition) and ſpeaketh that
which indeed is true, but yet beſides our caſe: Nor have I ever
ſaid the contrary; and withall doth not apply it to his purpoſe.
Nay I ſay, that if he had well applyed it, this alone had been a­
ble to have made him change his opinion. And becauſe he ſaith,
that I ſaid, that it is true, when the abatement proceedeth from
ſome cauſe above, as namely by Rain, or opening of Lakes;
But when the cauſe is from below, that is, by ſome ſtop, as for
inſtance ſome Fiſhers Wears or Locks, or ſome impediment re­
mote from the Sea, although at the Level it ſhall riſe ſome Braces
where the impediment is, yet that riſing ſhall go upwards; and
here he finiſheth his Diſcourſe, and concludeth not any thing
more. To which I ſay firſt, that I have alſo ſaid the ſame in the
Propoſition, namely, that a Flood coming (which maketh Arno
to riſe in Piſa ſix or ſeven Braces (which I take to be a ſuperiour
cauſe whether it be Rain or the opening of Lakes, as beſt plea­
ſeth Bartolotti) in ſuch a caſe I ſay, and in no other (for towards
the Sea-coaſts it ſhall not cauſe a riſing of full half a Brace; and
therefore ſeeing Arno at the Sea-ſide to be raiſed by a Flood, whe­
ther of Rain, or of opening of Lakes half a Brace) it may be
inferred, that at Piſa it ſhall be raiſed thoſe ſix or ſeven Braces;
which variety, well conſidered, explaineth all this affair in favour
of my opinion: For the riſing that is made by the impediment
placed below, of Fiſhing Weares and Locks, operateth at the be­
ginning, raiſing the Waters that are neer to the impediment;
and afterwards leſs and leſs, as we retire upwards from the im­
pediment: provided yet that we ſpeak not of a Flood that com­
meth by acceſſion, but onely of the ordinary Water impeded.
But there being a new acceſſion, as in our caſe, then the Water
of the Flood, I ſay, ſhall make a greater riſing in the parts ſuperi­
our, far from the impediment; and theſe impediments ſhall
come to be thoſe that ſhall overflow the Plains, as happened
eighteen or nineteen years ago, before the opening of Fiume
morto into the Sea, The ſame will certainly follow, if Fiume
morto be let into Serchio. Here I could alledge a very pretty
caſe that befell me in la ^{*} Campagna di Roma, neer to the Sea­

ſide. where I drained a Bog or Fen, of the nature of the Wa­
ters of Piſa, and I ſucceeded in the enterprize, the Waters in their
ſite towards the Sea abating only three Palmes, and yet in the
1Fen they fell more than fifteen Palmes. But the buſineſſe
would be long, and not ſo eaſily to be declared, and I am cer­
tain that Sig. Bartolotti having conſidered this, would alter his
judgment, and withall would know that remitting that impedi­
ment anew, which I had left for leſſe than three Palmes towards
the Sea, the Waters in the Fen would return with the firſt Floods
and Raines to the ſame height as before, as likewiſe Fiume morto
will do if it ſhall be let again into Serchio.
* The Countrey
or Province lying
round the City,
heretofore called
Latium
Here I intreat your Honour to do me the favour to importune
P. Franceſco in my behalf, that he would be pleaſed to deelare
my meaning in the aforeſaid Letter to Sig. Bartolotti, for I hope
that if he will underſtand this point, he will be no longer ſo te­
nacious in his opinion.
Next that theſe Lords in the Commiſſion of Sewers, with the
Right Honourable the Marqueſſe of S. Angelo, and your Honour
do approve of my judgment, doth very much rejoyce me; but
becauſe that I know that they do it not in deſign to complement
me, but onely to ſerve his Highneſs our Grand Duke, I freely
profeſs that I will pretend no farther obligations from them there­
in, than I account my ſelf to owe to thoſe whoſe opinions are
contrary to mine, for that I know that they have the ſame end.
The definitive ſentence of this whole buſineſs is, that they give
theſe Plains, theſe Draines, and theſe Waters farre fetcht ap­
pellations.
11. As to the quantity of the Water that Fiume morto diſ­
chargeth into the Sea, there are very great diſputes about it, and
I have been preſent at ſome of them. But let your Honour be­
lieve me, that as this is not continual, but only during a few
dayes, ſo it will never be of any great prejudice to theſe Fields;
and if your Lordſhip would be aſcertained thereof, you may
pleaſe to go to Fiume morto at about a mile's diſtance from the
Sea, in the time of theſe ſtrong Windes, and obſerve the cur­
rent from thence upwards, for you ſhall finde it extream ſlow,
and conſequently will know that the quantity of the Water that
is repuls'd is very ſmall. And this ſeems to be contradicted by the
rule of Riſings proceeding from cauſes below, which occaſion no
conſiderable alteration far from the Sea.
I am neceſſitated to go to morrow out of Rome with his Emi­
nence Cardinal Gaetano about certain affairs touching Waters,
therefore I ſhall not farther inlarge, but for a cloſe to this tedious
Diſcourſe, I conclude in few words, that Fiume morto is by no
means to be let into Serchio, nor are there any means intermedi­
ate courſes to be taken, for they will alwayes be prejudicial; but
Fiume morto is to be diſcharged immediately into the Sea. When
it is ſtopt up by the fury of the Sea waves, I affirm that it is a
1ſign that there is no need of opening it; and if there be any oc­
caſion to open it, it is eaſily done. As for the reſt your Lordſhip
may pleaſe to keep account of all the particulars that occur, for
the memory of things paſt is our Tutreſſe in thoſe that are to
come. If occaſion ſhall offer, I intreat you to bow humbly in
my name to His Highneſs the Grand Duke, and the moſt Serene
Prince Leopold; and to attend the ſervice of Their Highneſſes, for
you ſerve I rinces of extraordinary merit; And to whom I my
ſelf am alſo exceedingly obliged. In the controverſies that ariſe
reſpect the pious end of ſpeaking the Truth, for then every
thing will ſucceed happily. I kiſs the hands of Padre Franceſco,
of Sig. Bartolotti, and of your Lordſhip.
Rome, 14. March 1642.
Your Honours
most Obliged Servant
D. BENEDETTO CASTELLI.
Vpon this occaſion I will here inſert a Diſcourſe that I made
upon the Draining and improvement of the Pontine Fens,
for that I think that whatſoever may be done well and to pur­
poſe in this matter hath abſolute dependance on the perfect know­
ledge of that ſo important Propoſition, by me demonſtrated and
explained in my Treatiſe of the Menſuration of Running Wa­
ters, namely, That the ſame water of a River doth continually
change Meaſures, according as it altereth and changeth the ve­
locity of its courſe; ſo that the meaſure of the thickneſſe of a
River in one Site, to the meaſure of the ſame River in another
Site, hath the ſame proportion reciprocally that the velocity in
this ſite hath to the velocity in the firſt ſite. And this is a Truth
ſo conſtant and unchangeable, that it altereth not in the leaſt
point on any occurrences of the Waters that change: and
being well underſtood, it openeth the way to the knowledge of
ſundry advertiſements in theſe matters, which are all reſolved by
this ſole Principle; and from it are derived very conſiderable be­
nefits; and without theſe it is impoſſible to do any thing with
abſolute perfection
1
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1
A
CONSIDERATION
Upon the
DRAINING
OF THE
Pontine Fenns.
BY
D. BENEDETTO CASTELLI, Abbot
of S. BENEDETTO ALOISIO, and Profeſſor
of the Mathematicks to P. Urban VIII. in the
Univerſity of ROME.
CONSIDERATION III.
Amongſt the enterprizes by me eſteemed, if not ab­
ſolutely impoſſible, , at leaſt exceeding difficult,
one was that famous one of Draining the Pontine
Fenns; and therefore I was thorowly reſolved
never to apply my minde thereunto, although
by my Patrons I ſhould be commanded to the
ſame: accounting that it was an occaſion rather of loſing repu­
tation by the miſcarriage of the attempt, than of gaining fame by
reducing things to a better paſs then they now are at. Yet never­
theleſs, having of late years obſerved the place, and ſailed through
thoſe Chanels, and thoſe Waters; after I had made ſome reflection
thereupon, I thought that the enterprize was not ſo difficult as
I had at firſt conceited it to be; and I am the more confirmed in
this opinion, upon the inducement of that which I have written
1Geometrically in my Treatiſe of the Menſuration of Running
Waters; ſo that talking with ſeveral perſons, I adventured to
affirm, in diſcoures, that this improvement might poſſibly be
brought into a good eſtate.
Now I have reſolved to ſet down my thoughts in writing, and
to honour this my Paper with the Noble Name of your Lordſhip,
to render it the more credible and conſpicuous at the firſt view,
if it ſhould chance that the Subject I treat of, were not of ſuch
moment, as that it did deſerve to be valued for any other reaſon.
Pardon me, Sir, if I have been too bold, and continue me in the
number of your Servants.
The enterprize of Draining a great part of the Territories of
the Pontine Fenns, hath been undertaken both in the time of
the antient Romans, and laſt of all, in our days; yea in the late
times by Sixtus V. I do not doubt in the leaſt, but that it will
be poſſible yet to reduce things to a very good paſs; and if I be not
miſtaken, with a very ſmall charge in compariſon of the profit that
would be received from thoſe rich Grounds. This improvement
was of great expence in the time of Sixtus Quintus, but by rea­
ſon the thing was not rightly underſtood, there were made many
Drains; a great part of which were unprofitable and vain: and
amongſt ſo many operations, there hapned ſome to be made that
ſucceeded, as was deſired; but not being underſtood, they were
held in no account; and thus the buſineſs being neglected, the
waters are returned into the ſame ſtate as they were at firſt, be­
fore the improvement. Here I have by familiar diſcourſes
with my friends, explained this enterprize undertaken by Six­
tus V. and haply alſo by ſome more antient, with the example of
the Fable of Orilo, in Arioſto. This Monſter was made up with
ſuch enchantment, that men fought with him alwayes in vain;
for though in the Combate he were cut in pieces, thoſe divided
Members preſently re-united, and returned to the fight more
fierce then ever. But the Paladine Aſtolfo coming to undertake
him, after a long diſpute, at the end he cut his head ſheer off
from the ſhoulders at one blow; and nimbly alighting from his
Horſe, took the Monſtrous head, and mounting again, as he rid
away he fell to ſhave the Pole of that Monſter, and ſo he loſt
the Lock of Hair, in which alone the enchantment lay; and then
the horrible Head in an inſtant manifeſted ſigns of death, and the
trunk which ran, ſeeking to reunite to it anew, gave the laſt gaſp,
and in this manner the enchantment ended. The Book of Fate
ſerved admirably to the Paladine, whereby he came to under­
ſtand that Charm; for by ſhaving his whole head, the enchanted
hairs came to be cut off amongſt the reſt: In the ſame manner, I
ſay, that it hath ſometimes happened in Draining thoſe Fields;
1for that amongſt ſo many tryals as have been made, that alſo
was light upon, on which the improvement and remedy to the
diſorder did depend. And to us my fore-named Treatiſe ſhall
ſerve for a Rule, which being well underſtood, ſhall make us to
know wherein conſiſteth, and whereon dependeth this miſcarri­
age, and conſequently it will be eaſie to apply thereunto a ſeaſo­
nable remedy.
And firſt I ſay, That there is no doubt but that the waters
continue ſo high on thoſe Plains becauſe they are ſo high in the
principal River, which ought to receive them, and carry them
into the Sea. Now the Cauſes of the height of the River, may
in my judgement be reduced to one alone; which is that by me
ſo often mentioned for the moſt Potent one, and declared in my
afore-named Tractate; to wit, The tardity of the motion of the
waters, which doth alwayes infallibly, and preciſely cauſe the
ſelf ſame Running Water to change the meaſure of its thickneſs
at ſuch a rate, that the more it encreaſeth in velocity, the more
it decreaſeth in meaſure; and the more it decreaſeth in velocity,
the more it encreaſeth in meaſure: As for example; If a River
run in ſuch a place with the velocity of moving a mile in the
ſpace of an hour, and afterwards the ſame River in another place
doth encreaſe in velocity, ſo as to make three miles an hour;
that ſame River ſhall diminiſh in thickneſs two thirds: And on
the contrary, If it ſhall diminiſh in velocity ſo, as that it runneth
but half a mile in the ſame time, it ſhall encreaſe the double in
thickneſs and meaſure. And in a word, look what proportion
the velocity in the firſt place, hath to the velocity in the ſecond,
and ſuch hath reciprocally the meaſure of the thickneſs in the
ſecond place, to the meaſure in the firſt; as I have clearly demon­
ſtrated in my Treatiſe: Which I repeat ſo frequently, that I
fear the Profeſſors of Polite Learning will charge me with Tua­
tologie, and vain Repetition. But I am ſo deſirous in this moſt
important point to be well underſtood, becauſe it will then be
eaſie to comprehend all the reſt; and without this it is impoſſible
(I will not ſay difficult, but abſolutely impoſſible) to underſtand,
or ever to effect any thing to purpoſe. And the better to ex­
plain the example, let it be ſuppoſed,
50[Figure 50]
That the water of a River A D,
runneth high at the level of A F,
with ſuch a certain velocity; and let
it, by the ſame water, be velocitated
three times more; I ſay, that it will
abate 1/3, and ſhall ſtand at the level
in B E; and if it ſhall more veloci­
tate, it will abate the more at the Sea; But if it ſhould retard
1more than it did at the level AF, it would riſe yet more above
the ſaid level A F; although that the ſelf ſame quantity of water
runneth all the while. By the above-named ſolid Principle I
reſolve extravagant Problems in my Treatiſe, and aſſign the Rea­
ſons of admirable effects of Running Waters: But as for what
concerneth our purpoſe of the Pontine Fenns, we have the Cau­
ſes very plain and clear; for which, by the trampling of Cattle
which paſs thorow the Draining River, the waters abate ſo nota­
bly, that it is as it were a miracle for thoſe Reeds, Flags, and
Weeds that ſpring up, encreaſe, and ſpread all over the River,
ſtop and impede that velocity of the waters which they would
have by means of their declivity. But that paſſage of thoſe Beaſts,
treading down thoſe Weeds unto the bottom of the River, in ſuch
ſort, as that they no longer hinder the Current of the Water;
and the ſame Waters increaſing in their courſe, they do dimi­
niſh in meaſure and height; and by this meanes the Ditches of the
Plains empty into the ſame ſucceſsfully, and leave them free
from Waters, and Drained. But theſe Weeds in a ſhort
time ſprouting up anew, and raiſing their ſtalkes thorow the
body of the Waters, they reduce things to the ſame evil
ſtate, as before, retarding the velocity of the Water, ma­
king it to increaſe in height, and perhaps do occaſion grea­
ter miſchiefs; ſeeing that thoſe many knots which each plant
ſhoots forth, begets a greater multitude of Stalks, which much
more incumbering the Water of the River, are a greater impe­
diment unto its velocity, and conſequently make the height
of the waters to encreaſe ſo much the more, and do more miſchief
than before.
Another head to which theſe harms may be reduced, but pro­
ceeding from the ſame Root, which hath a great part in this
diſorder, is the impediment of thoſe Wears in the River which
are made by heightning the bed of the ſame, for placing of fiſh­
ing-nets; of which Piſcaries I reckoned above ten, when I made
a voyage thorow thoſe waters to Sandolo. And theſe Fiſhing­
Wears are ſuch impediments, that ſome one of them makes the
water of the River in the upper part to riſe half a Palm, and
ſometimes a whole Palm, and more; ſo that when they are all
gathered together, theſe impediments amount to more than ſeven,
or poſſibly than eight Palms.
There concurreth for a third moſt Potent Cauſe of the waters
continuing high in the evacuating, or Draining Chanel, and con­
ſequently on the Plains; The great abundance of water that iſſu­
eth from Fiume Siſto, the waters of which do not keep within its
Banks when they are abundant; but encreaſing above its Chanel,
they unite with thoſe of the Evacuator, and diſperſing thorow
1the Fens are raiſed with great prejudice, and much grea­
ter than is conceived, according to what hath been demon­
ſtrated in the Second Conſideration upon the Lake of Venice.
Nor is it to any purpoſe to ſay, that if we ſhould meaſure
all the Waters that disimbogue from Fiume Siſto, and gather
them into one ſumme, we ſhould not finde them to be ſuch,
as that they ſhall be able to make the Waters of the Fens
to increaſe, by reaſon of the great expanſion of them, over
which that body of water is to diſtend: for to this inſtance we
anſwer wich that which we have given notice of in the Firſt Con­
ſideration touching the Lake of Venice, treating of the abate­
ment that is cauſed by the Brent let into the Lake. And more­
over, if I ſhall adde thereto that which I write in the Second
Conſideration, it will be very apparent how greatly harmfull
and prejudicial theſe excurfions of Waters from Fiume Siſto
may be, which are not kept under, and confined within the
River: Therefore, proceeding to the proviſions, and ope­
rations that are to be accounted Principall, I reduce them to
three Heads.
In the firſt place it is neceſſary to throw down thoſe Weares,
and to take the Piſciaries quite away, obſerving a Maxime, in
my judgment, infallible, that Fiſhing and Sowing are two things
that can never conſiſt together; Fiſhing being on the Water, and
Sowing on land.
Secondly, it will be neceſſary to cut under Water in the bot­
tome of the River thoſe Weeds and Plants that grow and in­
creaſe in the River, and leave them to be carried into the Sea by
the Stream; for by this means theſe Reeds ſhall not ſpring up
and diſtend along the bottome of the River, by means of the
Beaſts treading upon them; And the ſame ought to be done
often, and with care, and muſt not be delaied till the miſ­
chief increaſe, and the Champain Grounds be drowned, but
one ought to order matters ſo, as that they may not drown.
And I will affirm, that otherwiſe this principal point would be­
come a moſt conſiderable inconvenience.
Thirdly, it is neceſſary to make good the Banks of Fiume Siſto
on the left hand, and to procure that thoſe Waters may run in
the Chanel, and not break forth. And it is to be noted, that
it is not enough to do one or two of thoſe things, but we are to
put them all in execution; for omitting any thing, the whole
machine will be out of tune, and ſpoiled. But proceeding with
due care, you ſhall not only Drain the Pontine Fens, but by
means of this laſt particular the Current of Fiums Sisto ſhall
ſcowr its own Chanel of its ſelf, even to the carrying part of it
away: and haply with this abundance of water that it ſhall
1bear, the Mouth della Torre may be opened, and kept open
into the Sea. And it would, laſt of all, be of admirable bene­
fit to cleanſe Fiume Sisto from many Trees and Buſhes where­
with it is overgrown.
And with this I conclude, that the Improvement or Drain
poſſible to be made conſiſteth in theſe three particulars. Firſt,
in taking away the Fiſhing Weares, leaving the Courſe
of the Waters free. Secondly, in keeping the Principal
Rivers clear from Weeds and Plants. Thirdly, in keeping
the water of Fiume Sisto in its own Chanel. All which are
things that may be done with very little charge, and to the
manifeſt benefit of the whole Country, and to the rendering
the Air wholſomer in all thoſe Places adjoyning to the Pon­
tine Fens.
51[Figure 51]
1
A
CONSIDERATION
Upon the
DRAINING
Of the Territories of
Bologna, Ferrara,
AND
Romagna.
BY
D. BENEDETTO CASTELLI, Abbot
of S. BENEDETTO ALOISIO, Mathematician
to P. Vrban VIII. and Profeſſor in the
Univerſity of ROME.
The weghty buſineſſe of the Draining of
the Territories of Bologna, Ferrara,
and Romagna having been punctually
handled and declared in writing from
the excellent memory of the Right Ho­
nourable and Noble Monſignore Corſini,
who was heretofore Deputed Commiſ­
ſary General, and Viſitor of thoſe Wa­
ters; I am not able to make ſuch ano­
ther Diſcourſe upon the ſame Subject, but will only ſay ſome­
what for farther confirmation of that which I have ſaid in this
Book upon the Lake of Venice, upon the Pontine Fens, and up­
on the Draining of thoſe Plains of Piſa, lying between the Ri­
vers Arno and Serchio; whereby it is manifeſt, that in all the
1aforementioned Caſes, and in the preſent one that we are in hand
with, there have, in times paſt, very groſſe Errours been com­
mitted, through the not having ever well underſtood the true
meaſure of Running waters; and here it is to be noted, that the
buſineſſe is, that in Venice, the diverſion of the waters of the
Lake, by diverting the Brent was debated, and in part executed,
without conſideration had how great abatement of water might
follow in the Lake, if the Brent were diverted, as I have ſhewn
in the firſt Conſideration upon this particular, from which act
there hath inſued very bad conſequences, not only the difficulty
of Navigation, but it hath infected the wholſomneſſe of the Air,
and cauſed the ſtoppage of the Ports of Venice. And on the
contrary, the ſame inadvertency of not conſidering what riſing of
the Water the Reno, and other Rivers being opened into the Val­
leys of Bologna and Ferrara, might cauſe in the ſaid Valleys, is
the certain cauſe that ſo many rich and fertile Fields are drown­
ed under water, converting the happy habitations and dwellings
of men into miſerable receptacles for Fiſhes: Things which
doubtleſſe would never have happened, if thoſe Rivers had been
kept at their height, and Reno had been turn'd into Main-Po,
and the other Rivers into that of Argenta, and of Volano. Now
there having ſufficient been ſpoken by the above-named Monſig.
Corſini in his Relation, I will only adde one conceit of my own,
which after the Rivers ſhould be regulated, as hath been ſaid, I
verily believe would be of extraordinary profit, I much doubt in­
deed that I ſhall finde it a hard matter to perſwade men to be of
my mind, but yet nevertheleſs I will not queſtion, but that thoſe,
at leaſt, who ſhall have underſtood what I have ſaid and demon­
ſtrated concerning the manners and proportions, according to
which the abatements and riſings of Running waters proceed,
that are made by the Diverſions and Introductions of Waters,
will apprehend that my conjecture is grounded upon Reaſon.
And although I deſcend not to the exactneſſe of particulars, I
will open the way to others, who having obſerved the requiſite
Rules of conſidering the quantity of the waters that are intro­
duced, or that happen to be diverted, ſhall be able with punctu­
ality to examine the whole buſineſſe, and then reſolve on that
which ſhall be expedient to be done.
Reflecting therefore upon the firſt Propoſition, that the
Riſings of a Running Water made by the acceſſion of new water
into the River, are to one another, as the Square-Roots of the
quantity of the water that runneth; and conſequently, that the
ſame cometh to paſs in the Diverſions: Inſomuch, that a River
running in height one ſuch a certain meaſure, to make it encreaſe
double in height, the water is to be encreaſed to three times as
1much as it ran before; ſo that when the water ſhall be quadru­
ple, the height ſhall be double; and if the water were centuple,
the height would be decuple onely, and ſo from one quantity
to another: And on the contrary, in the Diverſions; If of the
100. parts of water that run thorow a River, there ſhall be di­
verted 19/160, the height of the River diminiſheth onely 1/10, and con­
tinuing to divert 17/100, the height of the River abateth likewiſe 1/10,
and ſo proceeding to divert 15/100 and then 13/100, and then 11/100, and
then 9/100, and then 7/100, and then 5/100, and then 3/106, alwaies by
each of theſe diverſions, the height of the Running Water di­
miniſheth the tenth part: although that the diverſions be ſo une.
qual. Reflecting I ſay upon this infallible Truth, I have had a
conceit, that though the Reno and other Rivers were diverted
from the Valleyes, and there was onely left the Chanel of Navi­
gation, which was onely the 1/20 part of the whole water that fal­
leth into the Valleys; yet nevertheleſs, the water in thoſe ſame
Valleyes would retain a tenth part of that height that became
conjoyned by the concourſe of all the Rivers: And therefore I
ſhould think that it were the beſt reſolution to maintain the Gha­
nel of Navigation (if it were poſſible) continuate unto the Po of
Ferrara, and from thence to carry it into the Po of Volano; for
beſides that it would be of very great eaſe in the Navigation of
Bologna, and Ferrara, the ſaid water would render the Po oſ
Volano navigable as far as to the very Walls of Ferrara, and con­
ſequently the Navigation would be continuate from Bologna to
the Sea-ſide.
But to manage this enterprize well, it is neceſſary to meaſure
the quantity of the Water that the Rivers diſcharge into the Val­
leys, and that which the Chanel of Navigation carryeth, in man­
ner as I have demonſtrated at the beginning of this Book; for this
once known, we ſhall alſo come to know, how profitable this di­
verſion of the Chanel of Navigation from the Valleys is like to
prove; which yet would ſtill be unprofitable, if ſo be that all
the Rivers that diſcharge their waters into the Valleys, ſhould
not ſirſt be Drained, according to what hath been above ad­
vertiſed.
Abbot CASTELLI, in the preſent conſideration referring
himfelf to the Relation of Monſig. Corſini, grounded upon the Ob­
ſervations and Precepts of the ſaid Abbot; as is ſeen in the pre­
ſent Diſcourſe. I thought it convenient for the compleating of the
Work of our Aulhour, upon theſe ſubjects, to inſert it in this
place.
1
A
Relation of the Waters in the Territories
of Bologna and Ferrara.
BY
The Right Honourable and Illuſtrious, Monſig­
nore CORSINI, a Native of Juſcany, Su­
perintendent of the general DRAINS,
and Preſident of Romagna-
The Rheno, and other Brooks of Romagna, were by the
advice of P. Agoſtino Spernazzati the Jeſuite, towards
the latter end of the time of Pope Clement VIII. notwith­
ſtanding the oppoſition of the Bologneſi, and others concerned
therein, diverted from their Chanels, for the more commodious
cleanſing of the Po of Ferrara, and of its two Branches of Prima­
ro, and Volano; in order to the introducing the water of the
Main-Po into them, to the end that their wonted Torrents being
reſtored, they might carry the Muddy-water thence into the Sea,
and reſtore to the City the Navigation which was laſt, as is ma­
nifeſt by the Brief of the ſaid Pope Clement, directed to the Car­
dinal San Clemence, bearing date the 22. of Auguſt, 1604.
The work of the ſaid cleanſing, and introducing of the ſaid
Po, either as being ſuch in it ſelf, or by the contention of the
Cardinal Legates then in theſe parts; and the jarrings that hap­
ned betwixt them, proved ſo difficult, that after the expence of
vaſt ſumms in the ſpace of 21. years, there hath been nothing
done, ſave the rendring of it the more difficult to be effected.
Interim, the Torrents with their waters, both muddy and
clear, have damaged the Grounds lying on the right hand of the
Po of Argenta, and the Rheno thoſe on its Banks; of which I
will ſpeak in the firſt place, as of that which is of greater impor­
tance, and from which the principal cauſe of the miſchiefs that
reſult from the reſt doth proceed.
* Or Lordſhip.
This Rbeno having overflowed the ^{*} Tennency of Sanmartina,
in circumference about fourteen miles given it before, and part
of that of Cominale given it afterwards, as it were, for a recepta­
cle; from whence, having depoſed the matter of its muddineſs,
it iſſued clear by the Mouths of Maſi, and of Lievaloro, into
the Po of Primaro, and of Volano; did break down the encom­
1paſſing Bank or Dam towards S. Martino, and that of its new
Chanel on the right hand neer to Torre del Fondo.
By the breaches on this ſide it ſtreamed out in great abun­
dance from the upper part of Cominale, and in the parts about
Raveda, Pioggio, Caprara, Chiare di Reno, Sant' Agoſtino, San
Proſpero, San Vincenzo, and others, and made them to become
incultivable: it made alſo thoſe places above but little fruitful,
by reaſon of the impediments that their Draines received, finding
the Conveyances called Riolo and Scorſuro, not only filled by la
Motta and la Belletta, but that they turned backwards of them­
ſelves.
But by the Mouths in the incloſing Bank or Dam at Borgo di
S. Martino iſſuing with violence, it firſt gave obſtruction to the
ancient Navigation of la Torre del la Foſſa, and afterwards to
the moderne of the mouth of Maſi, ſo that at preſent the Com­
merce between Bologna and Ferrara is loſt, nor can it ever be
in any durable way renewed, whilſt that this exceeds its due
bounds, and what ever moneys ſhall be imployed about the ſame
ſhall be without any equivalent benefit, and to the manifeſt

and notable prejudice of the ^{*} Apoſtolick Chamber.
* The Popes
Exchequer.
Thence paſſing into the Valley of Marzara, it ſwelleth high­
er, not only by the riſing of the water, but by the raiſing of the
bottome, by reaſon of the matter ſunk thither after Land­
floods, and dilateth ſo, that it covereth all the Meadows there­
abouts, nor doth it receive with the wonted facility the Drains of
the upper Grounds, of which the next unto it lying under the wa­
ters that return upwards by the Conveyances, and the more re­
mote, not finding a paſſage for Rain-waters that ſettle, become
either altogether unproſitable or little better.
From this Valley, by the Trench or Ditch of Marzara, or of
la Duca by la Buova, or mouth of Caſtaldo de Roſſi, and by the
new paſſage it falleth into the Po of Argenta, which being to re­
ceive it clear, that ſo it may ſink farther therein, and receiving
it muddy, becauſe it hath acquired a quicker courſe, there will
ariſe a very contrary effect.
Here therefore the ſuperficies of the water keeping high, until
it come to the Sea, hindereth the Valleys of Ravenna, where
the River Senio, thoſe of San Bernardino where Santerno was
turned, thoſe of Buon' acquiſto, and thoſe of Marmorto, where
the Idice, Quaderna, Sellero ſall in, from ſwallowing and taking
in their Waters by their uſual In-lets, yet many times, as I my
ſelf have ſeen in the Viſitation, they drink them up plentifully,
whereupon, being conjoyned with the muddineſſe of thoſe Ri­
vers that fall into the ſame, they ſwell, and dilate, and overflow
ſome grounds, and deprive others of their Drains in like manner
1as hath been ſaid of that of Marrara, inſomuch that from the
Point of S. Giorgio, as far as S. Alberto all thoſe that are between
the Valleys and Po are ſpoiled, of thoſe that are between Valley
and Valley many are in a very bad condition, and thoſe that are
ſome conſiderable ſpace above not a little damnified.
In fine, by raiſing the bottom or ſand of the Valleys, and the
bed of Reno, and the too great repletion of the Po of Primaro
with waters, the Valleys of Comacchio (on which ſide the Banks
are very bad) and ^{*} Poleſine di S. Giorgio are threatned with a

danger, that may in time, if it be not remedied, become irrepa­
rable, and at preſent feeleth the incommodity of the Waters,
which penetrating thorow the pores of the Earth do ſpring up in
the ſame, which they call Purlings, which is all likely to redound
to the prejudice of Ferrara, ſo noble a City of Italy, and ſo im­
portant to the Eccleſtaſtick State.
+ Poleſine is a
plat of Ground al­
moſt ſurrounded
with Bogs or wa­
ters, like an Iſland
Which particulars all appear to be atteſted under the hand of
a Notary in the Viſitation which I made upon the command of
His Holineſſe, and are withall known to be true by the ^{*}Ferrareſt

themſelves, of whom (beſides the requeſt of the Bologneſi) the
greater part beg compaſſion with ſundry Memorials, and reme­
dies, aſwell for the miſchiefs paſt, as alſo for thoſe in time to
come, from which I hold it a duty of Conſcience, and of Cha­
rity to deliver them.
* People of Fer­
rara.
Pope Clement judged, that the ſufficient means to effect this
was the ſaid Introduction of the Main Po into the Chancl of
Ferrara; a reſolution truly Heroical, and of no leſſe beauty
than benefit to that City, of which I ſpeak not at preſent, be­
cauſe I think that there is need of a readier and more acco­
modate remedy.
So that I ſee not how any other thing can be ſo much conſide­
rable as the removal of Reno, omitting for this time to ſpeak of

^{*} incloſing it from Valley to Valley untill it come to the Sea, as
the Dukes of Ferrara did deſign, foraſmuch as all thoſe Ferra­
reſi that have intereſt in the Poleſine di S. Giorgio, and on the
right hand of the Po of Argenta do not deſire it, and do, but too
openly, proteſt againſt it; and becauſe that before the Chanel
were made as far as the Sea, many hundreds of years would be
ſpent, and yet would not remedy the dammages of thoſe who
now are agrieved, but would much increaſe them, in regard the
Valleys would continue ſubmerged, the Drains ſtopped, and the
other Brooks obſtructed, which would of neceſſity drown not a
few Lands that lie between Valley and Valley; and in fine, in
regard it hath not from San Martina to the Sea for a ſpace of ſif­
ty miles a greater fall then 19, 8, 6, feet, it would want that force
which they themſelves who propound this project do require it to
1have, that ſo it may not depoſe the matter of the muddineſs when
it is intended to be let into Volana.
* In Chanels
made by hand.
So that making the Line of the bottome neer to Vigarano, it
would riſe to thoſe prodigious termes that they do make bigger,
and they may thence expect thoſe miſchiefs, for which they
will not admit of introducing it into the ſaid Po of Volana.
Amongſt the wayes therefore that I have thought of for effect­
ing that ſame remotion, and which I have cauſed to be viewed by
skilful men that have taken a level thereof, (with the aſſiſtance of
the venerable Father, D. Benedetto Caſtelli of Caſina, a man of
much fidelity and honeſty, and no leſs expert in ſuch like affairs
touching waters, than perfect in the Mathematick Diſciplines) two
onely, the reſt being either too tedious, or too dangerous to the
City, have ſeemed to me worthy, and one of them alſo more than
the other, to offer to your Lordſhip.
The one is to remit it into the Chanel of Volana, thorow which
it goeth of its own accord to the Sea.
The other is to turn it into Main-Po at Stellata, for, as at other
times it hath done, it will carry it to the Sea happily.
As to what concerns the making choice of the firſt way, that
which ſeemeth to perſwade us to it is, that we therein do nothing
that is new, in that it is but reſtored to the place whence it was
removed in the year 1522. in the time of Pope Adrian, by an
agreement made in way of contract, between Alfonſo, Duke of
Ferrara, and the Bologneſi; and that it was diverted for reaſons,
that are either out of date, or elſe have been too long time
deferred.
In like manner the facility wherewith it may be effected, let­
ting it run into the divided Po, whereby it will be turned to Fer­
rara, or elſe carrying it by Torre del Fondo, to the mouth of Maſi,
and from thence thorow the Trench made by the Ferrareſi,
along by Panaro, where alſo finding an ample Bed, and high and
thick Banks, that will ſerve at other times for it, and for the wa­
ters of Po, there may a great expence be ſpared.
That what ever its Fall be, it would maintain the ſame, not
having other Rivers, which with their Floods can hinder it; and
that running confined between good Banks, without doubt it
would not leave la Motto by the way; but eſpecially, that it
would be ſufficient if it came to Codigoro, where being aſſiſted by
the Ebbing and Flowing of the Sea, it would run no hazard of
having its Chanel filled up from thence downwards.
That there might thence many benefits be derived to the City,
by means of the Running Waters, and alſo no mean Navigation
might be expected.
On the contrary it is objected, That it is not convenient to
1think of returning this Torrent into the divided Po, by reaſon of
the peril that would thence redound to this City.
And that going by Torre del Fondo, through Sanmartina to
the Mouth de Maſi by the Chappel of Vigarano unto the Sea, it is
by this way 70. miles; nor is the Fall greater than 26. 5. 6. Feet, ſo
that it would come to fall but 4. inches & an half, or thereabouts
in a mile; whereas the common opinion of the skilfull (to the
end that the Torrents may not depoſe their ſand that they bring
with them in Land-Floods) requireth the twenty fourth part of
the hundredth part of their whole length, which in our caſe,
accounting according to the meaſure of theſe places, is 16. inches

a ^{*} mile; whereupon the ſinking of the Mud and Sand would
moſt certainly follow, and ſo an immenſe heightning of the Line
of the Bottom, and conſequently a neceſſity of raiſing the Banks,
the impoſſibility of maintaining them, the danger of breaches
and decayes, things very prejudicial to the Iſlets of this City, and
of San Giorgio, the obſtruction of the Drains, which from the
Tower of Tienne downwards, fall into the ſaid Chanel; to wit,
thoſe of the Sluices of Goro, and the Drains, of the Meadows of
Ferrara: And moreover, the damages that would ariſe unto the
ſaid Iſlet of S. Giorgio, and the Valleys of Comachio, by the wa­
ters that ſhould enter into the Goro or Dam of the Mills of Belri­
guardo, thorow the Trenches of Quadrea, which cannot be ſtopt,
becauſe they belong to the Duke of Modena, who hath right of
diverting the waters of that place at his pleaſure to the work of
turning Mills.
* The inch of
theſe places is
ſomewhat bigger
than ours.
The greater part of which Objections, others pretend to prove
frivolous, by ſaying, that its running there till at the laſt it was
turned another way, is a ſign that it had made ſuch an elevation
of the Line, of its Bed as it required; denying that it needeth
ſo great a declivity as is mentioned above; and that for the fu­
ture it would riſe no more.
That the ſaid Dra ns and Ditches did empty into the ſame,
whilſt Po was there; ſo that they muſt needs be more able to do
ſo when onely Reno runs that way.
That there would no Breaches follow, or if they did, they
would be onely of the water of Reno, which in few hours might
be taken away (in thoſe parts they call damming up of Breaches,
and mending the Bank, taking away the Breaches) and its a que­
ſtion whether they would procure more inconvenience than bene­
fit, for that its Mud and Sand might in many places, by filling
them up, occaſion a ſeaſonable improvement.
Now omitting to diſcourſe of the ſolidity of the reaſons on the
oneſide, or on the other, I will produce thoſe that move me to
ſuſpend my allowance of this deſign.
1
The firſt is, that although I dare not ſubſcribe to the opinion
of thoſe that require 16. inches Declivity in a mile to Reno, to
prevent its depoſing of Mud; yet would I not be the Author that
ſhould make a trial of it with ſo much hazard, for having to ſa­
tisfie my ſelf in ſome particulars cauſed a Level to be taken of
the Rivers L'amone, Senio, and Santerno, by Bernardino Aleotti,
we found that they have more Declivity by much than Artiſts re­
quire, as alſo the Reno hath from la Botta de Ghiſlieri to the
Chappel of Vigarano, for in the ſpace of four miles its Bottom­
Line falleth five feet and five inches. So that I hold it greater
prudence to depend upon that example, than to go contrary to a
common opinion, eſpecially ſince, that the effects cauſed by Reno
it ſelf do confirm me in the ſame, for when it was forſaken by
the Po, after a few years, either becauſe it had choaked up its
Chanel with Sand, or becauſe its too long journey did increaſe
it, it alſo naturally turned aſide, and took the way of the ſaid
Po towards Stellata. Nay, in thoſe very years that it did run that
way, it only began (as relations ſay) to make Breaches, an evi­
dent ſign that it doth depoſe Sand, and raiſe its Bed; which a­
greeth with the teſtimony of ſome that were examined in the
Viſitation of the Publique Notary, who found great benefit by
having Running Water, and ſome kind of paſſage for Boats,
and yet nevertheleſs affirm that it for want of Running Water
had made too high Stoppages and Shelfes of Sand; ſo that if
it ſhould be reſtored to the Courſe that it forſook, I much fear
that after a ſhort time, if not ſuddenly, it would leave it a­
again.
The ſecond I take from the obſervation of what happened to
Panaro, when with ſo great applauſe of the Ferareſi, it was
brought by Cardinal Serra into the ſaid Chanel of Volana; for
that notwithſtanding that it had Running Waters in much grea­
ter abundance than Reno; yet in the time that it continued in
that Chanel it raiſed its Bed well neer five feet, as is to be ſeen
below the Sluice made by Cardinal Capponi to his new Chanel;
yea, the ſaid Cardinal Serra who deſired that this his under taking
ſhould appear to have been of no danger nor damage, was con­
ſtrained at its Overflowings, to give it Vent into Sanmartina, that
it might not break in upon, and prejudice the City; which dan­
ger I ſhould more fear from Reno, in regard it carrieth a greater
abundance of Water and Sand
Thirdly, I am much troubled (in the uncertainty of the ſuc­
ceſs of the affair) at the great expence thereto required; For in
regard I do not approve of letting it in, neer to the Fortreſſe,
for many reſpects, and carrying it by la Torre del Fondo to the
Month de Maſt, it will take up eight miles of double Banks, a
1thing not eaſie to be procured, by reaſon that the Grounds lie
under Water; but from the Mouth de Maſi unto Codigoro, it
would alſo be neceſſary to make new Scowrings of the Chanel;
to the end, that the Water approaching (by wearing and carry­
ing away the Earth on both ſhores, might make a Bed ſufficient
for its Body, the depth made for Panaro not ſerving the turn, as
I conceive; and if it ſhould ſuffice, when could the people of
Ferrara hope to be re-imburſed and ſatisfied for the charge
thereof?
Fourthly, it ſerves as an Argument with me, to ſee that the
very individual perſons concerned in the Remotion or Diverſion
of the ſaid Torrent, namely, the Bologneſi do not incline unto it,
and that the whole City of Ferrara, even thoſe very perſons who
at preſent receive damage by it, cannot indure to hear thereof.
The reaſon that induceth theſe laſt named to be ſo averſe thereto,
is, either becauſe that this undertaking will render the introducti­
on of the Water of Main-Po more difficult; or becauſe they fear
the danger thereof; The others decline the Project, either for
that they know that Reno cannot long continue in that Courſe,
or becauſe they fear that it is too much expoſed to thoſe mens re­
vengeful Cutting of it who do not deſire it ſhould; and if a
man have any other wayes, he ought, in my opinion, to forbear
that, which to ſuch as ſtand in need of its Removal, is leſſe ſatiſ­
factory, and to ſuch as oppoſe it, more prejudicial.
To conclude, I exceedingly honour the judgment of Cardinal
Capponi, who having to his Natural Ability and Prudence added
a particular Study, Obſervation, and Experience of theſe Wa­
ters for the ſpace of three years together, doth not think that
Reno can go by Volana; to which agreeth the opinion of Car­
dinal S. Marcello, Legate of this City, of whom, for his exqui­
ſite underſtanding, we ought to make great account. But if e­
ver this ſhould be reſolved on, it would be materially neceſſary
to unite the Quick and Running Waters of the little Chanel of
Cento, of the Chanel Navilio, of Guazzaloca, and at its very
beginning thoſe of Dardagna, which at preſent, is one of the
Springs or Heads of Panaro, that ſo they might aſſiſt it in carry­
ing its Sand, and the matter of its Muddineſs into the Sea; and
then there would not fail to be a greater evacuation and ſcowr­
ing; but withall the Proprietors in the Iſlet of San Giorgio and
of Ferrara muſt prepare themſelves to indure the inconveniences
of Purlings or Sewings of the Water from the River thorow
the Boggy Ground thereabouts.
I ſhould more eaſily incline therefore to carry it into Main-Po
at Stellata, for the Reaſons that Cardinal Capponi moſt ingeni­
ouſly enumerates in a ſhort, but well-grounded Tract of his: not
1becauſe that indeed it would not both by Purlings and by Brea­
ches occaſion ſome inconvenience; eſpecially, in the beginning:
but becauſe I hold this for the incomodities of it, to be a far leſs
evil than any of the reſt; and becauſe that by this means there is
no occaſion given to them of Ferrara, to explain that they are
deprived of the hope of ever ſeeing the Po again under the Walls
of their City: To whom, where it may be done, it is but reaſon
that ſatisfaction ſhould be given.
It is certain that Po was placed by Nature in the midſt of this
great Valley made by the Appennine Hills, and by the Alps, to
carry, as the Maſter-Drain to the Sea, that is the grand receptacle
of all Waters; thoſe particular ſtreams which deſcend from
them.
That the Reno by all Geographers, Strabo, Pliuy, Solimas,
Mella, and others is enumerated among the Rivers that fall into
the ſaid Po.
That although Po ſhould of it ſelf change its courſe, yet would
Reno go to look it out, if the works erected by humane ind uſtry
did not obſtruct its paſſage; ſo that it neither is, nor ought to
ſeem ſtrange, if one for the greater common good ſhould turn it
into the ſame.
Now at Stellata it may go ſeveral waies into Po, as appeareth
by the levels that were taken by my Order; of all which I ſhould
beſt like the turning of it to la Botta de' Ghiſlieri, carrying it
above Bondeno to the Church of Gambarone, or a little higher or
lower, as ſhall be judged leaſt prejudicial, when it cometh to the
execution, and this for two principal reaſons: The one becauſe
that then it will run along by the confines of the Church P tri­
mony, without ſeparating Ferrara from the reſt of it; The other
is, Becauſe the Line is ſhorter, and conſequently the fall greater;
for that in a ſpace of ten miles and one third, it falleth twenty ſix
feet, more by much than is required by Artiſts; and would go
by places where it could do but little hurt, notwithſtanding that
the perſons interreſſed ſtudy to amplifie it incredibly.
On the contrary, there are but onely two objections that are
worthy to be examined; One, That the Drains and Ditches of
S. Bianca, of the Chanel of Cento, and of Burana, and all thoſe
others that enter into Po, do hinder this diverſion of Reno, by the
encreaſing of the waters in the Po. The other is that Po riſing
about the Tranſom of the Pilaſter-Sluice, very near 20 feet, the
Reno would have no fall into the ſame; whereupon it would riſe
to a terrible height, at which it would not be poſſible to make, or
keep the Banks made, ſo that it would break out and drown
the Meadowes, and cauſe miſchiefs, and damages unſpeakable
and irreparable; as is evident by the experiment made upon
1Panaro, which being confined between Banks, that it might go
into Po, this not being neither in its greateſt excreſcenſe, it broke
out into the territories of Final, and of Ferrara. And though
that might be done, it would thereupon enſue, that there being
let into the Chanel of Po, 2800, ſquare feet of water (for ſo much
we account thoſe of Reno and Panaro, taken together in their
greateſt heights) the ſuperficies of it would riſe at leaſt four feet,
inſomuch that either it would be requiſite to raiſe its Banks all the
way unto the Sea, to the ſame height, which the treaſures of the
Indies would not ſuffice to effect; or elſe there would be a neceſ­
ſity of enduring exceſſive Breaches. To theſe two Heads are the
Arguments reduced, which are largely amplified againſt our opi­
nion; and I ſhall anſwer firſt to the laſt, as moſt material.
I ſay therefore, that there are three caſes to be conſidered:
Firſt, Po high, and Reno low. Secondly, Reno high, and Po
low. Thirdly, Reno and Po both high together.
As to the firſt and ſecond, there is no difficulty in them; for if
Po ſhall not be at its greateſt height, Reno ſhall ever have a fall
into it, and there ſhall need no humane Artifice about the Banks:
And if Reno ſhall be low, Po ſhall regurgitate and flow up into
the Chanel of it; and alſo from thence no inconvenience ſhall
follow. The third remains, from which there are expected ma­
ny miſchiefs; but it is a moſt undoubted truth, that the excreſcen­
cies of Reno, as coming from the adjacent Appennines and Rains,
are to continue but ſeven, or eight hours at moſt, and ſo would
never, or very rarely happen to be at the ſame time with thoſe of
Po, cauſed by the melting of the ſnowes of the Alps, at leaſt 400.
miles diſtance from thence. But becauſe it ſometimes may hap­
pen, I reply, that when it cometh to paſs, Reno ſhall not go into
Po, but it ſhall have allowed it one or two Vents; namely, into
the Chanel of Ferrara, as it hath ever had; and into Sanmartina,
where it runneth at preſent, and wherewith there is no doubt, but
that the perſons concerned will be well pleaſed, it being a great
benefit to them, to have the water over-flow their grounds once
every four or five years, inſtead of ſeeing it anoy them continu­
ally. Yea, the Vent may be regulated, reſerving for it the Cha­
nel in which Reno at preſent runneth; and inſtead of turning it
by a Dam at la Betta de Chiſlieri, perhaps, to turn it by help of
ſtrong Sluices, that may upon all occaſions be opened and ſhut.
And for my part, I do not queſtion but that the Proprietors
themſelves in Sanmartina would make a Chanel for it; which
receiving, and confining it in the time of the Vents, might carry
the Sand into the Po of Primaro: Nor need there thence be fear­
ed any ſtoppage by Mud and Sand, ſince that it is ſuppoſed that
there will but very ſeldom be any neceſſity of uſing it; ſo that
1time would be allowed, upon occaſion, to ſcowr and cleanſe
it.
And in this manner all thoſe Prodigies vaniſh that are raiſed
with ſo much fear from the enterance of the Water of Reno
ſwelled into Po, when it is high, to which there needeth no other
anſwer; yet nevertheleſſe we do not take that quantity of Wa­
ter, that is carried by Reno, and by Panaro, to be ſo great as is affir­
med: For that P. D. Benedetto Caſtelli hath no leſſe accutely
than accurately obſerved the meaſures of this kind, noting that
the breadth and depth of a River is not enough to reſolve the
queſtion truly, but that there is reſpect to be had to the velocity
of the Waters, and the term of time, things hitherto not conſi­
dered by the Skilful in theſe affairs; and therefore they are not
able to ſay what quantity of Waters the ſaid Rivers carry, nor
to conclude of the riſings that will follow thereupon. Nay, it
is moſt certain, that if all the Rivers that fall into Po, which are
above thirty, ſhould riſe at the rate that theſe compute Reno to
do, an hundred feet of Banks would not ſuffice, and yet they
have far fewer: So that this confirmes the Rule of R. P. D. Bene­
detto, namely, that the proportion of the height of the Water
of Reno in Reno to the height of the Water of Reno in Po, is
compounded of the proportion of the breadth of the Chanel of
Po to that of Reno, and of the velocity of the Water of Reno
in Po to the velccity of the Water of Reno in Reno; a manifeſt
argument that there cannot in it, by this new augmentation of
Waters follow any alteration that neceſſitates the raiſing of its
Banks, as appeareth by the example of Panaro, which hath been
ſo far from ſwelling Po, that it hath rather aſſwaged it, for it hath
carried away many Shelfs and many Iſlets that had grown in its
Bed, for want of Waters ſufficient to bear away the matter of
Land-floods in ſo broad a Chanel; and as is learnt by the trial
made by us in Panaro with the Water of Burana; for erecting
in the River ſtanding marks, and ſhutting the ſaid Sluice, we could
ſee no ſenſible abatement, nor much leſs after we had opened it
ſenſible increaſment; by which we judge that the ſame is to ſuc­
ceed to Po, by letting in of Reno, Burana having greater pro­
portion to Panaro than Reno to Po, conſidering the ſtate of thoſe
Rivers in which the Obſervation was made. So that there is no
longer any occaſion for thoſe great raiſings of Banks, and the
danger of the ruptures as well of Reno as of Po do vaniſh, as al­
ſo the fear leſt that the Sluices which empty into Po ſhould re­
ceive obſtruction: which if they ſhould, yet it would be over in
a few hours. And as to the Breaches of Panaro which happened
in 1623. I know not why, ſeeing that it is confeſſed that the Po
was not, at that time, at its height, one ſhould rather charge it
1with the crime, than quit it thereof. The truth is, that the
Bank was not made of proof, ſince that the ſame now continu­
eth whole and good, and Panaro doth not break out; nay, there
was, when it brake more than a foot and half of its Banks above
the Water, and to ſpare; but it broke thorow by a Moles wor­
king, or by the hole of a Water-Rat, or ſome ſuch vermine;
and by occaſion of the badneſs of the ſaid Banks, as I finde by
the teſtimony of ſome witneſſes examined by my command, that
I might know the truth thereof. Nor can I here forbear to ſay,
that it would be better, if in ſuch matters men were more candid
and ſincere. But to ſecure our ſelves nevertheleſſe, to the ut­
moſt of our power, from ſuch like Breaches which may happen
at the firſt, by reaſon of the newneſſe of the Banks, I preſuppoſe
that from Po unto the place whence Reno is cut, there ought to
be a high and thick Fence made with its Banks, ſo that there
would be no cauſe to fear any whatſoever acceſſions of Water,
although that concurrence of three Rivers, which was by ſome
more ingeniouſly aggravated than faithfully ſtated by that which
was ſaid above were true; to whom I think not my ſelf bound
to make any farther reply, neither to thoſe who ſay that Po will
aſcend upwards into Reno, ſince that theſe are the ſame perſons
who would introduce a ſmall branch of the ſaid Po into the
Chanel of Ferrara, that ſo it may conveigh to the Sea, not Reno
onely, but alſo all the other Brooks of which we complained;
and becauſe that withal it is impoſſible, that a River ſo capacious
as Po ſhould be incommoded by a Torrent, that, as I may ſay,
hath no proportion to it.
I come now to the buſineſſe of the Ditches and Draines; and
as to the Conveyance of Burana, it hath heretofore been deba­
ted to turn it into Main-Po, ſo that in this caſe it will receive no
harm, and though it were not removed, yet would it by a Trench
under ground purſue the courſe that it now holdeth, and alſo
would be able to diſ-imbogue again into the ſaid new Chanel of
Reno, which conforming to the ſuperficies of the Water of Po,
would continue at a lower level than that which Panara had
when it came to Ferrara, into which Burana did nevertheleſſe
empty it ſelf for ſome time.
The Conveyance or Drain of Santa Bianca, and the little
Chanel of Cento may alſo empty themſelves by two ſubterranean
Trenches, without any prejudice where they run at preſent, or
without any more works of that nature, they may be turned into
the ſaid new Chanel, although with ſomewhat more of incon­
venience; and withall, the Chanel of Ferrara, left dry, would
be a ſufficient receptacle for any other Sewer or Drain whatſoe­
ver, that ſhould remain there.
1
All which Operations might be brought to perfection with
150. thouſand Crowns, well and faithfully laid out; which ſumm
the Bologneſi will not be unwilling to provide; beſides that thoſe
Ferrareſi ought to contribute to it, who ſhall partake of the
benefit.
Let me be permitted in this place to propoſe a thing which I
have thought of, and which peradventure might occaſion two
benefits at once, although it be not wholly new. It was in the
time of Pope Paul V. propounded by one Creſcenzio an Ingi­
neer, to cut the Main-Po, above le Papozze; and having made a
ſufficient evacuation to derive the water thereof into the Po of
Adriano, and ſo to procure it to be Navigable, which was not at
that time effected, either by reaſon of the oppoſitions of thoſe,
whoſe poſſeſſions were to be cut thorow, or by reaſon of the
great ſum of money that was neceſſary for the effecting of it: But
in viewing thoſe Rivers, we have obſerved, that the ſedge cutting
might eaſily be made below le Papozze, in digging thorow the
Bank called Santa Maria, & drawing a Trench of the bigneſs that
skilful Artiſts ſhall judge meet unto the Po ^{*} of Ariano, below the

Secche of the ſaid S. Maria; which as being a work of not
above 160. Perches in length, would be finiſhed with onely
12000. Crowns.
* Of Adriano.
Firſt; it is to be believed, that the waters running that way,
would not fail to open that Mouth into the Sea, which at pre­
ſent is almoſt choakt up by the Shelf of Sand, which the new
Mouth of Ponto Virro hath brought thither; and that it would
again bring into uſe the Port Goro, and its Navigation.
And haply experience might teach us, that the ſuperficies of
Po might come to fall by this aſſwagement of Water, ſo that the
acceſſion of Reno would queſtionleſs make no riſing in it:
Whereupon, if it ſhould ſo fall out, thoſe Princes would have
no reaſon to complain; who ſeem to queſtion, leſt by this new
acceſſion of water into Po, the Sluices might be endangered.
Which I thought not fit to omit to repreſent to your Lordſhip;
not, that I propoſe it to you as a thing abſolutely certain, but that
you might, if you ſo pleaſed, lay it before perſons whoſe judge­
ments are approved in theſe affairs.
I return now from where I degreſt, and affirm it as indubita­
ble, that Reno neither can, nor ought to continue longer where
it at this day is; and that it cannot go into any other place but
that, whither Cardinal Capponi deſigned to carry it, and which
at preſent pleaſeth me better than any other; or into Volana,
whence it was taken away; the vigilance of Men being able to
obviate part of thoſe miſchiefs, which it may do there.
But from its Removal, beſides the alleviation of the harm
1which by it ſelf is cauſed, there would alſo reſult the diminution
of that which is occaſioned by the other Brooks, to the right hand
of the Po of Argenta; foraſmuch as the ſaid Po wanting all the
water of Reno, it would of neceſſity come to ebb in ſuch man­
ner, that the Valleys would have a greater Fall into the ſame,
and conſequently it would take in, and ſwallow greater abun­
dance of water; and by this means the Ditches and Draines
of the Up-Lands would likewiſe more eaſily Fall into them; eſ­
pecially if the ſcouring of Zenzalino were brought to perfection,
by which the waters of Marrara would fall into Marmorta: And
if alſo that of Baſtia were enlarged, and finiſhed, by which there
might enter as much water into the ſaid Po of Argenta, as is taken
from it by the removal of Reno; although that by that meanes
the water of the Valleys would aſſwage double: Nor would the
people of Argenta, the Iſles of S. Giorgio, and Comacchio have any
cauſe to complain; for that there would not be given to them
more water than was taken away: Nay ſometimes whereas they
had Muddy waters, they would have clear; nor need they to fear
any riſing: And furthermore, by this means a very great quan­
tity of ground would be reſtored to culture; For the effecting of
all which, the ſumm of 50. thouſand Crowns would go very far,
and would ſerve the turn at preſent touching thoſe Brooks, car­
rying them a little farther in the mean time, to fill up the greater
cavities of the Valleys, that we might not enter upon a vaſter
and harder work, that would bring with it the difficulties of other
operations, and ſo would hinder the benefit which theſe people
expect from the paternal charity of His Holineſs.
1
TO
The Right Honourable,
MONSIGNORE
D. Ferrante Ceſarini.
My Treatiſe of the MENSURATION of RUN­
NING WATERS, Right Honourable, and
moſt Noble Sir, hath not a greater Preroga­
tive than its having been the production of the
command of Pope Vrban VIII. when His Ho­
lineſs was pleaſed to enjoyn me to go with
Monſignore Corſini, in the Viſitation that was
impoſed upon him in the year 1625. of the Waters of Ferrara,
Bologna, Romagna, and Romagnola; for that, on that occaſion
applying my whole Study to my ſervice and duty, I publiſhed in
that Treatiſe ſome particulars till then not rightly underſtood and
conſidered (that I knew) by any one; although they be in them­
ſelves moſt important, and of extraordinary conſequence. Yet
I muſt render thanks to Your Lordſhip for the honour you have
done to that my Tract; but wiſh withal, that your Eſteem of it
may not prejudice the univerſal Eſteem that the World hath of
Your Honours moſt refined judgement.
As to that Point which I touch upon in the Concluſion, name­
ly, That the conſideration of the Velocity of Running Water ſup­
plyeth the conſideration of the ^{*} Length omitted in the common

way of meaſuring Running Waters; Your Lordſhip having com­
manded me that in favour of Practiſe, and for the perfect diſco­
very of the diſorder that commonly happeneth now adayes in
the diſtribution of the Waters of Fountains, I ſhould demon­
ſtrate that the knowledge of the Velocity ſerveth for the finding
of the Length: I have thought fit to ſatisfie your Command by
relating a Fable; which, if I do not deceive my ſelf, will make
out to us the truth thereof; inſomuch that the reſt of my Treatiſe
ſhall thereby alſo become more manifeſt and intelligible, even to
1thoſe who finde therein ſome kinde of obſcurity.
* Larghezza, but
miſprinted.
In the dayes of yore, before that the admirable Art of Wea­
ving was in uſe, there was found in Perſia a vaſtand unvaluable
Treaſure, which conſiſted in an huge multitude of pieces of Er­
meſin, or Damask, I know not whether; which, as I take it,
amounted to near two thouſand pieces; which were of ſuch a
nature, that though their Breadth and Thickneſs were finite and
determinate, as they uſe to be at this day; yet nevertheleſs, their
Length was in a certain ſenſe infinite, for that thoſe two thouſand
pieces, day and night without ceaſing, iſſued out with their ends
at ſuch a rate, that of each piece there iſſued 100. Ells a day, from
a deep and dark Cave, conſecrated by the Superſtition of thoſe
people, to the fabulous Arachne. In thoſe innocent and early
times (I take it to have been, in that ſo much applauded and
deſired Golden age) it was left to the liberty of any one, to cut
off of thoſe pieces what quantity they pleaſed without any diffi­
culty: But that felicity decaying and degenerating, which was
altogether ignorant of Meum and Tuum; terms certainly moſt
pernicious, the Original of all evils, and cauſe of all diſcords;
there were by thoſe people ſtrong and vigilant Guards placed
upon the Cave, who reſolved to make merchandize of the Stuffes;
and in this manner they began to ſet a price upon that ineſtima­
ble Treaſure, ſelling the propriety in thoſe pieces to divers Mer­
chants; to ſome they ſold a right in one, to ſome in two, and to
ſome in more. But that which was the worſt of all, There was
found out by the inſatiable avarice of theſe men crafty inventions
to deceive the Merchants alſo; who came to buy the aforeſaid
commodity, and to make themſelves Maſters, ſome of one
ſome of two, and ſome of more ends of thoſe pieces of ſtuff;
and in particular, there were certain ingenuous Machines placed
in the more ſecret places of the Cave, with which at the pleaſure
of the Guards, they did retard the velocity of thoſe Stuffs, in
their iſſuing out of the Cave; inſomuch, that he who ought to have
had 100. Ells of Stuff in a day, had not above 50, and he who
ſhould have had 400, enjoyed the benefit of 50. onely; and ſo all
the reſt were defrauded of their Rights, the ſurpluſage being ſold,
appropriated, and ſhared at the will of the corrupt Officers: So
that the buſineſs was without all order or juſtice, inſomuch that
the Goddeſs Arachne being diſpleaſed at thoſe people, deprived
every one of their benefit, and with a dreadful Earthquake for
ever cloſing the mouth of the Cave, in puniſhment of ſo much
impiety and malice: Nor did it avail them to excuſe themſelves,
by ſaying that they allowed the Buyer the Breadth and Thick­
neſs bargained for; and that of the Length, which was infinite,
1there could no account be kept: For the wiſe and prudent
Prieſt of the Sacred Grotto anſwered, That the deceit lay in the
length, which they were defrauded of, in that the velocity of the
ftuffe was retarded, as it iſſued out of the Cave: and although
the total length of the Piece was infinite, for that it never cea­
ſed coming forth, and ſo was not to be computed; yet never­
theleſs its length conſidered, part by part, as it came out of the
Cave, and was bargained for, continued ſtill finite, and might
be one while greater, and another while leſſer, according as the
Piece was conſtituted in greater or leſſer velocity; and he added
withall, that exact Juſtice required, that when they ſold a piece
of ſtuff, and the propriety or dominion therein, they ought not
only to have aſcertained the breadth and thickneſſe of the Piece,
but alſo to have determined the length, determining its ve­
locity.
The ſame diſorder and confuſion, that was repreſented in the
Fable, doth come to paſſe in the Hiſtory of the Diſtribution of
the Waters of Conduits and Fountains, ſeeing that they are ſold
and bought, having regard only to the two Dimenſions, I mean
of Breadth and Height of the Mouth that diſchargeth the Wa­
ter; and to remedy ſuch an inconvenience, it is neceſſary to de­
termine the length in the velocity; for never ſhall we be able to
make a gueſſe at the quantity of the Body of Running Water,
with the two Dimenſions only of Breadth and Height, without
Length.
And to the end, that the whole buſineſs may be reduced
to a moſt eaſie practice, by which the waters of Aqueducts
may be bought and ſold juſtly, and with meaſures alwayes ex­
act and conſtant.
Firſt, the quantity of the Water ought diligently to be exa­
mined, which the whole principal ^{*} Pipe diſchargeth in a time
certain, as for inſtance, in an hour, in half an hour, or in a leſſe
interval of time, (for knowing which I have a moſt exact and
eaſie Rule) and finding that the whole principal pipe diſchar­
geth v. g. a thouſand Tuns of Water in the ſpace of one or
more hours, in ſelling of this water, it ought not to be uttered by
the ordinary and falſe meaſure, but the diſtribution is to be
made with agreement to give and maintain to the buyer ten or
twenty, or a greater number of Tuns, as the bargain ſhall be
made, in the ſpace of an hour, or of ſome other ſet and deter­
minate time. And here I adde, that if I were to undertake to
make ſuch an adjuſtment, I would make uſe of a way to divide
and meaſure the time with ſuch accurateneſſe, that the ſpace of
an hour ſhould be divided into four, ſix, or eight thouſand parts
1without the leaſt errour; which Rule was taught me by my
Maſter Sign. Galilæo Galilæi, Chief Philoſopher to the moſt Se­
rene Grand Duke of Tuſcany. And this way will ſerve eaſily and
admirably to our purpoſe and occaſion; ſo that we ſhall
thereby be able to know how many Quarts of Water an A­
queduct will diſcharge in a given time of hours, moneths, or
years. And in this manner we may conſtitute a Cock that ſhall
diſcharge a certain and determinate quantity of water in a time
given.
And becauſe daily experience ſhews us, that the Springs of A­
queducts do not maintain them alwayes equally high, and full
of Water, but that ſometimes they increaſe, and ſometimes de­
creaſe, which accident might poſſibly procure ſome difficulty in
our diſtribution: Therefore, to the end that all manner of ſcru­
ple may be removed, I conceive that it would be convenient to
provide a Ciſtern, according to the occaſion, into which there
might alwayes fall one certain quantity of water, which ſhould
not be greater than that which the principal pipe diſchargeth in
times of drought, when the Springs are bare of water, that ſo in
this Ciſtern the water might alwayes keep at one conſtant height.
Then to the Ciſtern ſo prepared we are to faſten the Cocks of
particular perſons, to whom the Water is ſold by the Reverend
Apoſtolique Chamber, according to what hath been obſerved
before; and that quantity of Water which remaineth over and
above, is to be diſcharged into another Ciſtern, in which the
Cocks of the Waters for publick ſervices, and of thoſe which
people buy upon particular occaſions are to be placed. And
when the buſineſſe ſhall have been brought to this paſſe, there
will likewiſe a remedy be found to the ſo many diſorders that
continually happen; of which, for brevity ſake, I will inſtance
in but four only, which concern both publique and private bene­
fit, as being, in my judgment, the moſt enormous and intole­
rable.
The firſt inconvenience is, that in the common way of meaſu­
ring, diſpenſing, and ſelling the Waters of Aqueducts, it is not
underſtood, neither by the Buyer nor Seller, what the quantity
truly is that is bought and ſold; nor could I ever meet with any
either Engineer or Architect, or Artiſt, or other that was able to
decypher to me, what one, or two, or ten inches of water was.
But by our above declared Rule, for diſpenſing the Waters of
Aqueducts we may very eaſily know the true quantity of Water
that is bought or ſold, as that it is ſo many Tuns an hour, ſo ma­
ny a day, ſo many in a year, &c.
The ſecond diſorder that happeneth, at preſent, in the diſtri­
1bution of Aqueducts is, that as the buſineſſe is now governed, it
lieth in the power of a ſordid Maſon to take unjuſtly from one,
and give undeſervedly to another more or leſſe Water than be­
longeth to them of right: And I have ſeen it done, of my
own experience. But in our way of meaſuring and diſtri­
buting Waters, there can no fraud be committed; and put­
ting the caſe that they ſhould be committed, its an eaſie mat­
ter to know it, and amend it, by repairing to the Tribunal
appointed.
Thirdly, it happens very often, (and we have examples there­
of both antient and modern) that in diſpenſing the Water after
the common and vulgar way; there is ſometimes more Water diſ­
pended than there is in the Regiſter, in which there will be regi­
ſtred, as they ſay, two hundred inches (for example) and there
will be diſpenſed two hundred and fifty inches, or more. Which
paſſage happened in the time of Nerva the Emperour, as Giulio
Frontino writes, in his 2. Book, De Aquaductibus Vrbis Romæ,
where he obſerveth that they had in Commentariis 12755. Qui­
naries of Water; and found that they diſpenſed 14018. Qui­
naries. And the like Errour hath continued, and is in uſe alſo
modernly until our times. But if our Rule ſhall be obſerved,
we ſhall incur no ſuch diſorder, nay there will alwayes be given
to every one his ſhare, according to the holy end of exact juſtice,
which dat unicuique quod ſuum eſt. As on the contrary, it is
manifeſt, that His Divine Majeſty hateth and abominateth Pon­
dus & pondus, Menſura & menſura, as the Holy Ghoſt ſpeak­
eth by the mouth of Solomon in the Proverbs, Chap. 20. Pondus
& Pondus, Menſura & Menſura, utrumque abominabile eſt apud
Deum. And therefore who is it that ſeeth not that the way of
dividing and meaſuring of Waters, commonly uſed, is expreſly
againſt the Law of God. Since that thereby the ſame meaſure
is made ſometimes greater, and ſometimes leſſer; A diſorder ſo
enormous and execrable, that I ſhall take the boldneſs to ſay, that
for this ſole reſpect it ought to be condemned and prohibited like­
wiſe by human Law, which ſhould Enact that in this buſineſs there
ſhould be imployed either this our Rule, or ſome other that
is more exquiſite and practicable, whereby the meaſure
might keep one conſtant and determinate tenor, as we make it,
and not, as it is now, to make Pondus & Pondus, Menſur a &
Menſura.
And this is all that I had to offer to Your moſt Illuſtrious
Lordſhip, in obedience to your commands, reſerving to my ſelf
the giving of a more exact account of this my invention, when
the occaſion ſhall offer, of reducing to practice ſo holy, juſt, and
1neceſſary a reformation of the Meaſure of Running Waters and
of Aqueducts in particular: which Rule may alſo be of great
benefit in the diviſion of the greater Waters to over-flow
Grounds, and for other uſes: I humbly bow,
Your Most Devoted,
and
Moſt Obliged Servant,
D. Benedetto Caſtelli, Abb. Caſin.
FINIS.
1
A TABLE
Of the moſt obſervable matters in this Treatiſe of the
MENSURATION of RUNNING
WATERS.
AAbatements of a River in different and unequal Diverſions, is alwaies equal, which is proved with 100. Syphons.Page 75Arno River when it riſeth upon a Land-Flood near the Sea one third of a Brace, it riſeth about Piſa 6. or 7. Braces.82BBanks near to the Sea lower, than far from thence. Corollary XIV.16Brent River diverted from the Lake of Venice, and its effects.64Brent ſuppoſed inſufficient to remedy the inconveniences of the Lake, and the falſity of that ſuppoſition.67Brent, and its benefits in the Lake.70Its Depoſition of Sand in the Lake, bow great it is.78, 79Bridges over Rivers, and how they are to be made. Appendix VIII.20Burana River, its riſing, and falling in Panaro.110CCaſtelli applyed himſelf to this Study by Order of Urban VIII.2Chanel of Navigation in the Valleys of Bologna, and its inconveniences.99Carried into the Po of Ferrara, and its benefitsibid.Ciampoli alover of theſe Obſervations of Waters.3DDifficulty of this buſineſs of Meaſuring Waters.2Diſorders that happen in the diſtribution of the Waters of Aqueducts, and their re-medies.113Diſtribution of the Waters of Fountains, and Aqueducts. Appendix X.22Diſtribution of Water to over-flow Grounds. Appendix XI.23, 69, 70Diverſion of Reno and other Brooks of Romagna, adviſed by P. Spernazzati to what end it was.100Drains and Ditches, the benefit they receive by cutting away the Weeds and Reeds. Appendix IX.21Drains and Sewers obſtructed, in the Diverſion of Reno into Main Po, and a remedy for the ſame.110EEngineers unverſ'd in the matters of Waters.2Erour found in the common way of Meaſuring Running Waters.68, 69Errour in deriving the Water of Acqua Paola. Appendix II.17, 18
1Errour of Bartolotti.86, 87Errours of Engineers in the Derivation of Chenels. Corollary XII.12Errour of Engineers in Meaſuring of Reno in Po. Appendix III.ibid.Errour of other Engineers, contrary to the precedent. Appendix IV.Ibid.Errour of Giovanni Fontana in Meaſuring Waters, Corollary XI.9Errour of Giulio Frontino in Meaſuring the Waters of Aqueducts. Appen-dix I.17Errours committed in cutting the Bank at Bondeno, in the ſwellings of Po: CorollaryXIII.81FFenns Pontine, Drained by Pope Sixtus Quintus, with vaſt expence.92The ruine and miſcarriage thereof.93Tardity of the principal Chanel that Drains them, cauſe of the Drowning.ibid.They are obſtructed by the Fiſhing-Wears, which ſuell the River.94Waters of Fiume Siſto, which flow in great abundance into the Evacuator of the ſaid Fenns.94, 95Remedies to the diſorders of thoſe Fenns.95, 96Fontana Giovanni, his errours in Meaſuring Waters. Corollary XI.9Fiume Morto, whether it ought to fall into the Sea, or into Serchio,79Let into Serchio and its inconveniences.79, 80The dangerous riſing of its Waters, when to be expected.81Its inconveniences when it is higher in level than Serchio, and why it riſeth moſt On the Sea-coaſts, at ſuch time as the Winds make the Sea to ſuell.83GGalilæo Galilæi. hoxourably mentioned.Page 2, 28His Rule for meaſuring the time.49HHeight, vide QuickHeights different, made by the ſame ſtream of a Brock or Torrent, according to the divers Velocities in the entrance of the River. Corollary I.6Heights different, made by the Torrent in the River, according to the different heights of the River. Corollary II.ibid.KKnowledge of Motion how much it importeth.1LtLake of Perugia, and, he Obſervation made on it. Appendix XII.42Lake of Thraſimenus and Conſiderations upon it, a Letter written to Sig. Galilæo Galilæi.28Lake of Venice, and Conſiderations upon it.63, 73Low Waters which let the bottom of it be diſcovered.64The ſtoppage and choaking of the Ports, a main cauſe of the diſorders of the Lake, and the grand remedy to thoſe diſorders what it is.66Lakes and Metrs along the Sea-coaſts, and the cauſes thereof.65Length of Waters, how it is to be Meaſured.70MMeaſure and Diſtributions of Waters. Appendix V.18
1Meaſure of Rivers that fall into others difficult. Coroll. X:9Meaſure of the Running Water of a Chanel of an height known by a Regulator of a Mea-ſure given, in a time aſſigned. Propoſition I. Problem I.50Meaſure of the Water of any River, of any greatneſs, in a time given. Propoſition V. Problem III.60Meaſure that ſhewes how much Water a River diſchargeth in a time given.48Mole-holes,Motion the principal ſubject of Philoſophy.1Mud. Vide Sand.NNavigation from Bologna to Ferrara, is become impoſſible, till ſuch time as Reno be diverted.101Navigation in the Lake of Venice endangered, and how restored.65, 70PPerpendicularity of the Banks of the River, to the upper ſuperficies of it.37Perpendicularity of the Banks to the bottom.37Perugia. Vide Lake.Pontine. Vide Fenns.Ports of Venice, Malamocco, Bondolo, and Chiozza, choaked up for want of Water in the Lake.65Proportions of unequal Sections of equal Velocity, and of equal Sections of unequal Velo-city. Axiome IV. and V.38Proportions of equal and unequal quantities of Water, which paſs by the Sections of dif-ferent Rivers. Propoſition II.39Proportions of unequal Sections that in equal times diſcharge equal quantities of Water. Propoſition III.41Proportion wherewith one River falling into another, varieth in height. Propo-ſition IV.44Proportion of the Water diſcharged by a River in the time of Flood, to the Water diſcharged in an equal time by the ſaid River, before or after the Flood. Propoſition V.44Proportion of the Heights made by two equal Brooks or Streams falling into the ſame River. Propoſition VI.45Proportion of the Water which a River diſchargeth encreaſing in Quick-height by the ad-dition of new Water, to that which it diſchargeth after the encreaſe is made. Propo-ſition IV. Theor. II.54Proportion of a River when high, to it ſelf when low. Coroll. I.55QQuantity of Running Waters is never certain, if with the Vulgar way of Meaſuring them, their Velocities be not conſidered.32Quantities of Waters which are diſcharged by a River, anſwer in equality to the Velocities and times in which they are diſcharged. Axiome I, II, III.38Quick-Height of a River, what it is. Definition V.48RReaſon of the Proverb, Take heed of the ſtill Waters. Coroll. VI.7Reaſons of Monſignore Corſini againſt the diverſion of Reno into the Po ofVolano.105Reaſons of Cardinal Capponi and Monſig. Corſini, for the turning of Reno into Main Po.106
1Two objections on the contrary, and anſwers to them.104 & 105What ought to be the proportion of the Heights of Reno in Reno, and of Reno inPo.110Regulator what it is. Definition IV.48Relation of the Waters of Bologna and Ferrara, by Monſignore Corſini100Reno in the Valleys, and its bad effects.100, 101Two wayes to divert it.103The facility and utility of thoſe wayes.Ibid.The difficulties objected.104Reply to Bartolotti touching the dangers of turning Fiume Morto into Serchio.83Retardment of the courſe of a River cauſed by its Banks. Appendix VII.19Riſings made by Flood-Gates but ſmall. Appendix XIII.26Rivers that are ſhallow ſwell much upon ſmall ſhowers, ſuch as are deep riſe but little upon great Floods. Corollary III.6Rivers the higher they are, the ſwifter.Ibid.Rivers the higher they are, theleſſe they encreaſe upon Floods.49Rivers when they are to have equal and when like Velocity.Ibid.Rivers in falling into the Sea, form a Shelf of Sand called Cavallo.65Five Rivers to be diverted from the Lake of Venice, and the inconveniences that would enſue thereupon.74, 75A River of Quick-height, and Velocity in its Regulator being given, if the Height be redoubled by new Water, it redoubleth alſo in Velocity. Propoſition II. The-orem I.51Keepeth the proportion of the heights, to the Velocities. Corollary52SSand and Mud that entereth into the Lake of Venice, and the way to examine it.76Seas agitated and driven by the Winds ſtop up the Ports.64, 65Sections of a River what they are. Definition I.37Sections equally ſwift what they are. Definition II.Ibid.Sections of a River being given, to conceive others equal to them, of different breadth, height and Velocity. Petition.38Sections of the ſame River, and their Proportions to their Velocities. Coroll. I.42Sections of a River diſcharge in any whatſoever place of the ſaid River, equal quantities of Water in equal times. Propoſition I.39Sile River what miſchiefes it threatneth, diverted from the Lake.74Spirtings of Waters grow bigger the higher they go. Coroll. XVI.16Sreams of Rivers how they encreaſe and vary. Coroll. I.6Streams retarded, and the effects thereof. Coroll. IX.8TTable of the Heights, Additions, and Quantities of Waters, and its uſe.56Thraſimenus. Vide Lake.Time how its meaſured in theſe Operations of the Waters.49Torrents encreaſe at the encreaſing of a River, though they carry no more Water than before: Coroll. IV.6Torrents when they depoſe and carry away the Sand. Coroll. V.7Torrents and their effects in a River.6, 7Torrents that fall into the Valleys, or into Po of Volano, and their miſchiefs prevent-ed, by the diverting of Reno into Main Po.100Tyber and the cauſes of its inundations. Coroll. VIII.8
1VValleys of Bologna and Ferrara, their inundations and diſorders, whence they pro-ceed.97Velocity of the Water ſhewn by ſeveral Examples.3Its proportion to the Meaſure.5Velocities equal, what they are.47Velocities like, what they are.47, 48Velocities of Water known, how they help us in finding the Lengths.113A Fable to explain the truth thereof.Ibid.Venice. Vide Lake.Vſe of the Regulator in meaſuring great Rivers. Conſideration I.60WWaters falling, why they diſgroß. Coroll. XVI.16Waters, how the Length of them is Meaſured.70Waters that are imployed to flow Grounds, how they are to be diſtributed.19, 53, 54Waters to be carryed in Pipes, to ſerve Aquaducts and Conduits, how they are to be Mea-ſured.115, 116Way to know the riſing of Lakes by Raines.28Way of the Vulgar to Meaſure the Waters of Rivers.68Wind Gun, and Tortable Fountain of Vincenzo Vincenti of Urbin.11Windes contrary, retard, and make Rivers encreaſe. Coroll. VII.8
The END of the TABLE of the Second Part
of the Firſt TOME.
MATHEMATICAL
Collections and Tranſlations:
THE SECOND
TOME:
IN TWO PARTS.
THE FIRST PART,
Containing,
I. GALILEUS GALILEUS His MATHEMATI­
CAL Diſcourſes and Demonſtrations, touching two
NEW SCIENCES, pertaining to the MECHA­
NICKS and LOCAL MOTIONS: With an
Appendix of the CENTRE of GRAVITY of ſome
SOLIDS.
II. GALILEUS His MECHANICKS: with ſome
Additionall Pieces.
III. RHENATUS DES CARTES His MECHA­
NICKS, Tranſlated from the FRENCH Manuſcript.
IV. ARCHIMEDES His Tract De Insidentibus Humido, or of
the NATATION of BODIES: With the Notes
and Demonſtrations of NICHOLAUS TARTALEA, and
FEDERICUS COMMANDINUS.
V. GALILEUS His Diſcourſe of NATATION.
VI. NICOLAUS TARTALEA, His Inventions for Diving un­
der Water, Raiſing of Ships ſunk, &c.
By THOMAS SALUSBURY, Eſq;
LONDON,
Printed by WILLIAM LEYBOURN, Anno Dom.
MD CLXV.
1
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1
MATHEMATICAL
DISCOURSES
AND
DEMONSTRATIONS,
TOVCHING
Two NEW SCIENCES; pertaining to
THE
MECHANICKS
AND
LOCAL MOTION:
BY
GALILÆVS GALILÆVS LYNCEVS,
Chiefe Phyloſopher and Mathematitian to the moſt
Serene GRAND DVKE of TVSCANY.
WITH
AN APPENDIX OF THE
Centre of Gravity
Of ſome SOLIDS.
Engliſhed from the Originall Latine and Italian,
By THOMAS SALUSBURY, Eſq;
LONDON,
Printed by WILLIAM LEYBOURN, Anno Dom.
MDCLXV.
1
GALILEUS,
HIS
DIALOGUES
OF
MOTION.
1
The Firſt Dialogue.
INTERLOCUTORS,
SALVIATUS, SAGREDUS, and SIMPLICIUS.
SALVIATUS.
The frequent reſort (Gentlemen) to

your Famous Arſenal of Venice, preſen­
teth, in my thinking, to your Speculative

Wits, a large field to Philoſophate in:
and more particularly, as to that part
which is called the Mechanicks: in re­
gard that there all kinds of Engines, and
Machines are continually put in uſe, by a
huge number of Artificers of all ſorts;
amongſt whom, as well through the obſervations of their Prede­
ceſſors, as thoſe, which through their own care they continually
are making, it's probable, that there are ſome very learned, and
bravely diſcours'd Men.
A Deſcription of
the Arſenal of
Venice.
It is a large field
for Wits to Philo­
ſophate in.
SAGR. Sir, you are not therein miſtaken: and I my ſelf, out of
1a natural Curioſitie, do frequentlie for my Recreation viſit that
place, and confer with theſe perſons; which for a certain prehe­

minence that they have above the reſt we call ^{*} Overſeers: whoſe
diſcourſe hath oft helped me in the inveſtigation of not only won­
derful, but abſtruce, and incredible Effects: and indeed I have been
at a loſſe ſometimes, and deſpaired to penetrate how that could
poſſibly come to paſſe, which far from all expectation my ſenſes
demonſtrated to be true; and yet that which not long ſince that
good Old man told us, is a ſaying and propoſition, though com­

mon enough, yet in my opinion wholly vain, as are many others,
often in the mouths of unskilful perſons; introduced by them, as
I ſuppoſe, to ſhew that they underſtand how to ſpeak ſomething
about that, of which nevertheleſſe they are incapable.
* Proti.
The Opinion of
Common Artificers
are often falſe.
SALV. It may be Sir, you ſpeak of that laſt propoſition which
he affirmed, when we deſired to underſtand, why they made

ſo much greater proviſion of ſupporters, and other proviſions,
and reinforcements about that Galeaſſe, which was to be launcht
than is made about leſſer Veſſels, and he anſwered us, that they did
ſo to avoid the peril of breaking its Keel, through the mighty
weight of its vaſt bulk, an inconvenience to which leſſer ſhips are
not subject.
Great Ships apter
than others to break
their Keels in
Launching, accor­
ding to ſome.
SAGR. I do intend the ſame, and chiefly that laſt concluſion,
which he added to his others, and which I alwaies eſteemed a vain
conceit of the Vulgar, namely, That in theſe and other Machines
we muſt not argue from the leſſe to the greater, becauſe many
Mechanical Inventions take in little, which hold not in great. But
being that all the Reaſons of the Mechanicks, have their founda­
tions from Geometry; in which I ſee not that greatneſſe and
ſmalneſſe make Circles, Triangles, Cilinders, Cones, or any other
ſolid Figures ſubject to different paſſions: when the great Ma­
chine is conformed in all its members to the proportions of the
leſſe that is uſeful, and fit for exerciſe to which it is deſigned; I
cannot ſee why it alſo ſhould not be exempt from the unlucky,
ſiniſter, and deſtructive accidents that may befall it.
SALV The ſaying of the Vulgar is abſolutely vain, and ſo
falſe, that its contrary may be affirmed with equal truth, ſaying,

That many Machines may be made more perfect in great than lit­
tle: As for inſtance, a Clock that ſhews and ſtrikes the Houres,
may be made more exact in one certain ſize, than in another leſſe.
With better ground is that ſame concluſion uſurped by other more
intelligent perſons, who refer the cauſe of ſuch effects in theſe
great Machines different from what is collected from the pure, and
abſtracted Demonſtrations of Geometry, to the imperfection of
the matter, which is ſubject to many alterations, and defects.
But here, I know not whether I may without contracting ſome
1ſuſpition of Arrogance ſay, that thither alſo doth the recourſe to
the defects of the matter (able to blemiſh the perfecteſt Mathe­
matical Demonſtrations) ſuffice to excuſe the diſobedience of

Machines in concrete, to the ſame abſtracted and Ideal: yet not­
withſtanding I will ſpeak it, affirming, That abſtracting all imper­
fections from the Matter, and ſuppoſing it moſt perfect, and unal­
terable, and from all accidental mutation exempt, yet neverthe­
leſſe its only being Material, cauſeth, that the greater Machine,
made of the ſame matter, and with the ſame proportions, as the
leſſer; ſhall anſwer in all other conditions to the leſſer in exact
Symetry, except in ſtrength, and reſiſtance againſt violent invaſi­
ons: but the greater it is, ſo much in proportion ſhall it be wea­
ker. And becauſe I ſuppoſe the Matter to be unalterable, that is
alwaies the ſame, it is manifeſt, that one may produce Demonſtra­
tions of it, no leſſe ſimply and purely Mathematical, then of eter­
nal, and neceſſary Affections: Therefore, Sagredus, Revoke the
opinion which you, and, it may be, all the reſt hold, that have ſtu­
died the Mechanicks; that Machines, and Frames compoſed of the
ſame Matter, with punctual obſervation of the ſelf ſame proporti­
on between their parts, ought to be equally, or to ſay better, pro­
portionally diſpoſed to Reſiſt; and to yield to External injuries
and aſſaults: For if it may be Geometrically demonſtrated, that
the greater are alwaies in proportion leſs able to reſiſt, than the
leſſe; ſo that in fine there is not only in all Machines & Fabricks
Artiſicial, but Natural alſo, a term neceſſarily aſcribed, beyond
which neither Art, nor Nature may paſſe; may paſſe, I ſay, al­
waies obſerving the ſame proportions with the Identity of the
Matter.
Many Machines
may be made more
exact in great than
in little.
Great Material
Machines, al­
though framed In
the ſame proportion
as others of the
ſame Matter that
are leſſer, are leſſe
ſtrong and able to
reſiſt external Im­
petuſs's than the
leſſer.
SAGR. I already feel my Brains to turn round, and my Mind,
(like a Cloud unwillingly opened by the Lightning,) I perceive
to be ſurprized with a tranſcient, and unuſual Light, which from
affar off twinkleth, and ſuddenly aſtoniſheth me; and with ab­
ſtruce, ſtrange, and indigeſted imaginations. And from what hath
been ſpoken, it ſeems to follow, that, it is a thing impoſſible to
frame two Fabricks of the ſame Matter, alike, and unequal, and
between themſelves in proportion equally able to Reſiſt; and
were it to be done, yet it would be impoſſible to find two only
Launces of the ſame wood, alike between themſelves in ſtrength,

and toughneſſe, but unequal in bigneſſe.
A Wooden Launce
fixed in a Wall at
Right-Angles, and
reduced to ſuch a
length and thick­
neſſe as that it may
endure, but made a
hairs breadth big­
ger, breaketh with
its own weight, is
ſingly one and no
more.
SALV. So it is Sir; and the better to aſſure you that we con­
cur in opinion, I ſay, that if we take a Launce of wood of ſuch a
length and thickneſſe, that being fixed faſt (v. g.) in a Wall at
Right Angles, that is parallel to the Horizon, it is reduced to the
utmoſt length, that it will hold at, ſo that lengthened never­
ſo-little more, it would break, being over-burthened with its own
1weight, there could not be another ſuch-a-one in the World: So
that if its length (for example) were Centuple to its thickneſſe,
there cannot be found another Launce of the ſame Matter, that
being in length Centuple to its thickneſſe, ſhall be able to ſuſtain
it ſelf preciſely, as that did, and no more: for all that are bigger
ſhall break, and the leſſer ſhall be able, beſides their own, to ſuſtain
ſome additional weight. And this that I ſay of the State of bear­
ing it ſelf, I would have underſtood to be ſpoken of every other
Conſtitution, and thus if one Tranſome bear or ſuſtain the force
often Tranſomes equal to it, ſuch another Beam cannot bear the
weight of ten that are equal to it. Now be pleaſed, Sir, and you

Simplicius to obſerve, how true Concluſions, though at the firſt
ſight they ſeem improbable, yet never ſo little glanced at, do depoſe
the Vailes which obſcure them, and make a voluntary ſhew of their
ſecrets nakedly, and ſimply. Who ſees not, that a Horſe falling

from a height of three or four yards, will break his bones, but a
Dog falling ſo many yards, or a Cat eight or ten, will receive no
hurt; nor likewiſe a Graſhopper from a Tower, nor an Ant thrown
from the Orbe of the Moon? Little Children eſcape all harm in
their falls, whereas perſons grown up break either their ſhins or
faces. And as leſſer Animals are in proportion more robuſtious,
and ſtrong than greater, ſo the leſſer Plants better ſupport them­
ſelves: and I already believe, that both of you think, that an Oake
two hundred foot high could not ſupport its branches ſpread like

one of an indifferent ſize; and that Nature could not have made
an Horſe as big as twenty Horſes, nor a Giant ten times as tall as a
Man, unleſſe ſhe did it either miraculouſly, or elſe by much alte­
ring the proportion of the Members, and particularly of the Bones,
enlarging them very much above the Symetry of common Bones.
To ſuppoſe likewiſe, that in Artificial Machines, the greater and
leſſer are with equal facility made, and preſerved, is a manifeſt Er­
rour: and thus for inſtance, ſmall Spires, Pillars, and other ſolid
figures may be ſafely moved, laid along, and reared upright, with­
out danger of breaking them; but the very great upon every ſini­
ſter accident fall in pieces, and for no other reaſon but their own
weight. And here it is neceſſary that I relate an accident, worthy
of notice, as are all thoſe events that occur unexpectedly, eſpecial­
ly when the means uſed to prevent an inconvenience, proveth in

fine the moſt potent cauſe of the diſorder. There was a very great
Pillar of Marble laid along, and two Rowlers were put under the
ſame neer to the ends of it; it came into the mind of a certain In­
gineer ſome time after, that it would be expedient, the better to
ſecure it from breaking in the midſt through its own weight, to
put under it in that part yet another Rowler: the counſel ſeemed
generally very ſeaſonable, but the ſucceſſe demonſtrated it to be
1wholly contrary: for many moneths had not paſt, before the Pil­
lar crackt, and broke in the middle juſt upon the new Rowler.
Truth upon a little
Courting, throweth
off her Vail, and
ſhews her Secrets
maked.
Great Animals
receive more harm
by a fall than leſ­
ſer.
Nature could not
have made of mea­
ner Horſes bigger,
and have retained
the ſame ſtrength,
but by altering
their Symetry.
A great Marble
Pillar broken by
its own weight,
and why.
SIMP. This was an accident truly ſtrange, and indeed preter
ſpem, eſpecially if it were derived from the addition of new ſup­
port in the middle.
SALV. From that doubtleſs it did proceed; and the known cauſe
of the Effect removeth the wonder: for the two pieces of the Pillar
being taken from off the Rowlers, one of thoſe bearers on which
one end of the Column had reſted, was by length of time rotten, and
ſunk away; and that in the midſt continuing ſound, and ſtrong,
occaſioned that half the Column lay hollow in the air without any
ſupport at the end; ſo that its own unweildy weight, made it do
that, which it would not have done, if it had reſted only upon the
two firſt Bearers, for as they had ſhrunk away it would have fol­
lowed. And here none can think that this would have faln out in
a little Column, though of the ſame ſtone, and of a length anſwe­
rable to its thickneſſe, in the very ſame proportion as the thick­
neſs, and length of the great Pillar.
SAGR. I am now aſſured of the effect, but do not yet compre­
hend the cauſe, how in the augmentation of Matter, the Reſiſtance
and Strength ought not alſo to multiply at the ſame rate. And I
admire at it ſo much the more, in regard I ſee, on the contrary, in
other caſes the ſtrength of Reſiſtance againſt Fraction to encreaſe
much more than the enlargement of the matter encreaſeth. For if
(for example) there be two Nailes faſtned in a Wall, the one twice
asthick as the other, that ſhall bear a weight not only double to this,
but triple, and quadruple.
SALV. You may ſay octuple, and not be wide of the truth:

nor is this effect contrary to the former, though in appearance it
ſeemeth ſo different.
A Naile double
in thickneſſe to
another being faſt­
ned in a Wall, ſu­
ſtains a Weight
octuple to that of
the leſſer.
SAGR. Therefore Salviatus, explain unto us theſe Riddles, and
level us theſe Rocks, if you can do it: for indeed I gueſſe this mat­
ter of Reſiſtance to be a field repleniſhed with rare, and uſeful Con­
templations, and if you be content that this be the ſubject of our
this-daies diſcourſe, it will be to me, and I believe to Simplicius,
very acceptable.
SALV. I cannot refuſe to ſerve you, ſince my Memory ſerveth

me, in minding me of that which I formerly learnt of our Accade­
mick, who hath made many Speculations on this ſubject, and all
conformable (as his manner is) to Geometrical Demonſtration:
inſomuch that, not without reaſon, this of his may be called a New
Science; for though ſome of the Concluſions have been obſerved

by others, and in the firſt place by Ariſtotle, yet nevertheleſſe are
they not any of the moſt curious, or (which more importeth)
proved by neceſſary Demonſtrations deduced from their primary,
1and indubitable fundamentals. And becauſe, as I ſay, I deſire de­
monſtratively to aſſure you, and not with only probable diſcour­
ſes to perſwade you; preſuppoſing, that you have ſo much know­
ledge of the Mechanical Concluſions, by others heretofore funda­
mentally handled, as ſufficeth for our purpoſe; it is requiſite, that
before we proceed any further, we conſider what effect that is which
opperates in the Fraction of a Beam of Wood, or other Solid, whoſe
parts are firmly connected; becauſe this is the firſt Notion, where­
on the firſt and ſimple principle dependeth, which as familiarly
known, we may take for granted. For the clearer explanation
whereof; let us take the Cilinder, or Priſme, A. B. of Wood, or
other ſolid and coherent matter, faſtned above in A, and hanging
perpendicular; to which, at the other end B, let there hang the
Weight C: It is manifeſt, that how great ſoever the Tenacity and
coherence of the parts of the ſaid Solid to one another be, ſo it be
not infinite, it may be overcome by the
Force of the drawing Weight C: whoſe
Gravity I ſuppoſe may be encreaſed as much
52[Figure 52]
as we pleaſe; by the encreaſe whereof the
ſaid Solid in fine ſhall break, like as if it had
been a Cord. And, as in a Cord, we under­
ſtand its reſiſtance to proceed from the mul­
titude of the ſtrings or threads in the Hemp
that compoſe it, ſo in Wood we ſee its veins,
and grain diſtended lengthwaies, that render
it far more reſiſting againſt Fraction, then any
Rope would be, of the ſame thickneſſe: but
in a Cylinder of ſtone or Metal the Tenacity
of its parts, (which yet ſeemeth greater) de­
pendeth on another kind of Cement,
than of ſtrings, or grains, and yet they alſo
being drawn with equivalent force, break.
By Accademick
here, as in his
Dialogues of the
Syſteme, Galile­
us meaneth him­
ſelf.
Ariſtotle the firſt
Obſerver of Me­
chanical Concluſi­
ons, but they nei­
ther not the moſt
curious nor ſolidly
demonſtrated.
SIMP. If the thing ſucceed as you ſay, I underſtand well
enough, that the thread or grain of the Wood which is as long as
the ſaid Wood may make it ſtrong and able to Reſiſt a great vio­
lence done to it to break it: But a Cord compoſed of ſtrings of
Hemp, no longer than two, or three foot a piece, how can it be ſo
ſtrong when it is ſpun out, it may be, to a hundred times that
length? Now I would farther underſtand your opinion concern­
ing the Connection of the parts of Metals, Stones, and other mat­
ters deprived of ſuch Ligatures, which nevertheleſſe, if I be not
deceived, are yet more tenacious.
SALV. We muſt be neceſſitated to digreſſe into new Specu­
lations, and not much to our purpoſe, if we ſhould reſolve thoſe
difficulties you ſtart.
1
SAGR. But if Digreſſions may lead us to the knowledge of
new Truths, what prejudice is it to us, that are not obliged to a
ſtrict and conciſe method, but that make our Congreſſions only
for our divertiſement to digreſſe ſometimes, leſt we let ſlip thoſe
Notions, which perhaps the offered occaſion being paſt, may never
meet with another opportunity of remembrance? Nay, who knows
not, that many times curioſity may thereby diſcover hints of more
worth, than the primarily intended Concluſions? Therefore I
entreat you to give ſatisfaction to Simplicius, and my ſelf alſo,
no leſſe curious than he, and deſirous to underſtand what that
Cement is, that holdeth the parts of thoſe Solids ſo tenaciouſly
conjoyned, which yet nevertheleſſe in concluſion are diſſoluble:
a knowledge which furthermore is neceſſary for the underſtanding
of the coherence of the parts of thoſe very ligaments, whereof
ſome Solids are compoſed.
SALV. Well, ſince it is your pleaſure, I will herein ſerve you.

And the firſt difficulty is, how the threads of a Cord or Rope
an hundred foot long ſhould ſo cloſely connect together (none
of them exceeding two or three foot) that it requireth a great
violence to break them. But tell me, Simplicius, cannot you hold
one ſingle ſtring of Hemp ſo faſt between your fingers by one

end, that I pulling by the other end ſhould break it ſooner than
get it from you? Queſtionleſſe you might: when then, thoſe
threads are not only at the end, but alſo in every part of their
length, held faſt with much ſtrength by him that graſpeth them, is
it not apparent, that it is a much harder matter to pluck them
from him that holds them, then to break them? Now in the Cord,

the ſame act of twiſting, binds the threads mutually within one
another, in ſuch ſort, that pulling the Cord with great force, the
threads of it break inſunder, but ſeparate and part not from one
another; as is plainly ſeen by viewing the ſhort ends of the ſaid
threads in the broken place, that are not a ſpan long; as they
would be, if the diviſion of the Cord had been made by the ſole
ſeperating of them in drawing the Cord, and not by breaking
them.
What that Cement
is that Connecteth
the parts of Solids.
How a Rope or
Cord reſiſteth Fra­
ction.
In breaking a Rope
the parts are not
ſeparated, but bro­
kon.
SAGR. For confirmation of this, let me add, that the Cord is
ſometimes ſeen to break, not by pulling it length-waies, but by
over-twiſting it: an argument, in my judgment, concluding that
the threads are ſo enterchangeably compreſt by one another, that
thoſe compreſſings permit not the compreſſed to ſlip ſo very little,
as is requiſite to lengthen it out that it wind about the Cord,
which in the twining breaketh, and conſequently in ſome ſinall
meaſure ſwels in thickneſſe.
SALV. You ſay very well; but conſider by the way, how one
truth draweth on another. That thread, which griped between the
1fingers, did not yield to follow him that would have forceably
drawn it from between them, reſiſted, becauſe it was ſtayed by a
double compreſſion, ſince the upper finger preſt no leſſe againſt
the nether, than it preſſed againſt that. And there is no queſtion,
that if of theſe two preſſures, one alone might be retained, there
would remain half of that Reſiſtance, which depended conjunctive­
ly on them both: but becauſe you cannot with removing, v.g. the
upper finger take away its preſſion, without taking away the other
part alſo; it will be neceſſary by ſome new Artifice to retain one
of them, and to find a way that the ſame thread may compreſſe it
ſelf againſt the finger or other ſolid body upon which it is put; and
this is done by winding the ſame thread about the Solid. For the
better underſtanding whereof, I will briefly give it you in Figure;
and let A B and CD be two Cilinders, and between them let there
be diſtended the thread E F, which for greater plainneſſe I will
repreſent to be a ſmall Cord: there is no doubt but that the two
Cylinders being preſſed hard one againſt the other, the Cord
E F pulled by the end F will Reſiſt no ſmal force before
it will ſlip from between the two Solids compreſſing it: but if
we remove one of them, though the Cord
53[Figure 53]
continue touching the other, yet ſhall it not
by ſuch contact be hindered from ſlipping
away. But if holding it faſt, though but
gently in the point A, towards the top of the
Cylinder, we wind, or belay it about the
ſame ſpirally in A F L O T R, and pull it by
the end R: it is manifeſt, that it will begin
to preſſe the Cylinder, and if the windings
and wreathes be many, it ſhall in its effectual
drawing alwaies preſſe it ſo much the ſtrai­
ter about the Cylinder: and by multiplying
the wreathes if you make the contact longer,
and conſequently more invincible, the more
difficult ſtill ſhall it be to withdraw the
Cord, and make it yield to the force that
pulls it. Now who ſeeth not, that the ſame
Reſiſtance is in the threads, which with many thouſand ſuch
twinings ſpin the thick Cord? Yea, the ſtreſſe of ſuch twiſting
bindeth with ſuch Tenacity, that a few Ruſhes, and of no great
length, (ſo that the wreaths and windings are but few where­
with they entertwine) make very ſtrong bands, called, as I take it,

^{*} Thum-ropes.
* Fuſta.
SAGR. Your Diſcourſe hath removed the wonder out of my
mind at two effects, whereof I did not well underſtand the rea­
ſon; One was to ſee, how two, or at the moſt three twines of the
1Rope about the Axis of a Crane did not only hold it, that be­
ing drawn by the immenſe force of the weight, which it held, it
ſlipt nor ſhrunk not; but that moreover turning the Crane about,
the ſaid Axis with the ſole touch of the Rope which begirteth it,
did in the after-turnings, draw and raiſe up vaſt ſtones, whilſt the
ſtrength of a little Boy ſufficed to hold and ſtay the other end of
the ſame Cord. The other is at a plain, but cunning, Inſtrument found
out by a young Kinſman of mine, by which with a Cord he could
let himſelf down from a window without much gauling the palmes
of his hands, as to his great ſmart not long before he had done. For

the better underſtanding whereof, rake this Scheame: About ſuch
a Cylinder of Wood as A B, two Inches
thick, and ſix or eight Inches long, he cut a
hollow notch ſpirally, for one turn and a
54[Figure 54]
half and no more, and of wideneſſe fit for
the Cord he would uſe; which he made to
enter through the notch at the end A, and
to come out at the other B, incircling after­
wards the Cylinder in a barrel or ſocket of
Wood, or rather Tin, but divided length­
waies, and made with Claſpes or Hinges to
open and ſhut at pleaſure: and then graſp­
ing and holding the ſaid Barrel or Caſe with
both his hands, the rope being made faſt
above, he hung by his arms; and ſuch was
the compreſſion of the Cord between the
moving Socket and the Cylinder, that at
pleaſure griping his hands cloſer he could
ſtay himſelf without deſcending, and ſlacking his hold a little, he
could let himſelf down as he pleaſed.
An Hand-Pully
or Inſtrument in­
vented by an ama­
rous perſon to let
himſelf down from
any great height
with a Cord with­
out gauling his
hands.
SALV. Aningenious invention verily, and for a full explanati­
on of its nature, me-thinks I diſcover, as it were by a ſhadow, the
light of ſome other additional diſcoveries: but I will not at this
time deviate any more from my purpoſe upon this particular: and
the rather in regard you are deſirous to hear my opinion of the
Reſiſtance of other Bodies againſt Fraction, whoſe texture is not

with threads, and fibrous ſtrings, as is that of Ropes, and moſt
kinds of Wood: but the connection of their parts ſeem to de­
pend on other Cauſes; which in my judgment may be reduced to
two heads; one is the much talked-of Repugnance that Nature
hath againſt the admiſſion of Vacuity: for another (this of Va­
cuity not ſufficing) there muſt be introduced ſome glue, viſcous
matter, or Cement, that tenaciouſly connecteth the Corpuſcles of
which the ſaid Body is compacted.
Why ſuch Bodies
reſiſt Fraction that
are not connected
with Fibrous fila­
ments.
I will firſt ſpeak of Vacuity, ſhewing by plain experiments,
1
what and how great its virtue is. And firſt of all the ſeeing at
pleaſure two flat pieces of either Marble, Metal, or Glaſſe, exqui­
ſitely planed, ſlickt, and poliſhed, that being laid upon one the
other, without any difficulty ſlide along upon each other, if drawn

ſidewaies, (a certain argument that no glue connects them,) but
that going about to ſeperate them, keeping them equidiſtant,
there is found ſuch repugnance, that the uppermoſt will be lif­
ted up, and will draw the other after it, and keep it perperually
raiſed, though it be pretty thick, and heavy, evidently proveth to
us, how much Nature abhorreth to admit, though for a ſhort mo­
ment of time, the void ſpace, that would be between them, till
the concourſe of the parts of the Circum-Ambient Air ſhould have
poſſeſt, and repleated it. We ſee likewiſe, that if thoſe two Plates
be not exactly poliſhed, and conſequently their contact not every
where exquiſite; in going about to ſeparate them gently, there will
be found no Renitence more than that of their meer weight, but in
the ſudden raiſing, the nether Stone will riſe, and inſtantly fall
down again, following the upper only for that very ſmall time
which ſerveth for the expanſion of that little Air which interpo­
ſeth betwixt the Plates, that did not every where touch, and for
the ingreſſion of the other circumfuſed. The like Reſiſtance, which
ſo ſenſibly diſcovers it ſelf betwixt the two Plates, cannot be
doubted to reſide alſo between the parts of a Solid, and that it en­
tereth into their connection, at leaſt in part, and as their Concomi­
tant Cauſe.
The firſt Cauſe of
the Cohorence of
Bodies is their Re­
pugnance to Vacu­
ity.
This is proved by
the Coherence of
two poliſhed Mar­
bles.
SAGR. Hold, I pray you, and permit me to impart unto you a
particular Conſideration, juſt now come into my Mind, and this it
is; That ſeeing how the lower Plate followeth the upper, and is
by a ſpeedy motion raiſed, we are thereby aſcertained that (con­
trary to the ſaying of many Philoſophers, and perchance of Ari­
ſtotle himſelf) the Motion in Vacuity would not be Inſtantaneous;
for ſhould in be ſuch, the propoſed Plates without the leaſt repug­
nance would Seperate; ſince the ſelf ſame inſtant of time would
ſuffice for their ſeparation, and for the concourſe of the Ambient
Air to repleat that Vacuity, which might remain between them.
By the Inferiour Plates following the Superiour therefore may be
gathered, that in the Vacuity the Motion would not be Inſtanta­

neous. And alſo it may be inferred, that even betwixt thoſe Plates
there reſteth ſome Vacuity, at leaſt for ſome very ſhort time; that
is, for ſo long as the Ambient Air is moving whilſt it concurreth to
replete the Vacuum: for if there did no Vacuity remain, there
would be no need either of the Concourſe, or Motion of the Am­
bient We muſt therefore ſay that Vacuity ſometimes is admit­
ted, though by Violence or againſt Nature, (albeit it is my opi­
nion, that nothing is contrary to Nature, but that which is im­
1poſſible, which again never is.) But here ſtarts up another diffi­
culty, and it is, That though Experience aſſures me of the truth of
the Concluſion, yet my Judgment is not thorowly ſatisfied of the
Cauſe, to which ſuch an effect may be aſcribed. For as much as
the effect of the Seperation of the two Plates, is in time before the
Vacuity which ſhould ſucceed by conſequence upon the Separa­
tion. And becauſe, in my opinion, the Cauſe ought, if not in

Time, at leaſt in Nature, to precede the Effect: and that of a Po­
ſitive Effect, the Cauſe ought alſo to be Poſitive; I cannot con­
ceive, how the Cauſe of the Adheſion of the two Plates, and of
their Repugnance to Separation, (Effects that are already in
Act) ſhould be aſſigned to Vacuity, which yet is not, but ſhould
follow. And of things that are not in being, there can be no Ope­

ration; according to the infallible Maxime of Philoſophy.
Vacuity partly the
cauſe of the Cohe­
rence between the
parts of Solids.
Of a Poſitive Ef­
fect the Cauſe is
Poſitive.
Non-entity is at­
tended with Non­
operation.
SIMP. But ſince you grant Ariſtotle this Axiome, I do not
think you will deny another that is moſt excellent, and true; to

wit, That Nature doth not attempt Impoſſibilities: Upon which
Axiom I think the Solution of our doubt depends: becauſe there­
fore a void ſpace is of it ſelf impoſſible, Nature forbids the doing
that, in conſequence of which Vacuity would neceſſarily ſucceed;
and ſuch an act is the ſeparation of the two Plates.
Nature doth not
attempt Impoſſibi­
lities.
SAGR. Now, (admitting this which Simplicius alledgeth is a
ſufficient Solution of my Doubt) in perſuance of the diſcourſe
with which I began, it ſeemeth to me, that this ſame Repugnance
to Vacuity ſhould be a ſufficient Cement in the parts of a Solid of
Stone, Metal, or what other ſubſtance is more firmly conjoyned,
and averſe to Diviſion. For if a ſingle Effect, hath but one ſole
Cauſe, as I underſtand, and think; or if many be aſſigned, they
are reducible to one alone: why ſhould not this of Vacuity, which
certainly is one, be ſufficient to anſwer all Reſiſtances?
SALV. I will not at this time enter upon this conteſt, whether
Vacuity, without other Cement, be in it ſelf alone ſufficient to
keep together the ſeparable parts of firm Bodies; but yet this I
ſay, that the Reaſon of the Vacuity, which is of force, and con­
oluding in the two Plates, ſufficeth not of it ſelf alone for the
firm connection of the parts of a ſolid Cylinder of Marble, or
Metal, the which forced with great violence, pulling them ſtreight
out, in fine, divide and ſeparate. And in caſe I have found a way
to diſtinguiſh this already-known Reſiſtance dependent on Va­
ouity, from all others whatſoever that may concur with it in
ſtrengthening the Connection, and make you ſee how that it alone
is not neer ſufficient for ſuch an Effect, would not you grant that
it would be neceſſary to introduce ſome other? Help him out, Sim­
plicius, for he ſtands ſtudying what to anſwer.
SIMP. The Suſpenſion of Sagredus muſt needs be upon ano­
1ther account, there being no place left for doubting of ſo clear, and
neceſſary a Conſequence.
SAGR. You Divine Simplicius, I was thinking if a Million of
Gold per annum, coming from Spaine, not being ſufficient to pay
the Army, whether it was neceſſary to make any other proviſion
than of Money to pay the Souldiers. But proceed, Salviatus, and
ſuppoſing that I admit of your Conſequence, ſhew us how to ſe­
parate the opperation of Vacuity from the other, that meaſuring
it we may ſee how it's inſufficient for the Effect of which we ſpeak.
SALV. Your Genius hath prompted you. Well, I will tell you
the way to part the Virtue of Vacuity from the reſt, and then how
to meaſure it. And to ſever it, we will take a continuate matter,

whoſe parts are deſtitute of all other Reſiſtance to Separation, ſave
only that of Vacuity, ſuch as Water at large hath been demon­
ſtrated to be in a certain Tractate of our Accademick. So that
when ever a Cylinder of Water is ſo diſpoſed, that being drawn
we find a Reſiſtance againſt the ſeparation of its parts, this muſt
be acknowledged to proceed from no other cauſe, but from re­
pugnance to Vacuity. But to make ſuch an experiment, I have
imagined a device, which with the help of a ſmall Diagram, may
be better expreſt than by my bare words. Let this Figure C A B D
be the Profile of a Cylinder of Metal, or of Glaſs, which muſt
be made hollow within, but turned exactly round; into whoſe
Concave muſt enter a Cylinder of Wood, exquiſitely fitted to
touch every where, whoſe Profile is noted by
E G H F, which Cylinder may be thruſt up­
55[Figure 55]
wards, and downwards: and this I would
have bored in the middle, ſo that there may
a rod of Iron paſs thorow, hooked in the end
K, and the other end I, ſhall grow thicker in
faſhion of a Cone, or Top; and let the
hole made for the ſame thorow the Cylinder
of Wood be alſo cut hollow in the upper
part, like a Conical Superficies, and exactly
fitted to receive the Conick end I, of the
Iron I K, as oft as it is drawn down by the
part K. Then I put the Cylinder of Wood
E H into the Concave Cylinder A D, and
would not have it come to touch the upper­
moſt Superficies of the ſaid hollow Cylinder,
but that it ſtay two or three fingers breadth
from it: and I would have that ſpace filled with Water; which
ſhould be put therein, holding the Veſſel with the mouth C D up­
wards; and thereupon preſs down the Stopper E H, holding the
Conical part I ſomewhat diſtant from the hollow that was made
1for it in the Wood, to leave way for the Air to go out, which in
thruſting down the Stopper will iſſue out by the hole of the
Wood, which therefore ſhould be made a little wider than the
thickneſs of the Hook of Iron I K. The Air being let out, and the
Iron pull'd back, which cloſe ſtoppeth the wood with its Conick
part I, then turn the veſſel with its mouth downwards, and faſten to
the hook K a Bucket that may receive into it ſand, or other weigh­
ty matter, and you may hang ſo much weight thereat, that at length
the Superiour ſurface of the Stopper E F will ſeparate and forſake
the inferiour part of the Water; to which nothing elſe held it con­
nected but the Repugnance againſt Vacuity: afterwards weighing
the Stopper with the Iron, the Bucket, and all that was in it, you
will have the quantity of the Force of the Vacuity. And if affixing
to a Cylinder of Marble, or Chriſtal, as thick as the Cylinder of
Water, ſuch a weight, that together with the proper weight of the
Marble or Chriſtal it ſelf, equalleth the gravity of all thoſe fore­
named things, a Rupture follow thereupon; we may without
doubt affirm, that the only reaſon of Vacuity holdeth the parts of
Marble and Chriſtal conjoyned: but not ſufficing; and ſeeing
that to break it there muſt be added four times as much weight,
it muſt be confeſſed, that the Reſiſtance of Vacuity is one part of
ſive, and that the other Reſiſtance is quadruple to that of Vacuity.
How to meaſure
the Virtue of Va­
cuity in Solids di­
ſtinct from other
convenient Cauſes
of their Coherence.
Water a Continu­
ate Matter, and
void of all other a­
verſion to ſeparati­
on, ſave that of Va­
cuity.
SIMP. It cannot be denied, but that the Invention is Ingen­
ous: but I hold it to be ſubject to many difficulties, which makes
me queſtion it; for who ſhall aſſure us, that the Air cannot pene­
trate between the Glaſs, and the Stopper, though it be cloſe ſtopt
with Flax, or other pliant matter? And alſo it's a Queſtion, whe­
ther Wax or Turpentine will ſerve to make the Cone I, ſtop the
hole cloſe: Again, Why may not the parts of the Water with­
draw and rarefie themſelves? Why may not the Air, or Exhalati­
ons, or other more ſubtil Subſtances penetrate through the Poroſi­
ties of the Wood, or Glaſs it ſelf?
SALV. Simplicius is very nimble at raiſing doubts, and, in part,
helping us to reſolve them, as to the Penetration of the Air through
the Wood, or between the Wood and Glaſs. But I moreover
obſerve, that we may at the ſame time ſecure our ſelves, and with­
all acquire new Notions, if the fore-named doubts take place; for
if the Water be by Nature, howbeit with violence, capable of ex­
tention, as it falleth out in Air, you ſhall ſee the Stopper to de­
ſcend: and if in the upper part of the Glaſs we make a ſmall pro­
minent Boſs, as this V; in caſe any Air, or other more Tenuous or
Spirituous Matter ſhould penetrate thorow the Subſtance, or Poroſi­
ty of the Glaſs, or Wood, it would be ſeen to reunite (the water
giving place) in the eminence V: which things not being percei­
ved, we reſt aſſured that the Experiment was made with due
1caution: and ſee that the Water is not capable oſ extenſion, nor
the Glaſs permeable by any matter, though never ſo ſubtil.
SAGR. And I, by means of theſe Diſcourſes have found the
Cauſe of an Effect, that hath for a long time puzled my mind

with wonder, and kept it in Ignorance. I have heretofore ob­
ſerved a Ciſtern, wherein, for the drawing thence of Water, there
was made a Pump, by ſome one that thought, perhaps, (but in
vain) to be thereby able to draw, with leſs labour, the ſame, or
greater quantity of Water, than with the ordinary Buckets; and
this Pump had its Sucker and Value on high, ſo that the Water
was made to aſcend by Attraction, and not by Impulſe, as do the
Pumps that work below. This, whilſt there is any Water in the
Ciſtern to ſuch a determinate height, will draw it plentifully; but
when the Water ebbeth below a certain Mark, the Pump will
work no more. I conceited, the firſt time that I obſerved this ac­
cident, that the Engine ____ had been ſpoyled, and looking for
the Workman, that he might amend it; he told me, that there was
no defect at all, other than what was in the Water, which being
fallen too low, permitted not it ſelf to be raiſed to ſuch a height;

and farther ſaid, that neither Pump, or other Machine, that raiſeth
the water by Attraction, was poſſibly able to make it riſe a hair
more than eighteen Braces, and be the Pumps wide or narrow, this
is the utmoſt limited meaſure of their height. And I have hitherto
been ſo dull of apprehenſion, that though I knew that a Rope, a
Stick, and a Rod of Iron might be ſo and ſo lengthened, that at
laſt, holding it up on high in the Air, its own weight would break
it, yet I never remembred, that the ſame would much more eaſily
happen in a Rope, or Thread of Water. And what other is that
which is attracted in the Pump than a Cylinder of Water, which
having its contraction above, prolonged more and more, in the end
arriveth to that term, beyond which being drawn, it breaketh by
its foregoing over-weight, juſt as if it was a Rope.
The Nature of the
attraction of Wa­
ter by Pumps.
Water raiſed or at­
tracted by a Pump
riſeth not above
eleven yards.
SALV. It is even ſo as you ſay; and becauſe the ſaid height of
eighteen Braces is the prefixed term of the Elevation, to which any
quantity of Water, be it (that is to ſay, be the Pump) broad,
narrow, or even, ſo narrow as to the thickneſs of a ſtraw, can ſu­
ſtain it ſelf; when ever we weigh the water contained in eighteen
Braces of Pipe, be it broad or narrow, we have the value of Reſi­
ſtance of Vacuity in Cylinders of whatſoever ſolid matter, of the
thickneſs of the propoſed Pipes. And ſince I have ſaid ſo much,

we will ſhew, that a man may eaſily find in all Metals, Stones, Tim­
bers, Glaſſes, &c. How far one may lengthen out Cylinders,
ſtrings, or rods of any thickneſs, beyond which, being oppreſt with
their own weight, they can no longer hold, but break in pieces.
Take for example a Braſs wyer of any certain thickneſs, and length,
1and fixing one of its ends on high, add gradually more and more
weight to the other, till at laſt it break, and let the greateſt weight
that it can bear be v. gr. fifty pounds. It is manifeſt that fifty
pound of Braſs more than its own weight, which let us ſuppoſe,
for example, to be one eighth of an Ounce, drawn out into a
Wyer of the like thickneſs, would be the greateſt length of the
Wyer that could bear it ſelf. Then meaſure how long the Wyer
was which brake, and let it be for inſtance a y ard; and becauſe it
weighed one eighth of an Ounce; and poiſed, or bore it ſelf, and
fifty pounds more; which are Four Thouſand Eight Hundred
eighths of Ounces; we ſay, that all Wyers of Braſs, whatever
thickneſs they be of, can hold, at the length of Four Thouſand
Eight Hundred and one yards, and no more: and ſo, a Braſs Wyer
being able to hold to the length of 4801 yards; the Reſiſtance it
findeth dependent on Vacuity, in reſpect of the remainder, is as
much as is equivalent to the weight of a Rope of Water eighteen
Braces long, and of the ſame thickneſs with the ſaid Braſs Wyer:
and finding Braſs to be v. gr. nine times heavier than Water, in
any Wyer of Braſs, the Reſiſtance againſt Fraction dependent on
the reaſon of Vacuity, importeth as much as two Braces of the
ſame Wyer weigheth. And thus arguing, and operating, we may
find the length of the Wyers, or Threads of all Solid Matters re­
duced to the utmoſt length that they can ſubſiſt of, and alſo what
part Vacuity hath in their Reſiſtance.
To what length Cy­
linders or Ropes of
any Matter may
be prolonged, be­
yond which being
charged they break
by their own weight
SAGR. It reſteth now, that you declare to us wherein conſiſts
the remainder of that Tenacity, that is, what that Glue or Reni­
tence is, which connecteth together the parts of a Solid, beſides
that which is derived from Vacuity; becauſe I cannot imagine
what that Cement is, that cannot be burnt, or conſumed in a ve­
ry hot Furnace in two, three, or four Moneths, nor ten, nor an hun­
dred; and yet Gold, Silver, and Glaſs, ſtanding ſo long Liquiſi­
ed, when it is taken out, its parts return, upon cooling, to reunite,
and conjoyn, as before. And again, becauſe the ſame difficulty
which I meet within the Connection of the parts of the Glaſs, I
find alſo in the parts of the Cement, that is, what thing that
ſhould be which maketh them cleave ſo cloſs together.
SALV. I told you but even now, that your Genius prompted
you: I am alſo in the ſame ſtrait: and alſo whereas I have in gene­
ral told you, how that Repugnance againſt Vacuity is unqueſti­
onably that which permits not, nnleſs with great violence, the ſe­
paration of the two Plates, and moreover of the two great pieces of
the Pillar of Marble, or Braſs, I cannot ſee why it ſhould not alſo
take place, and be likewiſe the Cauſe of the Coherence of the leſ­
ſer parts, and even of the very leaſt and laſt, of the ſame Matters:

and being that of one ſole Effect, there is but one only true, and
1moſt potent Cauſe; if I can find no other Cement, why may I not
try whether this of Vacuity, which I have already found, may be
ſufficient?
There is but one
ſole Cauſe of one
ſole Effect.
SIMP. But when you have already demonſtrated the Reſi­
ſtance of the great Vacuity in the ſeparation of the two great
parts of a Solid to be very ſmall in compariſon of that which con­
necteth, and conſolidates the little Particles, or Atomes, why will
you not ſtill hold, for certain, that this is extreamly differing from
that?
SALV. To this Sagredus anſwereth, That every particular
Souldier is ſtill paid with money collected by the general Impoſi­
tions of Shillings and Pence, although a Million of Gold ſufficeth
not to pay the whole Army. And who knows, but that other ex­
ceeding ſmall Vacuities may operate amongſt thoſe ſmall Atomes,
(even like as that was of the ſelf-ſame money) wherewith all
the parts are connected? I will tell you what I have ſometimes
fancied: and I give it you, not as an unqueſtionable Truth, but as a
kind of Conjecture very undigeſted, ſubmitting it to exacter con­
ſiderations: Pick out of it what pleaſeth you, and judge of the reſt

as you think fit. Conſidering ſometimes how the Fire, penetra­
ting and inſinuating between the ſmall Atomes of this or that Me­
tal, which were before ſo cloſely conſolidated, in the end ſepa­
rates, and diſunites them; and how, the Fire being gone, they re­
turn with the ſame Tenacity as before to Conſolidation, without
diminiſhing in quantity, (at all in Gold, and very little in other
Metals,) though they continue a long time melted; I have thought
that that might happen, by reaſon the extream ſmall parts of the
Fire, penetrating through the narrow pores of the Metal (through
which the leaſt parts of Air, or of many other Fluids, could not
for their cloſeneſs perforate) by repleating the ſmall interpoſing
Vacuities might free the minute parts of the ſame from the vio­
lence, wherewith the ſaid Vacuities attract them one to another,
prohibiting their ſeparation: and thus becoming able to move
freely, their Maſs might become fluid, and continue ſuch, as long
as the ſmall parts of the Fire ſhould abide betwixt them: and that
thoſe departing, and leaving the former Vacuities, their wonted
attractions might return, and conſequently the Coheſion of the
parts. And, as to the Allegation made by Simplicius, it may, in
my opinion, be thus reſolved; That although ſuch Vacuities ſhould
be very ſmall, and conſequently each of them eaſie to be over­
come, yet nevertheleſs their innumerable multitude innumerably

(if it be proper ſo to ſpeak) multiplieth the Reſiſtances: and we
have an evident proof what, and how great is the Force that reſul­
teth from the conjunction of an immenſe number of very weak
Moments, in ſeeing a Weight of many thouſands of pounds, held
1by mighty Cables, to yield, and ſuffer it ſelf at laſt to be over­
come by the aſſault of the innumerable Atomes of Water; which,
either carryed by the South-wind, or elſe by being diſtended into
very thin Miſts that move to and fro in the Air, inſinuate them­
ſelves between ſtring and ſtring of the Hemp of the hardeſt twi­
ſted Cables; nor can the immenſe force of the pendent Weight
prohibit their enterance; ſo that perforating the ſtrict paſſages be­
tween the Pores, they ſwell the Ropes, and by conſequence ſhor­
ten them, whereupon that huge Maſs is forcibly raiſed.
Moſt ſmall Va­
cuities diſſemina­
ted and interpoſed
between the ſmall
Corpuſcles of So­
lids the probable
cauſe of the conſi­
ſtence or connecti­
on of thoſe Corpuſ­
cles to one another,
Innumerable A­
tomes of Water in­
ſinuating into Ca­
bles draw and raiſe
an immenſe weight
SAGR. There's no doubt but that ſo long as a Reſiſtance is not

infinite, it may by a multitude of moſt minute Forces be over­
come; inſomuch that a competent number even of Ants would
be able to carry to ſhore a whole ſhips lading of Corn: for Senſe
giveth us quotidian examples, that an Ant carrieth a ſingle grain
with eaſe; and its cleer, that in the Ship there are not infinite
grains, but that they are compriſed in a certain number; and if you
take another number four or ſix times bigger than that, and take
alſo another of Ants equal to it, and ſet them to work, they ſhall
carry the Corn, and the Ship alſo. It is true indeed, that it will be
needful that the number be great, as alſo in my judgment that of
the Vacuities, which hold together the ſinall parts of the
Mettal.
Any finite Reſi­
ſtance is ſuperable
by any the leaſt
Force, multiplied.
SALV. But though they were required to be infinite, do you
think it impoſſible?
SAGR. Not if the Mettal were of an infinite maſſe; other­
wiſe ----
SALV. Otherwiſe what? Go to, feeing we are faln upon
Paradoxes, let us ſee if we can any way demonſtrate, how that
in a continuate finite extenſion, it is not impoſſible to finde infi­
nite Vacuities: and then, if we gain nothing elſe, yet at leaſt we

ſhall finde a ſolution of that moſt admirable Problem propound­
ed by Ariſtotle amongſt thoſe which he himſelf calleth admirable,
I mean amongſt his Mechanical Queſtions; and the Solution may
haply be no leſſe plain and concluding, than that which he himſelf
brings thereupon, and different alſo from that which Learned

Monſig. di Guevara very acutely diſcuſſeth. But it is firſt requiſite
to declare a Propoſition not toucht by others, on which the ſolution
of the queſtion dependeth, which afterwards, if I deceive not my
ſelf, will draw along with it other new and admirable Notions; for
underſtanding whereof the more exactly, we will give it you in
a Scheme: We ſuppoſe, therefore an equilateral, and equian­
gled Poligon of any number of Sides at pleaſure, deſcribed
about this Center G; and in this example let it be a Hexagon
A B C D E F; like to which, and concentrick with the ſame
muſt be diſtributed another leſſer, which we mark H I K L M N;
1and let one Side of the greater A B be prolonged indeterminately
towards S, and of the leſſe the correſpondent Side H I is to be
produced in like manner towards the ſame part, repreſenting the
Line H T, parallel to A S; and let another paſſe by the Center
equidiſtant from the former, namely G V. This done, we ſuppoſe
the greater Poligon to turn about upon the Line A S, carrying
with it the other leſſer Poligon. It is manifeſt, that the point B,
the term of the Side A B, ſtanding ſtill, whilſt the Revolution
begins, the angle A riſeth, and the point C deſcendeth, deſcribing
the arch C que ſo that the Side B C is applyed to the line B Q,
equal to it ſelf: but in ſuch converſion the angle I of the leſſer
Poligon riſeth above the Line I T. for that I B is oblique upon
A S: nor will the point I fall upon the parallel I T, before the
point C come to Q: and by that time I ſhall be deſcended unto
O after it had deſcribed the Arch I O, without the Line H T: and
at the ſame time the Side I K ſhall have paſs'd to O P. But the Cen­
ter G ſhall have gone all this time out of the Line G V, on which it
ſhal not fall, until it ſhall firſt have deſcribed the Arch G C. Having
made this firſt ſtep, the greater Poligon ſhall be tranſpoſed to reſt
with the Side B C upon the Line B que the Side I K of the leſſer
upon the Line O P, having skipt all the Line I O without touching
56[Figure 56]
it; and the Center G ſhall be removed to C, making its whole
courſe without the Parallel G V: And in fine all the Figure ſhall
be remitted into a Poſition like the firſt; ſo that the Revolution
being continued, and coming to the ſecond ſtep, the Side of the
greater Poligon D C ſhall remove to Q X; K L of the leſſer (ha­
ving firſt skipt the Arch P Y) ſhall fall upon Y Z, and the Center
proceeding evermore without G V ſhall fall on it in R, after the
great skip C R. And in the laſt place, having finiſhed an entire
Converſion, the greater Poligon will have impreſſed upon A S, ſix
1Lines equal to its Perimeter without any interpoſitions or skips:
the leſſer Poligon likewiſe ſhall have traced ſix Lines equal to its
Perimeter, but diſcontinued by the interpoſition of five Arches,
under which are the Chords, parts of the parallel H T not toucht
by the Poligon: And laſtly, the Center G never hath toucht the
Parallel G V except in ſix points. From hence you may compre­
hend, how that the Space paſſed by the leſſer Poligon, is almoſt
equal to that paſſed by the greater, that is the Line H T is almoſt
equal to A S, then which it is leſſer only the quantity of one of
theſe Arches, taking the Line H T, together with all its Arches.
Now, this which I have declared and explained to you in the exam­
ple of theſe Hexagons, I would have you underſtand to hold true
in all other Poligons, of what number of Sides ſoever they be, ſo
that they be like Concentrick, and Conjoyned; and that at the
Converſion of the greater, the other, how much ſoever leſſer, be
ſuppoſed to revolve therewith: that is, you muſt underſtand, I ſay,
that the Lines by them paſſed are very near equal, computing in­
to the Space paſt by the leſſer, the Intervals under the little Ar­
ches not toucht by any part of the Perimeter of the ſaid leſſer Po­
ligon. Let therefore the greater Poligon, of a thouſand Sides, paſs
round, and meaſure out a continued Line equal to its Perimeter;
and in the ſame time the leſs paſſeth a Line almoſt as long, but
compounded of a thouſand Particles equal to its thouſand Sides,
but diſcontinued with the interpoſition of a thouſand void Spaces:
for ſuch may we call them, in relation to the thouſand little Lines
toucht by the Sides of the Poligon. And what hath been ſpoken
hitherto admits of no doubt or ſcruple. But tell me, in caſe that
about a Center, as ſuppoſe the point A, (in the former Scheme)
we ſhould deſcribe two Circles concentrick, and united together;
and that from the points C and B of their Semi-Diameters, there
be drawn the Tangents C E, and B F, and by the Center A the Pa­
rallel A D; ſuppoſing the greater Circle to be turned upon the
Line B F, (drawn equal to its Circumference, as likewiſe the other
two C E, and A D;) when it hath compleated one Revolution,
what ſhall the leſſer Circle, and Center have done? The Center
ſhall doubtleſs have run over, and touched the whole Line A D,
and the leſs Circumference ſhall with its touches have meaſured
all C E, doing the ſame as did the Poligons above; and different
only in this, that the Line H T was not touched in all its Parts by
the Perimeter of the leſſer Poligon, but there were as many parts
left untoucht with the interpoſition of ſalts, or skipped ſpaces; as
were theſe parts touched by the Sides: but here in the Circles,
the Circumference of the leſſer Circle, never ſeparates from the
Line C E, ſo as to leave any of its parts untou cht; nor is the parts
touching of the Circumference, leſs than the part toucht of the
1Right-line. Now how is it poſſible that the leſſer Circle ſhould
without skips run a Line ſo much bigger than its Circumfe­
rence?
Ariſtotles admi­
rable Problem of
two Concentrick
Circles that turn
round, and its true
reſolution.
Monſig. Gueva
ra honourably men­
tioned.
SAGR. I was conſidering whether one might not ſay, that like
as the Center of the Circle trailed alone upon A D toucht, it all
being yet but one ſole Point; ſo likewiſe might the Points of the
leſſer Circumference, drawn by the revolution of the greater, go
gliding along ſome ſmall part of the Line C E.
SALV. This cannot be, for two reaſons; firſt, becauſe there is
no reaſon why ſome of the touches like to C ſhould go gliding
along ſome part of the Line C E, more than others: and though
there ſhould; ſuch touches being (becauſe they are points) inſi­
nite, the glidings along upon C E would be infinite; and ſo being,
they would make an infinite Line, but the Line C E is finite. The
other reaſon is, that the greater Circle, in its Revolution continu­
ally changing contact, the leſſer Circle muſt of neceſſity do the
like; there being no other Point but B, by which a Right Line can
be drawn to the Center A, and paſſing through C; ſo that the
greater Circumference changing Contact, the leſs doth change it
alſo; nor doth any Point of the leſs touch more than one Point of
its Right-Line C E: beſides, that alſo in the converſion of the Po­
ligons, no Point of the Perimeter of the leſs falls on more than one
Point of the Line, which was by the ſaid Perimeter traced, as may
be eaſily underſtood, conſidering the Line I K is parallel to B C,
whereupon, till juſt that B C fall on B R, I K continueth elevated
above I P, and toucheth it not before B C is on the very Point of
uniting with B Q, and then all in the ſame inſtant I K uniteth
with O P, and afterwards immediately riſeth above it again.
SAGR. The buſineſs is really very intricate, nor can I think on
any Solution of it, therefore do you explain it to us as far as you
judge needful.
SALV. I ſhould, for the evincing hereof, have recourſe to the
conſideration of the fore-deſcribed Poligons, the effect of which is
intelligible and already comprehended, and would ſay, that like as
in the Poligons of an hundred thouſand Sides, the Line paſſed and
meaſured by the Perimeter of the greater, that is by its hundred
thouſand Sides continually diſtended, is not conſiderably bigger
than that meaſured by the hundred thouſand Sides of the leſs, but
with the interpoſition of an hundred thouſand void ſpaces interve­
ning; fo I would ſay in the Circles (which are Poligons of innu­
merable Sides) that the Line meaſured by the infinite Sides of the
great Circle, lying continued one with another, to be equalled in
length by the Line traced by the infinite Sides of the leſs, but by
theſe including the interpoſition of the like number of intervening
Spaces: and like as the Sides are not quantitative, but yet infinite
1in number, ſo the interpoſing Vacuitics are not quantitative, but
infinite in number; that is, thoſe are infinite Points all filled, and
theſe are infinite points, part filled, and part empty. And here I
would have you note, that reſolving, and dividing a Line into quan­
titative parts, and conſequently of a finite number, it is not poſſible
to diſpoſe them into a greater extention than that which they poſ­
ſeſt whilſt they were continued, and connected, without the inter­
poſition of a like number of void Spaces; but imagining it to be
reſolved into parts not quantitative, namely, into its infinite indivi­
ſibles, we may conceive it produced to immenſity without the in­
terpoſition of quantitative void ſpaces, but yet of infinite indiviſi­
ble Vacuities. And this which is ſpoken of ſimple lines, ſhould alſo
be underſtood of Superficies, and Solid Bodies, conſidering that they
are compoſed of infinite Atomes not non-quantitative; if we would
divide them into certain quantitative parts, there's no queſtion, but
that we cannot diſpoſe them into Spaces more ample than the Solid
before occupied, unleſs with the interpoſition of a certain number
of quantitative void Spaces; void, I ſay, at leaſt of the matter of the
Solid: but if we ſhould propoſe the higheſt, and ultimate reſolution
made into the firſt, non-quantitative, but infinite firſt compoun­
ding parts, we may be able to conceive ſuch compounding parts
extended unto an immenſe Space without the interpoſition of
quantitative void Spaces; but only of infinite non-quantitative Va­
cuities: and in this manner a man may draw out, v. gr. a little Ball
of Gold into a very vaſt expanſion without admitting any quan­
titative void Spaces; yet nevertheleſs we may admit the Gold to
be compounded of infinite induciſſible ones.
SIMP. Me thinks that in this point you go the way of thoſe diſ­
ſeminated Vacuities of a certain Ancient Philoſopher ------
SALV. But you add not: [who denied Divine Providence:)
as on ſuch another occaſion, ſufficiently beſides his purpoſe, a cer­
tain Antagoniſt of our Accademick did ſubjoyn.
SIMP. I ſee very well, and not without indignation, the malice
of ſuch contradictors; but I ſhall forbear theſe Cenſures, not only
upon the ſcore of Good-Manners, but becauſe I know how diſa­
greeing ſuch Tenets are to the well-tempered, and well-diſpoſed
mind of a perſon, ſo Religious and Pious, yea, Orthodox and Ho­
ly, as you, Sir. But returning to my purpoſe; I find many ſcruples
to ariſe in my mind about your laſt Diſcourſe, which I know not
how to reſolve. And this preſents its ſelf for one, that if the Cir­
cumferences of two Circles are equall to the two Right Lines
C E, and B F, this taken continually, and that, with the interpoſi­
tion of infinite void Points; how can A D, deſcribed by the Center,
which is but one ſole Point, be ſaid to be equal to the ſame, it con­
taining infinite of them? Again, that ſame compoſing the Line of
1Points, the diviſible of indiviſibles, the quantitative of non-quan­
titative, is a rock very hard, in my judgment, to paſs over: And
the very admitting of Vacuity, ſo thorowly confuted by Ariſtotle,
no leſs puzleth me than thoſe difficulties themſelves.
SALV. There be, indeed, theſe and other difficulties; but re­
member, that we are amongſt Infinites, and Indiviſibles: thoſe in­
comprehenſible by our finite underſtanding for their Grandure;
and theſe for their minuteneſs: nevertheleſs we ſee that Humane
Diſcourſe will not be beat off from ruminating upon them, in
which regard, I alſo aſſuming ſome liberty, will produce ſome of
my conceits, if not neceſſarily concluding, yet for novelty ſake,
which is ever the meſſenger of ſome wonder: but perhaps the car­
rying you ſo far out of your way begun, may ſeem to you imper­
tinent, and conſequently little pleaſing.
SAGR. Pray you let us enjoy the benefit, and priviledge, of free
ſpeaking which is allowed to the living, and amongſt friends; eſpe­
cially, in things arbitrary, and not neceſſary; different from Diſcourſe
with dead Books, which ſtart us a thouſand doubts, and reſolve not
one of them. Make us therefore partakers of thoſe Conſiderations,
which the courſe of our Conferences ſuggeſt unto you; for we
want no time, ſeeing we are diſengaged from urgent buſineſſes, to
continue and diſcuſſe the other things mentioned; and particular­
ly, the doubts, hinted by Simplicius, muſt by no means eſcape us.
SAIV. It ſhall be ſo, ſince it pleaſeth you: and beginning at
the firſt, which was, how it's poſſible to imagine that a ſingle Point
is equal to a Line; in regard I can do no more for the preſent, I
will attempt to ſatisfie, or, at leaſt, qualifie one improbability with
another like it, or greater; as ſome times a Wonder is ſwallowed
up in a Miracle. And this ſhall be by ſhewing you two equal Su­
perficies, and at the ſame time two Bodies, likewiſe equal, and
placed upon thoſe Superficies as their Baſes; and that go (both
theſe and thoſe) continually and equally diminiſhing in the ſelf­

ſame time, and that in their remainders reſt alwaies equal between
themſelves, and (laſtly) that, as well Superſicies, as Solids, deter­
mine their perpetual precedent equalities, one of the Solids with
one of the Superficies in a very long Line; and the other Solid
with the other Superficies in a ſingle Point: that is, the latter in
one Point alone, the other in infinite.
The equal Super­
ficies of two Solids
continually ſub­
ſtracting from
them both equal
parts, are reduced,
the one into the
Circumference of a
Circle, and the o­
ther into a Point.
SAGR. An admirable propoſal, really, yet let us hear you ex­
plain and demonſtrate it.
SALV. It is neceſſary to give you it in Figure, becauſe the proof
is purely Geometrical. Therefore ſuppoſe the Semicircle A F B,
and its Center to be C, and about it deſcribe the Rectangle
A D E B, and from the Center unto the Points D and E let there
be drawn the Lines C D, and C E; Then drawing the Semi-Dia­
1meter C F, perpendicular to one of the two Lines A B, or D E
and immoveable; we ſuppoſe all this Figure to turn round about
that Perpendicular: It is manifeſt, that there will be deſcribed by
the Parallelogram A D E B, a Cylinder; by the Semi-circle A F B,
an Hemi-Sphære; and by the Triangle C D E a Cone. This pre­
ſuppoſed, I would have you imagine the Hemiſphære to be taken
away, leaving behind the Cone, and that which ſhall remain of
the Cylinder; which for the Figure, which it ſhall retain like to a
Diſh, we will hereafter call a Diſh: touching which, and the
Cone, we will ſirſt demonſtrate that they are equal; and next
a Plain being drawn parallel to the Circle, which is the foot or
Baſe of the Diſh, whoſe Diameter is the Line D E, and its Center
F; we will demonſtrate, that ſhould the ſaid Plain paſs, v. gr. by
the Line G H, cutting the Diſh in the points G I, and O N; and
the Cone in the points H and L; it would cut the part of the
Cone C H L, equal alwaies to the part of the Diſh, whoſe Profile
is repreſented to us by the Triangles G A I, and B O N: and more­
over we will prove the Baſe alſo of the ſame Cone, (that is the
Circle, whoſe Diameter is H L) to be equal to that circular Su­
perficies, which is Baſe of the part of the Diſh; which is, as we
may ſay, a Rimme as broad as G I; (note here by the way what
Mathematical Definitions are: they be an impoſition of names, or,
we may ſay, abreviations of ſpeech, ordain'd and introduced to
prevent the trouble and pains, which you and I meet with, at pre­
ſent, in that we have not agreed together to call v. gr. this Super­
ficies a circular Rimme, and that very ſharp Solid of the Diſh a
round Razor:) now howſoever you pleaſe to call them, it ſufficeth
you to know, that the Plain produced to any diſtance at pleaſure,
ſo that it be parallel to the Baſe, viz. to the Circle whoſe Diame­
ter D E cuts alwaies the two Solids, namely, the part of the Cone
C H L, and the upper part of the Diſh equal to one another: and
likewiſe the two Superficies, Baſis of the ſaid Solids, viz. the ſaid
Rimme, and the Circle H L, equal alſo to one another. Whence
followeth the forementioned Wonder; namely, that if we ſhould
ſuppoſe the cutting-plain to be
ſucceſſively raiſed towards the
57[Figure 57]
Line A B, the parts of the Solid
cut are alwaies equall, as alſo the
Superficies, that are their Baſes,
are evermore equal; and, in
fine, raiſing the ſaid Plain higher
and higher, the two Solids (ever
equal) as alſo their Baſes, (Su­
perficies ever equal) ſhall one couple of them terminate in a Cir­
cumference of a Circle, and the other couple in one ſole point;
1for ſuch are the upper Verge or Rim of the Diſh, and the Vertex
of the Cone. Now whilſt that in the diminution of the two So­
lids, they till the very laſt maintain their equality to one another, it
is, in my thoughts, proper to ſay, that the higheſt and ultimate terms
of ſuch Diminutions are equal, and not one infinitely bigger than
the other. It ſeemeth therefore, that the Circumference of an im­
menſe Circle may be ſaid to be equal to one ſingle point; and
this that befalls in Solids, holdeth likewiſe in the Superficies their
Baſes; that they alſo in the common Diminution conſerving al­
waies equality, in fine, determine at the inſtant of their ultimate
Diminution the one, (that is, that of the Diſh) in their Circum­
ference of a Circle, the other (to wit, that of the Cone) in one
ſole point. And why may not theſe be called equal, if they be the
laſt remainders, and footſteps left by equal Magnitudes? And note
again, that were ſuch Veſſels capable of the immenſe Cœleſtial
Hemiſpheres: both their upper Rims, and the points of the contai­
ned Cones (keeping evermore equally to one another) would fi­
nally determine, thoſe, in Circumferences equal to thoſe of the
greateſt Circles of the Cœleſtial Orbes, and theſe in ſimplo points.
Whence, according to that which ſuch Speculations perſwade us
to, all Circumferences of Circles, how unequal ſoever, may be
ſaid to be equal to one another, and each of them equal to one ſole
point.
SAGR. The Speculation is, in my eſteem, ſo quaint and curi­
ous, that, for my part, though I could, yet would I not oppoſe it,
for I take it for a piece of Sacriledge to deface ſo fine a Structure,
by ſpurning at it with any pedantick contradiction; yet for our en­
tire ſatisfaction, give us the proof (which you ſay is Geometrical)
of the equality alwaies retained between thoſe Solids, and thoſe
their Baſes, which I think muſt needs be very ſubtil, the philoſo­
phical Contemplation being ſo nice, which depends on the ſaid
Concluſion.
SALV. The Demonſtration is but ſhort, and eaſie. Let us keep
to the former Figure, in which the Angle I P C being a Right An­
gle, the Square of the Semi-Diameter I C is equal to the two
Squares of the Sides I P, and P C. But the Semi-Diameter I C, is
equal to A C, and this to G P; and C P is equal to P H; therefore
the Square of the Line G P is equal to the two Squares of I P, and
P H, and the Quadruple to the Quadruples; that is, the Quadrate
of the Diameter G N is equal to the two Quadrates I O, and H L:
and becauſe Circles are to each other, as the Squares of their Dia­
meters; the Circle whoſe Diameter is G N, ſhall be equall to the
two Circles whoſe Diameters are I O, and H L; and taking away
the Common Circle, whoſe Diameter is I O; the reſidue of the
Circle G N ſhall be equal to the Circle, whoſe Diameter is H L.
1And this is as to the firſt part: Now as for the other part, we will,
for the preſent, omit its Demonſtration, as well becauſe that if you
would ſee it, you ſhall find it in the twelfth Propoſition of the Se­

cond Book De centro Gravitatis Solidorum, publiſhed by Signeur
Lucas Valerius, the new Archimedes of our Age; who upon ano­
ther occaſion hath made uſe of it; as becauſe in our caſe it ſuffi­
ceth to have ſeen, how the Superficies, already explained, are ever­
more equal; and that alwaies diminiſhing equally, they in the end
determine, one in a ſingle point, and the other in the Circumfe­
rence of a Circle, be it never-ſomuch bigger, for in this lyeth our
Wonder.
Lucas Valerius,
the other Archi­
chimedes of our
Age, hath written
admirably, De
Centro Gravita­
tis Solidorum.
SAGR. The Demonſtration is as ingenious, as the reflection
grounded upon it is admirable. Now let us hear ſomewhat about
the other Doubt ſuggeſted by Simplicius, if you have any particu­
lars worth note to hint thereupon, but I ſhould incline to think it
impoſſible to be, in regard it is a Controverſie that hath been ſo
canvaſſed.
SALV. You ſhall have ſome of my particular thoughts thereon;
firſt repeating what but even now I told you, namely, that Infini­
ty alone, as alſo Indiviſibility, are things incompre henſible to us:
now think how they will be conjoyned together: and yet if you
would compound the Line of indiviſible points, you muſt make
them infinite; and thus it will be requiſite to apprehend in the
ſame inſtant both Infinite, and Indiviſible. The things that ar ſe­
veral times have come into my mind, on this occaſion, are many;
part whereof, and the more conſiderable, it may be, I cannot upon
ſuch a ſudden remember; but it may happen, that in the ſequal
of the Diſcourſe, coming to put queſtions and doubts to you, and
particularly to Simplicius, they may, on the other ſide, re-mind
me of that, which without ſuch excitement would have lain dor­
mant in my Fancy: and therefore, with my wonted freedom, per­
mit me that I produce any wild conjectures, for ſuch may we fitly
call them in compariſon of ſupernatural Doctrines, the only true
and certain determiners of our Controverſies, and unerring guides
in our obſcure, and dubious paths, or rather Laberinths.
Amongſt the firſt Inſtances that are wont to be produced

againſt thoſe that compound Continuum of Indiviſibles, this is uſu­
ally one; That an Indiviſible, added to another Indiviſible, produ­
ceth not a thing diviſible; for if that were ſo, it would follow, that
even the Indiviſibles were diviſible: for if two Indiviſibles, as for
example, two Points conjoyned, ſhould make a Quantity that
ſhould be a diviſible Line, much more ſuch ſhould one be that is
compounded of three, five, ſeven, or others, that are odd num­
bers; the which Lines, being to be cut in two equal parts, render
diviſible that Indiviſible which was placed in the middle. In this
1and other Objections of this kind you may ſatisfie the propoſer of
them, telling him, that neither two Indiviſibles, nor ten, nor an
hundred, no, nor a thouſand can compound a Magnitude diviſible,
and quantitative, but being infinite they may.
Continuum com­
pounded of Indivi­
ſibles.
SIMP. Here already riſeth a doubt, which I think unreſolvable;
and it is, that we being certain to find Lines one bigger than ano­
ther, although both contain infinite Points, we muſt of neceſſity
confeſs, that we have found in the ſame Species a thing bigger than
infinite; becauſe the Infinity of the Points of the greater Line, ſhall
exceed the Infinity of the Points of the leſſer. Now this aſſigning
of an Infinite bigger than an Infinite is, in my opinion, a conceit
that can never by any means be apprehended.
SALV. Theſe are ſome of thoſe difficulties, which reſult from
the Diſcourſes that our finite Judgments make about Infinites, gi­
ving them thoſe attributes which we give to things finite and ter­
minate; which I think is inconvenient; for I judge that theſe
terms of Majority, Minority, and Equality ſute not with Infinites,
of which we cannot ſay that one is greater, or leſs, or equal to ano­
ther: for proof of which there cometh to my mind a Diſcourſe,
which, the better to explain, I will propound by way of Interroga­
tories to Simplicius that ſtarted the queſtion.
I ſuppoſe that you very well underſtand which are Square Num­
bers, and which not Square.
SIMP. I know very well, that the Square Number is that which
proceeds from the multiplication of another Number into it ſelf;
and ſo four, and nine, are Square Numbers, that ariſing from two,
and this from three multiplied into themſelves.
SALV. Very well; And you know alſo, that as the Products are
called Squares: the Produſors, that is, thoſe that are multiplied, are
called Sides, or Roots; and the others, which proceed not from
Numbers multiplied into themſelves, are not Squares. So that if I
ſhould ſay, all Numbers comprehending the Square, and the not
Square Numbers, are more than the Square alone, I ſhould ſpeak a
moſt unqueſtionable truth: Is it not ſo?
SIMP. It cannot be denied.
SALV. Farther queſtioning, if I ask you how many are the
Numbers Square, you can anſwer me truly, that they be as many,
as are their propper Roots; ſince every Square hath its Root, and
every Root its Square, nor hath any Square more than one ſole
Root, or any Root more than one ſole Square.
SIMP. True.
An Infinite Num­
ber, as it contains
infinite Square
and Cupe Roots, ſo
it conta neth infi­
nite Square and
Cube Numbers.
SALV. But if I ſhall demand how many Roots there be, you
cannot deny but that they be as many as all Numbers, ſince there
is no Number that is not the Root of ſome Square: And this be­
ing granted, it is requiſite to affirm, that Square Numbers are as
1many as their Roots, and Roots are all Numbers: and yet in the
beginning we ſaid, that all Numbers are far more than all Squares,
the greater part not being Squares: and yet nevertheleſs the num­
ber of the Squares goeth diminiſhing alwaies with greater propor­
tion, by how much the greater number it riſeth to; for in an hun­
dred there are ten Squares, which is as much as to ſay, the tenth
part are Squares: in ten thouſand only the hundredth part are
Squares: in a Million only the thouſandth, and yet in an Infinite
Number, if we are able to comprehend it, we may ſay the Squares
are as many, as all Numbers put together.
SAGR. What is to be reſolved then on this occaſion?
SALV. I ſee no other deciſion that it may admit, but to ſay,
that all Numbers are infinite, Squares are infinite, their Roots are
infinite; and that neither is the multitude of Squares leſs than all
Numbers, nor this greater than that: and in concluſion, that the
Attributes of Equality, Majority, and Minority, have no place
in Infinites, but only in terminate quantities. And therefore when
Simplicius propoundeth to me many unequal Lines, and demand­
eth of me, how it can be, that in the greater there are no more
Points than in the leſs: I anſwer him, That there are neither more,
nor leſs, nor juſt ſo many; but in each of them infinite. Or if I
had anſwered him, that the Points in one, are as many as there are
Square Numbers; in another bigger, as many as all Numbers; in
a leſs, as many as the Cubick Numbers, might not I have given ſa­
tisfaction, by aſſigning more to one, than to another, and yet to
every one infinite? And thus much as to the firſt difficulty.
SAGR. Hold, I pray you, and give me leave to add unto what hath
been ſpoken hitherto, a thought which I juſt now light on, and it
is this, that granting what hath been ſaid, me-thinks, that not on­
ly it's improper to ſay, one Infinite is greater than another Infinite,
but alſo, that it's greater than a Finite; for if an Infinite Number
were greater, v. gr. than a Million; it would thereupon follow,
that paſſing from the Million to others, and ſo to others continual­
ly greater, one ſhould paſs on towards Infinity; which is not ſo: but
on the contrary, to how much the greater Numbers we go, ſo
much the more we depart from Infinite Number; becauſe in Num­
bers, the greater you take, ſo much the rarer and rarer alwaies are
Square Numbers contained in them; but in Infinite Number the
Squares can be no leſs than all Numbers, as but juſt now was con­
cluded: therefore the going towards Numbers alwaies greater, and
greater, is a departing farther from Infinite Number.
SALV. And ſo by your ingenious Diſcourſe we may conclude,
that the Attributes of Greater, Leſſer, or Equal, have no place,
not only amongſt Infinites; but alſo betwixt Infinites, and Fi­
nites.
1
I paſs now to another Conſideration; and it is, that in regard
that the Line, and every continued quantity are divideable conti­
nually into diviſibles, I ſee not how we can avoid granting that the
compoſition is of infinite Indiviſibles: becauſe a diviſion and ſub­
diviſion that may be proſecuted perpetually ſuppoſeth that the
parts are infinite; for otherwiſe the ſubdiviſion would be termina­
ble: and the parts being Infinite, it followeth of conſequence
that they be non-quantitative; for infinite quantitative parts make
an infinite extenſion: and thus we have a Continuum compoun­
ded of infinite Indiviſibles.
SIMP. But if we may continually proſecute the diviſion in
quantitative parts, what need have we, for ſuch reſpect, to intro­
duce the non-quantitative?
SALV. The very poſſibility of perpetually proſecuting the di­
viſion in quantitative parts induceth the neceſſity of the compoſiti­
on of infinite non-quantitative. Therefore, coming cloſer to you,
I demand you to tell me reſolutely, whether the quantitative parts
in Continuum be in your judgment finite or infinite?
SIMP. I reply, that they are both Infinite, and Finite; Infinite
in Power, and Finite in Act. Infinite in Power, that is, before the
Diviſion; but Finite in Act, that is, after they are divided: for the
parts are not actually underſtood to be in the whole, till it is di­
vided, or at leaſt marked; otherwiſe we ſay that they are in
Power.
SALV. So that a Line v. gr. twenty foot long, is not ſaid to
contain twenty Lines of one foot a piece, actually, but only after
it is divided into twenty equal parts: but is till then ſaid to contain
them only in power. Now be it as you pleaſe; and tell me whe­
ther, when the actual Diviſion of ſuch parts is made, that firſt
whole encreaſeth or diminiſheth, or elſe continueth of the ſame
bigneſs?
SIMP. It neither encreaſeth, nor diminiſheth.
SALV. So I think alſo. Therefore the quantitative parts in Con­
tinuum quantity, be they in Act, or be they in Power, make not its
quantity bigger or leſſer: but it is very plain that theſe quantita­
tive parts, actually contained in their whole, if they be infinite,
make it an infinite Magnitude; therefore quantitative parts,
though infinite only in power, cannot be contained, but only in an
infinite Magnitude: therefore in a finite Magnitude infinite quan­
titative parts can be contained neither in Act, nor Power.
SAGR. How then can it be true, that the Continuum may be
inceſſantly divided into parts ſtill capable of new diviſions?
SALV. It ſeems that that diſtinction of Power, and Act, makes
that feaſible one way, which another way would be impoſſible.
But I will ſee to adjuſt theſe matters by making another account:
1And to the Queſtion, which was put, Whether the quantitative
parts in a terminated Continuum be finite or infinite; I will anſwer
directly contrary to that which Simplicius replied, namely, that
they be neither finite, nor infinite.
SIMP. I ſhould never have found ſuch an anſwer, not imagi­
ning that there was any mean term between finite and infinite;
ſo that the diviſion or diſtinction which makes a thing to be either
Finite, or Infinite, is imperfect and deficient.
SALV. In my opinion it is; and ſpeaking of ^{*} Diſcrete Quan­

tities, me thinks that there is a third mean term between Finite and
Infinite, which is that which anſwereth to every aſſigned Number:
So that being demanded in our preſent caſe, Whether the quanti­
tative parts in Continuum be Finite, or Infinite, the moſt congru­
ous reply is to ſay, that they are neither Finite, nor Infinite, but ſo
many, as that they Anſwer to any number aſſigned: the which to
do, it is neceſſary that they be not comprehended in a limited
Number, for then they would not anſwer to a greater: nor, again,
is it neceſſary, that they be infinite, for no aſſigned Number is infi­
nite. And thus at the pleaſure of the Demander, a Line being
propounded, we may be able to aſſign in it an hundred quantita­
tive parts, or a thouſand, or an hundred thouſand, according to
the number which he beſt likes; ſo that it be not divided into in­
finite. I grant therefore to the Philoſophers, that Continuum con­
taineth as many quantitative parts as they pleaſe, and grant them
that it containeth the ſame either in Act, or in Power, which they
beſt like: but this I add again, that in like manner, as in a Line of
ten yards, there are contained ten Lines of one yard a piece, and
thirty Lines of a foot a piece, and three hundred and ſixty Lines
of an inch a piece, ſo it contains infinite Points; denominate them
in Act, or in Power, as you will: and I remit my ſelf in this matter
to your opinion and judgment, Simplicius.
Quantitative parts
in Diſcrete Quan­
tity are neither fi­
nite nor infinite,
but anſwerable to
every given Num­
ber.
SIMP. I cannot but commend your Diſcourſe: but am great­
ly afraid, that this parity of the Points, being contained in the like
manner as the quantitative parts, will not agree with abſolute ex­
actneſs; nor ſhall it be ſo eaſie a matter for you to divide the gi­
ven Line into infinite Points, as for thoſe Philoſophers to divide it
into ten yards, or thirty feet, nay, I hold it wholly impoſſible to
effect ſuch a diviſion: ſo that this will be one of thoſe Powers that
are never reduced to Act.
SALV. The trouble, pains, and long time without which a
thing is not feaſible, render it not impoſſible; for I think alſo, that
you cannot ſo eaſily effect a diviſion to be made of a Line into a
thouſand parts; and much leſs being to divide it into 937, or ſome
other great Prime Number. But if I diſpatch this, which you, it may
be, judge an impoſſible diviſion, in as ſhort a time, as another
1would require to divide it into forty, you will be content more
willingly to admit of it in our future Diſcourſe?
SIMP. I am pleaſed with your way of arguing, as you now do
mix it with ſome pleaſantneſs: and to your queſtion I reply, that
the facility would ſeem more than ſufficient, if the reſolving it into
Points were but as eaſie, as to divide it into a thouſand parts.
SALV. Here I will tell you a thing, which haply will make you
wonder in this matter of going about, or being able to reſolve the
Line into its Infinites, keeping that order which others obſerve in
dividing it into forty, ſixty, or an hundred parts; namely, by di­
viding it firſt into two, then into four: in which order he that
ſhould think to find its infinite Points would groſly delude himſelf;
for by that progreſſion, though continued to eternity, he ſhould
never arrive to the diviſion of all its quantitative parts: yea, he is
in that way ſo far from being able to arrive at the intended term
of Indiviſibility, that he rather goeth farther from it; and whilſt
he thinks by continuing the diviſion, and multiplying the multi­
tudes of the parts, to approach to Infinite, I am of opinion, that he
more and more removes from it: and my reaſon is this; In the
Diſcourſe, we had even now, we concluded, that, in an infinite
Number, there was, of neceſſity, as many Square, or Cube Num­
bers, as there were Numbers; ſince that thoſe and theſe were as ma­
ny as their Roots, and Roots comprehend all Numbers: Next we
did ſee, that the greater the Numbers were that were taken, the
ſeldomer are their Squares to be found in them, and ſeldomer yet
their Cubes: Therefore it is manifeſt, that the greater the Number
is to which you paſs, the farther you remove from Infinite Num­
ber: from whence it followeth, that turning backwards, (ſeeing
that ſuch a progreſſion more removes us from the deſired term) if

any number may be ſaid to be infinite it is the Unite: and, indeed,
there are in it thoſe conditions, and neceſſary qualities of the Infi­
nite Number, I mean, of containing in it as many Squares as Cubes,
and as Numbers.
The Unite of all
Numbers may
moſt properly be
ſaid to be Infinite.
SIMP. I do not apprehend very well, how this buſineſs ſhould
be underſtood.
SALV. The thing hath no difficulty at all in it, for the Unite
is a Square, a Cube, a Squared Square, and all other Powers; nor
is there any particular whatſoever eſſential to the Square, or to the
Cube, which doth not agree with the Unite; as v. gr. one proper­
ty of two Square-numbers is to have between them a Number
mean-proportional; take any Square number for one of the terms,
and the Unite for the other, and you ſhall likewiſe ever find be­
tween them a Number Mean-proportional. Let the two Square
Numbers be 9 and 4, you ſee that between 9 and 1 the Mean­
proportional is 3, and between 4 and 1 the Mean-proportional
1is 2, and between the two Squares 9 and 4, 6 is the Mean. The
property of Cubes is to have neceſſarily between them two Num­
bers Mean-proportional. Suppoſe 8, and 27, the Means between
them are 12 and 18; and between the Unite and 8 the Means
are 2 and 4; betwixt the Unite and 27 there are 3, and 9. We
therefore conclude, That there is no other Infinite Number but the
Vnite. And theſe be ſome of thoſe Wonders, that ſurmount the
comprehenſion of our Imagination, and that advertize us how ex­
ceedingly they err, who diſcourſe about Infinites with thoſe very
Attributes, that are uſed about Finites; the Natures of which have
no congruity with each other. In which affair I will not conceal
from you an admirable accident, that I met with ſome time ſince,
explaining the vaſt difference, yea, repugnance and contrariety of
Nature, that a terminate quantity would incur by changing or paſ­
ſing into Infinite. We aſſign this Right Line A B, of any length at
pleaſure, and any point in the ſame, as C being taken, dividing it
into two unequal parts: I ſay, that many couples Lines, (hold­
ing the ſame proportion between themſelves as have the parts
A C, and B C,) departing from the terms A and B to meet with
one another; the points of their Interſection ſhall all fall in the
Circumference of one and the ſame Circle: as for example, A L
and B L departing [or being drawn] from the Points A and B, and
having between themſelves the ſame proportion, as have the parts
A C and B C, and concurring in the point L: and the ſame pro­
portion being between two others A K, and B K, concurring in K,
alſo others as A I, and B I; A H, and B H; A G, and B G; A F,
and B F; A E, and B E: I ſay, that the points of their Interſecti­
on L, K, I, H, G, F, E, do all fall in the Circumference of one
and the ſame Semi-circle: ſo that we ſhould imagine the point
C to mve conti­
58[Figure 58]
nuallyafter ſuch
a ſort, that the
Lines produced
from it to the fix­
ed terms A and
B retain alwaies
the ſame propor­
tion that is be­
tween the firſt
parts A C and C B, that point C ſhall decribe the Circumference
of a Circle, as we ſhall ſhew you preſently. And the Circle in ſuch
ſort deſcribed ſhall be alwaies greater and greater ſucceſſively,
according as the point C is taken nearer to the middle point
which is O; and the Circle ſhall be leſſer which ſhall be deſcribed
from a point nearer to the extremity B, inſomuch, that from the
1infinite Points which may be taken in the Line O B, there may be
deſcribed Circles (moving them in ſuch ſort as above is preſcri­
bed) of any Magnitude; leſſer than the Pupil of the eye of a
Flea, and bigger than the Equinoctial of the Primum Mobile.
Now, if raiſing any of the Points comprehended betwixt the terms
O and B, from every one we may deſcribe Circles, and vaſt ones
from the Points nearer to O; then if we raiſe the Point O it ſelf,
and continue to move it in ſuch ſort as aforeſaid, that is, that the
Lines drawn from it to the terms A and B keep the ſame proporti­
on as have the firſt Lines A O, and O B, what Line ſhall be deſcri­
bed? There would be deſcribed the Circumference of a Circle,
but of a Circle bigger than the biggeſt of all Circles, therefore of
a Circle that is infinite: but it doth alſo deſcribe a Right Line, and
perpendicular upon A B, erected from the Point O, and produced
in infinitum without ever turning to reunite its laſt term with the
firſt, as the others did; for the limited motion of the Point C, after
it had deſigned the upper Semi-circle C H E, continued to de­
ſcribe the Lower E M C, reuniting its extream terms in the point
C: But the Point O being moved to deſign (as all the other Points
of the Line A B, for the Points taken in the other part O A
ſhall deſign their Circles, and thoſe Points neareſt to O the
greateſt) its Circle; to make it the biggeſt of all, and conſe­
quently infinite, it can never return any more to its firſt term, and

in a word deſigneth an Infinite Right-Line for the Circumference
of its Infinite Circle. Conſider now, what difference there is be­
tween a finite Circle, and an infinite; ſeeing that this in ſuch man­
ner changeth its being that it wholly loſeth both its being, and
power of being; for we have already well comprehended, that
there cannot be aſſigned an infinite Circle; by which we may
conſequently know that there can be no infinite Sphære, or other
Body, or figured Superficies. Now what ſhall we ſay to this Meta­
morphoſis in paſſing from Finite to Infinite? And why ſhould we
find greater repugnance, whilſt ſeeking Infinity in Numbers, we

come to conclude it to be in the Unite? And whilſt that breaking
a Solid into many pieces, and purſuing to reduce it into very ſmall
powder, it were reſolved into its infinite Atomes, admitting no far­
ther diviſion, why may we not ſay that it is returned into one ſole
Continuum, but perhaps fluid, as the Water, or Quickſilver, or
other Metall melted? And do we not ſee Stones liquified into
Glaſs, and Glaſs it ſelf with much Fire to become more fluid than
Water?
The difference be­
twixt a finite and
infinite Circle.
Vnity participates
of Infinity.
SAGR. Should we therefore think Fluids to be ſo called, be­
cauſe they are reſolved into their firſt, infinite, indiviſible com­
pounding parts?
SALV. I know not how to find a better anſwer to reſolve cer­
1tain ſenſible appearances, amongſt which this is one: When I take
a hard Body, be it either Stone, or Metal, and with a Hammer, or
very fine File, endeavour to divide it, as much as is poſſible, into
its moſt minute and impalpable powder; it is very clear, that its
leaſt Atomes, albeit for their ſmalneſs they are imperceptible, one by
one, to our ſight and touch; yet are they quantitative, figured, and
numerable: and it happens in them, that being accumulated to­
gether, they continue in heap; and being laid hollow, or with a
pit in the midſt, the hollowneſs or pit remains, the parts heaped
about it not returning to fill it up; and being ſtirr'd, or ſhaken,
they ſuddenly ſettle ſo ſoon as their external mover leaves them,
And the like effects are ſeen in all the Aggregates of ſmall Bodies,
bigger, and bigger, and of any kind of Figure, although Sphærical;
as we ſee in heaps of Peaſe, Wheat, Bird ſhot, and other matters. But
if we try to find the like accidents in Water, you will meet with
none of them; but, being raiſed, it inſtantly returns to a level, if
it be not by a veſſel, or ſome other external ſtay upheld; being
made hollow, it preſently diffuſeth to fill up the Cavity; and be­
ing long moved, it continually undulates, and ſpreads its waves very
far. From this, I think, we may very rationally infer, that the minute

parts of Water, into which it ſeemeth to be reſolved, (ſince it hath
leſs conſiſtence than any the fineſt powder, yea, hath no conſi­
ſtence at all) are vaſtly differing from Atomes quantitative and
diviſible; nor know I how to find any other difference therein
than that of being indiviſible. Methinks, alſo, that its moſt exqui­
ſite tranſparency, affords us ſufficient grounds to conjecture there­
of; for if we take the moſt diaphanous Chriſtal that is, and begin
to break, and pound it to powder, when it is in powder it loſeth
its tranſparency, and ſo much the more, the ſmaller it is pounded;
but yet Water which is ground to the higheſt degree, hath alſo the
higheſt degree of Diaphaneity Gold and Silver, reduced by Aqua­
fortis into a ſmaller Powder than any File can make, yet they con­
tinue powder, and become not fluid; nor do they liquifie till the
Indiviſibles of the Fire, or of the Sun-beams diſſolve them, as, I be­
lieve, into their firſt and higheſt infinite and indiviſible compoun­
ding parts.
Fluid Bodies are
ſuch, for that they
are reſolved into
their firſt Indiviſi­
ble Atomes.
SAGR. This which you have hinted of the Light I have many
times obſerved with admiration: I have ſeen, I ſay, a burning­
Glaſs, of a foot Diameter, liquifie or melt lead in an inſtant;
whence I came to be of opinion, that if the Glaſſes were very big,
and very polite, and of Parabolical Figure, they would no leſs melt
every other Metal in a very ſhort time; ſeeing that that, not very
big, nor very clear, and of a Sphærical Concave, with ſuch force
melted Lead, and burnt every combuſtible matter: effects, that
make the wonders, reported of the Burning-glaſſes of Archimedes,
credible to me.
1
Archimedes his
Burning — Glaſſes
admirable.
SALV. Touching the Effects of the Glaſſes, invented by Ar­
chimedes, all the Miracles, that ſeveral Writers record of them,
are to me rendred credible by the reading of Archimedes his own
Books, which I have with infinite amazement peruſed and ſtudied:
and if any doubts had been left me; that which laſt of all Father

Buonaventura Cavalieri hath publiſhed, touching Lo Specehio
Vſtorio, (or the Burning glaſs) and which I have read with ad­
miration, is ſufficient to reſolve them all.
Buonaventura
Cavalieri, the Je­
ſuate, a famous
Mathematician,
and his Book en­
titled, Lo Spec­
chio Uſtorio.
SAGR. I have alſo ſeen that Tract, and peruſed it with much
delight and wonder; and becauſe I formerly had knowledge of
the Author, I was confirmed in the opinion which I had conceived
of him, that he was like to prove one of the principal Mathemati­
cians of our Age. But returning to the admirable effects of the
Sun-Beams in melting of Metals, are we to believe that ſuch, and
ſo violent an operation is without Motion, or elſe that it is with
Motion, but extream ſwift?
Burnings are per­
formed with a moſt
ſwift Motion.
SALV. We ſee other burnings, and meltings to be performed
with Motion, and with a moſt ſwift Motion. Obſerve the ope­
rations of Lightnings, of Powder in Mines, and in Petards,
and, in ſum, how by quickning the flame of Coles, mixt with
groſs and impure vapours, by Bellows, encreaſeth its force in
the melting of Metals: ſo that I cannot ſee how the Action of
Light, albeit moſt pure, can be without Motion, and that alſo ve­
ry ſwift.
SAGR. But what and how great ought we to judge this Velo­
city of the Light? Is it haply Inſtantaneous, and done in a moment,
or, as the reſt of Motions, performed in Time? May we not by
Experiment be aſſured what it is?
SIMP. Quotidian experience ſhews the expanſion of Light to
be Inſtantaneous; in that beholding a Cannon, let off at a great
diſtance, the flaſh of the fire, without interpoſition of time, is tranſ­
mitted to our eye, but ſo is not the Report to our ear untill a con­
ſiderable time after.
SAGR. True, but, I pray you, what doth this obvious experi­
ment evince; but only this, that the Report is longer in arriving at
our Ear, than the Flaſh at our Eye; but it aſſures me not, that the
tranſmiſſion of the Light is therefore Inſtantaneous rather than in
Time, but only moſt ſwift. Nor doth ſuch an obſervation con­
clude more than that other, of ſuch who ſay, that as ſoon as the
Sun cometh to the Horizon, its Light arriveth at our eye: for who
ſhall aſſure me, that its beams arrive not at the ſaid term, afore they
reach our ſight?
SALV. The inconcludency of theſe, and other obſervations of
the like Nature, made me once think of ſome other way, whereby
we may without errour be aſcertained whether the illumination,
1that is, whether the expanſion of the Light were really Inſtantane­
ous; ſeeing that the very ſwift Motion of Sound, aſſureth us, that
that of Light cannot but be extream ſwift. And the experiment I

hit upon, was this; I would have two perſons take each of them a
Light, which, by holding it in a Lanthorn, or other coverture, they
may cover, and diſcover at pleaſure by interpoſing their hand to the
fight of each other; and, that placing themſelvs againſt one another,
ſome few paces diſtance, they may practice the ſpeedy diſcovery,
and occultation of their Lights from the ſight of each other: So
that when one ſeeth the others Light, he immediatly diſcloſe his:
which correſpondence, after ſome Reſponſes mutually made, will
become ſo exactly Inſtantaneous, that, without ſenſible variation,
at the diſcovery of the one, the other ſhall at the ſame time ap­
pear to the ſight of him that diſclos'd the firſt. Having adjuſted
this practice at this ſmall diſtance, let us place the two perſons with
two ſuch Lights at two or three miles diſtance; and by night re­
newing the ſame experiment; Let them intenſely obſerve if the
Reſponſes of the diſcloſures, and occultations do follow the ſame
tenour which they did near hand: for if they keep the ſame pro­
portion, it may be with certainty enough concluded, that the ex­
panſion of Light is Inſtantaneous; but if it ſhould require time in
a diſtance of three miles, which importeth ſix for the going of
one, and return of the other, the ſtay would be ſufficiently obſer­
vable. And if this Experiment be made at greater diſtances,
namely, at eight or ten miles, we may make uſe of the Teleſcope,
the Obſervators accommodating each of them one at the places,
where by night the Lights are to be obſerved; which though not
very big, and ſo not viſible, at that great diſtance, to the eye at
large; (though eaſie to be diſcloſed, and hid) by help of the
Teleſcopes before admitted, and fixed they may commodiouſly be
diſcerned.
The Velocity of
Light, how to find
by Experiment
whether it be In­
ſtantaneosu or not.
SAGR. The Invention ſeems to me no leſs certain than ingenu­
ous; but tell us what upon experimenting it you concluded.
SALV. Really, I have not tryed it, ſave only at a ſmall diſtance,
namely, leſs than a Mile: whereby I could come to no certainty
whether the apparence of the oppoſite Light was truly Inſtantane­
ous; But if not Inſtantaneous, yet it was of exceeding great Velo­
city, and I may ſay Momentary: and for the preſent, I would re­
ſemble it to that Motion which we ſee a flaſh of Lightning make
in the Clouds ten or more Miles off: of which Light we diſtin­
guiſh the beginning, and, I may fay, the ſource and riſe of it, in a
particular place in thoſe Clouds; but yet its wide expanſion imme­
diatly ſucceeds amongſt thoſe adjacent: which to me ſeems an ar­
gument that it is ſome ſmall time in doing; becauſe had the illu­
mination been made all at once, and not by degrees, it feems to
1me that we could not have diſtinguiſhed its original, or rather the
Center of its flake, and extream Dilatations. But into what Oceans
do we by degrees engage our ſelves? Amongſt Vacuities, Infinites,
Indiviſibles, and Instantaneous Motions; ſo that we ſhall not be
able by a thouſand Diſcourſes to recover the Shore?
SAGR. They are things, indeed, very diſproportionate to our
underſtanding. Behold Infinite, ſought amongſt Numbers, ſeemeth
to determine in the Unite: From Indiviſibles ariſeth things that
are continually diviſible: Vacuity ſeems only to reſide indiviſibly
mixt with Repletion: and, in brief, theſe things ſo change the
nature of thoſe underſtood by us, that even the Circumference of
a Circle becometh an Infinite Right-Line; which, if I well re­
member, is that Propoſition which you, Salviatus, are to mani­
feſt by Geometrical Demonſtration. Therefore, if you think fit,
it would be well, without any more digreſſions, to make it out
to us.
SALV. I am ready to ſerve you in demonſtrating the enſuing
Problem for your fuller information.
PROPOSITION.
A Right-Line being given, divided, according to any
proportion, into unequal parts, to deſcribe a Circle, to
the Circumference of which, at any point of the ſame,
two Right-Lines being produced from the terms of
the given Right Line, they may retain the ſame pro­
portion that the parts of the ſaid Line given have to
one another, ſo that thoſe be Homologous which de­
part ſrom the ſame terms.
Let the given Right-Line be AB, unequally divided ac­
cording to any proportion in the point C; it is required to
deſcribe a Circle at any point of whoſe Circumference two
Right Lines, produced from the terms A and B, concurring, have
the ſame proportion to each other, that A C, hath to B C, ſo that
thoſe be Homologous which depart from the ſame term. Upon
the Center C, at the diſtance of the leſſer part C B, let a Circle be
ſuppoſed to be deſcribed, to the Circumference of which from the
point A the Right-line A D is made a Tangent, and indetermi­
nately prolonged towards E: and let the Contact be in D, and
draw a Line from C to D, which ſhall be perpendicular to A E;
and let B E be perpendicular to B A, which produced, ſhall inter­
1ſect A E, the Angle A being acute: Let the interſection be in E,
from whence let fall a Perpendicular to A E, which produced, will
meet with A B infinitely prolonged in F. I ſay, firſt, that the
Right-lines F E, and F C are equal: ſo that drawing the Line
E C, we ſhall, in the
59[Figure 59]
two Triangles D E C,
B E C, have the two
Sides of the one, D E,
and C E, equal to the
two Sides of the other
B E, and E C; the
two Sides, D E, and
E B, being Tangents
to the Circle D B,
and the Baſes D C,
and C B, are likewiſe
equal: wherefore the
two Angles D E C,
and B E C, ſhall be
equal. And becauſe the Angle B C E wanteth of being a Right­
Angle, as much as the Angle B E C; and the Angle C E F, to
make it a Right-Angle, wants the Angle C E D, thoſe Supple­
ments being equal, the Angles F C E, and F E C ſhall be equal,
and ſo conſequently the Sides F E, and F C; wherefore making
the point F a Center, and at the diſtance F E, deſcribing a Circle,
it ſhall paſs by the point C. Deſcribe it, and let it be C E G. I ſay,
that this is the Circle required, by any point of the Circumfe­
rence of which, any two Lines that ſhall interſect, departing from
the terms A and B, ſhall be in proportion to each other, as are the
two parts A C, and B C, which beſore did concur in the point C.
This is manifeſt in the two that concur or interſect in the point E,
that is A E, and B E; the Angle E of the Triangle A E B being
divided in the midſt by C E; ſo that as A C is to C B, ſo is A E
to B E. The ſame we prove in the two A G, and B G, determined
in the point G. Therefore being (by the Similitude of the Tri­
angles A F E, and E F B) that as A F is to E F, ſo is E F to F B;
that is, as A F is to F C, ſo is C F to F B: So by Diviſion; as A C
is to C F, (that is, to F G) ſo is C B to B F; and the whole A B
is to the whole B G, as the part C B to the part B F: and by Com­
poſition; as A G is to G B, ſo is C F to F B; that is, as E F to
F B, that is, as A E to E B, and A C to C B: Which was to be de­
monſtrated. Again, let any other Point be taken in the Circum­
ference, as H; in which the two Lines A H and B H concur. I ſay, in
like manner as before, that as A C is to C B, ſo is A H to B H.
Continue H B untill it interſect the Circumference in I, and draw
1a Line joyning I to F. And becauſe it hath been proved already
that as A B is to B G, ſo is C B to B F, the Rectangle A B F ſhall be
equall to the Rectangle C B G, that is I B H: and therefore, as
A B is to B H, ſo is I B to B F, and the Angles at B are equal:
Therefore A H is to H B, as I F, that is E F, to F B, and as A E
to E B.
I ſay moreover, that it is impoſſible, that the Lines, which have
this ſame proportion, departing from the terms A and B, ſhould
meet in any point, either within or without the ſaid Circle: For­
aſmuch as if it be poſſible that two Lines ſhould concur in the
point L, placed without; let them be A L, and B L; and continue
L B to the Circumference in M, and conjoyn M to F. If therefore
A L is to B L, as A C to B C, that is, as M F to F B, we ſhall have
two Triangles A L B, and M F B, which about the two Angles
A L B and M F B have their Sides proportional, their upper Angles
in the point B equal, and the two remaining Angles F M B and
L A B leſs than Right Angles (for that the Right-angle at the
point M hath for its Baſe the whole Diameter C G, and not the
ſole part B F, and the other at the point A is acute by reaſon the
Line A L Homologous to A C, is greater than B L Homologous to
B C) Therefore the Triangles A B L, and M B F are like: and
therefore as A B is to B L, ſo is M B to B F; Wherefore the
Rectangle A B F ſhall be equall to the Rectangle M B L. But the
Rectangle A B F hath been demonſtrated to be equal to that of
C B G: Therefore the Rectangle M B L is equal to the Rectangle
C B G, which is impoſſible: Therefore the Concourſe of the Lines
cannot fall without the Circle. And in like manner it may be de­
monſtrated that it cannot fall within; Therefore all the Concour­
ſes fall in the Circumference it ſelf.
But it is time that we return to give ſatisfaction to the Intreaty
of Simplicius, ſhewing him that the reſolving the Line into its in­
finite Points is not only not impoſſible, but that it hath in it no
more difficulty than to diſtinguiſh its quantitative parts; preſup­
poſing one thing (notwithſtanding) which I think, Simplicius,
you will not deny me, and that is this; that you will not require me
to ſever the Points one from another, and ſhew you them one by
one diſtinctly upon this paper: for I my ſelfe ſhould be content,
if without enjoyning to pull the four or ſix parts of a Line from
one another, you ſhould but ſhew me its diviſions marked, or at
moſt inclined to Angles, framing them into a Square, or a Hexa­
gon; therefore I perſwade my ſelf, that for the preſent you will
grant them then ſufficiently, and actually diſtinguiſhed.
SIMP. I ſhall indeed.
SALV. Now if the inclining of a Line to Angles, framing

therewith ſometimes a Square ſometimes an Octagon, ſometimes
1a Poligon of Forty, of an Hundred, of a Thouſand Angles be a
mutation ſufficient to reduce into Act thoſe four, eight, forty,
hundred, or thouſand parts, which were, as you ſay, Potentially
in the ſaid Line at firſt: if I make thereof a Poligon of infinite
Sides, namely, when I bend it into the Circumference of a Circle,
may not I, with the like leave, ſay, that I have reduced thoſe infi­
nite parts into Act, which you before, whilſt it was ſtraight, ſaid
were Potentially contained in it? Nor may ſuch a Reſolution be
denied to be made into its Infinite Points, as well as that of its four
parts in forming thereof a Square, or into its thouſand parts in
forming thereof a Mill-angular Figure; by reaſon that there wants
not in it any of the Conditions found in the Poligon of a thou­
ſand, or of an hundred thouſand Sides. This applied or layed to a
Right-Line covereth it, touching it with one of its Sides, that is,
with one of its hundred thouſandth parts; the Circle, which is a
Poligon of infinite Sides, toucheth the ſaid Right-line with one of
its Sides, that is one ſingle Point divers from all its Colaterals, and
therefore divided, and diſtinct from them, no leſs than a Side of
the Poligon from its Conterminals. And as the Poligon turned
round upon a Plane deſcribes, with the conſequent tacts of its Sides,
a Right-line equal to its Perimeter: ſo the Circle, rowled upon
ſuch a Plane, deſcribes or ſtamps upon it, by its infinite ſucceſſive
Contacts, a Right-line, equall to its own Circumference. I know
not at preſent, Simplicius, whether or no the Peripateticks, (to
whom I grant, as a thing moſt certain, that Continuum may be di­
vided into parts alwaies diviſible, ſo that continuing the diviſion
and ſubdiviſion there can be no end thereof) will be content to
yield to me, that none of thoſe diviſions are the ultimate, as in­
deed they be not, ſince that there alwaies remains another; but
that only to be the laſt, which reſolves it into infinite Indiviſibles;
to which I yield we can never attain, dividing and ſubdividing it
ſucceſſively into a greater, and greater multitude of parts: but
making uſe of the way which I propound to diſtinguiſh and re­
ſolve all the infinite parts at one only draught, (an Artifice which
ought not to be denied me) I could perſwade my ſelf they
would ſatisfie themſelves, and admit this compoſition of Continu-

um to conſiſt of Atomes abſolutely indiviſible: And eſpecially,
this one path being more current than any other to extricate us
out of very intricate Laberinths; ſuch as are, (beſides that alrea­
dy touched of the Coherence of the parts of Solids) the concei­
ving the buſineſs of Rarefaction and Condenſation, without
running into the inconvenience of being forced to admit forth of
void Spaces or Vacuities; and for this a Penetration of Bodies: in­
conveniences, which both, in my opinion, may eaſily be avoided,
by granting the foreſaid Compoſition of Indiviſibles.
1
How infinite points
are aſſigned in a
finite Line.
Continuum com­
pounded of Indivi­
ſibles.
SIMP. I know not what the Peripateticks would ſay, in regard
that the Conſiderations you have propoſed would be, for the moſt
part, new unto them, and as ſuch, it is requiſite that they be exa­
mined: and it may be, that they would find you anſwers, and
powerful Solutions, to unty theſe knots, which I, by reaſon of the
want of time and ingenuity proportionate, cannot for the preſent
reſolve. Therefore, ſuſpending this particular for this time, I
would gladly underſtand how the introduction of theſe Indiviſi­
bles facilitateth the knowledge of Condenſation, and Rarefa­
ction, avoiding at the ſame time a Vacuum, and the Penetration of
Bodies.
SAGR. I alſo much long to underſtand the ſame, it being to
my Capacity ſo obſcure: with this proviſo, that I be not couzen­
ed of hearing (as Simplicius ſaid but even now) the Reaſons of
Ariſtotle in confutation of a Vacuum, and conſequently the Solu­
tions which you bring, as ought to be done, whilſt that you ad­
mit what he denieth.
SALV. I will do both the one and the other. And as to the firſt
it's neceſſary, that like as in favour of Rarefaction, we make uſe of
the Line deſcribed by the leſſer Circle bigger than its own Cir­
cumference, whilſt it was moved at the Revolution of the greater;
ſo, for the underſtanding of Condenſation, we ſhall ſhew, how that,
at the converſion made by the leſſer Circle, the greater deſcribeth
a Right-line leſs than its Circumference; for the clearer explicati­
on of which, let us ſet before us the conſideration of that which
befalls in the Poligons. In a deſcription like to that other; ſup­
poſe two Hexagons about the common Center L, which let be
A B C, and H I K, with the Parallel-lines H O M, and A B C, up­
on which they are to make their Revolutions; and the Angle I, of
the leſſer Poligon, reſting at a ſtay, turn the ſaid Poligon till ſuch
time as I K fall upon the Parallel, in which motion the point K
ſhall deſcribe the Arch K M, and the Side K I, ſhall unite with the
part I M; while this is in doing, you muſt obſerve what the Side
C B of the greater Poligon will do. And becauſe the Revolution
is made upon the Point I, the Line I B with its term B ſhall de­
ſcribe, turning backward the Arch B b, below the Parallel c A, ſo
that when the Side K I ſhall fall upon the Line M I, the Line B C
ſhall fall upon the Line b c, advancing forwards only ſo much as
is the Line B c, and retiring back the part ſubtended by the Arch
B b, which falls upon the Line B A, and intending to continue af­
ter the ſame manner the Revolution of the leſſer Poligon, this will
deſcribe, and paſs upon its Parallel, a Line equal to its Perimeter;
but the greater ſhall paſs a Line leſs than its Perimeter, the quan­
tity of ſo many of the lines B b as it hath Sides, wanting one;
and that ſame line ſhall be very near equal to that deſcribed by
1the leſſer Poligon, exceeding it only the quantity of b B. Here
then, without the leaſt repugnance the cauſe is ſeen, why the grea­
ter Poligon paſſeth or moveth not (being carried by the leſs)
with its Sides a greater Line than that paſſed by the leſs; that is,
becauſe that one part of each of them falleth upon its next coter­
minal and precedent.
But if we ſhould conſider the two Circles about the Center A,
reſting upon their Parallels, the leſſer touching his in the point B,
and the greater his in the
60[Figure 60]
point C; here, in begin­
ning to make the Revolu­
tion of the leſs, it ſhall not
occur as before, that the
point B reſt for ſome time
immoveable, ſo that the
Line B C giving back,
carry with it the point C,
as it befell in the Poligons,
which reſting fixed in the
point I till that the Side
K I falling upon the Line
I M, the Line I B carried
back B, the term of the
Side C B, as far as b, by
which means the Side B C
fell on b c, ſuper-poſing or
reſting the part B b upon
the Line B A, and advancing forwards only the part B c, equal to
I M, that is to one Side of the leſſer Poligon: by which ſuperpoſi­
tions, which are the exceſſes of the greater Sides above the leſs, the
advancements which remain equal to the Sides of the leſſer Poli­
gon come to compoſe in the whole Revolution the Right-line
equal to that traced, and meaſured by the leſſer Poligon. But

now, I ſay, that if we would apply this ſame diſcourſe to the ef­
fect of the Circles, it will be requiſite to confeſs, that whereas the
Sides of whatſoever Poligon are comprehended by ſome Number,
the Sides of the Circle are infinite; thoſe are quantitative and di­
viſible, theſe non-quantitative and Indiviſible: the terms of the
Sides of a Poligon in the Revolution ſtand ſtill for ſome time, that
is, each ſuch part of the time of an entire Converſion, as it is of
the whole Perimeter: in the Circles likewiſe the ſtay oſ the terms

of its infinite Sides are momentary, for a Moment is ſuch part of a
limited Time, as a Point is of a Line, which containeth infinite of
them; the regreſſions made by the Sides of the greater Poligon, are
not of the whole Side, but only of its exceſs above the Side of the
1leſſer, getting forwards as much ſpace as the ſaid leſſer Side: in
Circles, the Point, or Side C in the inſtantaneous reſt of B recedeth
as much as is its exceſs above the Side B, advancing forward as
much as the quantity of the ſame B: And in ſhort, the infinite
indiviſible Sides of the greater Circle with their infinite indiviſible
Regreſſions, made in the infinite inſtantaneous ſtaies of the infi­
nite terms of the infinite Sides of the leſſer Circle, and with their
infinite Progreſſes, equal to the infinite Sides of the ſaid leſſer
Circle, they compoſe and meaſure a Line equall to that deſcribed
by the leſſer Circle, containing in it ſelf infinite ſuperpoſitious
non-quantitative, which make a Conſtipation and Condenſation
without any penctration of quantitative parts: which cannot be
contrived to be done in the Line divided into quantitative parts,
as is the Perimeter of any Poligon, which being diſtended in a
Right-line at length, cannot be reduced to a leſſer length, unleſs
the Sides fall upon and Penetrate one the other. This Conſtipati­
on of parts non-quantitative, but infinite without Penetration of
quantitative parts, and the former Diſtraction above declared of

infinite Indiviſibles by the interpoſition of indiviſible Vacui­
ties, I believe, is the moſt that can be ſaid for the Condenſation
and Rarefaction of Bodies, without being driven to introduce Pe­
netration of Bodies, or quantitative Void Spaces. If there be any
thing therein that pleaſeth you, make uſe of it, if not, account it

vain, and my diſcourſe alſo; and ſeek out ſome other explanation
that may better ſatisfie your Judgment. Only theſe two words
by the way, let us remember that we are amongſt Infinites, and In­
diviſibles.
A Circle is a Poli­
gon of infinite in­
diviſible quantita­
tive Sides.
An Inſtant or Mo­
ment of quantita­
tive Time, is the
ſame as a Point of
a quantitative
Line.
Rarefaction is the
diſtraction of infi­
nite Indiviſibles
by the interpoſition
of infinite indiviſi­
ble Vaeuities.
Condenſation, ac­
cording to the ope­
ration of the Au­
thor, proceeds from
the Conſtipation of
quantitative and
indiviſible parts.
SAGR. That the Conceit is ingenious, and to my eares wholly
new, and ſtrange, I freely confeſs, but whether or no Nature pro­
ceed in this order, I know not how to reſolve; Truth is, that till
ſuch time as I hear ſomething that may better ſatisfie me, that I
may not ſtand ſilent, I will adhere to this. But haply Simplicius
may have ſomwhat, which I have not yet met with, to explicate
the explication, which is produced by Philoſophers in ſo abſtruce
a matter; for, indeed, what I have hitherto read about Condenſa­
tion, is to me ſo denſe, and that of Rarefaction ſo ſubtill, that
my weak ſight neither penetrates the one, nor comprehends the
other.
SIMP. I am full of confuſion, and find great Rubbs in the one
path, and in the other, and more particularly in this new one: for
according to this Rule, an Ounce of Gold might be rarefied and
drawn forth into a Maſs bigger than the whole Earth, and the
whole Earth condenſed and reduced into a leſs Maſs than a Nut;
which I neither believe, nor think that you your ſelf do believe:
and the Conſiderations and Demonſtrations by you hitherto de­
1livered, as they are things Mathematical, abſtract and ſeparate
from Senſible Matter, I believe, that when they come to be apply­
ed to Matters Phyſical and Natural, they will not exactly comply
with theſe Rules.
SALV. It is not in my power, nor, as I believe, do you deſire,
that I ſhould make that viſible which is inviſible; but as to ſuch
things as may be comprehended by our Senſes, in regard that you

have inſtanced in Gold, do we not ſee an immenſe extenſion to
be made of its parts? I know not whether you may have ſeen the
Method that Wyer-drawers obſerve in diſgroſſing Gold Wyer:
which in reality is not Gold, ſave only in the Superficies, for the
internal ſubſtance is Silver; and the way of diſgroſſing it is this.
They take a Cylinder, or, if you will, Ingot of Silver, about half
a yard long, and about three or four Inches thick, and this they

gild or over-lay with Leaves of beaten Gold, which, you know,
is ſo thin that the Wind will blow it to and again, and of theſe
Leaves they lay on eight or ten, and no more. So ſoon as it is
gilded, they begin to draw it forth with extraordinary force, ma­
king it to paſs thorow the hole of the Drawing Iron, and then
reiterate this forceable diſgroſsment again and again thorow holes
ſucceſſively narrower, ſo that, after ſeveral of theſe diſgroſments,
they bring it to the ſmalneſs of the hair of a womans head, if not
ſmaller, and yet it ſtill continueth gilded in its Superficies or out­
ſide: Now I leave you to conſider to what a fineneſs and diſtenſi­
on the ſubſtance of the Gold is brought.
Gold in the gilding
of Silver is drawn
forth and diſgroſ­
ſed immenſly.
* Or Thumb­
breadths.
SIMP. I do not ſee how it can be inferred from this Experi­
ment, that there may be a diſgroſment of the matter of the Gold
ſufficient to effect thoſe wonders which you ſpeak of: Firſt, For
that the firſt gilding was with ten Leaves of Gold, which make a
conſiderable thickneſs: Secondly, howbeit in the extenſion and
diſgroſment that Silver encreaſeth in length, it yet withall dimi­
niſheth ſo much in thickneſs, that compenſating the one dimenſi­
on with the other, the Superficies doth not ſo enlarge, as that for
overlaying the Silver with Gold, the ſaid Gold need to be reduced
to a greater thinneſs than that of its firſt Leaves.
SALV. You much deceive your ſelf, Simplicius, for the en­
creaſe of the Superficies is Subduple to the extenſion in length, as
I could Geometrically demonſtrate to you.
SAGR. I beſeech you, both in the behalf of my ſelf, and of
Simplicius, to favour us with that Demonſtration, if ſo be you
think that we can comprehend it.
SALV. I will ſee whether I can, thus upon the ſudden, recall
it to mind. It is already manifeſt, that that ſame firſt groſs Cylin­
der of Silver, and the Wyer diſtended to ſo great a length are two
equal Cylinders, in regard that they are the ſame Silver; ſo that
1if I ſhall ſhew you what proportion the Superficies of equall Cy­
linders have to one another, we ſhall obtain our deſire. I ſay there­
fore, that
PROPOSITION.
The Superficies of Equal Cylinders, their Baſes being
ſubſtracted, are to one another in ſubduple proportion
of their lengths.
Take two equall Cylinders, the heights of which let be A B,
and C D: and let the Line E be a Mean-proportional
between them. I ſay, the Superficies of the Cylinder A B,
the Baſes ſubſtracted, hath the ſame proportion to the Superficies
of the Cylinder C D, the Baſes in like manner ſubſtracted, as the
Line A B hath to the Line E, which is ſubduple of the proportion
of A B to C D. Cut the part of the Cylinder A B in F, and let the
height A F be equal to C D: And becauſe the Baſes of equal Cy­
linders anſwer Reciprocally to their heights, the Circle, Baſe of
the Cylinder C D, to the Circle, Baſe of the
61[Figure 61]
Cylinder A B, ſhall be as the height B A to
D C: And becauſe Circles are to one ano­
ther as the Squares of their Diameters, the
ſaid Squares ſhall have the ſame proportion,
that B A hath to C D: But as B A, is to
C D, ſo is the Square B A to the Square of
E: Therefore thoſe four Squares are Pro­
portionals: And therefore their Sides ſhall
be Proportionals. And as the Line A B is to
E, ſo is the Diameter of the Circle C to the
Diameter of the Circle A: But as are the
Diameters, ſo are the Circumferences; and
as are the Circumferences, ſo likewiſe are the Superficies of Cylin­
ders equal in Height. Therefore as the Line A B is to E, ſo is the
Superficies of the Cylinder C D to the Superficies of the Cylinder
A F. Becauſe therefore the height A F to the height A B, is as the
Superficies A F to the Superficies A B: And as is the height A B
to the Line E, ſo is the Superficies C D to the Superficies A F:
Therefore by Perturbation of Proportion as the height A F is to
E, ſo is the Superficies C D to the Superficies A B: And, by Con­
verſion, as the Superficies of the Cylinder A B is to the Superficies
of the Cylinder C D, ſo is the Line E to the Line A F; that is, to
the Line C D: or as A B to E: Which is in ſubduple proportion
of A B to C D: Which is that which was to be proved.
1
Now if we apply this, that hath been demonſtrated, to our
purpoſe; preſuppoſing that that ſame Cylinder of Silver, that was
gilded whilſt it was no more than half a yard long, and four or five
Inches thick, being diſgroſſed to the ſineneſs of an hair, is prolon­
ged unto the extenſion of twenty thouſand yards (for its length
would be much greater) we ſhall find its Superficies augmented
to two hundred times its former greatneſs: and conſequently, thoſe
Leaves of Gold, which were laid on ten in number, being diſten­
ded on a Superficies two hundred times bigger, aſſure us that the
Gold which covereth the Superficies of the ſo many yards of Wyer
is left of no greater thickneſs than the twentieth part of a Leaf of
ordinary Beaten-Gold. Conſider, now, how great its thinneſs is, and
whether it is poſſible to imagine it done without an immenſe di­
ſtention of its parts: and whether this ſeem to you an Experi­
ment, that tendeth likewiſe towards a compoſition of infinite In­
diviſibles in Phyſical Matters: Howbeit there want not other more
ſtrong and neceſſary proofs of the ſame.
SAGR. The Demonſtration ſeemeth to me ſo ingenuous, that
although it ſhould not be of force enough to prove that firſt intent
for which it was produced, (and yet, in my opinion, it plainly
makes it out) yet nevertheleſs that ſhort ſpace of time was well
ſpent which hath been employed in hearing of it.
SALV. In regard I ſee, that you are ſo well pleaſed with theſe
Geometrical Demonſtrations, which bring with them certain pro.
fit, I will give you the fellow to this, which ſatisfieth to a very cu­
rious Queſtion. In the former we have that which hapneth in
Cylinders that are equall, but of different heights or lengths: it
will be convenient, that you alſo hear that which occurreth in Cy­
linders equal in Superficies, but unequal in heights; my meaning
alwaies is, in thoſe Superficies only that encompaſs them about,
that is, not comprehending the two Baſes ſuperiour and inferiour.
I ſay, therefore, that
PROPOSITION.
Upon Cylinders, the Superficies of which the Baſes be­
ing ſubſtracted are equal, have the ſame proportion
to one another as their heights Reciprocally taken.
Let the Superficies of the two Cylinders A E and C F be
equall; but the height of this C D greater than the height
of the other A B. I ſay, that the Cylinder A E hath the
ſame proportion to the Cylinder C F, that the height C D hath
to A B. Becauſe therefore the Superficies C F is equall to the
1ſuperficies A E, the Cylinder C F ſhall be leſſe than A E: For
if they were equal, its Superficies, by the laſt Propoſition would
be greater than the Superficies A E, and
62[Figure 62]
much the more, if the ſaid Cylinder C F
were greater than A E. Let the Cylinder
I D be ſuppoſed equal to A E: There­
fore, by the precedent Propoſition, the
Superficies of the Cylinder I D ſhall be
to the Superficies A E, as the height I F
to the Mean-proportional betwixt I F &
A B. But the Superficies A E being by
Suppoſition equal to C F and I D, ha­
ving the ſame proportion to C F that the
height I F hath to C D: Therefore
C D is the Mean-Proportional between
I F and A B. Moreover, the Cylinder
I D being equal to the Cylinder A E,
they ſhall both have the ſame proporti­
on to the Cylinder C F: But I D is to
C F, as the height I F is to C D: Therefore the Cylinder A E
ſhall have the ſame proportion to the Cylinder C F, that the line
I F hath to C D; that is, that C D hath to A B: Which was to be
demonſtrated.
Of Corn-ſacks
with a Board at
the Bottom, made
of the ſame Stuffe,
but different in
height, which are
the more capa­
cious.
From hence is collected the Cauſe of an Accident, which the
Vulgar do not hearken to without admiration; and it is, how it
is poſſible that the ſame piece of ^{*}Cloth, being longer one way than
another, if a Sack be made thereof to hold Corn, as the uſual
manner is, with a Board at the bottom, will hold more, making
uſe of the leſſer breadth of the Cloth, for the height of the Sack,

and with the other encompaſſing the Board at the bottom, than if
it be made up the other way: As if for Example, the Cloth were
one way ſix foot, and the other way twelve, it will hold more,
when with the length of twelve one encompaſſeth the Board at the
bottom, the Sack being ſix foot high, than if it encompaſſed a
bottom of ſix foot, having twelve for its height. Now, by what
hath been demonſtrated, there is added to the Knowledge in ge­
neral that it holds more that way than this, the Specifick, and
particular Knowledge of how much it holdeth more: which is,
That it will hold more in proportion as it is lower, and leſſer, as
it is higher. And thus in the meaſures afore taken, the Cloth be­
ing twice as long as broad, when it is ſewed the length-ways it will
hold but half ſo much, as it will do the other way. And likewiſe

having a Mat to make a ^{*} Frale or Basket twenty five foot long,
and ſuppoſe ſeven broad; made up the long-way it will hold but
onely ſeven of thoſe meaſures, whereof the other way it will hold
five and twenty.
1
* Or Sacking.
* Bugnola, any
Veſſel made of
Rushes or Wick­
er.
SAGR. And thus to our particular content we continually diſ­
cover new Notions of great Curioſity, and not unaccompanyed
with Utility. But in the particular glanced at but even now, I
really believe, that amongſt ſuch as are altogether void of the
knowledge of Geometry, there would not be found one in twen­
ty, but at the firſt daſh would not be miſtaken, and wonder
that thoſe Bodies that are contained within equal Superficies,
ſhould not likewiſe be in every reſpect equal; like as they run in­
to the ſame errour, ſpeaking of the Superficies, when for deter­
mining, as it frequently falls out, of the ampleneſſe of ſeveral
Cities, they think they have obtained their deſire ſo ſoon as they
know the ſpace of their Circuits, not knowing that one Circuit
may be equal to another, and yet the place conteined by this
much larger than the place of that: which befalleth not onely in
irregular Superficies, but in the regular; amongſt which thoſe
of more Sides are alwayes more capacious than thoſe of fewer;
ſo that in fine, the Circle, as being a Poligon of infinite Sides, is
more capacious than all other Poligons of equal Perimeter; of
which I remember, that I with particular delight ſaw the Demon­
ſtration on a time when I ſtudied the Sphere of Sacroboſco, with
a very learned Commentary upon the ſame.
SALV. It is moſt certain; and I having likewiſe light upon
that very place, it gave me occaſion to inveſtigate, how it may
with one ſole Demonſtration be concluded, that the Circle is
greater than all the reſt of regular Iſoperemitral Figures, and of
others, thoſe of more Sides bigger than thoſe of fewer.
SAGR. And I that take great pleaſure in certain ſelect and no­
wiſe-trivial Demonſtrations, entreat you with all importunity to
make me a partaker therein.
SALV. I ſhall diſpatch the ſame in few words, demonſtrating
the following Theorem, namely;
1
PROPOSITION.
The Circle is a Mean-Proportional betwixt any two
Regular Homogeneal Poligons, one of which is cir­
cumſcribed about it, and the other Iſoperimetral to
it: Moreover, it being leſſe than all the circumſcri­
bed, it is, on the contrary, bigger than all the Iſoperi­
metral. And, again of the circumſcribed, thoſe that
have more angles are leſſer than thoſe that have
fewer; and on the other ſide of the Iſoperimetral,
thoſe of more angles are bigger.
Of the two like Poligons A and B, let A be circumſcribed
about the Circle A, and let the other B, be Iſoperime­
tral to the ſaid Circle: I ſay, that the Circle is the Mean­
proportional betwixt them. For that (having drawn the Semidi­
ameter A C) the Circle being equal to that Right-angled Trian­
gle, of whoſe Sides including the Right angle, the one is equal
63[Figure 63]
to the Semidiameter A C, and the other to the Circumference:
And likewiſe the Poligon A being equal to the right angled Tri­
angle, that about the right angle hath one of its Sides equal to
the ſaid right line A C, and the other to the Perimeter of the ſaid
Poligon: It is manifeſt, that the circumſcribed Poligon hath the
ſame proportion to the Circle, that its Perimeter hath to the Cir­
cumference of the ſaid Circle; that is, to the Perimeter of the
Poligon B, which is ſuppoſed equal to the ſaid Circumference:
But the Poligon A hath a proportion to the Poligon B, double to
that of its Perimeter, to the Perimeter of B (they being like Fi­
gures:) Therefore the Circle A is the Mean-proportional be­
tween the two Poligons A and B. And the Poligon A being
bigger than the Circle A, it is manifeſt that the ſaid Circle
A is bigger than the Poligon B, its Iſoperimetral, and conſe­
quently the greateſt of all Regular Poligons that are Iſoperimetral
1to it. As to the other particular, that is to prove, that of the
Poligons circumſcribed about the ſame Circle, that of fewer
Sides is bigger than that of more Sides; but that, on the contrary, of
the Iſoperimetral Poligons, that of more Sides is bigger than that
of fewer Sides, we will thus demonſtrate. In the Circle whoſe
Center is O, and Semidiameter O A, let there be a Tangent
A D, and in it let it be ſuppoſed, for example, that A D is the
half of the Side of the Pentagon circumſcribed, and A C the half
of the Side of the Heptagon, and draw the right lines O G C,
and O F D; and on the Center O, at the diſtance O C, draw the
Arch E C I: And becauſe the Triangle D O C is greater than the
Sector E O C, and the Sector C O I greater than the Triangle
C O A; the Triangle D O C ſhall have greater proportion to
the Triangle C O A, than the Sector E O C, to the Secant C O I,
that is, than the Secant F O G to the Secant G O A. And, by
Compoſition, Permutation of Proportion, the Triangle D O A
ſhall have greater proportion to the Secant F O A, than the Tri­
angle C O A to the Secant G O A: And ten Triangles D O A
ſhall have greater proportion to ten Secants F O A, than four­
teen Triangles C O A to fourteen Sectors G O A: That is the
circumſcribed Pentagon ſhall have greater proportion to the Cir­
cle, than hath the Heptagon: And therefore the Pentagon ſhall
be greater than the Heptagon. Let us now ſuppoſe an Hep­
tagon and a Pentagon Iſoperimetral to the ſame Circle. I ſay, that
the Heptagon is bigger than the Pentagon. For that the ſaid Cir­
cle being the Mean proportional between the Pentagon circum­
ſcribed and the Pentagon its Iſoperimetral, and likewiſe the Mean
between the Circumſcribed and Iſoperimetral Heptagon: It ha­
ving been proved that the Circumſcribed Pentagon is greater then
the Circumſcribed Heptagon, the ſaid Pentagon ſhall have greater
proportion to the Circle, than the Heptagon: that is, the Circle
ſhall have greater proportion to its Iſoperimetral Pentagon, than
to its Iſoperimetral Heptagon: Therefore the Pentagon is leſſer
than the Iſoperimetral Heptagon. Which was to be demon­
ſtrated
SAGR. A moſt ingenious Demonſtration, and very acute. But
whither are we run to ingulph our ſelves in Geometry, when as
we were about to conſider the Difficulties propoſed by Simpli­
cius, which indeed are very conſiderable, and in particular, that
of Condenſation, is in my opinion, very abſtruce.
SALV. If Condenſation and Rarefaction are oppoſite Motions,
where there is ſeen an immenſe Rarefaction, one cannot deny an
extraordinary Condenſation: but immenſe Rarefactions, and,
which encreaſeth the wonder, almoſt Momentary, we ſee every
day: for what a boundleſſe Rarefaction is that of a little quan­
1
tity of Gunpowder reſolved into a vaſt maſſe of Fire? And what,
beyond this, the (I could almoſt ſay) indeterminate Expanſion
of its Light? And if that Fire and this Light ſhould reunite toge­
ther, which yet is no impoſſibility, in regard, that at the firſt
they lay in that little room, what a Condenſation would this be?
If you ſtudy for them, you will find hundreds of ſuch Rarefacti­
ons, which are much more readily obſerved, than Condenſati­
ons: for Denſe matters are more tractable, and ſubject to our
Senſes. For we can eaſily order Wood at pleaſure, and we ſee
it reſolved into Fire, and into Light, but we do not in the ſame
manner ſee the Fire and the Light Condenſe to the making of
Wood: We ſee Fruits, Flowers, and many other ſolid matters
reſolved in a great meaſure into Odors, but we do not after the
ſame manner ſee the odoriferous Atomes concurre to the conſtitu­
tion of the Oderate Solids; but where Senſible Obſervation is
wanting, we are to ſupply it with Reaſon, which will ſuffice to
make us apprehenſive, no leſſe of the Motion to the Rarefaction
and reſolution of Solids, than, to the Condenſation of rare and
moſt tenuous Subſtances. Moreover, we queſtion how to effect
the Condenſation and Rarefaction of the Bodies which may be
rarefied and condenſed, ſtudying in what manner it may be done
without introducing of a Vacuum, and Penetration of Bodies;
which doth not hinder, but that in Nature there may be matters
which admit no ſuch accidents, and conſequently do not allow
roome for thoſe things which you phraſe inconvenient and im­
poſſible. And laſtly, Simplicius, I have on the the ſcore of ſatis­
fying you, and thoſe Philoſophers that hold with you, taken
ſome pains in conſidering how Condenſation and Rarefaction
may be underſtood to be performed without admitting Penetra­
tion of Bodies, and introducing the Void Spaces called Vacuities,
Effects which you deny and abhorre: for if you would but grant
them, I would no longer ſo reſolutely contradict you. There­
fore either admit theſe Inconveniences, or accept of my Spe­
culations, or elſe finde out others more conducing to the
purpoſe.
Rarefaction im­
minſe is that of
a little Gunpow­
der into a vaſt
maſs of Fire.
SAGR. As to the denying of Penetration, I am wholly of opi­
nion with the Peripatetick Philoſophers; as to that of a Vacuum,
I would ſee the Demonſtration of Ariſtotle thorowly examined,
wherewith he oppoſeth the ſame, and what you, Salviatus, will
anſwer to it. Simplicius ſhall do me the favour punctually to
recite the proof of the Philoſopher; and you, Salviatus, to an­
ſwer it.
SIMP. Ariſtotle, as neer as I can remember, breaks out againſt
certain of the Ancients, who introduced Vacuity, as neceſſary
to Motion, ſaying, that this without that could not be effected;
1to this Ariſtotle making oppoſition, demonſtrateth, that on the
contrary, the effecting of Motion (as we ſee) deſtroyeth the Poſiti­
on of Vacuum; and his method therein is this. He maketh two
Suppoſitions, one is touching Moveables different in Gravity
moved in the ſame Medium: the other is concerning the ſame
Moveable moved in ſeveral Medium's. As to the firſt, he ſuppo­
ſeth that Moveables different in Gravity, move in the ſame
Medium with unequal Velocities, which bear to each other the
ſame proportion as their Gravities: ſo that, for example, a Move­
able ten times heavier than another, moveth ten times more ſwift­
ly. In the other Poſition he aſſumes, that the Velocity of the
ſame Moveable in different Medium's are in Reciprocal to that of
the thickneſſe or Denſity of the ſaid Medium's: ſo that ſuppo­
ſing v. gr. that the Craſſitude of the Water was ten times as great
as that of the Air, he will have the Velocity in the Air to be
ten times more than the Velocity in the Water. And from this ſe­
cond Aſſumption he draweth his Demonſtration in this manner.
Becauſe the tenuity of Vacuum infinitely ſurpaſſeth the corpu­
lence, though never ſo ſubtil, of any whatever Replete Medi­
um, every Moveable that in the Replete Medium moveth a cer­
tain ſpace in a certain time, in a Vacuum would paſſe the ſame
in an inſtant: But to make a Motion in an inſtant is impoſſible:
Therefore to introduce Vacuity in the accompt of Motion is im­
poſſible.
SALV. The Argument one may ſee to be ad hominem, that is,

againſt thoſe who would make a Vacuum neceſſary to Motion;
but if I ſhall admit of the Argument as concludent, granting
withal, that in Vacuity there would be no Motion; yet the Poſi­
tion of Vacuity taken abſolutely, and not in relation to Motion,
is not thereby overthrown. But to tell you what thoſe Ancients,
peradventure, might anſwer, that ſo we may the better diſcover
how far the Demonſtration of Ariſtotle holds good, methinks that
one might oppoſe his Aſſumptions, denying them both. And as
to the firſt: I greatly doubt that Ariſtotle never experimented
how true it is, that two ſtones, one ten times heavier than the o­
ther, let fall in the ſame inſtant from an height, v. gr. of an hun­
dred yards, were ſo different in their Velocity, that upon the
arrival of the greater to the ground, the other was found not to
have deſcended ſo much as ten yards.
Ariſtotle's Argu­
ment againſt a
Vacuum is ad
hominem.
SIMP. Why, it may be ſeen by his own words, that he confeſ­
ſeth he had made the Experiment, for he ſaith, [We ſee the more
grave] now that Seeing implieth that he had tried the Experi­
ment.
SAGR. But I, Simplicius, that have made proof thereof, do aſ­
ſure you, that a Cannon bullet that weigheth one hundred, rwo
1hundred, and more pounds, will not one Palme anticipate the ar­
rival of a Musket-bullet to the ground, that weigheth but half
a pound, falling likewiſe from an height of two hundred yards.
SALV. But without any other Experiments, we may by ſhort
and neceſſary Demonſtrations cleerly prove, that it is not true that
a Moveable more grave moveth more ſwiftly than another leſſe
grave, confining our meaning ſtill to Moveables of the ſame Mat­
ter; and, in ſhort, to thoſe of which Ariſtotle ſpeaketh. For tell
me, Simplicius whether you admit, that to every cadent grave
Body there belongeth by nature one determinate Velocity; ſo
as that it cannot be encreaſed or diminiſhed in it without uſing vi­
olence to it, or impoſing ſome impediment upon it?
SIMP. It cannot be doubted, but that the ſame Moveable in
the ſame Medium hath one eſtabliſhed and by-nature-determinate
Velocity, which cannot be increaſed, unleſſe with new Impetus
conferred on it, or diminiſhed, ſave onely by ſome impediment
that retards it.
SALV. If therefore we had two Moveables, the natural Velo­
cities of which were unequal, it is manifeſt, that if we joyned the
ſlower with the ſwifter, this would be in part retarded by the
ſlower, and that in part accelerated by the other more ſwift. Do
not you concur with me in this opinion?
SIMP. I think that it ought undoubtedly ſo to ſucceed.
SALV. But if this be ſo, and, it be likewiſe true that a great
Stone moveth with (ſuppoſe) eight degrees of Velocity, and a leſ­
ſer with fewer, then joyning them both together, the compound
of them will move with a Velocity leſſe than eight Degrees: But
the two Stones joyned together make one Stone greater than
that before, which moved with eight degrees of Velocity: There­
fore this greater Stone moveth leſſe ſwiftly than the leſſer, which
is contrary to your Suppoſition. You ſee therefore, that from the
ſuppoſing that the more grave Moveable moveth more ſwiftly
than the leſſe grave, I prove unto you that the more grave mo­
veth leſſe ſwiftly.
SIMP. I find my ſelf at a loſſe, for the truth is, that the leſ­
ſer Stone being joyned to the greater, weight is added unto it, and
weight being added to it, I cannot ſee why there ſhould not Ve­
locity be added to it, or at leaſt why it ſhould be diminiſhed
in it.
SALV. Here you run into another errour, Simplicius, for it
is not true, that that ſame leſſer Stone encreaſeth the weight of
the greater.
SIMP. Oh wonderful! this quite ſurpaſſeth my apprehenſion.
SALV. Not at all, if you will but ſtay till I have diſcovered
to you the Equivokes, of which you are in doubt: Therefore
1you muſt know that it is neceſſary to diſtinguiſh betwixt grave
Bodies ſet on Moving, and the ſame conſtituted in Reſt; a Stone
put into the Ballance not onely acquireth greater weight, by lay­
ing another Stone upon it, but alſo the addition of, a Flake of
Hemp will make it weigh more by thoſe ſix or ten ounces that
the Hemp ſhall weigh; but if you ſhould freely let fall the Stone
tied to the Hemp from an high place, do you think that in the
Motion the Hemp weigheth down the Stone, ſo as to accelerate
its Motion; or elſe do you believe that it will retard it, ſuſtain­
ing it in part? We indeed feel our ſhoulders laden, ſo long as we
will oppoſe the Motion that the weight would make which lyeth
upon our backs; but if we ſhould deſcend with the ſame Velocity
wherewith that ſame grave Body would naturally deſcend, in what
manner will you that it preſſe or bear upon us? Do not you ſee
that this would be a wounding one with a Lance that runneth
before you, with as much or more ſpeed than you purſue him.
You may conclude therefore that in the free and natural fall, the
leſſer Stone doth not bear upon the greater, and conſequently doth
not encreaſe their weight, as it doth in Reſt.
SIMP. But what if the greater was put upon the leſſer?
SALV. It would encreaſe their weight, in caſe its Motion were
more ſwift; but it hath been already concluded, that in caſe the
leſſer ſhould be more ſlow it would in part retard the Velocity of
the greater, ſo that there Compound would move leſſe ſwiftly;
being greater than the other, which is contrary to your Aſſumpti­
on: Let us conclude therefore, that great Moveables, and like­
wiſe little, being of the ſame Specifical Gravity, move with like
Velocity.
SIMP. Your diſcourſe really is full of ingenuity, yet methinks
it is hard to conceive that a drop of Bird-ſhot, ſhould move as
ſwiftly as a Canon-bullet.
SALV. You may ſay a grain of Sand as faſt as a Mill-ſtone.
I would not have you, Simplicius, to do as ſome others are wont
to do, and diverting the diſcourſe from the principal deſign, fa­
ſten upon ſome one ſaying of mine that may want an hairs-breadth
of the truth, and under this hair hide a defect of another man as
big as the Cable of a Ship. Aristotle ſaith, a Ball of Iron of an
hundred pounds weight falling, from an height of an hundred yards,
commeth to the ground before that one of one pound is deſcended
one ſole yard: I ſay, that they arrive at the earth both in the ſame
time: You find, that the bigger anticipates the leſſer two Inches,
that is to ſay, that when the great one falls to the ground, the o­
ther is diſtant from it two inches: you go about to hide under
theſe two inches the ninety nine yards of Ariſtotle, and ſpeaking
onely to my ſmall errour, paſſe over in ſilence the other great one.
1Ariſtotlee affirmeth, that Moveables of different Gravities in the
ſame Medium move (as far as concerneth Gravity) with Veloci­
ties proportionate to their Weights; and exemplifieth it by
Moveables, wherein one may diſcover the pure and abſolute effect
of Weight, omitting the other Conſiderations, as well of Figures,
as of the minute Motions; which things receive great alteration
from the Medium, which altereth the ſimple effect of the ſole
Gravity; wherefore we ſee Gold, that is heavier than any other
matter, being reduced into a very thin Leaf, to go flying to and
again through the Air, the like do Stones beaten to very ſmall
Powder. But if you would maintain the Univerſal Propoſition, it
is requiſite that you ſhew the proportion of the Velocities to be
obſerved in all grave Bodies, and that a Stone of twenty pounds
moveth ten times ſwifter than one of two: which, I tell you, is
falſe, and that falling from an height of fifty or an hundred yards,
they come to the ground in the ſame inſtant.
SIMP. Perhaps in very great heights of Thouſands of yards
that would happen, which is not ſeen to occur in theſe leſſer
heights.
SALV. If this was the Meaning of Ariſtotle, you have in­
volved him in another Errour, which will be found a Lie; for
there being no ſuch perpendicular altitudes found on the Earth,
its a clear caſe, that Ariſtotle was not able to have made an Experi­
ment thereof; and yet would perſwade us that he had, whilſt he
ſaith, that the ſaid effect is ſeen.
SIMP. Ariſtotle indeed makes no uſe of this Principle, but of
that other, which I believe is not obnoxious to theſe doubts.
SALV. Why that alſo is no leſſe falſe than this; and I admire
that you do not of your ſelf perceive the fallacy, and diſcern, that
ſhould it be true, that the ſame Moveable in Medium's of dif­
ferent Subtilty and Rarity, and, in a word, of different Ceſſion,
ſuch, for example, as are Water and Air, move with a greater
Velocity in the Air than in the Water, according to the propor­
tion of the Airs Rarity to the Rarity of the Water, it would
follow that every Moveable that deſcendeth in the Air would
deſcend alſo in the Water: Which is ſo falſe, that very many
Bodies deſcend in the Air, that in the Water do not onely not
deſcend, but alſo riſe upwards.
SIMP I do not underſtand the neceſſity of your Conſequence:
and I will ſay farther, that Ariſtotle ſpeaketh of thoſe Grave­
bodies that deſcend in the one Medium and in the other, and not
of thoſe that deſcend in the Air and aſcend in the Water.
SALV. You produce for the Philſopher ſuch Pleas as he, with­
out all doubt, would never alledge, for that they aggravate the
firſt miſtake. Therefore tell me, if the Craſsitude of the Water,
1or whatever it be that retardeth the Motion, hath any proporti­
on to the Craſſitude of the Air that leſſe retards it; and if it have;
do you aſſign it us, at pleaſure.
SIMP. It hath ſuch a proportion, and we will ſuppoſe it to be
decuple; and that therefore the Velocity of a Grave Body, that
deſcends in both the Elements, ſhall be ten times ſlower in the Wa­
ter than in the Air.
SALV. I will take one of thoſe Grave-Bodies that deſcend in
the Air, but not in the Water; as for inſtance, a Ball of Wood,
and deſire that you will aſſign it what Velocity you pleaſe, whilſt it
deſcends through the Air.
SIMP. Suppoſe we, that it move with twenty degrees of Velo­
city.
SALV. Very well: And it is manifeſt, that that Velocity to
ſome other leſſer, may have the ſame proportion, that the Craſſi­
tude of the Water hath to that of the Air; and that this ſhall be
the Velocity of the two only degrees: ſo that exactly to an hair,
and in direct conformity to the Aſſumption of Ariſtotle, it ſhould
be concluded, That the Ball of Wood, which in the Air, ten times
more yielding, moveth deſcending with twenty degrees of Veloci­
ty, in the Water ſhould deſcend with two, and not return from the
bottom to flote a-top, as it doth: unleſs you will ſay, that the
aſcending of the Wood to the top is the ſame in the Water, as its
ſinking to the bottom with two degrees of Velocity; which I do
not believe. But ſeeing that the Ball of Wood deſcends not to the
bottom, I rather think that you will grant me, that ſome other Ball,
of other matter different from Wood, might be found that deſcends
in the Water with two degrees of Velocity.
SIMP. Queſtionleſſe there might; but it muſt be of a matter
conſiderably more grave than Wood.
SALV. This is that which I deſired to know. But this ſecond
Ball, which in the Water deſcendeth with two degrees of Velocity,
with what Velocity will it deſcend in the Air? It is requiſite (if
you will maintain Ariſtotles Rule) that you anſwer that it will
move with twenty degrees: But you your ſelf have aſſigned twen­
ty degrees of Velocity to the Ball of Wood; Therefore this, and
the other that is much more grave, will move thorow the Air with
equall Velocity. Now how doth the Philoſopher reconcile this
Concluſion with that other of his, that the Moveables of different
Gravity, move in the ſame Medium with different Velocities, and
ſo different as are their Gravities? But, without any deep ſtudies,
how comes it to paſs that you have not obſerved very frequent,
and very palpable Accidents, and not conſidered two Bodies, that in
the Water will move one an hundred times more ſwiftly than the
other, but that again in the Air that ſwifter one will not out-go the
1other, one ſole Centeſm? As for example, an Egge of Marble will
deſcend in the Water an hundred times faſter than one of an Hen,
when as in the Air, at the height of twenty Yards it will not anti­
cipate it four Inches: and, in a word, ſuch a certain Grave Body
will ſink to the bottom in three hours in ten fathom Water, that
in the Air will paſs the ſame ſpace in one or two pulſes, and ſuch
another (as for inſtance a Ball of Lead) will paſs that number of
fathoms with eaſe in leſs than double the time. And here I ſee
plainly, Simplicius, that you find, that herein there is no place left
for any diſtinction, or reply. Conclude we therefore, that that
ſame Argument concludeth nothing againſt Vacuum; and if it
ſhould, it would only overthrow Spaces conſiderably great, which
neither I, nor, as I take it, thoſe Ancients did ſuppoſe to be natu­
rally allowed, though, perhaps, with violence they may be effe­
cted, as, me thinks, one may collect from ſeveral Experiments, which
it would be two tedious to go about at preſent to produce.
SAGR. Seeing that Simplicius is ſilent, I will take leave to ſay
ſomething. In regard you have with ſufficient plainneſſe demon­
ſtrated, that it is not true, That Moveables unequally grave move in
the ſame Medium with Velocities proportionate to their Gravities,
but with equal: deſiring to be underſtood to ſpeak of Bodies of the
ſame Matter, or of the ſame Specifick Gravity, but not (as I con­
ceive) of Gravities different in Spetie, (for I do not think that
you intend to prove unto us, that a Ball of Cork moveth with like
Velocity to one of Lead;) and having moreover very manifeſtly
demonſtrated, that it is not true, That the ſame Moveable in Me­
diums of different Reſiſtances retain in their Velocities and Tardi­
ties the ſame proportion as have their Reſiſtances: to me it would
be a very pleaſing thing to hear, what thoſe be which are obſerved
as well in the one caſe as in the other.
SALV. The Queſtions are ingenuous, and I have many times
thought of them: I will relate unto you the Contemplations made
upon them, and what at length I did from thence infer. After I
had aſſured my ſelf that it was not true, That the ſame Moveable
in Medium's of different Reſiſtance obſerveth in its Velocity the
proportion of the Ceſſion of thoſe Media; nor yet, again, That in
the ſame Medium Moveables of different Gravity retain in their
Velocities the proportion of thoſe Gravities (ſpeaking alwaies of
Gravitles different in ſpecie) I began to put both theſe Accidents
together, obſerving that which befell the Moveables different in
Gravity put into Mediums of different Reſiſtance, and I perceived
that the inequality of the Velocities were found to be alwaies
greater in the more reſiſting Medium's, than in the more yielding;
and that with ſuch a diverſity, that of two Moveables that, de­
ſcending thorow the Air, differ very little in Velocity of Motion,
1one will, in the Water, move ten times faſter than the other;
yea: that ſuch, as in the Air do ſwiftly deſcend, in the Water not
only will not deſcend, but will be wholly deprived of Motion,
and, which is yet more, will move upwards: for one ſhall ſome­
times find ſome kind of Wood, or ſome knot, or root of the ſame,
that in the Water will lye ſtill, when as in the Air it will ſwiftly
deſcend.
SAGR. I have many times ſet my ſelf with an extream patience
to ſee if I could reduce a Ball of Wax, (which of it ſelf doth not
go to the bottom) by adding to it grains of ſand, to ſuch a degree
of Gravity like to the Water, as to make it ſtand ſtill in the
midſt of that Element; but I could never, by all the care I
uſed, ſucceed in my attempt; ſo that I cannot tell, whether any
Solid matter may be found ſo naturally alike in Gravity to Wa­
ter, as that being put into any place of the ſame, it can reſt or lye
ſtill.
SALV. In this, as well as in a thouſand other actions, many
Animals are more ingenuous than we. And, in this caſe, Fiſhes

would have been able to have given you ſome light, being in this
affair ſo skilful, that at their pleaſure they ^{*} equilibrate themſelves,

not only with one kind of Water, but with ſuch, as, either of their
own nature, or by means of ſome ſupervenient muddineſs, or for
their ſaltneſs (which maketh a great alteration) are very diffe­
rent; equilibrate themſelves, I ſay, ſo exactly, that without ſtir­
ring in the leaſt they lye ſtill in every place: and this, in my opi­
nion, they do, by making uſe of the Inſtrument given them by Na­
ture to that end, ſcilicet, of that Bladder which they have in their
Bodies, which by a very narrow neck anſwereth to their mouth;
and by that they either, when they would ſtand ſtill, ſend forth
part of the Air that is contained in the ſaid Bladders, or, ſwimming
to the top they draw in more, making themſelves by that art one
while more, another while leſs heavy than the Water, and at their
pleaſures equilibrating themſelves to the ſame.
Fiſhes equilibrate
themſelves admi­
rably in the Water.
* Or poiſe.
SAGR I deceived ſome of my Friends with another device;
for I had made my boaſt unto them, that I would reduce that Ball
of Wax to an exact equilibrium with the Water, and having put
ſome ſalt Water in the bottom of the Veſſel, and a-top of that ſome
freſh, I ſhewed them the Ball, which in the midſt of the Water
ſtood ſtill, and being thruſt to the bottom, or to the top, ſtaid nei­
ther in this nor that ſcituation, but returned to the midſt.
SALV. This ſame Experiment is not void of utility; for Phyſi­

cians, in particular, treating of ſundry qualities of Waters, and
amongſt other things, principally of the more or leſs Gravity or
Levity of this or that: by ſuch a Ball, in ſuch manner poiſed and
adjuſted that it may reſt ambiguous, if I may ſo ſay, between
1aſcending and deſcending in a Water, upon the leaſt difference
of weight between two Waters, if that Ball ſhall deſcend in the
one; in the other, that is more grave, it ſhall aſcend. And the
Experiment is ſo exact, that the addition of but only two grains
of Salt, put into ſix pounds of Water, ſhall make that Ball to
aſcend from the bottom to the ſurface, which was but a little be­

fore deſcended thither. And moreover, I will tell you this in con­
firmation of the exactneſs of this Experiment, and withall for a
clear proof of the Non-reſiſtance of Water to diviſion, that not
only the ingravitating it with the mixture of ſome matter heavier
than it, maketh that ſo notable difference, but the warming or
cooling of it a little produceth the ſame effect, and with ſo ſubtil
an operation, that the infuſing four diops of other Water, a lit­
tle warmer, or a little colder, than the ſix pounds, ſhall cauſe the
Ball to riſe or ſink in the ſame; to ſink in it upon the infuſion of
the warm, and to riſe at the infuſion of the cold. Now ſee how
much thoſe Philoſophers are deceived, who would introduce in
Water viſcoſity, or other conjunction of parts which make it to
reſiſt Diviſion or Penetration.
A Ball of Wax
prepared to make
the Experiment of
the different Gra­
vities of Waters.
Water bath no
Reſiſtance to Di­
viſion.
SAGR. I have ſeen many Convincing Diſcourſes touching

this Argument in a ^{*} Treatiſe of our Accademick; yet never the leſs
there is reſting in me a ſtrong ſcruple, which I know not how to
remove: For if nothing of Tenacity, or Coherence reſides amongſt
the parts of Water, how can it bear it ſelf up in reaſonable big
and high Tumours; in particular, upon the leaves of Cole-worts
without diſperſing or levelling?
* The Tract cited
in this place is
that which we
diſpoſe firſt in
Order, in the
firſt part of this
Tome,
SALV. Although it be true, that he who is Maſter of a true
Concluſion, may reſolve all Objections that can be brought againſt
it, yet will not I arrogate to my ſelf the power ſo to do; nor
ought my inſufficiency becloud the ſplendour of Truth. Firſt,
therefore, I confeſs that I know not how it cometh to paſs, that
thoſe Globes of Water ſuſtain themſelves at ſuch an height and
bigneſs, albeit I certainly know that it doth not proceed from any

internal Tenacity that is between its parts; ſo that it remaineth
neœſſary, that the Cauſe of that Effect do reſide without. That it
is not Internal, beſides thoſe Experiments already ſhewn you, I can
prove by another moſt convincing one. If the parts of that Wa­
ter, which conſerveth it ſelf in a Globe or Tumour whilſt it is en­
compaſſed by the Air, had an internal Cauſe for ſo doing, they
would much better ſuſtain themſelves being environed by a Medi­
um, in which they had leſs propenſion to deſcend, than they have
in the Ambient Air: But every Fluid Body more grave than the
Air would be ſuch a Medium; as, for inſtance, Wine: And there­
fore, infuſing Wine about that Globe of Water, it might raiſe it
ſelf on every ſide, and yet the parts of the Water, conglutinated
1by the internal Viſcoſity, never diſſolve: But it doth not happen
ſo; nay, no ſooner doth the circumfuſed liquor approach thereto,
but, without ſtaying till it riſe much about it, the little globes of
Water will diſſolve and become flat, reſting under the Wine, if it
was red. The Cauſe therefore of this Effect is External, and per­
haps in the Ambient Air: and, indeed, one may obſerve a great
diſſention between the Air and Water; which I have obſerved
in another Experiment; and this it is: If I fill a ^{*} Ball of Chriſtal,

that hath a mouth as narrow as the hollow of a ſtraw, with water,
and when it is thus full, turn it with its mouth downwards, yet will
not the Water, although very heavy, and prone to deſcend tho­
row the Air, nor the Air, as much diſpoſed on the other hand, as
being very light, to aſcend thorow the Waters, yet will they not
(I ſay) agree that that ſhould deſcend, iſſuing out at the mouth,
and this aſcend, entering in at the ſame: but they both continue
averſe and contumacious. Again, on the contrary, if I preſent to
that mouth a veſſel of red Wine, which is almoſt inſenſibly leſs
grave than Water, we ſhall ſee it in an inſtant gently to aſcend by
red ſtreams thorow the Water, and the Water with like Tardity to
deſcend through the Wine, without ever mixing with each other,
till that in the end, the Ball will be full of Wine, and the Water
Will all ſink unto the bottom of the Veſſel underneath. Now
what are we to ſay, or what are we to infer, but a diſagreement
between the Water and Air, occult to me, but perhaps -----
Water formed into
great drops upon
the Leaves of Col­
worts, how they
conſiſt.
* Or bottle.
SIMP. I can ſcarce refrain my laughter to ſee the great Anti­
pathy that Salviatus hath to Antipathy, ſo that he will not ſo much
as name it, and yet it is ſo accommodate to reſolve the doubt.
SALV. Now let this, for the ſake of Simplicius be the ſoluti­
on of our ſcruple; and leaving the Digreſſion, let us return to our
purpoſe. Seeing that the difference of Velocity in Moveables of
divers Gravities is found to be more and more, as the Mediums are
more and more Reſiſting: And withall, that in a Medium of
Quickſilver, Gold doth not only go to the bottom more ſwiftly
than Lead, but it alone deſcends in it, and all other Metals and
Stones move upwards therein, and flote thereon; whereas between
Balls of Gold, Lead, Braſs, Porphiry, or other grave matters, the in­
equality of motion in the Air ſhall be almoſt wholly inſenſible, for
it is certain, that a Ball of Gold in the end of the deſcent of an

hundred yards ſhall not out-ſtrip one of Braſs four Inches: ſeeing
this, I ſay, I have thought, that if we wholly took away the
Reſiſtance of the Medium, all Matters would deſcend with equall
Velocity.
Reſiſtance of the
Medium remo­
ved, all Matters,
though of different
Gravities would
move with like
Velocity.
SIMP. This is a bold ſpeech, Salviatus, I ſhall never believe
that in Vacuity it ſelf, if ſo be one ſhould allow Motion in it, a lock
of Wooll would move as ſwiftly as a piece of Lead.
1
SALV. Fair and ſoftly, Simplicius, your ſcruple is not ſo ab­
ſtruce, nor I ſo incautelous, that you ſhould need to think that I
was not adviſed of it, and that conſequently I have not found a re­
ply to it. Therefore, for my explanation, and your information,
hearken to what I ſhall ſay. We are upon the examination of
what would befall Moveables exceeding different in weight in a
Medium, in caſe it ſhould have no Reſiſtance, ſo that all the diffe­
rence of Velocity that is found between the ſaid Moveables ought
to be referred to the ſole inequality of Weight. And becauſe on­
ly a Space altogether void of Air, and of every other, though te­
nuous and yielding Body, would be apt ſenſibly to ſhew us what
we ſeek, ſince we want ſuch a Space, let us ſucceſſively obſerve that
which happeneth in the more ſubtill and leſſe reſiſting Mediums,
in compariſon of that which we ſee to happen in others leſſe ſubtill
and more reſiſting: for if we ſhould really find the Moveables
different in Gravity to differ leſſe and leſſe in Velocity, according
as the Mediums are found more and more yielding; and that,
finally, although extreamly unequal in weight, in a Medium more
tenuous than any other, though not void, the difference of Velo­
city diſcovers it ſelf to be very ſmall, and almoſt unobſervable, I
conceive that we may, and that upon very probable conjecture,
believe, that in a Vacuum their Velocities would be exactly equal.
Therefore let us conſider that which hapneth in the Air; wherein
to have a Figure of an uniform Superficies, and very light Matter,
I will that we take a blown Bladder, in which the included Air
will weigh little or nothing in a Medium of the Air it ſelf, becauſe
it can make but very ſmall Compreſſion therein, ſo that the Gravi­
ty is only that little of the ſaid film, which would not be the thou­
ſandth part of the weight of a lump of Lead of the bigneſs of
the ſaid Bladder when blown. Theſe, Simplicius, being let fall
from the height of four or ſix yards, how great a ſpace, do you
judge, that the Lead would anticipate the Bladder in its deſcent?
Aſſure your ſelf that would not move thrice, no nor twice as faſt,
although even now you would have had it to have been a thou­
ſand times more ſwift.
SIMP. It is poſſible that at the beginning of the Motion, that
is, in the firſt five or ſix yards this might happen that you ſay; but
in the progreſſe, and in a long continuation I believe, that the Lead
would leave it behind, not only ſix, but alſo eight and ten parts of
twelve.
SALV. And I alſo believe the ſame: and make no queſtion,
but that in very great diſtances the Lead will have paſſed an hun­
dred miles of way, ere the Bladder will have paſſed ſo much as one.
But this, Simplicius, which you propound, as an effect contrary to
my Aſſertion, is that which moſt eſpecially confirmeth it. It is (I
1once more tell you) my intent to declare, That the difference of
Gravity is in no wiſe the cauſe of the divers velocities of Movea­
bles of different Gravity, but that the ſame dependeth on exteri­
our accidents, & in particular, on the Reſiſtance of the Medium, ſo
that, this being removed, all Moveables move with the ſame de­
grees of Velocity. And this I chiefly deduce from that which but
now you your ſelf did admit, and which is very true, namely, that
of two Moveables, very different in weight, the Velocities more and
more differ, according as the ^{*} Spaces are greater and greater that

they paſſe: an Effect which would not follow, if it did depend on
the different Gravities: for they being alwaies the ſame, the pro­
portion betwixt the Spaces would likewiſe alwaies continue the
ſame, which proportion we ſee ſtill ſucceſſively to encreaſe in the
continuance of the Motion; for that the heavieſt Moveable in the
deſcent of one yard will not anticipate the lighteſt the tenth part
of that Space or Way, but in the fall of twelve yards will out-go
it a third part, in that of an hundred will outſtrip it 90/100.
* Or Waies.
SIMP. Very well: But following you ſtep by ſtep, if the dif­
ference of weight in Moveables of different Gravities cannot
cauſe the difference of proportion in their Velocities, for that the
Gravities do not alter; neither then can the Medium, which is
ſuppoſed alwaies to continue the ſame, cauſe any alteration in the
proportion of the Velocities.
SALV. You wittily bring an inſtance againſt my Poſition, that

it is very neceſſary to remove. I ſay therefore, that a Grave Body
hath, by Nature, an intrinſick Principle of moving towards the
Common Center of heavy things, that is to that of our Terreſtrial
Globe, with a Motion continually accelerated, and accelerated
alwaies equally, ſcilicet, that in equal times there are made equal
^{*} additions of new Moments, and degrees of Velocities: and this
ought to be underſtood to hold true at all times when all acciden­

tal and external impediments are removed; amongſt which there
is one that we cannot obviate, that is the Impediment of the Me­
dium, which is Repleat, when as it ſhould be opened and latterally
moved by the falling Moveable, to which tranſverſe Motion the
Medium, though fluid, yielding and tranquile, oppoſeth it ſelf
with a Reſiſtance one while leſſer, and another while greater and
greater, according as it is more ſlowly or haſtily to open to give
paſſage to the Moveable, which, becauſe, as I have ſaid, it goeth
of its own nature continually accelerating, it cometh of conſe­
quence to encounter continually greater Reſiſtance in the Medi­
um, and therefore Retardment, and diminution in the acquiſt of
new degrees of Velocity; ſo that in the end, the Velocity arriveth
to that ſwiftneſſe, and the Reſiſtance of the Medium, to that
ſtrength, that ballancing each other, they take away all further
1Acceleration, and reduce the Moveable to an Equable and Uni­
form Motion, in which it afterwards continually abides. There is
therefore in the Medium augmentation of Reſiſtance, not becauſe
it changeth its Eſſence, but becauſe the Velocity altereth where­
with it ought to open, and laterally move, to give paſſage to the
falling Body, which goeth continually accelerating. Now the
obſerving, that the Reſiſtance of the Air to the ſmall Moment or
Impetus of the Bladder is very great, and to the great weight of
the Lead is very ſmall, makes me hold for certain, that if one ſhould
wholly remove it, by adding to the Bladder great aſſiſtance, and
but very little to the Lead, their Velocities would equalize each
other. Taking this Principle therefore for granted, That in the
Medium wherein, either by reaſon of Vacuity, or otherwiſe, there
were no Reſiſtance that might abate the Velocity of the Motion,
ſo that of all Moveables the Velocities were alike, we might con­

gruouſly enough aſſign the proportions of the Velocities of like
and unlike Moveables, in the ſame and in different, Replear, and
therefore Reſiſting Medium's. And this we might effect by ſtudy­
ing how much the Gravity of the Medium abateth from the Gra­
vity of the Moveable, which Gravity is the Inſtrument wherewith
the Moveable makes its Way, repelling the parts of the Medium
on each Side: an operation that doth not occur in void Mediums;
and therefore there is no difference to be expected from the di­
verſe Gravity: and becauſe it is manifeſt, that the Medium abateth
from the Gravity of the Body by it contained, as much as is the
weight of ſuch another maſs of its own Matter, if the Velocities of
the Moveables that in a non-reſiſting Medium would be (as hath
been ſuppoſed) equal, ſhould diminiſh in that proportion, we
ſhould have what we deſired. As for example; ſuppoſing that
Lead be ten thouſand times more grave than Air, but Ebony a
thouſand times only; of the Velocities of theſe two Matters, which
abſolutely taken, that is, all Reſiſtance being removed, would be
equal, the Air ſubſtracts from the ten thouſand degrees of the
Lead one, and from the thouſand degrees of the Ebony likewiſe
abateth one, or, if you will, of its ten thouſand, ten. If there­
fore the Lead and the Ebony ſhall deſcend thorow the Air from
any height, which, the retardment of the Air removed, they would
have paſſed in the ſame time, the Air will abate from the ten
thouſand degrees of the Leads Velocity one, but from the ten
thouſand degrees of Ebony's Velocity it will abate ten: which is
as much as to ſay, that dividing that Altitude, from which thoſe
Moveables departed into ten thouſand parts, the Lead will arrive
at the Earth, the Ebony being left behind, ten, nay, nine of thoſe
ſame ten thouſand parts. And what elſe is this, but that a Ball of
Lead, falling from a Tower two hundred yards high, to find how
1much it will anticipate one of Ebony of leſſe than four Inches?
The Ebony weigheth a thouſand times more than the Air, but that
Bladder ſo blown, weigheth only four times ſo much; the Air
therefore from the intrinſick and natural Velocity of the Ebony
ſubducteth one degree of a thouſand, but from that, which alſo in
the Bladder would abſolutely have been the ſame, the Air ſub­
ducts one part of four: ſo that by that time the Ball of Ebony
falling from the Tower, ſhall come to the ground, the Bladder
ſhall have paſſed but three quarters of that height. Lead is twelve
times heavier than Water, but Ivory only twice as heavy; the
Water therefore, from their abſolute Velocities which would be
equal, ſhall abate in the Lead the twelfth part, but in the Ivory
the half: when therefore, in the Water, the Lead ſhall have de­
ſcended eleven fathom, the Ivory ſhall have deſcended ſix. And,
arguing by this Rule, I believe, that we ſhall find the Experiment
much more exactly agree with this ſame Computation, than with
that of Ariſtotle. By the like method we might find the Veloci­
ties of the ſame Moveable in different fluid Mediums, not compa­
ring the different Reſiſtances of the Mediums, but conſidering the
exceſſes of the Gravity of the Moveable over and above the Gra­
vities of the Mediums: v. gr. ^{*} Tin is a thouſand times heavier than

Air, and ten times heavier than Water; therefore dividing the ab­
ſolute Velocity of the Tin into a thouſand degrees, it ſhall move
in the Air, (which deducteth from it the thouſandth part,) with nine
hundred ninety nine, but in the Water with nine hundred only;
being that the Water abateth the tenth part of its Gravity, and
the Air the thouſandth part. Take a Solid ſomewhat heavier than
Water, as for inſtance, the Wood called Oake, a Ball of which
weighing, as we will ſuppoſe, a thouſand drams, a like quantity
of Water will weigh nine hundred and fifty, but ſo much Air will
weigh but two drams,: it is manifeſt, that ſuppoſing that its abſo­
lute Velocity were of a thouſand degrees, in Air there would re­
main nine hundred ninety eight, but in the Water only fifty; be­
cauſe that the Water of the thouſand degrees of Gravity taketh
away nine hundred and fifty, and leaves fifty only; that Solid there­
fore would move well-near twenty times as faſt in the Air as Wa­
ter; like as the exceſſe of its Gravity above that of the Water is
the twentieth part of its own. And here I deſire that we may con­
ſider, that no matters, having a power to move downwards in the
Water, but ſuch as are more grave in Species than it; and conſe­
quently many hundreds of times, more grave than the Air, in
ſeeking what the proportions of their Velocities are in the Air and
Water, we may, without any conſiderable errour, make account
that the Air doth not deduct any thing of moment from the abſo­
lute Gravity, and conſequently, from the abſolute Velocity of ſuch
1matters: ſo that having eaſily found the exceſſe of their Gravi­
ty above the Gravity of the Water, we may ſay that their Velo­
city in the Air, to their Velocity in the Water hath the ſame propor­
tion, that their total Gravity hath to the exceſſe of this above
the Gravity of the Water. For example, a Ball of Ivory weigh­
eth twenty ounces, a like quantity of Water weigheth ſeventeen
ounces: therefore the Velocity of the Ivory in Air, to its Velocity
in Water is very neer as twenty to three.
The Velocity of
Grave Bodies de­
ſcending Natural­
ly to the Center do
go continually en­
creaſing till that
by the encreaſe of
the Reſiſtance of
the Medium it
becometh uniform.
* Or aquiſts.
To find the Pro­
portions of the Ve­
locities of different
Moveables in the
ſame, and in diffe­
rent Mediums.
* Or Pewter.
SAGR. I have made a great acquiſt in a buſineſſe of it ſelf cu­
rious, and in which, but without any benefit, I have many times
wearied my-thoughts: nor would there any thing be wanting for
the putting theſe Speculations in practice, ſave onely the way
how one ſhould come to know of what Gravity the Air, is in com­
pariſon to the Water, and conſequently to other heavy matters.
SIMP. But in caſe one ſhould finde, that the Air inſtead of
Gravity had Levity, what ought one to ſay of the foregoing diſ­
courſes, otherwiſe very ingenuous?
SALV. It would be neceſſary to confeſſe that they were truly
Aerial, Light, and Vain. But will you queſtion whether the Air
be heavy, having the expreſſe Text of Ariſtotle that affirmeth it,
ſaying, That all the Elements have Gravity, even the Air it ſelf;

a ſigne of which (ſubjoyns he) we have in that a ^{*} Bladder blown,
weigheth heavier than unſwell'd.
* Or Boracho; a
bottle made of a
Goat skin, uſed
to hold wine and
other Liquids.
SIMP. That a Boracho, or Bladder blown, weigheth more,
might proceed, as I could ſuppoſe, not from the Gravity that is
in the Air, but in the many groſſe Vapours intermixed with it in
theſe our lower Regions; by means whereof I might ſay, that the
Gravity of the Bladder, or Boracho encreaſeth.
SALV. I would not have you ſay it, and much leſſe that you
ſhould make Aristotle ſpeak it, for he treating of the Elements,
and deſiring to perſwade me that the Element of Air is grave,
making me to ſee it by an Experement: if in comming to the proof
he ſhould ſay: Take a Bladder, and fill it with groſſe Vapours;
and obſerve that its weight will encreaſe; I would tell him that
it would weigh yet more if one ſhould fill it with bran; but would
afterwards adde; that thoſe Experiments prove, that bran, and
groſſe Vapours are grave: but as to the Element of Air, I ſhould
be left in the ſame doubt as before. The Experiment of Ariſtotle
therefore is good, and the Propoſition true. But I will not ſay ſo
much, for a certain other reaſon taken expreſly out of a Philoſo­
pher whoſe name I do not remember, but am ſure that I have read
it, who argueth the Air to be more grave than light, becauſe it
more eaſily carrieth grave Bodies downwards, than the light up­
wards.
SAGR. Good i-faith. By this reaſon then, the Air ſhall be
1much heavier than the Water, ſince, that all Bodies are carried
more eaſily downwards thorow the Air than thorow the Water,
and all light Bodies more eaſily upwards in this than in that: nay,
infinite matters aſcend in the Water, that in the Air deſcend.
But be the Gravity of the Bladder, Simplicius, either by reaſon of
the groſſe Vapours, or pure Air, this nothing concerns our pur­
poſe, for we ſeek that which happeneth to Moveables that move
in this our Vaporous Region. Therefore, returning to that which
more concerneth me, I would for a full and abſolute informati­
on in the preſent buſineſſe, not onely be aſſured that the Air is
grave, as I hold for certain, but I would, if it be poſſible, know
what its Gravity is. Therefore, Salviatus, if you have wherewith
to ſatisfie me in this alſo, I entreat you to favour me with the
ſame.
SALV. That there reſideth in the Air poſitive Gravity, and

not, as ſome have thought, Levity, which haply is in no Mat­
ter to be found, the Experiment of the Blown-Bladder, alledged
by Ariſtotle, affordeth us a ſufficiently-convincing Argument; for
if the quality of abſolute and poſitive Levity were in the Air,
then the Air being multiplied and compreſſed, the Levity would
encreaſe, and conſequently the propenſion of going upwards:
but Experience ſhews the contrary. As to the other demand, that

is, of the Method how to inveſtigate its Gravity, I have tried to
do it in this manner: I have taken a pretty bigge Glaſſe ^{*} Bottle,

with its neck bended, and a Finger-ſtall of Leather faſt about
it, having in the top of the ſaid Finger-ſtall inſerted and fa­
ſtened a Valve of Leather, by which with a Siringe I have made
paſſe into the Bottle by force a great quantity of Air, of which,
becauſe it admits of great Condenſation, it may take in two or
three other Bottles-ful over and above that which is naturally con­
tained therein. Then I have in an exact Ballance very preciſely
weighed that Bottle with the Air compreſſed within it, adjuſting
the weight with ſmall Sands. Afterwards, the Valve being opened,
and the Air let out, that was violently conteined in the Veſſel, I
have put it again into the Scales, and finding it notably aleviated,
I have by degrees taken ſo much Sand from the other Scale, keep­
ing it by it ſelf, that the Ballance hath at laſt ſtood in Equilibrio
with the remaining counter-poiſe, that is with the Bottle. And
here there is no queſtion, but that the weight of the reſerved Sand
is that of the Air that was forceably driven into the Bottle, and
which is at laſt gone out thence. But this Experiment hitherto aſ­
ſureth me of no more but this, that the Air violently deteined in
the Veſſel, weigheth as much as the reſerved Sand, but how much
the Air reſolutely and determinately weigheth in reſpect of the
Water, or other grave matter, I do not as yet know, nor can
1I tell, unleſſe I meaſure the quantity of the Air compreſſed: and
for the diſcovering of this a Rule is neceſſary, which I have
found may be performed two manner of wayes, one of which
is to take ſuch another Bottle or Flask as the former, and in like
manner bended, with a Finger-ſtall of Leather, the end of which
may cloſely imbrace the Volve of the other, and let it be very
faſt tied about it. It's requiſite, that this ſecond Bottle be bored in
the bottom, ſo that as by that hole we may thruſt in a Wier,
wherewith we may, at pleaſure, open the ſaid Volve, to let out
the ſuperfluous Air of the other Veſſel, after it hath been weighed:
but this ſecond Bottle ought to be full of Water. All being pre­
pared in the manner aforeſaid, and with the Wier opening the
Volve, the Air iſſuing out with impetuoſity, and paſſing into the
Veſſel of Water, ſhall drive it out by the hole at the Bottom:
and it is manifeſt, that the quantity of Water which ſhall be
thruſt out, is equal to the Maſſe and quantity of Air that ſhall
have iſſued from th'other Veſſel: that Water therefore being
kept, and returning to weigh the Veſſel lightned of the Air com­
preſſed (which I ſuppoſe to have been weighed likewiſe firſt with
the ſaid forced Air) and the ſuperfluous ſand being laid by, as I
directed before; it is manifeſt, that this is the juſt weight of ſo
much Air in maſſe, as is the maſſe of the expulſed and reſerved
Water; which we are to weigh, and ſee how many times its
weight ſhall contain the weight of the reſerved ſand: and we may
without errour affirme, that the Water is ſo many times heavier
than Air; which ſhall not be ten times, as it ſeemeth Ariſtotle
held, but very neer four hundred, as the ſaid Experiment ſheweth.
The Air hath Po­
ſitive Gravity.
How that Gravity
may be computed.
* Un Fiaſco, thoſe
long-neckt glaſſe
bottles in which
we have our
Florence Wine
brought to us.
The other way is more expeditious, and it may be done with
one Veſſel onely, that is with the firſt accomodated after the man­
ner before directed, into which I will not that any other Air be
put, more than that which naturally is found therein; but I will,
that we inject Water without ſuffering any Air to come out,
which being forced to yield to the ſupervenient Water muſt of
neceſſity be compreſſed: having gotten in, therefore, as much
Water as is poſſible, (but yet without great violence one cannot get
in three quarters of what the Bottle will hold) put it into the
Scales, and very carefully weigh it: which done, holding the
Veſſel with the neck upwards, open the Volve, letting out the
Air, of which there will preciſely iſſue forth ſo much as there is
Water in the Bottle. The Air being gone out, put the Veſſel again
into the Scales, which by the departure of the Air will be found
lightened, and abating from the oppoſite Scale the ſuperfluous
weight, it ſhall give us the weight of as much Air as there is
Water in the Bottle.
SIMP. The Contrivances you found out cannot but be con­
1feſſed to be witty and very ingenuous, but whilſt, me thinks, they
fully ſatisfie my underſtanding, they another way occaſion in
me much Confuſion, for it being undoubtedly true that the Ele­
ments in their proper Region are neither heavy nor light, I can­
not comprehend, how and which way that portion of Air, which
ſeemeth to have weighed v. gr. four drams of ſand, ſhould af­
terwards have that ſame Gravity in the Air, in which the ſand is
contained that weigheth againſt it: and therefore me thinks that
the Experiment ought not to be practiced in the Element of Air,
but in a Medium in which the Air it ſelf might exerciſe its quality
of Gravitation, if it really be owner thereof.
SALV. Certainly the Objection of Simplicius is very acute,
and therefore its neceſſary, either that it be unanſwerable, or that
the Solution be no leſſe acute. That that Air, which compreſ­
ſed, appeared to weigh as much as that ſand, left at liberty in its
Element is no longer to weigh any thing as the Sand doth, is a thing
manifeſt: and therefore for making of ſuch an Experiment, its
requiſite to chooſe a place and Medium wherein the Air as well as
the Sand might weigh: for, as hath ſeveral times been ſaid, the
Medium ſubſtracts from the Weight of every Matter that is im­
merged therein, ſo much, as ſuch another quantity of the ſaid
Medium, as is that of the maſſe immerſed, weigheth: ſo that
the Air depriveth the Air of all its Gravity. The operation, there­

fore, to the end it were made exactly, ought to be tried in a Va­
cuum, wherein every grave Body would exerciſe its Moment
without any diminution. In caſe therefore, Simplicius, that we
ſhould weigh a portion of Air in a Vacuum, would you then be
convinced and aſſured of the buſineſſe?
The Air compreſ­
ſed and violently
pent up, weigheth in
a Vacuum; and
how its weight is to
be eſtimated.
SIMP. Verily I ſhould: but this is to defire, or enjoyn that
which is impoſſible.
SALV. And therefore the obligation muſt needs be great that
you owe to me, when ever I ſhall for your ſake effect an impoſſibi­
lity: but I will not ſell you that which I have already given you:
for we, in the foregoing Experiment, weigh the Air in a Vacuum,
and not in the Air, or in any other Replete Medium. That from
the Maſs, Simplicius, that in the fluid Medium is immerged certain
Gravity is ſubſtracted by the ſaid Medium, this commeth to paſs
by reaſon that it reſiſteth its being opened, driven back, and in a
word commoved; a ſign of which is its proneneſs to return inſtant­
ly to fill the Space up again, that the immerſed maſs occupied in it,
as ſoon as ever it departeth thence; for if it ſuffered not by that
immerſion, it would not operate againſt the ſame. Now tell me,
when you have in the Air the Bottle before filled with the ſame Air
naturally contained therein, what diviſion, repulſe, or, in ſhort,
what mutation doth the external ambient Air receive from the ſe­
1cond Air that was newly infuſed with force into the Veſſel? Doth
it enlarge the Bottle, whereupon the Ambient ought the more to
retire it ſelf to make room for it? Certainly no: And therefore
we may ſay, that the ſecond Air is not immerſed in the Ambient,
not occupying any Space therein; but is as if it was in a Vacuum,
nay more, is really conſtituted in it, and is placed in Vacuities that
were not repleted by the former un-condenſed Air. And, really, I
know not how to diſcern any difference between the two Conſti
tutions of Incloſed and Ambient, whilſt in this the Ambient doth
no-ways preſs the Incloſed, and in that the Incloſed doth not re­
repulſe the Ambient: and ſuch is the placing of any matter in a
Vacuum, and the ſecond Air compreſsed in the Flask. The weight
therefore that is found in that ſame condenſed Air, is the ſame that
it would have, were it freely diſtended in a Vacuum. Tis true in­
deed, that the weight of the Sand that weigheth againſt it, as ha­
ving been in the open Air, would in a Vacuum have been a little
more than juſt ſo heavy; and therefore it is neceſſary to ſay, that
the weighed Air is in reality ſomewhat leſſe heavy than the Sand
that counterpoiſeth it, that is, ſo much, by how much the like
quantity of Air would weigh in a Vacuum.
SIMP. I had thought that there was ſomething to have been
wiſhed for in the Experiments before produced; but now I am
thorowly ſatisfied.
The difference,
though very great,
of the Gravity of
Moveables hath
no part in differer­
cing their Veloci­
ties.
SALV. The things by me hitherto alledged, and in particular,
this, That the difference of Gravity, although exceeding great,
hath no part in diverſifying the Velocities of Moveables, ſo that,
notwithſtanding any thing depending on that, they would all
move with equal Celerity, is ſo new, and at the firſt apprehenſi­
on ſo remote from probability, that, were there not a way to de­
lucidate it, and make it as clear as the Sun, it would be better
to paſſe it over in ſilence, than to divulge it: therefore ſeeing
that I have let it eſcape from me, its fit that I omit neither Expe­
riment nor Reaſon that may corroborate it.
SAGR. Not onely this, but many other alſo of your Aſſerti­
ons are ſo remote from the Opinions and Doctrines commonly
received, that ſending them abroad, you would ſtir up a great
number of Antagoniſts: in regard, that the innate Diſpoſition of
Men doth not ſee with good eyes, when others in their Studies
diſcover Truths or Fallacies, that were not diſcovered by them­
ſelves: and with the title of Innovators of Doctrines, little plea­
ſing to the ears of many, they ſtudy to cut thoſe knots which
they cannot untie, and with ſub-terranean Mines to blow up
thoſe Structures, which have been with the ordinary Tools by
patient Architects erected: but with us here, who are far from
any ſuch thoughts, your Experiments and Arguments are
1ſufficient to give full ſatisfaction: yet nevertheleſſe, if ſo be you
have other more palpable Experiments, and more convincing
Reaſons we would very gladly hear them.
SALV. The Experiment made with two Moveables, as different
in weight as may be, by letting them deſcend from a place on
high, thereby to ſee whether their Velocity be equal, meets with
ſome difficulty: for if the height ſhall be great, the Medium,
which is to be opened and laterally repelled by the Impetus of the
cadent Body, ſhall be of much greater prejudice to the ſmall Mo­
ment of the light Moveable, than to the violence of the heavy
one; whereupon in a long way the light one will be left behind:
and in a little altitude it might be doubted whether there were
really any difference, or if there were, whether it would be
ſenſible. Therefore I have oft been thinking to reiterate the de­
ſcent ſo many times from ſmall heights, and to accumulate toge­
ther ſo many of thoſe minute differences of time, as might inter­
cede between the arrival or fall of the heavy Body to the ground,
and the arrival of the light one, which ſo conjoyned, would make
a time not onely obſervable, but obſervable with much facility
Moreover, that I might help my ſelf with Motions as ſlow as poſ­
ſible may be, in which the Reſiſtance of the Medium operates
leſſe in altering the effect that dependeth on ſimple Gravity, I
have had thoughts to cauſe the Moveable to deſcend upon a de­
clining Plane, not much raiſed above the Plane of the Horizon;
for upon this, no leſſe than in perpendicularity, we may diſcover
that which is done by Grave Bodies different in weight: and pro­
ceeding farther, I have deſired to free my ſelf from any whatſo­
ever impediment, that might ariſe from the Contact of the ſaid
Moveables upon the ſaid declining Plane: and laſtly, I have ta­
ken two Balls, one of Lead, and one of Cork, that above an hun­
dred times more grave than this, and have faſtened them to two
ſmall threads, each equally four or five yards long, tyed on
high: and having removed aſwel the one as the other Ball from
the ſtate of Perpendicularity, I have let them both go in the ſame
Moment, and they deſcending by the Circumferences of Circles
deſcribed by the equal Strings their Semidiameters, and having
paſſed beyond the Perpendicular, they afterwards by the ſame
way returned back, and reiterating theſe Vibrations, and re­
turns of themſelves neer an hundred times, they have ſhewn ve­
ry ſenſibly, that the grave Pendulum moveth ſo exactly under the
time of the light one, that it doth not in an hundred, no nor in a
thouſand Vibrations, anticipate the time of one ſmall moment,
but that they keep an equal paſſe in their Recurſions. They alſo
ſhew the Operation of the Medium, which conferring ſome im­
pediment on the Motion, doth much more diminiſh the Vibrati­
1ons of the Cork, than that of the Lead: not that it maketh them
more or leſſe frequent, nay, when the Arches paſſed by the Cork
were not of above five or ſix degrees, and thoſe of the Lead fif­
ty, they did paſs them under the ſame times.
SIMP. If this be ſo, how is it then that the Velocity of the
Lead is not greater than that of the Cork? that paſſing a jour­
ney of ſixty degrees, in the time that this paſseth hardly ſix?
SALV. But what would you ſay, Simplicius, in caſe they
ſhould both diſpatch their Recurſions in the ſame time, when the
Cork being removed thirty degrees from the Perpendicular,
ſhould paſs an arch of ſixty, and the Lead removed from the
ſame middle point onely two degrees, ſhould run an arch of four?
would not then the Cork be ſo much more ſwift than the Lead?
and yet Experience ſhews that ſo it happeneth: therefore obſerve,
The Pendulum of Lead being carried v. gr. fifty degrees from the
Perpendicular, and thence let go, ſwingeth, and paſſing beyond
the Perpendicular, neer fifty more degrees, deſcribeth an arch
of well neer an hundred degrees; and returning of its ſelf back
again, it deſcribeth another arch, not much leſſe than the former,
and continuing its Vibrations, after a great number of them, it
finally returneth to Reſt: Each of thoſe Vibrations are made un­
der equal times aſwel thoſe of ninety degrees, as thoſe of fifty,
twenty, ten, or four; ſo that by conſequence, the Velocity of the
Moveable doth ſucceſſively languiſh and abate, in regard, that
under equal times it doth ſucceſſively paſſe arches continually
leſſer and leſſer. The like, yea the ſelf ſame effect is performed
by the Cork, hanging by a ſtring of the like length, ſave that
in a leſſe number of Vibracions it returneth to Reſt, as being leſs
apt, by means of its Levity, to overcome the obſtacle of the Air:
and yet nevertheleſs all the Vibrations, both great and ſmall, are
made under times equal to one another, and equal alſo to the
times of the times of the Vibrations of the Lead. Whereupon it
is true, that if whilſt the Lead paſſeth an arch of fifty degrees,
the Cork paſseth one but of ten, the Cork is then more ſlow
than the Lead: but it will alſo happen on the other ſide, that the
Cork paſseth the arch of fifty degrees, when the Lead paſseth
but that of ten or ſix; and ſo in ſeveral times the Lead ſhall be
ſwifter onewhile, and the Cork another while: but if the ſame
Moveables ſhall alſo under the ſame equal times, paſs arches that
are equal, one may then very ſafely ſay, that their Velocities are
equal.
SIMP. This diſcourſe ſeems to me concluding, and not con­
cluding, and I finde in my thoughts ſuch a Confuſion, ariſing
from the one-while ſwift, another-while ſlow, another-while ex­
treme ſlow motion of both the one and other Moveable; as that
1it permits me not to diſcern clearly, whether it be true, That their
Velocities are alwaies equal.
SAGR. Give me leave, I pray you, Salviatus, to interpoſe two
words. And tell me, Simplicius, whether you admit, that it may be
ſaid with abſolute verity that the Velocities of the Cork and of
the Lead are equal, in caſe, that both of them departing at the
ſame moment from Reſt, and moving by the ſame declivities, they
ſhould alwaies paſſe equal Spaces in equal times?
SIMP. This admits of no doubt, nor can it be contradicted.
SAGR. It hapneth now in the Pendulums that each of them
paſſeth now ſixty degrees, now fifty, now thirty, now ten, now
eight, four, and two; and when each of them paſſeth the Arch of
ſixty degrees they paſſe it in the ſame time; in the Arch of fifty the
ſame time is ſpent by both the one and the other Moveable; ſo in
the Arch of thirty, of ten, and of the reſt: and therefore it is con­
cluded, that the Velocity of the Lead in the Arch of ſixty degrees,
is equal to the Velocity of the Cork in the ſame Arch of ſixty de­
grees: and that the Velocities in the Arch of fifty, are likewiſe
equal to one the other, and ſo in the reſt. But it is not ſaid, that the
Velocity that is exerciſed in the Arch of ſixty is equal to the Ve­
locity that is exerciſed in the Arch of fifty, nor this to that of the
Arch of thirty. But the Velocities are alwaies leſſer, in the leſſer
Arches. And this is collected from our ſenſibly ſeeing the ſame
Moveable conſume as much time in paſſing the great Arch of ſixty
degrees, as in paſſing the leſſer of fifty, or the leaſt of ten: and, in a
word, in their being all paſſed alwaies under equal times. It is true
therefore, that both the Lead and the Cork ſucceſſively retard the
Motion, according to the Diminution of the Arches, but yet do
not alter their harmony in keeping the equality of Velocity in all
the ſame Arches by them paſſed. I deſired to ſay thus much, more
to try whether I have rightly apprehended the Conceit of Salvia­
tus, than out of any neceſſity that I thought Simplicius to ſtand in
of a more plain Explanation than that of Salviatus, which is, as
in all other things, extreamly clear, and ſuch, that, it being fre­
quent with him to reſolve Queſtions, in appearance not only ob­
ſcure, but repugnant to Nature, and to the Truth, with Reaſons,
or Obſervations, or Experiments very trite and familiar to every
one, it hath (as I have underſtood from divers) given occaſion to
one of the moſt eſteemed Profeſſors of our Age to put the leſſe
eſteem upon his Novelties, holding them to have as much of Sor­
didneſſe, for that they depend on over low and popular Funda­
mentals: as if the moſt admirable and moſt-to-be-prized Proper­
ty of the Demonſtrative Sciences, were not to ſpring and ariſe
from Principles known, underſtood, and granted by every one.
But let us, for all that, continue to banquet our ſelves with this diet
1that is ſo light of digeſtion; and ſuppoſing that Simplicius is fully
ſatisfied in underſtanding and admitting, That the intern Gravity
of different Moveables hath no ſhare in differencing their Veloci­
ties, ſo that all of them, for ought that dependeth on that, would
move with the ſame Velocities; tell us, Salviatus, in what you
place the ſenſible and apparent inequalities of Motion; and an­
ſwer to that Inſtance that Simplicius produceth, and which I like­
wiſe confirm, I mean, of ſeeing a Cannon Bullet move more ſwift­
ly than a drop of Bird-ſhot, for the difference of Velocity ſhall be
but ſmall, in reſpect of that which I object againſt you of Movea­
bles of the ſame matter, of which ſome of the greater will deſcend
in a Medium, in leſſe than one beat of the Pulſe, that ſpace, that
others which are leſſer will not paſſe in an hour, nor in four, nor in
twenty; ſuch are pebbles and minute gravel-ſtones, eſpecially,
that ſmall ſand which muddieth the Water; in which Medium
they will not deſcend in many hours ſo much as two fathoms,
which Stones, and thoſe of no great bigneſſe, do paſſe in one beat
of the Pulſe.
SALV. That which the Medium operates, in retarding Movea­
bles, the more according as they are compared to one another, leſs
grave in ſpecie, hath been already declared, ſhewing that it pro­
ceeds from the ſubſtraction of weight. But how one and the ſame
Medium can with ſo great difference diminiſh the Velocity in
Moveables that differ only in Magnitude, although they are of
the ſame Matter, and of the ſame Figure, requireth for its expli­
cation a more ſubtil diſcourſe, than that which ſufficeth for under­
ſtanding how the more dilated Figure of the Moveable, or the
Motion of the Medium that is made contrary to the Moveable, re­

tardeth the Velocity of the ſaid Moveable. I reduce the cauſe of
the ſaid Problem to the Scabroſity, and Poroſity, that is common­
ly, and, for the moſt part, neceſſarily found in the Superficies of
Solid Bodies, the which Scabroſities, in their Motion, go repulſing
and commoving the Air, or other Ambient Medium: of which we
have an evident teſtimony, in that we hear the Bodies, though made
as round as is poſſible for them to be, to hum whilſt they paſſe ve­
ry ſwiftly thorow the Air; and they are not only heard to hum, but
to whir and whiſtle, if there be but in them ſome more than ordi­
nary cavity or prominency. We ſee alſo, that in turning round
every rotund Solid maketh a little wind: And what need more?
Do we not hear a notable whirring, and in a very ſharp Accent,
made by a Top, while it turneth round on the ground with great
Celerity? The ſhrilneſs of which whizzing groweth flatter accor­
ding as the Velocity of the Vertigo doth by degrees more and
more ſlacken: a neceſſary Argument likewiſe of the commotion
and percuſſion of the Air by thoſe (though very ſmall) Scabroſi­
1ties of their Superficies. It is not to be doubted, but that theſe in the
deſcent of Moveables, grating upon, and repulſing the fluid Am­
bient, procure retardment in the Velocity, and ſo much the greater,
by how much the Superficies ſhall be greater, as is that of leſſer
Solids compared to bigger.
The greater or leſs
Scabroſity and Po­
roſity of the Super­
ficies of Movea­
bles, a probable
cauſe of their grea­
ter or leſſer Retar­
dation.
SIMP. Stay, I pray you, for here I begin to be at a loſſe: for
though I underſtand and admit, that the Confrication of the Medi­
um with the Superficies of the Moveable retardeth the Motion,
and that it more retardeth it where (ceteris paribus) the Superficies
is greater, yet do I not comprehend upon what ground you call the
Superficies of leſſer Solids greater: & farthermore if, as you affirm, the
greater Superficies ought to cauſe greater retardment, the greater
Solids ought to be the ſlower, which is not ſo: but this Objection
may eaſily be removed, by ſaying, that although the greater hath
a greater Superficies, it hath alſo a greater Gravity, upon which
the impediment of the greater Superficies hath not ſo much more
prevalent influence, than the impediment of the leſſer Superficies
hath upon the leſſer Gravity, as that the Velocity of the greater
Solid ſhould become the leſſer. And therefore I ſee no reaſon why
one ſhould alter the equality of the Velocities, whilſt, that looking
how much the Moving Gravity diminiſheth, the faculty of the Re­
tarding Superficies doth diminiſh at the ſame rate.
SALV. I will reſolve all that which you object in one word.
Therefore, Simplicius, you will without controverſie admit, that
when, of two equal Moveables of the ſame Matter, and alike in Fi­
gure (which undoubtedly would move with equal ſwiftneſſe) as
well the Gravity, as the Superficies of one of them diminiſheth,
(yet ſtill retaining the ſimilitude of Figure) the Velocity like­
wiſe, for the ſame reaſon, would not be diminiſhed in that which
was leſſened.
SIMP. Really, I think, that it ought ſo to follow as you ſay,
granting the preſent Doctrine with a ſalvo ſtill to our Doctrine,
which teacheth, that the greater or leſſer Gravity hath no operati­
on in accelerating or retarding Motion.
SALV. And this I confirm; and grant you likewiſe your Po­
ſition, from whence, in my opinion, may be inferred, That in caſe
the Gravity diminiſheth more than the Superficies, there may be
introduced in the Moveable, in that manner diminiſhed, ſome re­
tardment of Motion, and that greater and greater, by how much in
proportion, the diminution of the Weight was greater than the di­
minution of the Superficies
SIMP. I make not the leaſt queſtion of it.
Solids cannot be
diminiſhed at the
ſame rate in Super­
ficies as in Weight,
retaining the ſimi­
litude of the Fi­
gures.
SALV. Now know, Simplicius, that in Solids one cannot di­
miniſh the Superficies ſo much as the Weight keeping the ſimili­
tude of Figure. For it being manifeſt, that in diminiſhing of grave
1Solids, the Weight leſſeneth as much as the Bulk, when ever the
Bulk happens to be diminiſhed more than the Superficies, (care
being had to retain the ſimilitude of Figure) the Gravity likewiſe
would come to be more diminiſhed than the Superficies. But Geo­
metry teacheth us, that there is much greater proportion between
the Bulk and the Bulk in like Solids, than between their Superfi­
cies. Which for your better underſtanding, I ſhall explain in ſome
particular caſe. Therefore fancy to your ſelf, for example, a Dye,
one of the Sides of which is v. gr. two Inches long, ſo that one of
its Surfaces ſhall be four Square Inches, and all ſix, that is, all its
Superficies twenty four Square Inches. Then ſuppoſe the ſame
Dye at three ſawings cut into eight ſmall Dice, the Side of every
one of which will be one Inch, and one of its Surfaces an Inch
Square, and its whole Superficies ſix Square Inches, of which the
whole Dye contained twenty four in its Superficial content. Now,
you ſee, that the Superficial content of the little Dye is the fourth
part of the Superficial content of the great one, (for ſix is the
fourth part of twenty four) but the Solid content of the ſaid Dye
is only the eighth part: therefore the Bulk, and conſequently the
Weight, doth much more diminiſh than the Superficies. And if
you ſubdivide the little Dye into eight others, we ſhall have for
the whole Superficial content of one of theſe, one and an half
Square Inches, which is the ſixteenth part of the Superficies of the
firſt Dye; but its Bulk, or Maſs, is only the ſixty fourth part of that.
You ſee therefore, how that in only theſe two diviſions the Bulks
decreaſe four times faſter than their Superficies: and if we ſhould
proſecute the Subdiviſion, untill that we had reduced the firſt So­
lid into a ſmall powder, we ſhould find the Gravity of the minute
Atomes to be leſſened an hundred and an hundred times more
than their Superficies. And this which I have exemplified in
Cubes, hapneth in all like Solids, the Bulks of which are in Seſ­
quialter proportion of their Superficies. You ſee, therefore, in how
much greater proportion the Impediment of the Contact of the
Superficies of the Moveable with the Medium encreaſeth in ſmall
Moveables, than in greater: and if we ſhould add, that the Sca­
broſities in the very ſmall Superficies of the minute Atomes are
not happily leſſer than thoſe of the Superficies of greater Solids,
that are diligently poliſhed, obſerve how fluid, and void of all Re­
ſiſtance being opened, the Medium is required to be, when it is to
give paſſage to ſo feeble a Virtue. And therefore take notice, Sim­
plicius, that I did not equivocate, when even now I ſaid, That the
Superficies of leſſer Solids is greater, in compariſon of that of
bigger.
SIMP. I am wholly ſatisfied: and I verily believe, that if I were
to begin my Studies again, I ſhould follow the Counſel of Plato,
1and enter my ſelf firſt in the Mathematicks, which I ſee to proceed
very ſcrupulouſly, and refuſe to admit any thing for certain, ſave
that which they neceſſarily demonſtrate.
SAGR. I have taken great delight in this Diſcourſe; but, be­
fore we paſſe any further, I would be glad to be ſatisfied in one
particular, which newly came into my thoughts, when but juſt
now you ſaid, that Like-Solids are in Seſquialter proportion to
their Superficies for I have ſeen, and underſtood the Propoſition

with its Demonſtration, in which it is proved, That the Superficies
of Like-Solids are in duplicate proportion of their Sides; and ano­
ther that proveth the ſame Solids to be in triple proportion of the
ſame Sides; but the proportion of Solids to their Superficies, I do
not remember that I ever ſo much as heard it mentioned.
Solids are to each
other in Seſquial­
ter proportion to
their Superficies.
SALV. You your ſelf have anſwered and declared the doubt.
For that which is triple of a thing of which another is double, doth
it not come to be Seſquialter of this double? Yes doubtleſſe. Now,
if Superficies are in double proportion of the Lines, of which the
Solids are in triple proportion, may not we ſay, That the Solids are
in Seſquialter proportion of their Superficies?
SAGR. I underſtand you very well. And although other par­
ticulars, pertaining to the matter of which we have treated, do re­
main for me to ask, yet if we ſhould thus run from one Digreſſion
to another, it will be late before we ſhould come to the Queſtions
principally intended, which concern the diverſities of the Acci­
dents of the Reſiſtances of Solids againſt Fraction; and therefore,
if you ſo pleaſe, we may return to the firſt Theme, which we pro­
poſed in the beginning.
SALV. You ſay very well; but the ſo many, and ſo different
things that have been examined, have ſtoln ſo much of our time,
that there is but little of it left in this day to ſpend in our other
principal Argument, which is full of Geometrical Demonſtrati­
ons that are to be conſidered with attention: ſo that I ſhould think
it were better to adjourn our meeting till to morrow, as well for
this which I have told you, as alſo becauſe I might bring with me
ſome Papers, on which I have, in order, ſet down the Theorems and
Problems, in which are propoſed and demonſtrated the different
Paſſions of this Subject, which, it may be, would not otherwiſe
with requiſite Method come into my mind.
SAGR. I very gladly comply with your advice, and ſo much the
more willingly, in regard that, for a Concluſion of this daies Con­
ference, I ſhall have time to hear you reſolve ſome doubts that I
find in my mind concerning the Point laſt handled. Of which one
is, Whether we are to hold, that the Impediment of the Medium
may be ſufficient to aſſign bounds to the Acceleration of Bodies of
very grave Matter, that are of great Bulk, and of a Spherical Figure:
1and I inſtance in the Spherical Figure, that I might take that which
is contained under the leaſt Superficies, and therefore leſſe ſubject
to Retardment. Another ſhall be, touching the Vibrations of Pen­
dulums, and this hath many heads: One ſhall be, Whether all,
both Great, Mean, and Little, are made really and preciſely under
equal Times: And another, What is the proportion of the Times
of Moveables, ſuſpended at unequal ſtrings, of the Times of their
Vibrations I mean.
SALV. The Queſtions are ingenious, and, like as it is incident
to all Truths, I ſuppoſe, that, which ever of them we handle, it will
draw after it ſo many other Truths, and curious Conſequences,
that I cannot tell whether the remainder of this day may ſuffice
for the diſcuſſing of them all.
SAGR. If they ſhall be but as delightful as the precedent, it
would be more grateful for me to employ as many daies, not to ſay,
hours, as it is unto night, and I believe that Simplicius will not be
cloy'd with ſuch Argumentations as theſe.
SIMP. No certainly: and eſpecially, when the Queſtions trea­
ted of are Phyſical, touching which we read not the Opinions or
Diſcourſes of other Philoſophers.
Any Body, of any
Figure, Greatneſs,
and Gravity, is
checked by the Re­
nitence of the Me­
dium, though ne­
ver ſo tenuous, in
ſuch ſort, that the
Motion continuing,
it is reduced to
equability.
SALV. I come therefore to the firſt, affirming without any
hæſitation, that there is not a Sphere ſo big, nor of Matter ſo grave,
but that the Renitence of the Medium, though very tenuous, checks
its Acceleration, and in the continuation of the Motion reduceth
it to Equability, of which we may draw a very clear Argument
from Experience it ſelf. For if any falling Moveable were able in
its continuation of Motion to attain any degree of Velocity, no
Velocity that ſhould be conferred upon it, could be ſo great but
that it would depoſe it, and free it ſelf of it by help of the Impe­
diment of the Medium. And thus, a Cannon-bullet, that had de
ſcended through the Air, v. gr. four yards, and had, for example,
acquired ten degrees of Velocity, and that with theſe ſhould enter
into the Water, in caſe the Impediment of the Water were not
able to prohibit ſuch a certain Impetus in the Ball, it would en­
creaſe it, or at leaſt would continue it unto the bottom; which is
not obſerved to enſue: nay, the Water, although it were but a few
fathoms in depth, would impede and debilitate it in ſuch a man­
ner, that it will make but a ſmall impreſſion in the bottom of the
River or Lake. It is therefore manifeſt, that that Velocity, of
which the Water had ability to deprive it in a very ſhort way,
would never be permitted to be acquired by it, though in a depth
of a thouſand Fathoms. And why ſhould it be permitted to gain
it in a thouſand, to be taken from it again in four? What need we
more? Do we not ſee the immenſe Impetus of the Ball, ſhot from
the Cannon it ſelf, to be in ſuch a manner flatted by the interpo­
1ſition of a few Fathom of Water, that without any harm to the
Ship, it but very hardly reacheth to make a dent in it? The Air al­
ſo, though very yielding, doth nevertheleſſe repreſſe the Velocity
of the falling Moveable, although it be very heavy, as we may by
ſuch like Experiments collect; for if from the top of a very high
Tower we ſhould diſcharge a Muſquet downwards, this will make
a leſſer impreſſion on the ground, than if we ſhould diſcharge the
Muſquet at the height of four or ſix yards above the Plane: an
evident ſign, that the Impetus, wherewith the Bullet iſſueth from
the Gun, diſcharged on the top of the Tower, doth gradually di­
miniſh in deſcending thorow the Air: therefore the deſcending
from any whatſoever great height will not ſuffice to make it ac­
quire that Impetus, of which the Reſiſtance of the Air deprived
it, when it had in any manner been conferred upon it. The batte­
ry likewiſe that the force of a Bullet, ſhot from a Culverin, ſhall
make in a Wall at the diſtance of twenty Paces, would not, I be­
lieve, be ſo great, if the Bullet was ſhot perpendicularly from any
immenſe Altitude. I believe, therefore, that there is a Bound or
term belonging to the Acceleration of every Natural Moveable
that departs from Reſt, and that the Impediment of the Medium in
the end reduceth it to ^{*} Equality, in which it afterwards alwaies

continueth.
* Or Equability.
SAGR. The Experiments are really, in my opinion, much to
the purpoſe: nor doth any thing remain, unleſſe the Adverſary
ſhould fortifie himſelf, by denying, that they will hold true in great
and ponderous Maſſes, and that a Cannon-bullet coming from the
Concave of the Moon, or from the upper Region of the Air,
would make a greater percuſſion than coming from the Cannon.
SALV. There is no queſtion, but that many things may be
objected, and that they may not be all ſalved by Experiments; ne­
vertheleſſe in this contradiction, me thinks, there is ſomething that
may fall under conſideration; ſcilicet, that it is very probable,

that the Grave Body, falling from an Altitude, acquireth ſo much
Impetus, at its arrival to the ground, as would ſuffice to return it
to that height, as is plainly ſeen in a Pendulum reaſonable weighty,
that being removed fifty or ſixty degrees from the Perpendicular,
gaineth that Velocity and Virtue which exactly ſufficeth to force it
to the like Recurſion, that little abated, which is taken from it by
the Impediment of the Air. To conſtitute, therefore, the Cannon­
bullet in ſuch an Altitude as may ſuffice for the acquiſt of an Impe­
tus, as great as that which the Fire giveth it in its iſſuing from the
Piece, it would ſuffice to ſhoot it upwards perpendicularly with
the ſaid Cannon, and then obſerving, whether in its fall it maketh
an impreſſion equal to that of the percuſſion made near at hand in
its iſſuing forth; but, indeed, I believe, that it would not be any
1whit near ſo forcible. And therefore I hold that the Velocity,
which the Bullet hath near to its going out of the Piece, would
be one of thoſe that the Impediment of the Air would never ſuffer
it to acquire, whilſt it ſhould with a natural Motion deſcend, leaving
the ſtate of Reſt, from any great height. I come now to the other
Queſtions belonging to Pendulums, matters which to many would
ſeem very frivolous, and more eſpecially to thoſe Philoſophers that
are continually buſied in the more profound Queſtions of Natural
Philoſophy: yet, notwithſtanding, will not I contemn them, being
encouraged by the Example of Ariſtotle himſelf, in whom I admire
this above all things; that he hath not, as one may ſay, omitted any
matter that any waies merited conſideration, which he hath not
ſpoken of: and now upon the Queſtions you propounded, I think
I can tell you a certain conceit of mine upon ſome Problems con­
cerning Muſick, a noble Subject, of which ſo many famous men,
and Ariſtotle himſelf, have written; and touching it, he conſide­
reth many curious Problems: ſo that if I likewiſe ſhall from ſo fa­
miliar and ſenſible Experiments, draw Reaſons of admirable acci­
dents on the Argument of Sounds, I may hope that my diſcourſes
will be accepted by you.
A Grave Body,
falling from an
Altitude, acqui­
reth ſo much Im­
petus at its arri­
val to the ground,
as in all probabili­
ty, would ſuffice to
recarry it to the
ſame height from
whence it fell.
SAGR Not only accepted, but by me, in particular, moſt paſ­
ſionately deſired, in regard that I taking a great delight in all Mu­
ſical Inſtruments, and being reaſonably well inſtructed concerning
Conſonances, have alwaies been ignorant and perplexed with
endeavouring to know, whence it cometh that one ſhould more
pleaſe and delight me than another; and that ſome not only pro­
cure me no delight, but highly diſpleaſe me: the trite Ptoblem al­
ſo of the two Chords ſet to an Uniſon, one of which moveth and
actually ſoundeth at the touching of the other, I alſo am unreſol­
ved in: nor am I very clearly informed concerning the Forms of
Conſonances, and other particularities.
SALV. We will ſee, if from theſe our Peudulums one may ga­
ther any ſatisfaction in all theſe Doubts. And as to the firſt Que­
ſtion, that is, Whether the ſame Pendulum doth really and punctu­
ally perform all its Vibrations, great, leſſer, and leaſt, under Times
preciſely equal; I refer my ſelf to that which I have heretofore
learnt from our Academian, who plainly demonſtrateth, that the

Moveable that ſhould deſcend along the Chords, that are Subten­
ſes to any Arch, would neceſſarily paſſe them all in equal Times,
as well the Subtenſe under an hundred and eighty degrees, (that
is, the whole Diameter) as the Subtenſes of an hundred, ſixty, ten,
two, or half a degree, or of four minutes: ſtill ſuppoſing that they
all determine in the loweſt Point touching the Horizontal Plane.
Next as to the deſcendents by the Arches of the ſame Chords eli­
vated above the Horizon, and that are not greater than a Qua­
1drant, that is, than ninety degrees, Experience likewiſe ſhews, that

they paſſe all in Times equal, but yet ſhorter than the Times of
the paſſages by the Chords: an effect which hath ſo much of won­
der in it, by how much at the firſt apprehenſion one would think
the contrary ought to follow: For the terms of the beginning,
and the end of the Motion being common, and the Right-Line be­
ing the ſhorteſt, that can be comprehended between the ſaid
Terms, it ſeemeth reaſonable, that the Motion made by it ſhould
be finiſhed in the ſhorteſt Time, which yet is not ſo: but the ſhor­
teſt Time, and conſequently, the ſwifteſt Motion, is that made by
the Arch of which the ſaid Right-Line is Chord. In the next

place, as to the Times of the Vibrations of Moveables, ſuſpended
by ſtrings of different lengths, thoſe Times are in Subduple pro­
portion to the lengths of the ſtrings, or, if you will, the lengths
are in duplicate proportion to the Times, that is, are as the Squares
of the Times: ſo that if, for example, the Time of a Vibration
of one Pendulum is double to the Time of a Vibration of another,
it followeth, that the length of the ſtring of that is quadruple to
the length of the ſtring of this. And in the Time of one Vibration
of that, another ſhall then make three Vibrations, when the ſtring
of that ſhall be nine times as long as the other. From whence doth
follow, that the length of the ſtrings have to each other the ſame
proportion, that the Squares of the Numbers of the Vibrations that
are made in the ſame Times have.
Moveables deſcen­
ding along the
Chords, that are
Subtenſes to any
Arch of a Circle,
paſſe as well the
greater as the leſ­
ſer Chords in equal
Times.
Moveables and
Pendula deſcend­
ing along the Ar­
ches of the ſame
Chords, elivated as
far as 90 deg. paſs
the ſaid Arches in
Times equal, but
that are ſhorter
than the tranſiti­
ons along the
Chords.
The Times of the
Vibrations of Mo­
vables, hanging at
alonger or ſhorter
thread, are to one
another in propor­
tion ſubduple the
lengths of the
ſtrings, at which
they hang.
SAGR. Then, if I have rightly underſtood you, I may eaſily

know the length of a ſtring, hanging at any never-ſo-great height,
although the ſublime term of the ſuſpenſion were inviſible to me,
and I only ſaw the other lower extream. For if I ſhall faſten a
weight of ſufficient Gravity to the ſaid ſtring here below, and ſet
it on vibrating to and again, and a friend telling ſome of its Recur­
ſions, and I at the ſame time tell the Recurſions of another Movea­
ble, ſuſpended at a ſtring that is preciſely a yard long, by the
Numbers of the Vibrations of theſe Pendula, made in the ſame
Time, I will find the length of the ſtring. As for example, ſuppoſe
that in the time that my friend hath counted twenty Recurſions of
the long ſtring, I had told two hundred and forty of my ſtring,
that is one yard long: ſquaring the two numbers twenty and two
hundred and forty, which are 400, and 57600, I will ſay, that the
long ſtring containeth 57600 of thoſe Meaſures, of which my
ſtring containeth 400. and becauſe the ſtring is one ſole yard, I will
divide 57600 by 400, and the quotient will be 144, and I will af­
firm that ſtring to be 144 yards long.
To find the Length
of any Rope, or
ſtring, at which a
Moveable hang­
eth, by the frequen­
cy of its Vibrations
SALV. Nor will you be miſtaken one Inch; and eſpecially, if
you take a great Number of Vibrations.
SAGR. You give me frequent occaſion to admire the Riches,
1and withal the extraordinary bounty of Nature, whil'ſt by things
ſo common, and, I might in a certain ſence ſay, vile, you go col­
lecting of Notions very curious, new, and oftentimes, remote
from all imagination. I have an hundred times conſidered the Vi­
brations, in particular, of the Lamps in ſome Churches, hanging
by very long ropes, when they have been unawares ſtirred by
any one: but the moſt that I inferred from that ſame Obſervati­
on, was the improbability of the Opinion of thoſe who hold,
that ſuch-like Motions are maintained and continued by the Medi­
um, that is by the Air: for it ſhould ſeem to me, that the Air had
a great judgment, and withal but little buſineſſe to ſpend ſo ma­
ny hours time in vibrating an hanging Weight with ſo much Regu­
larity: but that I ſhould have learnt, that that ſame Moveable,
ſuſpended at a ſtring of an hundred yards long, being removed
from Perpendicularity one while ninety degrees, and another
while one degree onely, or half a degree, ſhould ſpend as much time
in paſſing this little, as in paſſing that great Arch, certainly would
never have come into my head, for I ſtill think, that it bordereth
upon Impoſsibility. Now I am in expectation to hear that theſe
petty Notions will aſsign me ſuch Reaſons of thoſe Muſical Pro­
blems, as may, in part at leaſt, give me ſatisfaction.
Every Pendulum
hath the Time of
its Vibration ſo li­
mited; that it is
not poſſible to make
it move under any
other Period.
SALV. Above all things, you are to know, that every Pendu­
lum hath the Time of its Vibrations ſo limited, and prefixed, that
it is impoſſible to make it move under any other Period, than that
onely one, which is natural unto it. Let any one take the ſtring in
hand, to which the Weight is faſtened, and trie all the wayes
he can to encreaſe or decreaſe the frequency of its Vibrations,
and he ſhall finde it labour in vain: but we may, on the contrary,
on a Pendulum, though grave and at reſt, by onely blowing up­
on it, conferre a Motion, and a Motion conſiderably great, by
reiterating the blaſts, but under the Time that is properly be­
longing to its Vibrations: for if at the firſt blaſt we ſhould have re­
moved it from Perpendicularity half an Inch, adding a ſecond,
after that it being returned towards us, is ready to begin the ſe­
cond Vibration, we ſhould conferre new Motion on it, and ſo
ſucceſſively with other blaſts, but given in Time, and not when
the Pendulum is comming towards us (for ſo we ſhould impede;
and not help the Motion) and ſo continuing with many Impul­
ſes, we ſhould confer upon it ſuch an Impetus, that a greater
force by much than that of a blaſt of our breath, will be required
to ſtay it.
SAGR. I have, from my childhood, obſerved, that one man a­
lone, by means of theſe Impulſes, given in Time, hath been able
to towl a very great Bell, and when it was to ceaſe, I have ſeen
four or ſix men more lay hold on the Bell-rope, and they have all
1been raiſed from the ground: ſo many together being unable to
arreſt that Impetus, which one alone, with regular Pulls, had con­
ferred upon the Bell.
SALV. An example, that declareth my meaning with no leſſe

propriety than this that I have premiſed, doth ſute to render the
reaſon of the admirable Problem of the Chord of the Lute or Viol,
which moveth, and maketh not onely that really to ſound, which
is tuned to the Uniſon, but that alſo which is ſet to an Eighth
and a Fifth. The Chord being toucht, its Vibrations begin, and
continue all the Time that its Sound is heard to endure: theſe
Vibrations make the Air neer adjacent to vibrate and tremble,
whoſe tremblings and quaverings diſtend themſelves a great way,
and ſtrike upon all the Chords of the Inſtrument, and alſo of o­

thers neer unto it: the Chord that is ſet to an Uniſon, with that
which is toucht, being diſpoſed to make its Vibrations ^{*} in the
ſame Time, beginneth at the firſt impulſe to move a little, and

a ſecond, a third, a twentieth, and many more, overtaking it, all
in juſt and Periodick Times, it receiveth at laſt, the ſame Tre­
mulation, with that firſt touched, and one may clearly ſee it go,
dilating its Vibrations exactly according to the Pace of its Mo­
ver. This Undulation that diſtendeth it ſelf thorow the Air, mo­
veth, and makes to vibrate, not onely the Chords, but likewiſe
any other Body diſpoſed to trembling, and to vibrate in the very
Time of the trembling Chord: ſo that if we fix in the Sides of
the Inſtrument ſeveral ſmall pieces of Briſtles, or of other flexible
matters, you ſhall ſee upon the ſounding of the Viol, now one,
now another of thoſe Corpuſcles tremble, according as that
Chord is toucht, whoſe Vibrations return in the ſame Time: the
others will not move at the ſtriking of this Chord, nor will that
Briſtle tremble at the ſtriking of another Chord. If with the Bow
one ſmartly ſtrike the Baſe-Chord of a Viol, and ſet a drinking
Glaſſe, thin and ſmooth, neer unto it, if the Tone of the Chord
be an Uniſon to the Tone of the Glaſſe, the Glaſſe ſhall dance,
and ſenſibly re-ſound. Again, the ample dilating of the Tremor
or Undulation of the Medium about the Body reſounding, is ap­
parently ſeen in making the Glaſſe to ſound, by putting a little
Water in it, and then chafing the brim or edge of it with the tip
of the finger: for the included Water is obſerved to undulate in
a moſt regular order: and the ſame effect will be yet more clearly
ſeen, by ſetting the foot of the Glaſſe in the bottom of a reaſo­
nable large Veſſel, in which there is Water as high almoſt as to
the brim of the Glaſſe, for making it to ſound, as before, with
the Confrication of the finger, we ſhall ſee the trembling of the
Water to diffuſe it ſelf moſt regularly, and with great Velocity,
to a great diſtance round about the Glaſſe; and it hath many
1times been my fortune, in making a reaſonable big Glaſſe, almoſt
full of Water, to ſound as aforeſaid, to ſee the Waves in the
Water, at firſt formed with an exact equality; and it hapning
ſometimes, that the Tone of the Glaſſe riſeth an Eighth higher, at
the ſame inſtant, I have ſeen every one of the ſaid Waves to divide
themſelves in two: an accident that very clearly proveth the
forme of the Octave to be the double.
The Chord of a
Muſical Inſtru­
ment touched, mo­
veth, and maketh
the Chords ſet to an
Uniſon, Fifth and
Eighth, with it to
ſound; and why.
Sundry Problems
touching Muſical
Proportions, and
their Solutions.
* Or under.
SAGR. The ſame hath alſo befaln me more than once, to my
delight, and alſo benefit: for I ſtood a long time perplexed a­
bout theſe Forms of Conſonants, not conceiving, that the Rea­
ſon, commonly given thereof by the Authours that have hither­
to written learnedly of Muſick, were ſufficiently convincing,
they tell us, that the Diapaſon, that is the Eighth, is contained
by the double, the Diapente, which we call the Fifth, by the
Seſquialter: for a Chord being diſtended on the ^{*} Monochord,

ſtriking it all; and afterwards ſtriking but the half of it, by pla­
cing a Bridge in the middle, one heareth an Eighth; and if the
Bridge be placed at a third of the whole Chord, touching the
whole, and then the two thirds, it ſoundeth a Fifth; whereupon
they infer, that the Eighth is contained between two and one, and
the Fifth between three and two. This Reaſon, I ſay, ſeemed to
me not neceſſarily concluding for the aſſigning juſtly the double
and the Seſquialter, for the natural Forms of the Diapaſon and
the Diapente. And that which moved me ſo to think, was this.
There are three ways, by which we may ſharpen the Tone of a
Chord: one is, by making it ſhorter, the other is by diſtending;
or making it more tenſe; and the third is by making it thinner. If,
retaining the ſame Tention and thickneſſe, we would hear an
Eighth, it is neceſſary to ſhorten it to one half, which is done by
ſtriking it all, and then half. But if, retaining the ſame length
and thickneſſe, we would have it riſe to an Eighth, by ſcrewing
it higher, it will not ſuffice to ſtretch it double as much, but we
ſhall need the quadruple, ſo that, if before it was ſtretched by a
Weight of one pound, it will be needful to faſten four pound
to it to ſharpen it to an Eighth. And laſtly, if, keeping the ſame
length and Tention, we would have a Chord, that by being ſmal­
ler, rendereth an Eighth, it will be neceſſary, that it retain onely
a fourth part of the thickneſſe of the other more Grave. And this
which I ſpeak of the Eighth, that is, that its form taken from the
Tention, or from the thickneſſe of the Chord, is in duplicate
proportion to that which it receiveth from the length, is to be
underſtoood of all other Muſical Intervals: for that which the
length giveth us in a Seſquialter proportion, i. e. by ſtriking it all,
and then the two thirds, if you would have it proceed from the
Tention, or from the diſgroſſing, you muſt double the Seſqui­
1alter proportion, taking the double Seſquiquartan: and if the
Grave Chord were ſtretched by four pound weight, faſten to the
Acute not ſix, but nine: and, as to the thickneſſe, make the Grave
Chord thicker than the Acute, according to the proportion of
nine to four, to have the Fifth. Theſe being moſt exact Experi­
ments, I thought, that I ſaw no reaſon, why theſe Sage Philoſo­
phers ſhould eſtabliſh the form of the Eighth to be rather the dou­
ble, than quadruple; and the Form of the Fifth to be rather the
Seſquialter, than the double Seſquiquartan. But becauſe the
numbring of the Vibrations of a Chord, which in giving a ſound,
are extreme frequent, is altogether impoſſible, I ſhould always
have been in doubt, whether or no it were true, that the more
Acute Chord of the Eighth, made in the ſame time, double the
number of the Vibrations of the more Grave, if the Waves,
which may be continued as long as you pleaſe, by making the
Glaſs to ſound and vibrate, had not ſenſibly ſhewn me, that in
the ſelf ſame moment that (ſometimes) the Sound is heard to riſe
to an Eighth, there are ſeen to ariſe other Waves more minute,
which with infinite ſmoothneſs cut in the middle each of thoſe
firſt.
* An Inſtrument
of but one ſtring;
called by Mar­
ſennus la Tromper­
te Marine.
SALV. An excellent Obſervation for diſtinguiſhing one by
one the Undulations ariſing from the Tremulation of the re­
ſounding Body: which are thoſe that diffuſing themſelves tho­
row the Air, make the titillation upon the Drum of our Ear, that
in our Soul becommeth a Sound: But whereas beholding and ob­
ſerving them in the Water, endure no longer than the confrica­
tion of the finger laſteth, and alſo in that time they are not per­
manent, but are continually made and diſſolved, would it not
be an ingenious undertaking, if one could make, with much
exquiſiteneſſe, ſuch, as would continue a long time; I mean
Moneths and Years, ſo as to give a man opportunity meaſure,
and with eaſe to number them?
SAGR. I aſſure you I ſhould highly value ſuch an Invention.
SALV. The diſcovery was accidental, and the Obſervation
and applicative improvement of it onely were mine, and I hold
it to be a Circumſtance of noble Contemplation, althongh a buſi­
neſſe in its ſelf ſufficiently homely. Scraping a Braſſe Plate with
an Iron Chizzel to fetch out ſome Spots, in moving the Chizzel to
and again upon it pretty quick, I heard it (once or twice amongſt
many gratings) to Sibilate and ſend forth a whiſtling noiſe, very
ſhrill and audible: and looking upon the Plate, I ſaw a long
row of ſmall ſtreaks, parallel to one another, and diſtant from
one another by moſt equal Intervals: returning to my ſcraping
again, I perceived by ſeveral trials, that in thoſe ſcrapings, and
thoſe onely that whiſtled, the Chizzel left the ſtreaks upon the
1Plate: but when the Scraping paſſed without any Sibilation,
there was not ſo much as the leaſt ſign of any ſuch ſtreaks. Re­
peating the Experiment ſeveral times afterwards, ſcraping now
with greater, now with leſſe velocity, the Sibilation hapned to
be of a Tone ſometimes acuter, ſometimes graver; and I obſerved
the marks made in the more acute ſounds to be cloſer together,
and thoſe of the more grave farther aſunder: and ſometimes alſo,
according as the ſelf ſame ſcrape was made towards the end, with
greater velocity than at the beginning, the ſound was heard to
grow ſharper, and the ſtreaks were obſerved to ſtand thicker,
but ever with extream neatneſſe, and marked with exact equidi­
ſtance: and farther-more, in the Sibilating ſcrapes; I felt the
Chizzel to ſhake or tremulate in my hand, and a certain chilneſſe
to run along my arm; and in ſhort, I ſaw the ſame effected upon
the Toole, which we uſe to obſerve in whiſpering, and after­
wards ſpeaking aloud, for ſending forth the breath without
forming a ſound, we do not perceive any moving in the throat
and mouth, in compariſon of that which we diſcern to be in the
Wind-pipe and Throat of every one, in ſending forth the voice;
and eſpecially in grave and loud Tones. I have likewiſe ſome­
times amongſt the Chords of the Viols, obſerved two that were
Uniſons to the Sibilations made by ſcraping after the manner I
told you, and that were moſt different in Tone, from which two
they preciſely were diſtant a perfect Fifth, and then meaſuring
the intervals of the ſtreaks of both the Scrapes, I ſaw the di­
ſtance that conteined forty five ſpaces of the one, conteined
thirty of the other: which, indeed, is the Form attributed to the
Diapente. But here, before I proceed any farther, I will tell you,
that of the three manners of rendring a Sound Acute, that which
you refer to the ſlenderneſſe or fineneſſe of the Chord, may
with more truth be aſcribed to the Weight. For the alteration ta­
ken from the thickneſſe, anſwereth, when the Chords are of the
ſame matter; and ſo a Gut-ſtring to make an Eighth, ought to be
four times thicker than the other Gut-ſtring; and one of Wier four
times thicker than another of Wier. But if I would make an Eighth
with one of Wier to one of Gut-ſtring, I am not to make it four
times thicker, but four times graver, ſo that, as to thickneſſe,
this of Wier ſhall not be four times thicker, but quadruple in
Gravity, for ſome times it ſhall be more ſmall than its reſpon­
dent to the Acuter Eighth, that is of Gut-ſtring. Hence it com­
meth to paſſe that, ſtringing an Inſtrument with Chords of Gold,
and another with Chords of Braſſe, if they ſhall be of the ſame
length, thickneſſe, and Tention, Gold being almoſt twice as
heavy, the Strings ſhall prove about a Fifth more Grave. And
here it is to be noted, that the Gravity of the Moveable more re­
1ſiſteth the Velocity, than the thickneſſe doth; contrary to what
others at the firſt would think: for indeed, in appearance, its more
reaſonable, that the Velocity ſhould be retarded by the Reſiſtance
of the Medium againſt Opening in a Moveable thick and light,
than in one grave and ſlender: and yet in this caſe it happeneth
quite contrary. But purſuing our firſt Intent, I ſay, That the
ncereſt and immediate reaſons of the Forms of Muſical Intervals,
is neither the length of the Chord, nor the Tention, nor the
thickneſſe, but the proportion of the numbers of the Vibrations,
and Percuſſions of the Undulations of the Air that beat upon the
Drum of our Ear, which it ſelf alſo doth tremulate under the
ſame meaſures of Time. Having eſtabliſhed this Point, we may,
perhaps, aſſign a very apt reaſon, whence it commeth, that of
thoſe Sounds that are different in Tone, ſome Couples are re­
ceived with great delight by our Sence, others with leſs, and
others occaſion in us a very great diſturbance; which is to ſeek a
reaſon of the Conſonances more or leſſe perfect, and of Diſlo­
nances. The moleſtation and harſhneſſe of theſe proceeds, as I
believe, from the diſcordant Pulſations of two different Tones,
which diſproportionally ſtrike the Drum of our Ear: and the
Diſſonances ſhall be extreme harſh, in caſe the Times of the Vi­
brations were incommenſurable. For one of which take that,
when of two Chords ſet to an Uniſon, one is ſounded, and ſuch
a part of another, as is the Side of the Square of its Diameter;
a Diſſonance like to the ^{*} Tritone, or Semi-diapente. Conſonan­

ces, and with pleaſure received, ſhall thoſe Couples of Sounds
be, that ſhall ſtrike in ſome order upon the Drum; which order
requireth, firſt, that the Pulſations made in the ſame Time be
commenſurable in number, to the end, the Cartillage of the Drum,
may not ſtand in the perpetual Torment of a double inflection of
allowing and obeying the ever diſagreeing Percuſſions. Therefore
the firſt and moſt grateful Conſonance ſhall be the Eighth, being,
that for every ſtroke, that the Grave-ſtring or Chord giveth upon
the Drum, the Acute giveth, two; ſo that both beat together
in every ſecond Vibration of the Acute Chord; and ſo of the
whole number of ſtrokes, the one half accord to ſtrike together,
but the ſtrokes of the Chords that are Uniſons, alwayes joyn
both together, and therefore they are, as if they were of the
ſame Chord, nor make they a Conſonance. The Fifth delighteth
likewiſe, in regard, that for every two ſtroaks of the Grave
Chord, the Acute giveth three: from whence it followeth, that
numbering the Vibrations of the Acute Chord, the third part of
that number will agree to beat together; that is, two Solitary ones
interpoſe between every couple of Conſonances; and in the Di­
ateſſeron there interpoſe three. In the ſecond, that is in the Seſ-
1quioctave Tone for every nine Pulſations, one onely ſtrikes in Con­
ſort with the other of the Graver Chord; all the reſt are Diſcords,
and received upon the Drum with regret, and are judged Diſſo­
nances by the Ear.
* Or a falſe Fifth.
SIMP. I could wiſh this Diſcourſe were a little explained.
SALV. Suppoſe this line A B the Space, and dilating of a Vi­
bration of the Grave Chord; and the line C D that of the Acute
Chord, which with the other giveth the Eighth: and let A B be
divided in the midſt in E. It is manifeſt, that the Chords begin­
ing to move at the terms A and C, by that time the Acute Vibra­
tion ſhall be come to the term D, the other
64[Figure 64]
ſhall be diſtended onely to the half E, which
not being the bound or term of the Motion,
it ſtrikes not: but yet a ſtroak is made in D.
The Vibrations afterwards returning from D
to C, the other paſſeth from E to B, where­
upon the two Percuſſions of B and C ſtrike
both together upon the Drum: and ſo con­
tinuing to reiterate the like ſubſequent Vi­
brations; one ſhall ſee, that the union of the
Percuſſions of the Vibrations C D with thoſe of A B, happen al­
ternately every other time: but the Pullations of the terms A B
are alwayes accompanied with one of C D, and that alwayes the
ſame: which is manifeſt, for ſuppoſing that A and C ſtrike to­
gether; in the time that A is paſſing to B, C goeth to D, and
returneth back to C: ſo that the ſtroaks at B and C are alſo
together. But now let the two Vibrations A B and C D be thoſe
that produce the Diapente, the times of which are in proportion
Seſquialter, and divide A B of the Grave Chord, in three equal
parts in E and O; And ſuppoſe the Vibrations to begin at the
ſame moment from the terms A and C: It is manifeſt, that at the
ſtroke that ſhall be made in D, the Vibration of A B ſhall have
got no farther than O, the Drum therefore receiveth the Pulſa­
tion D onely: again in the return from D to C, the other Vibra­
tion paſſeth from O to B, and returneth to O, making the Pul­
ſation in B, which likewiſe is ſolitary, and in Counter-time, (an
accident to be conſidered:) for we having ſuppoſed the firſt
Pulſations to be made at the ſame moment in the terms A and C,
the ſecond, which was onely by the term D, was made as long after
as the time of the tranſition C D, that is A O, imports; but
that which followeth, made in B, is diſtant from the other one­
ly ſo much as is the time O B, which is the half: afterwards con­
tinuing the Recurſion from O to A, whilſt the other goeth from
C to D, the two Pulſations come to be made both at once in A
and D. There afterwards follow other Periods like to theſe, that
1is, with the interpoſition of two ſingle and ſolitary Pulſations of
the Acute Chord, and one of the Grave Chord, likewiſe ſolita­
ry, is interpoſed between the two ſolitary ſtrokes of the Acute. So
that if we did but ſuppoſe the Time divided into Moments, that is,
into ſmall equal Particles: ſuppoſing that in the two firſt moments,
I paſſed from the Concordant Pulſations made in A and C to O
and D, and that in D, I make a Percuſſion: and that in the third
and fourth moment I return from D to C, ſtriking in C, and
that from O, I paſt to B, and returned to O, ſtriking in B; and
that laſtly in the fifth and ſixth moment from O and C, I paſt to
A and D ſtriking in both: we ſhall have the Pulſations diſtributed
with ſuch order upon the Drum, that ſuppoſing the Pulſations of
the two Chords in the ſame inſtant, it ſhall two moments after
receive a ſolitary Percuſſion, in the third moment anothor, ſoli­
tary likewiſe, in the fourth another ſingle one, and two moments
after, that is, in the ſixth, two together; and here ends the
Period, and, if I may ſo ſay, Anomaly; which Period is oft-times
afterwards replicated.
SAGR. I can hold no longer, but muſt needs expreſſe the con­
tent I take in hearing reaſons ſo appoſitely aſſigned of effects that
have ſo long time held me in darkneſſe and blindneſſe. Now I
know why the Uniſon differeth not at all from a ſingle Tone: I
ſee why the Eighth is the principal Conſonance, but withal ſo
like to an Uniſon, that, as an Uniſon, it is taken and cojoyned
with others: it reſembleth an Uniſon, for that whereas the Pul­
ſations of Chords ſet to an Uniſon, keep time in ſtriking, theſe
of the Grave Chord in an Eighth alwayes keep time with thoſe
of the Acute, and of theſe one interpoſeth alone, and in equal
diſtances, and as, one may ſay, without any variety, whereupon
that Conſonance is over ſweet. But the Fifth, with thoſe its
Counter-times, and with the interpoſures of two ſolitary Pulſa­
tions of the Acute Chord, and one of the Grave Chord,
between the Couples of Diſcordant Pulſations, and thoſe
three ſolitary ones, with an interval of time, as great as the half of
that which interpoſeth between each Couple, and the ſolitary
Percuſſions of the Acute Chord, maketh ſuch a Titillation and
Tickling upon the Cartillage of the Drum of the Ear, that al­
laying the Dulcity with a mixture of Acrimony, it ſeemeth at
one and the ſame time to kiſſe and bite.
SALV. It is convenient, in regard I ſee, that you take ſuch de­
light in theſe Novelties, that I ſhew you the way whereby the Eye
alſo, and not the Ear alone, may recreate it ſelf in beholding
the ſame ſports that the Ear feeleth. Suſpend Balls of Lead or o­
ther heavy matter on three ſtrings of different lengths, but in
ſuch proportion, that while the longer maketh two Vibrations,
1the ſhorter may make four, and the middle one three; which
will happen, when the longeſt containeth ſixteen feet, or other
meaſures, of which the middle one containeth nine, and the
ſhorteſt four: and removing them all together from Perpendi­
cularity, and then letting them go, you ſhall ſee a pleaſing In­
termixtion of the ſaid Pendulums with various encounters, but
ſuch, that, at every fourth Vibration of the longeſt, all the three
will concurre in one and the ſame term together, and then again
will depart from it, reiterating anew the ſame Period: the which
commixture of Vibrations, is the ſame, that being made by the
Chords, preſents to the Ear an Eighth, with a Fifth in the midſt.
And if you qualifie the length of other ſtrings in the like diſpo­
ſure, ſo that their Vibrations anſwer to thoſe of other Muſical,
but Conſonant Intervals, you ſhall ſee other and other Inter­
weavings, and alwaies ſuch, that in determinate times, and after
determinate numbers of Vibrations, all the ſtrings (be they three,
or be they four) will agree to joyn in the ſame moment, in the
term of their Recurſions, and from thence to begin ſuch another
Period: but if the Vibrations of two or more ſtrings are either
Incommenſurable, ſo, that they never return harmoniouſly to ter­
minate determinate numbers of Vibrations, or though they be
not Incommenſurable, yet if they return not till after a long time,
and after a great number of Vibrations, then the ſight is con­
founded in the diſorderly order of irregular Intermixtures, and
the Ear with wearineſſe and regret receiveth the intemperate Im­
pulſes of the Airs Tremulations, that without Order or Rule,
ſucceſſively beat upon its Drum.
But whither, my Maſters, have we been tranſported for ſo
many hours by various Problems, and unlook't for Diſcourſes?
We have made it Night, and yet we have handled few or none of
the points propounded; nay we have ſo loſt our way, that I
ſcarſe remember our firſt entrance, and that ſmall Introduction,
which we laid down, as the Hypotheſis and beginning of the fu­
ture Demonſtrations.
SAGR It will be convenient, therefore, that we break up our
Conference for this time, giving our Minds leave to compoſe
themſelves in the Nights Repoſe, that we may to Morrow (if
you pleaſe ſo far to favour us) reaſſume the Diſcourſes deſired,
and chiefly intended.
SALV. I ſhall not fail to be here to Morrow at the uſual
hour, to ſerve and enjoy you.
The End of the Firſt Dialogue.
1
GALILEUS,
HIS
DIALOGUES
OF
MOTION.
The Second Dialogue.
INTERLOCUTORS,
SALVIATUS, SAGREDUS, and SIMPLICIUS.
SAGREDUS.
Simplicius, and I, ſtaid expecting your com­
ing, and we have been trying to recall to
memory our laſt Conſideration, which, as
the Principle and Suppoſition, on which
you ground the Concluſions that you in­
tended to Demonſtrate to us, was that
Reſiſtance, that all Bodies have to Fracti­
on, depending on that Cement, that con­
nects and glutinates the parts, ſo, as that
they do not ſeparate and divide without a powerful attraction:
and our enquiry hath been, what might be the Cauſe of that
Coherence, which in ſome Solids is very vigorous; propounding
that of Vacuum for the principal, which afterwards occaſioned ſo
many Digreſſions as held us the whole day, and far from the
1matter at firſt propoſed, which was the Contemplation of the Re­
ſiſtances of Solids to Fraction.
SALV. I remember all that hath been ſaid, and returning to
our begun diſcourſe; What ever this Reſiſtance of Solids to brea­
king by a violent attraction, is ſuppoſed to be, it is ſufficient, that it
is to be found in them: which, though it be very great againſt the
ſtrength of one that draweth them ſtreight out, it is obſerved to be
leſſe in forcing them tranſverſely, or ſidewaies: and thus we ſee,
for example, a rod of Steel, or Glaſſe to ſuſtain the length-waies a
weight of a thouſand pounds, which, faſtned at Right-Angles in­
to a Wall, will break if you hang upon it but only fifty. And of
this ſecond Reſiſtance we are to ſpeak, enquiring, according to
what proportions it is found in Priſmes, and Cylinders of like and
unlike figure, length, and thickneſs, and, withal, of the ſame mat­
ter. In which Speculation, I take for a known Principle, that which
in the Mechanicks is demonſtrated amongſt the Paſſions of the
Vectis, which we call the Leaver: namely, That in that uſe of the
Leaver, the Force is to the Reſiſtance in Reciprocal proportion,
as the Diſtances from the Fulciment to the ſaid Force and the Re­
ſiſtance.
SIMP. This Ariſtotle, in his Mechanicks, demonſtrated before
any other man.
SALV. I am content to grant him the precedency in time, but
for the firmneſſe oſ Demonſtration, I think, that Archimedes
ought to be preferred far before him, on one ſole Propoſition of
whom, by him demonſtrated in his Book, De Equiponderantium,
depend the Reaſons, not only of the Leaver, but of the greater
part of the other Mechanick Inſtruments.
SAGR. But ſince that this Principle is the foundation of all
that which you intend to demonſtrate to us, it would be very re­
quiſite, that you produce us the proof of this ſame Suppoſition,
if it be not too long a work, giving us a full and perfect informati­
on thereof.
SALV. Though I am to do this, yet it will be better, that I lead
you into the field of all our future Speculations, by an enterance
ſomewhat different from that of Archimedes; and that, ſuppo­
ſing no more, but only that equal Weights, put into a Ballance of
equal Arms, make an Equilibrium, (a Principle likewiſe ſuppoſed
by Archimedes himſelf.) I come, in the next place, to demon­
ſtrate to you, that not only it is as true as the other, That unequal
Weights make an Equilibrium in a Stiliard of Armes unequal, ac­
cording to the proportion of thoſe Weights Reciprocally ſuſpen­
ded, but that it is one and the ſame thing to place equal Weights
at equal diſtances, as to place unequal Weights at diſtances that
are in Reciprocal Proportion to the Weights. Now for a plain
1Demonſtration of what I ſay, deſcribe a Solid Priſm or Cylinder
A B, [as in Figure 1. at the end of this Dialogue,] ſuſpended by
its ends at the Line H I, and ſuſtained by two Cords, H A, and I B.
It is manifeſt, that if I ſuſpend the whole by the Cord C, placed
in the middle of the Beam or Ballance H I, the Priſm A B will be
equilibrated, one half of its weight, being on one ſide, and the other
half on the other ſide of the Point of Suſpenſion C by the Princi­
ple that we preſuppoſed. Now let the Priſm be divided into un­
equal parts by the Line D, and let the part D A be grea­
ter, and D B leſſer; and to the end, that ſuch diviſion being made,
the Parts of the Priſm may reſt in the ſame ſcituation and conſti­
tution, in reſpect of the Line H I, let us help it with a Cord E D,
which, being faſtened in the Point E, ſuſtaineth the parts A D, and
D B: It is not to be doubted, but that there being no local muta­
tion in the Priſm, in reſpect of the Ballance H I, it ſhall remain in
the ſame ſtate of Equilibration. But it will reſt in the ſame Con­
ſtitution likewiſe, if the Part of the Priſm, that is now ſuſpended at
the two extreams, or ends with Cords A H and D E, be hanged at
one ſole Cord G L, placed in the midſt: and likewiſe the other
part D B, will not change ſtate, if ſuſpended by the middle, and
ſuſtained by the Cord F M. So that the Cords H A, E D, and I B
being untied, and only the two Cords G L, and F M being left, the
Equilibrium will ſtill remain, the Suſpenſion being ſtill made at
the Point C. Now, here let us confider, that we have two Grave
Bodies A D, and D B, hanging at the terms G and F of a Beam
G F, in which the Equilibrium is made at the Point C: in ſuch
manner, that the diſtance of the ſuſpenſion of the Weight A D
from the Point C, is the Line C G, and the other part C F, is the
diſtance at which the other Weight D B hangeth. It remaineth,
therefore, only to be demonſtrated, that thoſe Diſtances have the
ſame proportion to one another, as the Weights themſelves have,
but reciprocally taken: that is, that the diſtance G C is to the di­
ſtance C F, as the Priſm D B to the Priſm D A, which we prove
thus. The Line G E being the half of E H, and E F the half of
E I, all G F ſhall be equall to all H I, and therefore equal to C I:
and taking away the common part C F, the remainder G C ſhall
be equal to the remainder F I, that is, to F E: and C E taken in
common, the two Lines G E and C F ſhall be equal: and, there­
fore, as G E, is to E F, ſo is F C, to C G: but as G C is to E F, ſo is
the double to the double; that is H E to E I; that is, the Priſm
A D to the Priſm D B. Therefore by Equality of proportion,
and by Converſion, as the diſtance G C is to the diſtance C F, ſo
is the Weight B D to the Weight D A: which is that that I was to
demonſtrate. If you underſtand this, I believe that you will not
ſcruple to admit, that the two Priſmes A D, and D B make an
1Equilibrium in th Point C, for the half of the whole Solid A B is
on the right hand of the Suſpenſion C, and the other half on the
left; and that in this manner there are repreſented two equal
Weights, diſpoſed and diſtended at two equal diſtances. Again,
that the two Priſmes A D, and D B, being reduced into two Dice,
or two Balls, or into any two other Figures, (provided that they
keep the ſame Suſpenſions G and F) do continue to make their
Equilibrium in the Point C, I believe none can deny, for that it is
moſt manifeſt, that Figures change not weight, where the ſame
quantity of matter is retained. From which we may gather the
general Concluſion, That two Weights, whatever they be, make
an Equilibrium at Diſtances reciprocally anſwering to their Gra­
vities. This Principle, therefore, being eſtabliſhed, before we paſs
any farther, I am to propoſe to Conſideration, how theſe Forces,
Reſiſtances, Moments, Figures, may be conſidered in Abſtract,
and ſeparate from Matter, as alſo in Concrete and conjoyned
with Matter; and in this manner thoſe Accidents that agree with
Figures, conſidered as Immaterial, ſhall receive certain Modifica­
tions, when we ſhall come to add Matter to them, and conſequent­
ly Gravity. As for example, if we take a Leaver, as for inſtance
B A [as in Fig. 2.] which, reſting upon the Fulciment E, we ap­
ply to raiſe the heavy Stone D: It is manifeſt by the Principle de­
monſtrated, that the Force placed at the end B, ſhall ſuffice to
equal the Reſiſtance of the Weight D, if ſo be, that its Moment
have the ſame proportion to the Moment of the ſaid D, that the
Diſtance A C hath to the Diſtance C B: and this is true, if we
confider no other Moments than thoſe of the ſimple Force in B,
and of the Reſiſtance in D, as if the ſaid Leaver were immaterial,
and void of Gravity. But if we bring to account the Gravity alſo
of the Inſtrument or Leaver it ſelf, which hapneth ſometimes to be
of Wood, and ſometimes of Iron; it is manifeſt, that the weight
of the Leaver, being added to the Force in B, it will alter the pro­
portion, which it will be requiſite to deliver in other terms. And
therefore before we paſſe any farther, it is neceſſary, that we di­
ſtinguiſh between theſe two waies of Conſideration, calling that a
taking it abſolutely, when we ſuppoſe the Inſtrument to be taken
in Abſtract, that is, disjunct from the Gravity of its own Matter;
but conjoyning the Matter, as alſo the Gravity, with ſimple and
abſolute Figures, we will phraſe the Figures conjoyn'd with the
Matter, Moment, or Force compounded.
SAGR I muſt of neceſſity break the Reſolution I had taken,
not to give occaſion of digreſſing, for I ſhould not be able to ſet
my ſelf to hear what remaines with attention, if a certain ſcruple
were not removed that cometh into my head; and it is this, That
I gueſſe you make compariſon between the Force placed in B, and
1the total Gravity of the Stone D, of which Gravity me thinks, that
one, and that, very probably, the greater part, reſteth upon the
Plane of the Horizon: ſo that----
SALV. I have rightly apprehended you, ſo that you need ſay
no more, but only take notice, that I named not the total Gravity
of the Stone, but ſpake of the Moment that it hath, and exerciſeth
at the Point A, the extream term of the Leaver B A, which is ever
leſs than the entire weight of the Stone; and is variable according
to the Figure of the Stone, and according as it hapneth to be more
or leſſe elevated.
SAGR. I am ſatisfied in that particular, but I have one thing
more to deſire, namely, that for my perfect information, you would
demonſtrate to me the way, if there be one, how I may find what
part of the total weight that is, which cometh to be born by the
ſubjacent Plane, and what that which gravitates upon the Leaver
at the extream A.
SALV. Becauſe I can give you ſatisfaction in few words, I will
not fail to ſerve you: therefore, deſcribing a ſlight Figure thereof,
be pleaſed to ſuppoſe, that the Weight, whoſe Center of Gravity is
A, [as in Fig. 3.] reſteth upon the Horizon with the term B, and
at the other end is born up by the Leaver C G, on the Fulciment
N, by a Power placed in G: and that from the Center A, and term
C, Perpendiculars be let fall to the Horizon, A O, and C F. I ſay,
That the Moment of the whole Weight ſhall have to the Moment
of the whole Power in G, a proportion compounded of the Di­
ſtance G N to the Diſtance N C, and of F B to B O. Now, as the
Line F B is to B O, ſo let N C be to X. And the whole Weight A
being born by the two Powers placeed in B and C, the Power B is
to C, as the diſtance F O to O B: and by Compoſition, the
two Powers B and C together, that is, the total Moment of
the whole Weight A, is to the Power in C, as the Line F B is
to the Line B O; that is, as N C to X: But the Moment of
the Power in C is to the Moment of the Power in G, as the Di­
ſtance G N is to N C: Therefore, by Perturbation of proportion,
the whole Weight A is to the Moment of the Power in G, as G N
to X: But the proportion of G N to X is compounded of the pro­
portion G N to N C, and of that of N C to X; that is, of F B to
B O: Therefore the Weight A is to the Power that bears it up in
G, in a proportion compounded of G N to N C, and of that of
F B to B O: which is that that was to be demonſtrated. Now re­
turning to our firſt intended Argument, all things hitherto decla­
red being underſtood, it will not be hard to know the reaſon,
whence it cometh to paſſe that
1
PROPOSITION I.
A Solid Priſm or Cylinder of Glaſſe, Steel, Wood, or
other Frangible Matter, that being ſuſpended length­
waies, will ſuſtain a very great Weight hanged
Thereat, will, Sidewaies, (as we ſaid even now) be
broken in pieces by a far leſſer Weight, according as
its length ſhall exceed its thickneſs.
Wherefore let us deſcribe the Solid Priſm A B C D,
fixed into a Wall by the Part A B, and in the
other extream ſuppoſe the Force of the Weight E;
(alwaies underſtanding the Wall to be erect to the Horizon,
and the Priſm or Cylinder faſtened in the Wall at Right-An­
gles) it is manifeſt, that being to break, it will be broken in the place
B, where the Mortace in the Wall ſerveth for Fulciment, and B C
for the part of the Leaver in which lieth the force, and the thick­
neſſe of the Solid B A is the other part of the Leaver, in which
lieth the Reſiſtance, which conſiſteth in the unfaſtening, or divi­
ding, that is to be made of the part of the Solid B D, that is with­
out the Wall from that which is within: and by what hath been
declared, the Moment
65[Figure 65]
of the Force placed in
C, is to the Moment of
the Reſiſtance that lieth
in the thickneſſe of the
Priſm, that is, in the
Connection of the Baſe
B A, with the parts con­
tiguous to it, as the
length C B is to the half
of B A: And therefore
the abſolute Reſiſtance
againſt Fraction that is
in the Priſm B D,
(which abſolute Reſi­
ſtance is that which is
made by drawing it
downwards, for at that
time the motion of the Mover is the ſame with that of the Body
Moved) againſt the fracture to be made by help of the Leaver
1B C, is as the Length B C to the half of A B in the Priſm, which
in the Cylinder is the Semidiameter of its Baſe. And this is our firſt
Propoſition. And obſerve, that what I have ſaid ought to be un­
derſtood, when the Confideration of the proper Weight of the So­
lid B D is removed: which Solid I have taken as weighing nothing.
But in caſe we would bring its Gravity to account, conjoyning it
with the Weight E, we ought to add to the Weight E the half of
the Weight of the Solid B D: ſo that the Weight B D being
v. gr. two pounds, and the Weight of E ten pounds, we are to
take the Weight E, as if it were eleven pounds.
SIMP. And why not as if it were twelve?
SALV. The Weight E, Simplicius, hanging at the term C,
gravitates in reſpect of B C, with all its Moment of ten pounds,
whereas if only B D were pendent, it would weigh with its whole
Moment of two pounds; but, as you ſee, that Solid is diſtributed
thorow all the length B C, uniformly, ſo that its parts near to the
extream B, gravitate leſſe than the more remote: ſo that, in a word,
compenſating thoſe with theſe, the weight of the whole Priſm is
brought to operate under the Center of its Gravity, which anſwe­
reth to the middle of the Leaver B C: But a Weight hanging at
the end C, hath a Moment double to that which it would have
hanging at the middle: And therefore the half of the Weight of
the Priſm ought to be added to the Weight E, when we would uſe
the Moment of both, as placed in the Term C.
SIMP. I apprehend you very well, and, if I deceive not my ſelf,
me thinks, that the Power of both the Weights B D and E, ſo placed,
would have the ſame Moment, as if the whole Weight of B D, and
the double of E were hanged in the midſt of the Leaver B C.
SALV. It is exactly ſo, and you are to bear it in mind. Here we
may immediatly underſtand
PROPOSITION II.
How, and with what proportion, a Ruler, or Priſm,
more broad than thick, reſiſteth Fraction, better if it
be forced according to its breadth, than according to
its thickneſſe.
For underſtanding of which, let a Priſm be ſuppoſed A D:
[as in Fig. 4.] whoſe breadth is A C, and its thickneſs much
leſſer C B: It is demanded, why we would attempt to break
it edge-waies, as in the firſt Figure it will reſiſt the great Weight
T, but placed flat-waies, as in the ſecond Figure, it will not reſiſt
1X, leſſer than T: Which is manifeſted, ſince we underſtand the
Fulciment, one while under the Line B C, and another while under
C A, and the Diſtances of the Forces to be alike in both Caſes, to
wit, the length B D. But in the firſt Caſe, the Diſtance of the Re­
ſiſtance from the Fulciment, which is the half of the Line C A, is
greater than the Diſtance in the other Caſe, which is the half of B
C: Therefore the Force of the Weight T, muſt of neceſſity be grea­
ter than X, as much as the half of the breadth C A is greater than
half the thichneſſe B C, the firſt ſerving for the Counter-Leaver of
C A, and the ſecond of C B to overcome the ſame Reſiſtance, that
is the quantity of the Fibres, or ſtrings of the whole Baſe A B.
Conclude we therefore, that the ſaid Priſm or Ruler, which is
broader than it is thick, reſiſteth, bresking more the edge-waies
than the flat-waies, according to the Proportion of the breadth to
the thickneſs.
It is requiſite that we begin in the next place
PROPOSITION III.
To find according to what proportion the encreaſe of the
Moment of the proper Gravity is made in a Priſm
or Cylinder, in relation to the proper Reſiſtance
againſt Fraction, whilſt that being parallel to the
Horizon, it is made longer and longer: Which Mo­
ment I find to encreaſe ſucceſsively in duplicate Pro­
portion to that of the prolongation.
For demonſtration whereof, deſcribe the Priſm or Cylin­
der A D, firmly faſtned in the Wall at the end A, and let
it be equidiſtant from the Horizon, and let the ſame be
underſtood to be prolonged as far as E, adding thereto the part
B E. It is manifeſt, that the prolongation of the Leaver A B
to C encreaſeth, by it ſelf alone, that is taken abſolutely, the
Moment of the Force preſſing againſt the Reſiſtance of the
Separation and Rupture to be made in A, according to the pro­
portion of C A to B A: but, moreover, the Weight of the Solid
affixed B E, encreaſeth the Moment of the preſſing Gravity of
the Weight of the Solid A B, according to the Proportion of
the Priſm A E to the Priſm A B; which proportion is the ſame
as that of the length A C, to the length A B: Therefore it is clear
1that the two augmentations of the Lengths and of the Gravities
being put together, the Moment compounded of both is in double
66[Figure 66]
proportion to ei­
ther of them. We
conclude there­
fore, That the Mo­
ments of the For­
ces of Priſmes and
Cylinders of equal
thickneſſe, but of
unequal length, are
to one another in
duplicate proporti­
on to that of their
Lengths; that is,
are as the Squares of
their Lengths.
We will ſhew, in
the ſecond place,
according to what proportion the Reſiſtance of Fraction in Priſmes
and Cylinders encreaſeth, when they continue of the ſame length,
and encreaſe in thickneſs. And here I ſay, that
PROPOSITION IV.
In Priſmes and Cylinders of equal length, but unequal
thickneſs, the Reſiſtance againſt Fraction encreaſeth
in a proportion iriple to the Diameters of their
Thickneſſes, that is, of their Baſes.
Let the two Cylinders be theſe A and B, [as in Fig. 5.]
whoſe equal lengths are D G, and F H, the unequal Baſes
the Circles, whoſe Diameters are C D, and E F. I ſay,
that the Reſiſtance of the Cylinder B is to the Reſiſtance of the
Cylinder A againſt Fraction, in a proportion triple to that which
the Diameter F E hath to the Diameter D C. For if we conſider
the abſolute and ſimple Reſiſtance that reſides in the Baſes, that
is, in the Circles E F, and D C to breaking, offering them vio­
lence by pulling them end-waies, without all doubt, the Reſiſtance
of the Cylinder B, is ſo much greater than that of the Cylinder A,
by how much the Circle E F is greater than C D; for the Fibres,
Filaments, or tenacious parts, which hold together the Parts of the
Solid, are ſo many the more. But if we conſider, that in offering
1them violence tranſverſly we make uſe of two Leavers; of which
the Parts or Diſtances, at which the Forces are applied are the Lines
D G, and F H, the Fulciments are in the Points D and F; but the
other Parts or Diſtances, at which the Reſiſtances are placed, are
the Semidiameters of the Circles D C and E F, becauſe the Fila­
ments diſperſed thorow the whole Superficies of the Circles are as
if they were all reduced into the Centers: conſidering, I ſay, thoſe
Leavers, we would be underſtood to intend, that the Reſiſtance in
the Center of the Baſe E F againſt the Force of H, is ſo much grea­
ter than the Reſiſtance of the Baſe C D, againſt the Force placed
in G, (and the Forces in G and H are of equal Leavers D G, and
F H) as the Semidiameter F E is greater than the Semidiameter
D C, the Reſiſtance againſt Fraction, therefore, in the Cylinder
B, encreaſeth above the Reſiſtance of the Cylinder A, according
to both the proportions of the Circles E F and D C, and of their
Semidiameters, or, if you will, Diameters: But the proportion of
the Circles is double of that of the Diameters; Therefore the pro­
portion of the Reſiſtances, which is compounded of them, is in
triplicate proportion of the ſaid Diameters: Which is that which
I was to prove. But becauſe alſo the Cubes are in triplicate pro­
portion to their Sides, we may likewiſe conclude, That the Reſi­
ſtances of Cylinders of equal Length, are to one another as the Cubes
of their Diameters.
From that which we have Demonſtrated we may likewiſe con­
clude, that
COROLARY.
The Reſiſtances of Priſms, and Cylinders of equal length are in
Seſquialter proportion to that of the ſaid Cylinders.
The which is manifeſt, becauſe the Priſms and Cylinders,
equal in height, are to one another, in the ſame proportion as
their Baſes; that is, the double of the Sides or Diameters of the
ſaid Baſes: But the Reſiſtances (as hath been demonſtrated) are
in triplicate proportion to the ſaid Sides or Diameters: Therefore
the proportion of the Reſiſtances is Seſquialter to the proportion
of the ſaid Solids, and, conſequently, to the Weights of the ſaid
Solids.
SIMP. It is convenient, that, before we proceed any farther, I
be reſolved of a certain Doubt, and this it is, That I have not hi­
therto heard propoſed to Conſideration another certain kind of
Reſiſtance, that, in my opinion, is ſucceſſively diminiſhed in So­
lids, according as they are more and more prolonged, and not on­
ly in uſing them ſidelongs, but alſo leng thwaies, in the ſelf ſame
1manner juſt as we ſee a very long Cord to be much leſſe apt to
ſuſtain a great weight, than if it were ſhort: ſo that I believe, that
a Ruler of Wood or Iron will ſuſtain a much greater weight, if it
ſhall be ſhort, than if it ſhall be very long; underſtanding it al­
waies to be uſed lengthwaies, and not tranſverſly; and alſo
its own weight being accounted for, which in the longer is
greater.
SALV. I fear, Simplicius, that in this Point you, with many
others, are deceived, if ſo be, that I have rightly apprehended your
meaning, ſo that you would ſay, that a Cord v. gr. forty yards
long cannot ſuſtain ſo much, as if uſe were made but of one or two
yards of the ſame Rope.
SIMP. That is it, which I would have ſaid, and as yet it ſeemeth
a very probable Propoſition.
SALV. But I hold it not only improbable, but falſe: and think
that I can very eaſily reclaim you from your Errour. Therefore
let us ſuppoſe this Rope A B, [as in Fig. 6.] faſtned on high by
the end A, and by the other end let there hang the Weight C,
by the force of which, the ſaid Rope is to be broken. Do you
aſſign me the particular place, Simplicius, where the Rupture is
to happen.
SIMP. Let it be in the place D.
SALV. I ask what is the cauſe why it ſhould break in D.
SIMP. The reaſon thereof is, becauſe the Rope was not ſtrong
enough in that part, to ſuſtain v. gr. an hundred pounds of weight,
for ſo much is the Rope D B with the Stone C.
SALV. Therefore when ever ſuch a Rope ſhall come to be vio­
lently ſtretched by thoſe hundred pounds of weight, it ſhall break
in that place.
SIMP So I think.
SALV. But tell me now; if one did hang the ſame Weight, not
at the end of the Rope B, but near to the point D, as for inſtance,
in E, or elſe did tye the Rope not at the height A, but very near,
and almoſt at the Point D it ſelf, as in F, tell me, I ſay, whether
the Point D would feel the ſame weight of an hundred pounds.
SIMP. It would ſo, ſtill joyning the piece of Rope E B to the
Stone C.
SALV. If then the Rope in the Point D commeth to be drawn
by the ſaid hundred pounds of weight, it will break by your con­
ceſſion. And yet F E, is a ſmall piece of the length A B: why do
you ſay then, that the long Rope is weaker than the ſhort one?
Be content, therefore, to ſuffer your ſelf to be reclaimed from an
Errour, in which you have had many Companions, and thoſe in
other things very knowing. And let us go on: and having demon­
ſtrated, that Priſms and Cylinders encreaſe their Moments above
1their Reſiſtances, according to the Squares of their Lengths (alwaies
provided, that they retain the ſame thickneſſe) and that likewiſe,
theſe that are equally long, but different in thickneſſe, encreaſe
their Reſiſtances according to the proportion of the Cubes of the
Sides or Diameters of their Baſes, we may enquire what befal­
leth to thoſe Solids, being different in length and thickneſs, in which
I obſerve, that
PROPOSITION V.
Priſms and Cylinders, of different length and thickneſs,
have their Reſiſtances againſt Fraction, in a propor­
tion compounded of the proportion of the Cubes of the
Diameters of their Baſes, and of the proportion of
their lengths reciprocally taken.
Let theſe two A B C, and D E F, [as in Fig. 7.] be ſuch Cy­
linders. I ſay, the Reſiſtance of the Cylinder A C ſhall be to
the Reſiſtance of the Cylinder D F, in a proportion com­
pounded of the proportion of the Cube of the Diameter A B, to
the Gube of the Diameter D E, and of the proportion of the
Length E F to the Length B C. Suppoſe E G equal to B C, and to
the Lines A B, and D E, let C H be a third proportional, and I,
a fourth; and as E F is to B C, ſo let I be to S. And becauſe the
Reſiſtance of the Cylinder A C is to the Reſiſtance of the Cylin­
der D G, as the Cube A B to the Cube D E; that is, as the Line
A B to the Line I: and the Reſiſtance of the Cylinder G D is to
the Reſiſtance of the Cylinder D F, as the Length F E is to the
Length E G; that is, as the Line I is to S: Therefore by Equali­
ty of proportion, as the Reſiſtance of the Cylinder A C is to the
Reſiſtance of the Cylinder D F, ſo is the Line A B to S: But the
Line A B is to S, in a proportion compounded of A B to I, and of
I to S: Therefore the Reſiſtance of the Cylinder A C is to the Re­
ſiſtance of the Cylinder D F, in a proportion compounded of A B
to I, that is, as the Cube of A B to the Cube of D E, and of the
proportion of the Line I to S; that is, of the Length E F to the
Length B C: Which was to be demonſtrated.
After the Propoſition laſt demonſtrated, we will conſider what
hapneth between like Cylinders and Priſms, of which we will de­
monſtrate, how that
1
PROPOSITION VI.
Of like Cylinders and Priſms the Moments compoun­
ded, that is to ſay, reſulting from their Gravities,
and from their Lengths, which are, as it were, Lea­
vers, have to one another a proportion Seſquialter to
that which is between the Reſiſtances of their ſame
Baſes.
For demonſtration of which let us deſcribe the two like Cy­
linders A B, and C D, [as in Fig. 8.] I ſay, that the Mo­
ment of the Cylinder A B, to overcome the Reſiſtance of its
Baſe B, hath to the Moment of C D, to overcome the Reſiſtance
of its Baſe C, a proportion Seſquialter to that which the ſame Re­
ſiſtance of the Baſe B, hath to the Reſiſtance of the Baſe D:
And becauſe the Moments of the Solids A B, and C D, to over­
come the Reſiſtances of their Baſes B and D, are compounded of
their Gravities, and of the Forces of their Leavers, and the Force
of the Leaver A B is equal to the Force of the Leaver C D, and
that becauſe the length A B hath the ſame proportion to the Semi­
diameter of the Baſe B, (by the ſimilitude of the Cylinders) that
the Length C D hath to the Semidiameter of the Baſe D; it re­
maineth, that the total Moment of the Cylinder A B, be to the
total Moment of C D, as the ſole Gravity of the Cylinder A B is
to the ſole Gravity of the Cylinder C D; that is, as the ſaid Cy­
linder A B is to the ſaid C D: But theſe are in triplicate propor­
tion to the Diameters of their Baſes B and D; and the Reſiſtances
of the ſame Baſes, being to one another as the ſaid Baſes, they are
conſequently in duplicate proportion to their ſame Baſes: There­
fore the Moments of Cylinders are in Seſquialter proportion to
the Reſiſtances of their Baſes.
SIMP. This Propoſition, indeed, is not only new, but unexpe­
cted to me, and at firſt ſight, very remote from the judgment that
I ſhould have conjecturally paſt upon it: for in regard, that theſe
Figures are in all other reſpects alike, I ſhould have thought that
their Moments likewiſe ſhould have retained the ſame proportion
towards their proper Reſiſtances.
SAGR. This is the Demonſtration of that Propoſition, that in
the beginning of our Diſcourſes, I ſaid, I thought------I had ſome
glimps of.
SALV. That which now befalleth, Simplicius, hapned for ſome
1time to my ſelf, believing, that the Reſiſtances of like Solids were
alike, till that a certain, and that no very fixed or accurate Obſer­
vation ſeemed to repreſent unto me, that Solids do not contain
an equal tenure in their Toughneſs, but that the bigger are leſſe
apt to ſuffer violent accidents, as luſty men are more damnified by
their falls than little children; and, as in the begining we ſaid, we
ſee a great Beam or Column break to pieces falling from the ſame
height, and not a ſmall Priſin or little Cylinder of Marble. This
ſame Obſervation gave me the hint for finding of that which I am
now about to demonſtrate; a Quality truly admirable, for that
amongſt the infinite Solid-like Figures, there are not ſo much
as two, whoſe Moments retain the ſame proportion towards their
proper Reſiſtances.
SIMP. Now you put me in mind of ſomething inſerted by Ari­
ſtotle amongſt his Mechanical Queſtions, where he would give a
Reaſon, whence it is, that Beams the longer they are, they are by ſo
much the more weak, and bend more and more, although the ſhort
ones be the ſlendereſt, and the long ones thickeſt: and, if I well re­
member, he reduceth the Reaſon to the ſimple Leaver.
SALV. It is very true, and becauſe the Solution ſeemeth not
wholly to remove the cauſe of doubting Monſignore di Guevara,
who, the truth is, with his moſt learned Commentaries hath highly
enobled and illuſtrated that Work, enlargeth himſelf with other
accute Speculations for the obviating all difficulties, yet himſelf
alſo remaining perplexed in this point, whether, the lengths and
thickneſſes of ſuch Solid Figures, encreaſing with the ſelf ſame
proportion, they ought to retain the ſame tenure in their Tough­
neſſes and Reſiſtances againſt their breaking, and likewiſe againſt
their bending. After I had long conſidered thereon, I have, in
this manner found, that which I am about to tell you. And firſt
I will demonſtrate that
1
PROPOSITION VII.
Of like and heavy Priſms or Cylinders there is one only,
and no more, that is reduced (being charged with its
own weight) to the ultimate ſtate between breaking
and holding it ſelf together: ſothat every greater, as
being unable to reſiſt its own weight, will break,
and every leſſer reſiſteth ſome Force that is employed
againſt it to break, it.
Let the heavy Priſm be A B [as in Fig 9.] reduced to the
utmoſt length of its Conſiſtance, ſo that being lengthned
never ſo little more it will break: I ſay, that this is the only
one amongſt all thoſe that are like unto it, (which yet are infinite)
that is capable of being reduced to that dubious and tickliſh ſtate;
ſo that every greater being oppreſſed with its own weight will
break, and every leſſer not, nay, will be able to reſiſt ſome additi­
on of a new violence, over and above that of its own weight.
Firſt, take the Priſm C E, like to, and greater than A B. I ſay, that
this cannot conſiſt, but will break, being overcome by its own
Gravity. Suppoſe the part C D as long as A B. And becauſe the
Reſiſtance C D is to that of A B, as the Cube of the thickneſſe of
C D to the Cube of the thickneſs of A B; that is, as the Priſm
C E to the Priſm A B (being alike:) Therefore the Weight of
C E is the greateſt that can be ſuſtained at the length of the Priſm
C D: But the Length C E is greater: Therefore the Priſm C E
will break. But let F G be leſſet: it ſhall be demonſtrated like­
wiſe (ſuppoſing F H equal to B A) that the Reſiſtance of F G is
to that of A B, as the Priſm F G is to the Priſm A B, in caſe that the
Diſtance A B, that is F H, were equal to F G, but it is greater:
Therefore the Moment of the Priſm F G, placed in G, doth not
ſuffice to break the Priſm F G.
SAGR. A moſt manifeſt and brief Demonſtration, inferring the
truth and neceſſity of a Propoſition that at firſt ſight ſeemeth far
from probability. It would be requiſite, therefore, to alter much
the proportion betwixt the Length and Thickneſſe of the greater
Priſm by making it thicker or ſhorter, to the end it might be re­
duced to that nice ſtate of indifferency between holding and brea­
king; and the Inveſtigation of that ſame State, as I think, would
be no leſſe ingenuous.
SALV. Nay, rather more, as it is alſo more laborious: and I am
1ſure I have ſpent no ſmall time to find it; and I will now impart it
to you: Therefore
PROP. VIII. PROBL. I.
A Cylinder or Priſm of the utmoſt length not to be bro­
ken by its own weight, and alſo a greaver length, be­
ing given, to find the thickneſſe of another Cylinder
or Priſm that under-given length is the only one, and
biggeſt, that can reſiſt its own weight.
Let the Cylinder B C [as in Fig. 10.] be the biggeſt that
can reſiſt its own weight, and let D E be a Length greater
than A C; it is required to find the Thickneſſe of the Cylin­
der, that under the Length D E is the greateſt reſiſting its own
weight. Let I be a third proportional to the Lengths D E, and
A C; and as D E is to I, ſo let the Diameter F D be to the Dia­
meter B A: and make the Cylinder F E. I ſay, that this is the big­
geſt, and only one amongſt all that are like to it that reſiſteth its
own weight. To the Lines D C and I let M be a third propor­
tional, and O a fourth. And ſuppoſe F G equal to A C. And be­
cauſe the Diameter F D is to the Diameter A B, as the Line D E
to I, and O is a fourth proportional to D E and I, the Cube of
F D ſhall be to the Cube of B A as D E is to O: But as the Cube of
F D is to the Cube of B A, ſo is the Reſiſtance of the Cylinder
D G to the Reſiſtance of the Cylinder B C: Therefore the Reſi­
ſtance of the Cylinder D G is to that of the Cylinder B C, as the
Line D F is to O. And becauſe the Moment of the Cylinder B C
is equal to its Reſiſtance, if we ſhew that the Moment of the Cylin­
der F E is to the Moment of the Cylinder B C, as the Reſiſtance
D F to the Reſiſtance B A; that is, as the Cube of F D to the Cube
of B A; that is, as the Line D E to O, we ſhall have our intent:
that is, that the Moment of the Cylinder F E is equal to the Reſi­
ſtance placed in F D. The Moment of the Cylinder F E is to the
Moment of the Cylinder D G, as the Square of D E is to the
Square of A C; that is, as the Line D E to I: But the Moment of
the Cylinder D G is to the Moment of the Cylinder B C, as the
Square D F to the Square B A; that is, as the Square of D E to the
Square of I; that is, as the Square of I to the Square of M; that
is, as I to O: Therefore, by Equality of proportion, as the Mo­
ment of the Cylinder F E is to the Moment of the Cylinder B C,
ſo is the Line D E to O; that is, the Cube D F to the Cube
B A; that is, the Reſiſtance of the Baſe D F to the Reſiſtance
1of the Baſe B A: Which is that that was ſought.
SAGR This, Salviatus, is a long Demonſtration, and very hard
to be born in mind at the firſt hearing, therefore I could wiſh, that
you would pleaſe to repeat it.
SALV. I will do what you ſhall command; but haply it would
be better to produce one more conciſe and ſhort: but then it will
be requiſite to deſcribe a Figure ſomewhat different.
SAGR. The favour will then be the greater: and beſtow upon
me the draught of that already explained, that I may at my leaſure
conſider it again.
SALV. I will not fail to ſerve you. Now, ſuppoſe a Cylinder A,

[as in Fig. 11.] the Diameter of whoſe Baſe let be the Line D C,
and let this A be the greateſt that can ſuſtain it ſelf and not break,
than which we will find a bigger, which likewiſe ſhall be the big­
geſt alſo, and the only one that ſuſtaineth it ſelf. Let us deſire one
like to the ſaid A, and as long as the aſſigned Line, and let this be
v. gr. E, the Diameter of whoſe Baſe let be K L; and to the two
Lines D C, and K L let M N be a third proportional; which let be
the Diameter of the Baſe of the Cylinder X, in length equal to E.
I ſay, that this X is that which we ſeek. And becauſe the Reſi­
ſtance D C is to the Reſiſtance K L, as the Square D C to the
Square K L; that is, as the Square K L to the Square M N; that
is, as the Cylinder E to the Cylinder X; that is, as the Moment E
to the Moment X: But the Reſiſtance K L is to M N, as the Cube
of K L is to the Cube of M N; that is, as the Cube B C to the
Cube K L; that is, as the Cylinder A to the Cylinder E; that is,
as the Moment A to the Moment E: Therefore, by Perturbation
of proportion, as the Reſiſtance D C is to M N, ſo is the Moment
A to the Moment X: Therefore the Priſm X, is in the ſame Conſti­
tution of Moment and Reſiſtance as the Priſm A.
The laſt Problem
performed another
way.
But let us make the Problem more general, and let the Propo­
ſition be this:
The Cylinder A C being given, and its Moment to-

wards its Reſiſtance being ſuppoſed at pleaſure, and
any Length D E being aſsigned, to find the Thick­
neſſe af the Cylinder whoſe Length is D E, and whoſe
Moment towards its Reſiſtance retaineth the ſame
proportion, that the Moment of the Cylinder A C
doth to its Reſiſtance.
1
The laſt Propoſi­
tion made more ge­
neral.
Reaſſuming the above ſaid Figure and almoſt the ſame Me­
thod, we will ſay: Becauſe the Moment of the Cylinder
F E hath the ſame proportion to the Moment of the part
D G, that the Square E D hath to the Square F G; that is that
the Line D E hath to I: and becauſe the Moment of the Cylinder
F G is to the Moment of the Cylinder A C, as the Square F D to
the Square A B; that is, as the Square D E to the Square I; that
is, as the Square I to the Square M; that is, as the Line I to O:
Therefore, ex æquali, the Moment of the Cylinder F E hath the
ſame proportion to the Moment of the Cylinder A C, that the
Line D E hath to the Line O; that is, that the Cube D E hath
to the Cube of I; that is, that the Cube of F D hath to the
Cube of A B; that is, that the Reſiſtance of the Baſe F D hath to
the Reſiſtance of the Baſe A B: Which was to be performed.
Now, let it be obſerved, that from the things hitherto demonſtra­
ted, we may plainly gather, how Impoſſible it is, not only for Art, but

for Nature her ſelf to encreaſe her Machines to an immenſe Vaſt­
neſſe: ſo that it would be impoſſible by Art to build extraordina­
ry vaſt Ships, Palaces, or Temples, whoſe ^{*} Oars, Sail-yards, Beams,
Iron Bolts, and, in a word, their other parts ſhould conſiſt or hold
together: neither again could Nature make Trees of unmeaſura­

ble greatneſſe, for that their Arms or Bows being oppreſſed with
their own weight would at laſt break: and likewiſe it would be
impoſſible for her to make ſtructures of Bones for men, Horſes, or
other Animals, that might ſubſiſt, and proportionatly perform
their Offices, when thoſe Animals ſhould be augmented to im­
menſe heights, unleſſe ſhe ſhould take Matter much more hard and
Refiſting than that which ſhe commonly uſeth, or elſe ſhould de­
form thoſe Bones by augmenting them beyond their due Symetry,
and making the Figure or ſhape of the Animal to become mon­
ſtrouſly big: Which haply was hinted by my moſt Witty Poet,
where deſcribing an huge Giant, he ſaith,
* Oares are uſed
in the Ships or
Gallies of the
Mediterrane, up­
on which our
Author was a
Coaſter.
Bones of Animals
magnified beyond
their ratural ſize,
would not ſubſiſt, if
it be required to
retain the ſame
proportion of thick­
neſs and hardneſs
in them that is in
thoſe of Natural
Animals.
Non ſi puo compartir quanto ſia lungo,
Si ſmiſuratamente è tutto groſſo.
Example of the
Bone of an Animal
enlarged to thrice
the Natural pro­
portion, how much
thicker it ought to
be to perform its
office.
And for a ſhort example of this that I ſay, [as in Fig. 12.] I
have heretofore drawn the Figure of a Bone only trebled in
Length, and augmented in Thickneſſe in ſuch proportion, as that
it may in its great Animal perform the office proportionate to that
of the leſſer Bone in a ſmaller Animal, and the Figures are theſe:
whereby you ſee what a diſproportionate Figure that of the aug­
mented Bone becometh. Whence it is manifeſt, that he that would
in an huge Giant keep the proportions that the Members have in
1an ordinary Man, muſt either find Matter much more hard and re­
ſiſting to make Bone of, or elſe muſt admit that its Strength is in
proportion much more weak than in Men of middle Stature: other­
wiſe, encreaſing the Giant to an immeaſurable height he would be
oppreſſed, and fall under his own weight. Whereas on the con­
trary, in diminiſhing of Bodies we do not ſee the Strength and
Forces to diminiſh in the ſame proportion, nay, in the leſſer the
Robuſtiouſneſſe encreaſeth with a great proportion. So that I
believe, that a little Dog could carry on his back two or three Dogs
equal to himſelf, but I do not think that an Horſe could carry ſo
much as one ſingle Horſe of his own ſize.
SIMP. But if it be ſo, I have great reaſon to doubt the Im­
menſe bulks that we ſee in Fiſhes, for (if I rightly underſtand
you) a Whale ſhall be as big as ten Elephants, and yet they ſu­
ſtain themſelves.
SALV. Your doubt, Simplicius, prompts me with another Con­
dition which I perceived not before, which is alſo able to make
Giants and other very big Animals to conſiſt, and act themſelves
no leſſe than ſmaller, and this will happen when not only Strength
is added to the Bones and other Parts, whoſe office it is to ſuſtain
their own and the ſupervenient weight; but the ſtructure of the
Bones being left with the ſame proportions, the ſame Fabricks
would juſt in the ſame manner, yea, with much more eaſe, con­
ſiſt, when the Gravity of the matter of thoſe Bones, or that of
the Fleſh, or whatever elſe is to reſt it ſelf upon the Bones is dimini­
ſhed in that proportion: and of this ſecond Artifice, Nature hath
made uſe in the framing of Fiſhes, making their Bones, and Pulps,
not only very light, but without any Gravity.
SIMP. I ſee very well, Salviatus, whither your Diſcourſe ten­
deth: you will ſay, that becauſe the Element of Water is the Ha­
bitation of Fiſhes, which by its Corpulence, or, as others will, by
its Gravity diminiſheth the weight of Bodies demerged in it, for
that reaſon the Matter of Fiſhes, not weighing any thing, may be
ſuſtained without ſurcharging their Bones: but this doth not ſuf­
fice, for although the reſt of the ſubſtance of the Fiſh weigh not,
yet without doubt the matter of their Bones hath its weight:
and who will ſay, that the Rib of a Whale that is as big as a
Beam doth not weigh very much, and in Water ſinketh to the Bot­
tom? Theſe therefore ſhould not be able to ſubſiſt in ſo vaſt a
Bulk.
SALV. You argue very cunningly; and for an anſwer to your
Doubt, tell me, whether you have obſerved Fiſhes to ſtand im­
moveable under water at their pleaſures, and not to deſcend to­
wards the Bottom, or raiſe themſelves towards the top without
making ſome motion with their Fins?
1
SIMP. This is a very manifeſt Obſervation.
The Cauſe why
Fiſhes do equili­
brate themſelves
in the Water.
SALV. This power therefore that the Fiſhes have to ſtay them­
ſelves, as if they were immoveable in the midſt of the Water, is a
moſt infallible argument, that the Compofition of their Corporeal
Maſſe equalleth the Specifick Gravity of the Water, ſo that if
there be found in them ſome parts that are more grave than the
Water, it is neceſſarily requiſite that they have others ſo much
leſſe grave, ſo that the Equilibrium may be ballanced. If therefore
the Bones be more grave, it is neceſſary that the Pulps, or other
Matters that are in them, be more light; and theſe will with their
lightneſſe counterpoiſe and compenſate the weight of the Bones.
So that in Aquatick Animals the quite contrary hapneth to that
which befals the Terreſtrial, namely, that in the latter it is the of­
fice of the Bones to ſuſtain their own weight, and the weight of
the Fleſh; and in the former, the Fleſh [if one may ſo call it]

beareth up its own weight, and that of the Bones. And therefore
ceaſe to wonder how there may be moſt vaſt Animals in the Wa­
ter, but not on the Earth, that is, in the Air.
Aquatick Animals
greater than the
Terreſtrial, and for
what Reaſon.
SIMP. I am ſatisfied, and moreover obſerve, that theſe which
we call Terreſtrial Animals, ought with more reaſon to be called
Aerial; becauſe in the Air they really live, and by the Air they are
environ'd, and of the Air they breath.
SAGR. The Diſcourſe of Simplicius pleaſeth me, as alſo his
Doubt and its Solution. And farthermore I comprehend very ea­
ſily, that one of theſe huge Fiſhes being haul'd on ſhore, could not
perchance be able to ſuſtain it ſelf for any time; but that the Con­
nections of the Bones being relaxed, its Maſſe would be cruſh'd un­
der its own weight.
SALV. For the preſent, I encline to the ſame Opinion: nor am
I far from thinking that the ſame would happen to that huge Ship,
which floating in the Sea is not diſſolved by its weight, and the bur­
den of its Lading and Artilery, but on dry ground, and environed
with Air, it perhaps would fall in pieces. But let us purſue our bu­
ſineſſe, and demonſtrate, that
1
PROP. IX. PROBL. II.
A Priſme or Cylinder with its weight, and the great­
eſt Weight ſuſtained by it being given, to find the
greateſt Length, beyond which being prolonged. it
would break under its own Weight.
Let there be given the Priſme A C (as in Fig. 13.) with its
weight, and likewiſe let the Weight D be given, the great­
eſt that can be ſuſtained by the extreme C: it is required to
finde the greateſt Length unto which the ſaid Priſme may be pro­
longed, without breaking. As the weight of the Priſme A C is to
the Compound of the weights A C, with the double of the
Weight D, ſo let the length C A be to C A H: between which
let A G be a Mean-Proportional. I ſay that A G is the Length
ſought. For the depreſſing Moment of the Weight D in C, is
equal to the Moment of the double weight D, if it be placed in
the middle of A C, where is alſo the Center of the Moment of
the Priſme A C: The Moment, therefore, of the Reſiſtance of
the Priſme A C, which reſides in A, is equivalent to the gravi­
tation of the double of the Weight D with the weight A C, but
hanged in the midſt of A C. And becauſe it hath been made,
that as the Moment of the ſaid Weights ſo ſituated, that is, of
the double of D, with A C, is to the Moment of A C, ſo is H A
to A C, between which A G is a Mean Proportional: There­
fore the Moment of D doubled with the Moment of A C, is to
the Moment A C, as the Square G A to the Square A C: But the
preſſing Moment of the Priſme G A, is to the Moment of A C,
as the Square G A to the Square A C: Therefore the Length
A G is the greateſt that was ſought, namely, that unto which the
Priſme A G being prolonged, it would ſuſtain it ſelf, but beyond
it would break.
Hitherto we have conſidered the Moments and Reſiſtances of
ſolid Priſmes and Cylinders, one end of which is ſuppoſed im­
moveable, and to the other onely the Force of a preſſing weight
is applyed, conſidering it by it ſelf alone, or joyned with the
Gravity of the ſame Solid, or elſe the ſole Gravity of the ſaid
Solid. Now I deſire that we may ſpeak ſomething of thoſe ſame
Priſmes or Cylinders, in caſe they were ſuſtained at both ends, or
did reſt upon one ſole point taken between the ends. And firſt,
I ſay that,
1
PROPOSITION X.
The Cylinder that being charged with its own Weight
ſhall be reduced to its greateſt Length, beyond which
it would not ſuſtain it ſelf, whether it be born up in
the middle by one ſole Fulciment, or elſe by two at
the ends, may be double in length to that which
ſhould be faſtned in the Wall, that is ſuſtained at but
one end.
Which of it ſelt is very obvious; for if we ſhall ſup­
poſe of the Cylinder which I deſcribe A B C, its
half A B to be the utmoſt Length that is able to be
ſuſtained, being faſtened at the end B, it ſhall be ſuſtained in the
ſame manner, if being laid upon the Fulciment G, it ſhall be
counterpoiſed by its other half B C. And likewiſe, if of the Cy­
linder D E F, the Length ſhall be ſuch that onely one half of it
can be ſuſtained, being faſtened at the end D, and conſequent­
ly the other E F, fixed at the end F; it is manifeſt, that placing
the Fulciments H and I under the ends D and F, every Moment
of Force or of Weight that is added in E, will there make the
Fracture.
That which requireth a more ſubtil Speculation is, when ſub­
ſtracting from the proper Gravity of ſuch Solids, it were pro­
pounded to us
PROP. XI. PROBL. III.
To find whether that Force or weight, that being ap­
plied to the middle of a Cylinder ſuſtained at the
ends, would ſuffice to break it, could do the ſame,
applied in any other place, neerer to one end than to
the other.
As for Example, whether we deſiring to break a Staffe
and took it with the ends in our hands, and ſetting our
knee, to the midſt of it, the ſame Force that ſhould ſuf­
fice to break it in that manner, would alſo ſuffice in caſe the knee
1were ſet, not in the midſt, but neerer to one of the ends.
SAGR. I think the Problem is toucht upon by Ariſtotle in his
Mechanical Queſtions.
SALV. The Queſtion of Aristotle is not preciſely the ſame,
for he ſeeks no more, but to render a reaſon why leſſe labour is
required to break the Staffe, holding the hands at the ends of it,
that is, far diſtant from the Knee, than if we held them neerer:
and he giveth a general Reaſon of the ſame, reducing the cauſe
of it to the Leavers, which are longer when the Arms are ex­
tended, graſping the ends. Our Queſtion addeth ſomething
more, ſeeking whether, ſetting the Knee in the midſt, or in ano­
ther place, but alwayes keeping the hands at the ends, the ſame
Force ſerveth in all ſituations.
SAGR. At firſt apprehenſion it ſhould ſeem that it doth, for
that the two Leavers retain in a certain faſhion the ſame Moment,
ſeeing that as the one is ſhortned, the other is lengthened.
SALV. Now you ſee, how eaſie it is to make Equivocations,
and with what caution and circumſpection we are to walk, leaſt
we run into them. This that you ſay, and which indeed at the
firſt ſight carrieth with it ſo much of probability, is in the ſtrict­
neſſe of it ſo falſe, that whether the Knee, which is the Fulci­
ment of the two Leavers, be placed or not placed in the midſt,
it maketh ſuch alteration, that of that Force which would ſuffice
to make the Fracture in the midſt, it being to be made in ſome
other place, it will not ſuffice to apply four times ſo much, nor
ten, nor an hundred, no nor a thouſand. Upon this we will
make ſome general Conſideration, and then we will come to the
Specifick Determination of the Propoſition, according to which,
the Forces for making of Fractures gradually vary more in one
point than in another.
Let us firſt deſigne this Truncheon A B to be broken in the
midſt upon the Fulciment C, and neer unto that let us deſigne
it again, but under the Characters D E, to be broken on the
Fulciment F, remote from the middle. Firſt it is manifeſt, that
the Diſtances A C and C B being equal, the Force ſhall be ſha­
red equally in the ends B and A. Again, according as the Di­
ſtance D F groweth leſſe than the Diſtance A C, the Moment
of the Force placed in D groweth leſſe than the Moment in A,
that is placed at the Diſtance C A, and leſſeneth according to
the proportion of the Line D F to A C; and conſequently, it is
requiſite to encreaſe it to equalize or exceed the Reſiſtance of F:
But the Diſtance D F may diminiſh in infinitum, in relation to
the Diſtance A C: Therefore it is requiſite, that it be poſſible for
the Force to be applyed in D, to encreaſe in infinitum, that it
may countervail the Reſiſtance in F. But, on the contrary, ac­
1cording as the Diſtance F E encreaſeth above C B, it is requiſite
to diminiſh the Force in E, that it may compenſate the Reſi­
ſtance in F: But the Diſtance F E in relation to C B, cannot en­
creaſe in infinitum, by drawing the Fulciment F towards the end
D, no nor yet to the double: Therefore, the Force in E, that it
may compenſate the Reſiſtance in F, ſhall be alwayes more than
half of the Force in B. We may comprehend, therefore, the ne­
ceſſity of augmenting the Moments of the Collected Forces in E
and D infinitely to equalize or exceed the Reſiſtance placed in F,
according as the Fulciment F ſhall approach neerer and neerer
to the end D.
SAGR. What will Simplicius ſay to this? Muſt he not con­
feſſe the Virtue of Geometry to be a more powerful inſtrument
than all others, to ſharpen the Wit, and diſpoſe it to diſcourſe
and ſpeculate well? and that Plato had great reaſon to deſire that
his Scholars ſhould be well grounded in the Mathematicks? I
have very well underſtood the nature of the Leaver, and how
that its Length encreaſing or decreaſing, the Moment of the
Force and of the Reſiſtance augmented or diminiſhed, and yet in
the determination of the preſent Problem I deceived my ſelf, and
that not a little, but infinitely much.
SIMP. The truth is, I begin to ſee that Logick, although it
be a moſt appoſite Inſtrument to regulate our Diſcourſe, doth
not attain, as to the prompting of the Mind with Invention,
unto the acuteneſſe of Geometry.
SAGR. In my conceit, Logick giveth us to underſtand, whe­
ther the Diſcourfes and Demonſtrations already made and found
are concluding, but that it teacheth us how to finde concluding
Diſcourſes and Demonſtrations; the truth is, I do not believe:
But it will be better, that Salviatus ſhew us according to what pro­
portion the Moments of the Forces do go increaſing, to overcome
the Reſiſtance of the ſame Piece of Wood, according to the ſe­
veral places of the Fracture.
SALV. The proportion that you ſeek, proceedeth after ſuch
a manner, that
1
PROPOSITION XII.
If in the length of a Cylinder we ſhall marke two places,
upon which we would make the Fracture of the ſaid
Cylinder, the Reſiſtances of thoſe two places have
the ſame proportion to each other, as have the Re­
ctangles made by the Diſtances of thoſe places
reciprocally taken.
Let the two Forces (as in Fig. 16.) be A and B the leaſt, to
break in C, and E and F likewiſe the leaſt, to break in D.
I ſay the Forces A and B have the ſame proportion to the
Forces E and F, that the Rectangle A D B hath to the Rectan­
gle A C B. For the Forces A and B, have to the Forces E and F, a
proportion compounded of the Forces A and B, to the Force
B, of B to F, and of F to E and E: But as the Forces A and
B are to the Force B, ſo is the Length B A to A C; and as the
Force B is to F, ſo is the Line D B to B C; and as the Force F is
to F and E, ſo is the Line D A to A B: Therefore the Forces A
and B have to the Forces E and F a proportion compounded of
theſe three, namely, of B A to A C, of D B to B C, and of D A
A B. But of the two proportions D A to A B, and A B to A C,
is compounded the proportion of D A to A C: Therefore the
Forces A and B have to the Forces E and F, the proportion com­
pounded of this D A to A C, and of the other D B to D C.
But the Rectangle A D B hath to the Rectangle A C B, a pro­
portion compounded of the ſame D A to A C, and of D B to
B C: Therefore the Forces A and B are to the Forces E and F,
as the Rectangle A D B is to the Rectangle A C B; which is as
much as to ſay, the Reſiſtance againſt Fraction in C, hath the
ſame proportion to the Reſiſtance againſt Fraction in D, that
the Rectangle A D B hath to the Rectangle A C B: Which was
to be demonſtrated.
In conſequence of this Theorem we may reſolve a Problem of
great Curioſity; and it is this:
1
PROP. XIII. PROBL. IV.
There being given the greateſt Weight that can be ſup­
ported at the middle of a Cylinder or Priſme, where
the Reſiſtance is leafl; and there being given a
Weight greater than that, to find in the ſaid Cylin­
der, the point at which the given greater Weight may
be ſupporited as the greateſt Weight.
Let the given weight greater than the greateſt weight that
can be ſupported at the middle of the Cylinder A B, have
unto the ſaid greateſt weight, the proportion of the line E
to F: it is required to find the point in the Cylinder at which the
ſaid given weight commeth to be ſupported as the biggeſt. Be­
tween E and F let G be a Mean-Proportional; and as E is to G,
ſo let A D be to S, S ſhall be leſſer than A D. Let A D be the
Diameter of the Semicircle A H D: in which ſuppoſe A H equal
to S; and joyn together H and D, and take D R equal to it.
I ſay that R is the point ſought, at which the given weight,
greater than the greateſt that can be ſupported at the middle of the
Cylinder D, would become as the greateſt weight. On the length
BA deſcribe the Semicircle A N B, and raiſe the Perpendicular
RN, and conjoyn N and
D: And becauſe the two
67[Figure 67]
Squares N R and R D are
equal to the Square N D;
that is, to the Square A D;
that is, to the two A H and
and H D; and H D is equal
to the Square D R: There­
fore the Square N R, that
is, the Rectangle A R B
ſhall be equal to the Square A H; that is, to the Square S: But
the Square S is to the Square A D, as F to E; that is, as the
greateſt ſupportable Weight at D to the given greater Weight:
Therefore this greater ſhall be ſupported at R, as the greateſt
that can be there ſuſtained. Which is that that we ſought.
SAGR. I underſtand you very well, and am conſidering that
the Priſme A B having alwayes more ſtrength and reſiſtance a­
gainſt Preſſion in the parts that more and more recede from the
middle, whether in very great and heavy Beams one may take
1away a pretty big part towards the end with a notable alleviation
of the weight; which in Beams of great Rooms would be commo­
dious, and of no ſmall proſit. And it would be pretty, to find what
Figure that Solid ought to have, that it might have equal Reſi­
ſtance in all its parts; ſo as that it were not with more eaſe to be
broken by a weight that ſhould preſſe it in the midſt, than in any
other place.
SALV. I was juſt about to tell you a thing very notable and
pleaſant to this purpoſe. I will aſſume a brief Scheme for the bet­
ter explanation of my meaning. This Figure D B is a Priſm, whoſe
Reſiſtance againſt Fraction in the term A D by a Force preſſing
at the term B, is leſſe than the Reſiſtance that would be found in
the place C I, by how much the length C B is leſſer than B A; as
hath already been demon­
ſtrated. Now ſuppoſe the
68[Figure 68]
ſaid Priſme to be ſawed
Diagonally according to the
Line FB, ſo that the oppo­
ſite Surfaces may be two
Triangles, one of which to­
wards us is F A B. This So­
lid obtains a quality contrary to the Priſme, to wit, that it leſſe re­
ſiſteth Fraction by the Force placed in B at the term C than at A,
by as much the Length C B is leſſe than B A; Which we will ea
ſily prove: For imagining the Section C N O parallel to the other
A F D, the Line F A ſhall be to C N in the Triangle F A B in the
ſame proportion, as the Line A B is to B C: and therefore if we
ſuppoſe the Fulciment of the two Leavers to be in the Points A
and C, whoſe Diſtances are B A, A F, B C, and C N, theſe, I ſay,
ſhall be like: and therefore that Moment which the Force placed
at B hath at the Diſtance B A above the Reſiſtance placed at the
Diſtance A F, the ſaid Force at B ſhall have at the Diſtance BC
above the ſame Reſiſtance, were it placed at the Diſtance C N:
But the Reſiſtance to be overcome at the Fulciment C, being pla­
ced at the Diſtance C N, from the Force in B is leſſer than the
Reſiſtance in A ſo much as the Rectangle C O is leſſe than the
Rectangle A D; that is, ſo much as the Line C N is leſs than A F;
that is, C B than B A: Therefore the Reſiſtance of the part O C B
againſt Fraction in C is ſo much leſs than the Reſiſtance of the
whole D A O againſt Fracture in O, as the Length C B is leſs than
A B. We have therefore from the Beam or Priſme D B, taken
away a part, that is half, cutting it Diagonally, and left the Wedge
or triangular Priſm F B A; and they are two Solids of contrary
Qualities, namely, that more reſiſts the more it is ſhortned, and this
in ſhortning loſeth its toughneſs as faſt. Now this being granted,
1it ſeemeth very reaſonable, nay, neceſſary, that one may give it
a cut, by which taking away that which is ſuperfluous, there remai­
neth a Solid of ſuch a Figure, as in all its parts hath equal Reſi­
ſtance.
SIMP. It muſt needs be ſo; for where there is a tranſition from
the greater to the leſſer, one meeteth alſo with the equal.
SAGR. But the buſineſſe is to find how we are to guide the
Saw for making of this Section.
SIMP. This ſeemeth to me as if it were a very eaſie buſineſſe;
for if in ſawing the Priſm diagonally, taking away half of it, the
Figure that remains retaineth a contrary quality to that of the
whole Priſm, ſo as that in all places wherein this acquireth ſtrength,
that as faſt loſeth it, me thinks, that keeping the middle way, that
is, taking only the half of that half, which is the fourth part of the
whole, the remaining Figure will not gain or loſe ſtrength in any
of all thoſe places wherein the loſſe and the gain of the other two
Figures were alwaies equal.
SALV. You have not hit the mark, Simplicius; and as I ſhall
ſhew you, it will appear in reality, that that which may be cut off
from the Priſm, and taken away without weakening it is not its
fourth part, but the third. Now it remaineth (which is that that
was hinted by Sagredus)
PROP. XIV. PROBL. V.
To find according to what Line the Section is to be
made; Which I will prove to be a Parabolical
Line.
But firſt it is neceſſary to demonſtrate a certain Lemma, which
is this:
LEMMA I.
If there ſhall be two Ballances or Leavers divided by their Fulci­
ments in ſuch ſort that the two Distances where at the Forces
are to be placed, have to each other double the proportion of
the Diſtances at which the Reſiſtances ſball be, which Reſi­
ſtances are to each other as their Diſtances, the ſuſtaining
Powers ſhall be equal.
Let A B and C D be two Leavers divided upon their Fulciments
E and F, in ſuch ſort that the Diſtance E B hath to F D a pro­
portion double to that which the Diſtance E A hath to F C. I ſay,
1the Powers that in BD ſhall ſuſtain the Reſiſtances A and C ſhall
be equal to each other. Let E G be ſuppoſed a Mean-Proporti­
onal between E B and F D; therefore as B E is to E G, ſo ſhall
G E be to F D, and A E to C F; and ſo is ſuppoſed the Reſiſtance
of A to the Reſiſtance of C. And becauſe that as E G is to F D,
ſo is A E to C F; by Permutation as G E is to E A, ſo ſhall D F
be to F C: And therefore (in
regard that the two Leavers
69[Figure 69]
D C and G A are divided pro­
portionally in the Points F and
E) in caſe the Power that being
placed at D compenſates the
Reſiſtance of C were at G, it
would countervail the ſame Reſiſtance of C placed in A: But by
what hath been granted, the Reſiſtance of A hath the ſame propor­
tion to the Reſiſtance of C, that AE hath to C F; that is, B E
hath to E G: Therefore the Power G, or if you will D, placed at
B will ſuſtain the Reſiſtance placed at A: Which was to be de­
monſtrated.
This being underſtood: in the Surface F B of the Priſme D B,
let the Parabolical Line F N B be drawn, whoſe Vertex is B, ac­
cording to which let the ſaid Priſme be ſuppoſed to be ſawed, the
Solid compriſed between the Baſe A D, the Rectangular Plane
A G, the Bight Line B G, and the Superficies D G B F being leſt
incurvated according to the Curvity of the Parabolical Line
F N B. I ſay, that
that Solid is through­
70[Figure 70]
out of equal Reſi­
ſtance. Let it be cut
by the Plane C O pa­
rallel to A D; and
imagine two Leavers
divided and ſuppor­
ted upon the Fulciments A and C; and let the Diſtances of one
be B A and A F, and of the other B C, and C N. And becauſe in
the Parabola F B A, A B is to B C, as the Square of F A to the
Square of C N, it is manifeſt, that the Diſtance B A of one Leaver,
hath to the Diſtance B C of the other a proportion double to that
which the other Diſtance A F hath to the other C N, And be­
cauſe the Reſiſtance that is to be equal by help of the Leaver
B A hath the ſame proportion to the Reſiſtance that is to be
equal by help of the Leaver B C, that the Rectangle D A hath to
the Rectangle O C; which is the ſame that the Line A F hath to
N C, which are the other two Diſtances of the Leavers; it is ma­
nifeſt by the fore going Lemma, that the ſame Force that being
1applyed to the Line B G will equal the Reſiſtance D A, will like­
wiſe equal the Reſiſtance C O. And the ſame may be demonſtra­
ted, if one cut the Solid in any other place: therefore that Parabo­
lical Solid is throughout of equal Reſiſtance. In the next place,
that cutting the Priſme according to the Parabolical Line F N B,
the third part of it is taken away, appeareth, For that the Semi­
Parabola F N B A and the Rectangle F B are Baſes of two Solids
contained between two parallel Planes, that is, between the Rect­
angles F B and D G, whereby they retain the ſame Proportion, as
thoſe their Baſes: But the Rectangle F B is Seſquialter to the Se­
miparabola F N B A: Therefore cutting the Priſine according to
the Parabolick Line, we take away the third part of it. Hence we
ſee, that Beams may be made with the diminution of their Weight
more than thirty three in the hundred, without diminiſhing their
Strength in the leaſt; which in great Ships, in particular, for bea­
ring the Decks may be of no ſmall benefit; for that in ſuch kind
of Fabricks Lightneſſe is of infinite importance.
SAGR. The Commodities are ſo many, that it would be tedi­
ous, if not impoſſible, to mention them all. But I, laying aſide
theſe, would more gladly underſtand that the alleviation is made
according to the aſſigned proportions. That the Section, according
to the Diagonal Line, cuts away half of the weight I very well
know: but that the other Section according to the Parabolical Line
takes away the third part of the Priſme I can believe upon the
word of Salviatus, who evermore ſpeaks the truth, but in this
Caſe Science would better pleaſe me than Faith.
SALV. I ſee then that you would have the Demonſtration,
whether or no it be true, that the exceſſe of the Priſme over and
above this, which for this time we will call a Parabolical Solid, is
the third part of the whole Priſme. I am certain that I have for­
merly demoſtrated it; I will try now whether I can put the
Demonſtration together again: to which purpoſe I do remember
that I made uſe of a Certain Lemma of Archimedes, inſerted by
him in his Book de Spiralibus, and it is this:
LEMMA II.
If any number of Lines at pleaſure ſhall exceed one another equal­
ly, and the exceſſes be equal to the leaſt of them, and there be as
many more, each of them equal to the greateſt; the Squares of all
theſe ſhall be leſſe than the triple of the Squares of thoſe that
exceed one another: but they ſhall be more than triple to thoſe
others that remain, the Square of the greateſt being ſub­
ſtracted.
1
This being granted: Let the Parabolick Line A B be inſcribed
in this Rectangle A C B P: we are to prove the Mixt Triangle
B A P, whoſe ſides are B P and P A, and Baſe the Parabolical Line
B A, to be the third part of the whole Rectangle C P. For if it be
not ſo, it will be either more than the third part, or leſſe. Let it be
ſuppoſed that it may be
leſſe, and to that which is
71[Figure 71]
wanting ſuppoſe the Space
X to be equal. Then di­
viding the Rectangle con­
tinually into equal parts
with Lines parallel to the
Sides B P and C A, we
ſhall in the end arrive at
ſuch parts, as that one of them ſhall be leſſe than the Space X.
Now let one of them be the Rectangle O B, and by the Points
where the other Parallels interſect the Parabolick Line, let the Pa­
rallels to A P paſſe: and here I will ſuppoſe a Figure to be cir­
cumſcribed about our Mixt-Triangle, compoſed of Rectangles,
which are B O, I N, H M, F L, E K, G A; which Figure ſhall alſo
yet be leſs than the third part of the Rectangle C P, in regard that
the exceſſe of that Figure over and above the Mixed Triangle is
much leſſe than the Rectangle B O, which yet again is leſſe than
the Space X.
SAGR. Softly, I pray you, for I do not ſee how the exceſſe of
this circumſcribed Figure above the Mixt Triangle is conſiderably
leſſer than the Rectangle B O.
SALV. Is not the Rectangle B O equal to all theſe ſmall Rect­
angles by which our Parabolical Line paſſeth; I mean theſe, B I,
I H, H F, F E, E G, and G A, of which one part only lyeth with­
out the Mixt Triangle? And the Rectangle B O, is it not alſo ſup­
poſed to be leſſe than the Space X? Therefore if the Triangle to­
gether with X did, as the Adverſary ſuppoſeth, equalize the third
part of the Rectangle C P the circumſcribed Figure that adjoyns
to the Triangle ſo much leſſe than the Space X, will remain even
yet leſſe than the third part of the ſaid Rectangle C P. But this
cannot be, for it is more than a third part, therefore it is not true
that our Mixt Triangle is leſſe than one third of the Rectangle.
SAGR. I underſtand the Solution of my Doubt. But it is
requiſite now to prove unto us, that the Circumſcribed Figure is
more than a third part of the Rectangle C P; which, I believe, will
be harder to do.
SALV. Not at all. For in the Parabola the Square of the Line

D E hath the ſame proportion to the Square of Z G, that the Line
1D A hath to A Z; which is the ſame that the Rectangle K E hath to
the Rectangle A G, their heights A K and K L being equal. There­
fore the proportion that the Square E D hath to the Square Z G;
that is, the Square L A hath to the Square A K, the Rectangle K E
hath likewiſe to the Rectangle K Z. And in the ſelf-ſame manner
we might prove that the other Rectangles L F, M H, N I, O B are
to one another as the Squares of the Lines M A, N A, O A, P A.
Conſider we in the next place, how the Circumſcribed Figure is
compounded of certain Spaces that are to one another as the
Squares of the Lines that exceed with Exceſſes equal to the leaſt,
and how the Rectangle C P is compounded of ſo many other Spa­
ces each of them equal to the Greateſt, which are all the Rectan­
gles equal to O B. Therefore, by the Lemma of Archimedes, the
Circumſcribed Figure is more than the third part of the Rectangle
C P: But it was alſo leſſe, which is impoſſible: Therefore the
Mixt-Triangle is not leſſe than one third of the Rectangle C P.
I ſay likewiſe, that it is not more: For if it be more than one
third of the Rectangle C P, ſuppoſe the Space X equal to the ex­
ceſſe of the Triangle above the third part of the ſaid Rectangle
C P, and the diviſion and ſubdiviſion of the Rectangle into Rect­
angolets, but alwaies equal, being made, we ſhall meet with ſuch as
that one of them is leſſer than the Space X; which let be done:
and let the Rectangle B O be leſſer than X; and, having deſcribed
the Figure as before, we ſhall have inſcribed in the Mixt-Triangle
a Figure compounded of the Rectangles V O, T N, S M, N L, Q K,
which yet ſhall not be leſs
72[Figure 72]
than the third part of the
great Rectangle C P, for
the Mixt Triangle doth
much leſſe exceed the In­
ſcribed Figure than it doth
exceed the third part of
the Rectangle C P; Be­
cauſe the exceſſe of the
Triangle above the third part of the Rectangle C P is equal to
the Space X which is greater than the Rectangle B O, and this al­
ſo is conſiderably greater than the exceſſe of the Triangle above
the Inſcribed Figure: For to the Rectangle B O, all the Rectan­
golets A G, G E, E F, F H, H I, I B are equal, of which the Ex­
ceſſes of the Triangle above the Inſcribed Figure are leſſe than
half: And therefore the Triangle exceeding the third part of the
Rectangle C P, by much more (exceeding it by the Space X)
than it exceedeth its inſcribed Figure, that ſame Figure ſhall alſo
be greater than the third part of the Rectangle C P: But it is leſſer,
by the Lemma preſuppoſed: For that the Rectangle C P, as being
1the Aggregate of all the biggeſt Rectangles, hath the ſame pro­
portion to the Rectangles compounding the Inſcribed Figure, that
the Aggregate of of all the Squares of the Lines equal to the big­
geſt, hath to the Squares of the Lines that exceed equally, ſubſtra­
cting the Square of the biggeſt: And therefore (as it hapneth in
Squares) the whole Aggregate of the biggeſt (that is the Rectan­
gle C P) is more than triple the Aggregate of the exceeding
ones, the biggeſt deducted, that compound the Inſcribed Fi­
gure. Therefore the Mixt-Triangle is neither greater nor leſſer
than the third part of the Rectangle C P: It is therefore equal.
The Quadrature of
the Parabola ſhewn
by one ſingle De­
monſtration.
SAGR. A pretty and ingenuous Demonſtration: and ſo much
the more, in that it giveth us the Quadrature of the Parabola, ſhew­
ing it to be Seſquitertial of the Triangle inſcribed in the ſame;
proving that which Archimedes demonſtrateth by two very diffe­
rent, but both very admirable, methods of a great number of Pro­
poſitions. As hath likewiſe been demonſtrated lately by Lucas
Valerius, another ſecond Archimedes of our Age, which Demon­
ſtration is ſet down in the Book that he writ of the Center of the
Gravity of Solids.
SALV. A Treatiſe which verily is not to come behind any one
that hath been written by the moſt Famous Geometricians of the
preſent and all paſt Ages: which when it was read by our Acade­
mick, it made him deſiſt from proſecuting his Diſcoveries that he
was then proceeding to write on the ſame Subject: in regard he
ſaw the whole buſineſs ſo happily found and demonſtrated by the
ſaid Valerius.
SAGR. I was informed of all theſe things by our Academick;
and have beſought him withall that he would one day let me ſee
his Demonſtrations that he had ſound at the time when he met
with the Book of Valerius: but I never was ſo happy as to ſee them.
SALV. I have a Copy of them, and will impart them to you,
for you will be much pleaſed to ſee the variety of Methods, which
theſe two Authors take to inveſtigate the ſame Concluſions, and
their Demonſtrations: wherein alſo ſome of the Concluſions have
different Explanations, howbeit in effect equally true.
SAGR. I ſhall be very glad to ſee them, therefore when you re­
turn to our wonted Conferences you may do me the favour to
bring them with you. But in the mean time, this ſame of the Re­
fiſtance of the Solid taken from the Priſme by a Parabolick Secti­
on, being an Operation no leſſe ingenuous than beneficial in many
Mechanical Works, it would be good that Artificers had ſome ea­
ſie and expedite Rule how they may draw the ſaid Parabolick
Line upon the Plane of the Priſme.
SALV. There are ſeveral waies to draw thoſe Lines, but two

that are more expedite than all the reſt, I will deſcribe unto you.
1One of which is truly admirable, ſince that thereby, in leſſe time
than another can with Compaſſes ſlightly draw upon a paper
four or ſix Circles of different ſizes, I can deſign thirty or forty
Parabolick Lines no leſſe exact, ſmall, and ſmooth than the Cir­
cumferences of thoſe Circles. I have a Ball of Braſſe exquiſitely
round, no bigger than a Nut, this thrown upon a Steel Mirrour
held, not erect to the Horizon, but ſomewhat inclined, ſo that the
Ball in its motion may run along preſſing lightly upon it, leaveth
a Parabolical Line finely and ſmoothly deſcribed, and wider or
narrower according as the Projection ſhall be more or leſs elevated.
Whereby alſo we have a clear and ſenſible Experiment that the
Motion of Projects is made by Parabolick Lines: an Effect obſer­
ved by none before our Academick, who alſo layeth down the
Demonſtration of it in his Book of Motion, which we will joynt­
ly peruſe at our next meeting. Now the Ball, that it may deſcribe
by its motion thoſe Parabola's, muſt be rouled a little in the hands
that it may be warmed, and ſomewhat moyſtned, for by this
means it will leave its track more apparent upon the Mirrour. The
other way to draw the Line that we deſire upon the Priſme is after
this manner. Let two Nailes be faſtned on high in a Wall, at an
equal diſtance from the Horizon, and remote from one another
twice the breadth of the Rectangle upon which we would trace the
Semiparabola, and to theſe two Nails tye a ſmall thread of ſuch a
length that its doubling may reach as far as the length of the
Priſme; this ſtring will hang in a Parabolick Figure: ſo that tra­
cing out upon the Wall the way that the ſaid String maketh on it,
we ſhall have a whole Parabola deſcribed: which a Perpendicular
that hangeth in the midſt between theſe two Nailes will divide
into two equal parts. And for the transferring or ſetting off of
that Line afterwards upon the oppoſite Surfaces of the Priſme it is
not difficult at all, ſo that every indifferent Artiſt will know how
to do it. The ſame Line might be drawn upon the ſaid Sur­
face of the Priſme by help of the Geometrical Lines delineated up­
on the Compaſſe of our Friend, without any more ado.
Several waies to
deſcribe a Para­
bola.
We have hitherto demonſtrated ſo many Concluſions touching
the Contemplation of theſe Reſiſtances of Solids againſt Fraction
by having firſt opened the way unto the Science with ſuppoſing the
direct Reſiſtance for known, that we may in purſuance of them
proceed forwards to the finding of other, and other Concluſions,
with their Demonſtrations of thoſe which in Nature are infinite.
Only at preſent, for a final concluſion of this daies Conferences,
I will add the Speculation of the Reſiſtances of the Hollow Solids
which Art, and chiefly Nature, uſeth in an hundred Operations,
when without encreaſing the weight ſhe greatly augmenteth the
ſtrength: as is ſeen in the Bones of Birds, and in many Canes that
1are light and of great Reſiſtance againſt bending and breaking.
For if a Wheat Straw that ſupports an Ear that is heavier than the
whole Stalk, were made of the ſame quantity of matter but were
maſſie or ſolid, it would be much leſſe repugnant to Fraction or
Flection. And with the ſame Reaſon Art hath obſerved, and Ex­
perience confirmed, that an hollow Cane, or a Trunk of Wood
or Metal, is much more firm and tough than if being of the ſame
weight and length it were ſolid, which conſequently would be
more flender, and therefore Art hath contrived to make Lances hol­
low within when they are deſired to be ſtrong and light. We will
ſhew therefore, that
PROPOSITION XV.
The Reſiſtances of two Cylinders, equall, and equally
long, one of which is Hollow, and the other Maſsie,
have to each other the ſame proportion, as their Dia­
meters.
Let the Cane or Hollow Cylinder be A E, [as in Fig. 17.]
and the Cylinder I N Maſſie, and equall in weight and length.
I ſay, the Reſiſtance of the Cane A E hath the ſame propor­
tion to the Reſiſtance of the ſolid Cylinder, as the Diameter
A B hath to the Diameter I L. Which is very manifeſt; For the
Cane and the Cylinder I N being equal, and of equal lengths, the
Circle I L that is Baſe of the Cylinder ſhall be equal to the Ring
A B that is Baſe of the Cane A E, (I call the Superficies that re­
maineth when a leſſer Circle is taken out of a greater that is Con­
centrick with it a Ring:) and therefore their Abſolute Reſiſtan­
ces ſhall be equal: but becauſe in breaking croſſe-waies we make
uſe in the Cylinder I N of the length L N for a Leaver, and of the
point L for a Fulciment, and of the Semidiameter or Diameter L I
for a Counter-Leaver; and in the Cane the part of the Leaver,
that is the Line B E is equal to L N; but the Counter-Leaver at
the Fulciment B is the Diameter or Semidiameter A B: It is mani­
feſt therefore that the Reſiſtance of the Cane exceedeth that of
the Solid Cylinder as much as the Diameter A B exceeds the Dia­
meter I L; Which is that that we ſought. Toughneſs therefore is ac­
quired in the hollow Cane above the Toughneſs of the ſolid Cylin­
der according to the proportion of the Diameters: provided al­
waies that they be both of the ſame matter, weight, and length.
It would be well, that in conſequence of this we try to inveſtigate
that which hapneth in other Caſes indifferently between all Canes
and ſolid Cylinders of equal length, although unequal in quantity
of weight, and more or leſs evacuated. And firſt we will demon­
ſtrate, that
173[Figure 73]
Place this at the end of the ſecond Dialogue pag: 124,
1
PROP. XVI. PROBL. VI.
A Trunk or Hollow Cane being given, a Solid Cylinder
may be found equal to it.
This Operation is very eaſie. For let the Line A B, be the Dia­
meter of the Cane, and C D the Diameter of the Hollow or
Cavity. Let the Line A E be ſet off upon the greater Circle
equal to the Diameter C D, and conjoyn E B. And becauſe in
74[Figure 74]
the Semicircle A E B the Angle E is Right­
Angle, the Circle whoſe Diameter is A B
ſhall be equall to the two Circles of the Di­
ameters A E and E B: But A E is the Dia­
meter of the Hollow of the Cane: Therefore
the Circle whoſe Diameter is E B, ſhall be
equal to the Ring A C B D: And therefore
the ſolid Cylinder, the Circle of whoſe Baſe
hath the Diameter E B ſhall be equal to the
Cane, they being of the ſame length. This demonſtrated, we may
preſently be able
PROP. XVII. PROBL. VII.
To find what proportion is betwixt the Reſiſtances of
any whatſoever Cane and Cylinder, their lengths be­
ing equal.
LET the Cane A B E, and the Cylinder R S M, be of equal
length: it is required to find what proportion the Reſiſtances
have to each other. By the precedent let the Cylinder I L N
be found equal to the Cane, and of the ſame length; and to the
Lines I L and R S (Diameters of the Baſes of the Cylinders I N and
75[Figure 75]
R M) let the Line V be a fourth
Proportional. I ſay, the Reſiſtance
of the Cane A E is to the Reſi­
ſtance of the Cylinder R M, as the
Line A B is to V. For the Cane
A E being equal to, and of the
ſame length with the Cylinder
I N, the Reſiſtance of the Cane
ſhall be to the Reſiſtance of the
Cylinder, as the Line A B is to I L:
But the Reſiſtance of the Cylinder I N is to the Reſiſtance of the
Cylinder R M, as the Cube I L is to the Cube R S; that is, as the
Line I L to V: Therefore, ex æquali, the Reſiſtance of the Cane
A E hath the ſame proportion to the Reſiſtance of the Cylinder
R M, that the Line A B hath to V: Which is that that was ſought.
The End of the Second Dialogue.
1
GALILEUS,
HIS
DIALOGUES
OF
MOTION.
The Third Dialogue.
INTERLOCUTORS,
SALVIATUS, SAGREDUS, and SIMPLICIUS.
OF LOCAL MOTION.
We promote a very new Science, but of a very
old Subject. There is nothing in Nature more
antient than MOTION, of which
many and great Volumns have been written
by Philoſophers: But yet there are ſundry
Symptomes and Properties in it worthy of
our Notice, which I find not to have been hi­
therto obſerved, much leſſe demonſtrated by
any. Some ſlight particulars have been no­
ted: as that the Natural Motion of Grave Bodies continually accelle-
1rateth, as they deſcend towards their Center: but it hath not been as yet
declared in what proportion that Acceleration is made. For no man,
that I know, hath ever demonſtrated, That there is the ſame proportion
between the Spaces, thorow which a thing moveth in equal Times, as
there is between the Odde Numbers which follow in order after a Vnite.
It hath been obſerved that Projects [or things thrown or darted with vi­
olence] make a Line that is ſomewhat curved; but that this line is a Pa­
rabola, none have hinted: Yet theſe, and ſundry other things, no
leſſe worthy of our knowledg, will I here demonſtrate: And which
is more, I will open a way to a moſt ample and excellent Science,
of which theſe our Labours ſhall be the Elements: into which more
ſubtil and piercing Wits than mine will be better able to dive.
We divide this Treatiſe into three parts. In the firſt part we conſider
ſuch things as reſpect Equable or Vniforme Motion. In the ſecond we
write of Motion naturally accelerate. In the third we treat of Violent
Motion, or De Projectis.
OF EQVABLE MOTION.
Concerning Equable or Vniform Motion we have need of onely one
Definition, which I thus deliver.
DEFINITION.
By an Equable or Uniform Motion, I underſtand that by which a
Moveable in all equal Times paſſeth thorow equal Spaces.
ADVERTISEMENT.
I thought good to add to the old Definition (which ſimply termeth
that an Equable Motion, whereby equal Spaces are paſt in equal
Times) this Particle All, that is, any whatſoever Times that are equal:
for it may happen, that a Moveable may paſſe thorow equal Spaces in cer­
tain equal Times, though the Spaces be not equal which it hath gone in
leſſer, though equal parts of the ſame Time. From this our Definition
follow theſe four Axiomes: ſcilicet,
AXIOMEL
In the ſame Equable Motion that Space is greater which is paſſed
in a longer Time, and that leſſer which is paſt in a ſhorter.
1
AXIOME II.
In the ſame Equable Motion, the greater the Space is that hath
been gone thorow, the longer was the Time in which the Move­
able was going it.
AXIOME III.
The Space which a greater Velocity paſſeth in any Time, is great­
er than the Space which a leſſer Velocity paſſeth in the ſame
Time.
AXIOME IV.
The Velocity which paſſeth a greater Space, is greater than the
Velocity which paſſeth a leſſer Space in the ſame Time.
THEOR. I. PROP. I.
If a Moveable moving with an Equable Motion,
and with the ſame Velocity paſſe two ſeveral
Spaces, the Times of the Motion ſhall be to
one another as the ſaid Spaces.
Let the Moveable by an Equable Motion with the ſame Velocity paß
the two Spaces A B and B C: and let D E be the Time of the Moti­
on thorow A B; and let the Time of the Motion thorow B C be E F
I ſay that the Time D E to the Time E F, is as the Space A B to the
Space B C. Protract the Spaces and Times on both ſides, towards
G H and I K, and in A G take any number of Spaces equal to A B,
76[Figure 76]
and in D I the like number of Times equal to D E. Again, in C H take
any number of Spaces equal to B C, and in F K take the ſame number
of Times equal to the Time E F. This done, the Space B G will con­
tain juſt as many Spaces equal to B A, as the Time E I containeth
Times equal to E D, equimultiplied according to what ever Rate; And
likewiſe the Space B H will contain as many Spaces equal to B C, as
1the Time K E containeth Times equal to F E, at what ever rate equi­
multiplied. And foraſmuch as D E is the Time of the Motion thorow
A B, the whole Time E I, ſhall be the Time of the whole Space of the
Motion thorow B G, by reaſon that the Motion is Equable, and that the
number of the Times in E I equal to D E, is the ſame with the number
of Spaces in B G, equal to B A: For the ſame reaſon E K is the Time
of the Motion thorow H B. Now in regard the Motion is Equable, if the
Space G B were equal to H B, the Time I E would be equal to E K:
and if G B be greater than B H, I E ſhall likewiſe be greater than E K:
and if leſſer, leſſer. They are therefore four Magnitudes; A B the firſt,
B C the ſecond, D E the third, and E F the Fourth; and the firſt
and third, to wit, the Space A B, and Time D E, there were taken the
Time I E, and the Space G B equimultiple, according to any multi­
plication; and it hath been demonſtrated that theſe do at once either
equal, or fall ſhort of, or elſe exceed the Time E K, and Space B H,
which are equimultiple of the ſecond and fourth: Therefore the firſt
bath to the ſecond, to wit the Space A B to the Space B C, the ſame
proportion that the third hath to the fourth, to wit, the Time D E to
the Time E F. Which was to be demonſtrated.
THEOR. II. PROP. II.
If a Moveable in equal Times paſſe thorow two
Spaces, the ſaid Spaces will be to each other,
as the Velocities. And if the Spaces are to each
other as the Velocities, the Times will be
equal.
Let us ſuppoſe A B and B C in the former Figure, to be two
Spaces paſt, by the Moveable in equal times; the Space A B with
the Velocity D E, and the Space B C with the Velocity E F. I
ſay, that the Space A B is to the Space B C, as the Velocity D E is to
the Velocity E F: and thus I prove it. Take as before, of the Spaces
and Velocities equi-multiples, accordieg to any what ever Rate, ſci­
licet G B and I E, of A B and D E, and likewiſe H B and K E, of
B C and E F: It may be concluded as above, that G B and I E are
both at once either equal to, or fall ſhort of, or elſe exceed the equi-mul­
tiples of D H and E K. Therefore the Propoſition is proved.
1
THEOR. III. PROP. III.
The Times in which the ſame Space is paſt tho­
row by unequal Velocities, have the ſame pro­
portion to each other as their Velocities contra­
rily taken.
Let the two unequal Velocities be A the greater, and B the leſſe:
and according to both theſe let a Motion be made thorow the ſame
Space C D. I ſay the Time in which the Velocity A paſſeth the
Space C D, ſhall be to the Time in which the Velocity B paſſeth the
ſaid Space, as the Velocity B to the Velocity A. As A is to B, ſo let
C D be to C E: Then, by the
former Propoſition, the Time in
77[Figure 77]
which the Velocity A paſſeth
C D, ſhall be the ſame with
the Time in which B paſſeth
C E. But the Time in which
the Velocity B paſſeth C E, is
to the Time in which it paſſeth C D, as C E is to C D: Therefore
the Time in which the Velocity A paſſeth C D, is to the Time in which
the Velocity B paſſeth the ſame C D, as C E is to C D; that is, the Ve­
locity B is to the Velocity A: Which was to be proved.
THEOR. IV. PROP. IV.
If two Moveables move with an Equable Mo­
tion, but with unequal Velocities, the Spaces
which they paſſe in unequal Times, are to each
other in a proportion compounded of the pro­
portion of the Velocities, and of the propor­
tion of the Times.
Let the two Moveables moving with an Equable Motion, be E and
F: And let the proportion of the Velocity of the Moveable E be
to the Velocity of the Moveable F, as A is to B: And let the Time
in which E is moved, be unto the Time in which F is moved, as C is
to D. I ſay the Space paſſed by E, with the Velocity A in the Time C, is to
the Space paſſed by F, with the Velocity B in the Time D, in a proportion
compounded of the proportion of the Velocity A to the Velocity B, and of
1the proportion of the Time C to the Time D. Let the Space paſſed by the
Moveable E, with the Velocity A in the Time C, be G: And as the
Velocity A is to the Velocity B,
78[Figure 78]
ſo let G be to I: And as the
Time C is to the Time D, ſo
let I be to L: It is manifeſt,
that I is the Space paſſed by F
in the ſame Time in which E
paſſeth thorow G; ſeeing that
the Spaces G and I are as the
Velocities A and B; and ſeeing that as the Time C is to the Time D, ſo
is I unto L; and ſince that I is the Space paſſed by the Moveable F in the
Time C: Therefore L ſhall be the Space that F paſſeth in the Time D,
with the Velocity B: But the proportion of G to L, is compounded of the
proportions of G to I, and of I to L; that is, of the proportions of the
Velocity A to the Velocity B, and of the Time C to the Time D:
Therefore the Propoſition is demonſtrated.
THEOR. V. PROP. V.
If two Moveables move with an Equable Motion,
but with unequal Velocities, and if the Spaces
paſſed be alſo unequal, the Times ſhall be to
each other in a proportion compounded of the
proportion of the Spaces, and of the proporti­
on of the Velocities contrarily taken.
Let A and B be the two Moveables, and let the Velocity of A be to
the Velocity of B, as V to T, and let the Spaces paſſed, be as S to
R. I ſay the proportion of the Time in which A is moved to the
Time in which B is moved, ſhall be compounded of the proportions of the
Velocity T to the Velocity V, and of the Space S to the Space R. Let C be
the Time of the Motion A;
79[Figure 79]
and as the Velocity T is to
the Velocity V, ſo let the
Time C be to the Time E:
And for aſmuch as C is the
Time in which A with
the Velocity V paſſeth the
Space S; and that the
Time C is to the Time E, as the Velocity T of the Moveable B is to the
Velocity V, E ſhall be the Time in which the Moveable B would paſſe
1the ſame Space S. Again as the Space S is to the Space R, ſo let the
Time E be to the Time G: Therefore G is the Time in which B would
paſſe the Space R. And becauſe the proportion of C to G is compounded
of the proportions of C to E, and of E to G; And ſince the proportion
of C to E is the ſame with that of the Velocities of the Moveables A and
B contrarily taken; that is, with that of T and V; And the proportion
of E to G is the ſame with the proportion of the Spaces S and R: There­
fore the Propoſition is demonſtrated.
THEOR. VI. PROP. VI.
If two Moveables move with an Equable Motion,
the proportion of their Velocities ſhall be com­
pounded of the proportion of the Spaces paſ­
ſed, and of the proportion of the Times con­
trarily taken.
Let A and B be the two Moveables moving with an Equable
Motion; and let the Spaces by them paſſed, be as V to T; and
let the Times be as S to R. I ſay that the proportion of the Ve­
locity of the Moveable A, to that of the Velocity of B, ſhall be
compounded of the proportions of the Space V to the Space T, and
of the Time R to the Time S. Let C be the Velocity with which the
Moveable A paſſeth the Space V in the Time S: And let the Velocity C
be to the Velo-
80[Figure 80]
city E, as the
Space V is to
the Space T;
And E ſhall
be the Veloci­
ty with which
the Moveable
B paſſeth the Space T in the Time S: Again, let the Velocity E be to the
other Velocity G, as the Time R is to the Time S; And G ſhall be the
Velocity with which the Moveable B paſſeth the Space T in the Time R.
We have therefore the Velocity C, wherewith the Moveable A paſſeth
the Space V in the Time S; and the Velocity G, wherewith the Move­
able B paſſeth the Space T in the Time R: And the proportion of C to
G is compounded of the proportions of C to E and of E to G: But the
proportion of C to E, is ſuppoſed the ſame with that of the Space V to
the Space T; and the proportion of E to G, is the ſame with that of R
to S: Therefore the Propoſition is manifest.
1
* That is the A­
cademick, i. e.
Galileus.
SALV. This that we have read, is what our ^{*} Author hath written
of the Equable Motion. We will paſs therefore to a more ſubtil and
new Contemplation touching the Motion Naturally Accelerate:
and behold here the Title and Introduction.
OF MOTION
NATVRALLY ACCELERATE.
In the former Book we have conſidered the Accidents which ac­
company Equable Motion; we are now to treat of another kind of
Motion which we call Accelerate. And firſt it will be expedient to
find out and explain a Definition beſt agreeing to that which Nature
makes uſe of. For though it be not nconvenient to feign a Motion at plea­
ſure, and then to conſider the Accidents that attend it (as thoſe have
done, who having framed in their imagination Helixes and Conchoi­
des, which are Lines ariſing from certain Motions, although not uſed
by Nature, and upon that Suppoſition have laudably demonſtrated the
Symptomes thereof) yet in regard that Nature maketh uſe of a certain
kind of Acceleration in the deſcent of Grave Bodies, we are reſolved to
ſearch out and contemplate the paſſions thereof, and ſee whether the
Definition that we are about to produce of this our Accelerate Motion,
doth aptly and congruouſly ſute with the Eſſence of Motion Naturally
Accelerate. After many long and laborious Studies we have found out
a Definition which ſeemeth to expreſſe the true nature of this Accelerate
Motion, in regard that all the Natural Experiments that fall under
the Obſervation of our Senſes, do agree with thoſe its properties that
we intend anon to demonſtrate. In this Diſquiſition we have been aſſi­
ſted, and as it were led by the hand by that obſervation of the uſual
Method and common procedure of Nature her ſelf in her other Operati­
ons, wherein ſhe conſtantly makes uſe of the Firſt, Simpleſt, and Ea­
ſieſt Means that are: for I believe that no man can think that Swim­
ming or flying can be performed in a more ſimple or eaſie way, than that
which Fiſhes and Birds do uſe out of a Natural Inſtinct. Why there­
fore ſhall not I be perſwaded, that, when I ſee a Stone to acquire conti­
nually new additions of Velocity in its deſcending from its Reſt out of ſome
high place, this encreaſe made in the ſimpleſt eaſieſt and moſt obvious
manner that we can imagine? Now if we ſeriouſly examine all the ways
that can be deviſed, we ſhall find no encreaſes, no acquiſitions
leſſe intricate or more intelligible than that which ever encreaſeth or
makes its additions after the ſame manner. This appeareth by the great
Affinity that is between Time and Motion. For as the Equability or
Vniformity of Motion is defined and expreſſed by the Equability of the
1Times and Spaces, (for we call that Motion or Lation Equable, by which
equal Spaces are paſt in equal Times) ſo by the ſame Equability of the
parts of Time, we may perceive, that the encreaſe of Celerity in the Natu­
ral Motion of Grave Bodies, is made after a Simple and plain manner;
conceiving in our Mind that their Motion is continually accelerated uni­
formly and at the ſame Rate, whilſt equal additions of Celerity are
conferred upon them in all equal Times. So that taking any equal par­
ticles of Time beginning from the firſt Inſtant in which the Moveable
departeth from Reſt, and entereth upon its Deſcent, the Degree of
Velocity acquired in the firſt and ſecond Particles of Time, is double the
degree of Velocity that the Moveable acquired in the firſt Particle: and
the degree of Velocity that it acquireth in three Particles, is triple, and
that in four quadruple to the ſame Degree of the firſt Time: As, for
our better underſtanding, if a Moveable ſhould continue its Motion
according to the degree or moment of Velocity acquired in the firſt Parti­
cle of Time, and ſhould extend its courſe equably with that ſame De­
gree; this Motion would be twice as ſlow as that which it would obtain
according to the degree of Velocity acquired in two Particles of Time:
So that it will not be improper if we underſtand the Intention of the Ve­
locity, to proceed according to the Extenſion of the Time. From whence
we may frame this Definition of the Motion of which we are about to
treat.
DEFINITION.
Motion Accelerate in an Equable or Vniform
Proportion, I call that which departing from
Reſt, ſuperaddeth equal moments of Velocity
in equal Times.
SAGR. Though it were Irrational for me to oppoſe this or any
other Definition aſſigned by any whatſoever Author, they being all
Arbitrary, yet I may very well, without any offence, queſtion whe­
ther this Definition, which is underſtood and admitted in Abſtract,
doth ſute, agree, and hold true in that ſort of Accelerate Motion,
which Grave Bodies deſcending naturally do exerciſe. And becauſe
the Authour ſeemeth to promiſe us, that the Natural Motion of
Grave Bodies is ſuch as he hath defined it, I could wiſh that ſome
Scruples were removed that trouble my mind; that ſo I might apply
my ſelf afterwards with greater attention to the Proportions and
Demonſtrations which are expected.
SALV. I like well, that you and Simplicius do propound
Doubts as they come in the way: which I do imagine will be the
1ſame that I my ſelf did meet with when I firſt read this Treatiſe,
and that, either were reſolved by conferring with the Author, or
removed by my own conſidering of them.
SAGR. Whilſt I am fancying to my ſelf a Grave Deſcending
Moveable to depart from Reſt, that is from the privation of all
Velocity, and to enter into Motion, and in that to go encrea­
ſing, according to the proportion after which the Time encreaſeth
from the firſt inſtant of the Motion; and to have v. gr. in eight
Pulſations, acquired eight degrees of Velocity, of which in the
fourth Pulſation it had gained four, in the ſecond two, in the
firſt one, Time being ſubdiviſible in infinitum, it followeth, that
the Antecedent Velocity alwayes diminiſhing at that Rate, there
will bt no degree of Velocity ſo ſmall, or, if you will, of Tardity
ſo great, in which the ſaid Moveable is not found to be conſti­
tuted, after its departure from infinite Tardity, that is, from
Reſt. So that if that degree of Velocity which it had at four Pul­
ſations of Time, was ſuch, that maintaining it Equable, it would
have run two Miles in an hour, and with the degree of Velocity
that it had in the ſecond Pulſation, it would have gone one mile
an hour, it muſt be granted, that in the Inſtants of Time neeter
and neerer to its firſt Inſtant of moving from Reſt, it is ſo ſlow,
as that (continuing to move with that Tardity) it would not have
paſſed a Mile in an hour, nor in a day, nor in a year, nor in a
thouſand; nay, nor have gone one ſole foot in a greater time:
An accident to which me thinks the Imagination but very unea­
ſily accords, ſeeing that Senſe ſheweth us, that a Grave Falling
Body commeth down ſuddenly, and with great Velocity.
SALV. This is one of thoſe Doubts that alſo fell in my way
upon my firſt thinking on this affair, but not long after I remo­
ved it: and that removal was the effect of the ſelf ſame Expe­
riment which at preſent ſtarts it to you. You ſay, that in your
opinion, Experience ſheweth that the Moveable hath no ſooner
departed from Reſt, but it entereth into a very notable Velocity:
and I ſay, that this very Experiment proves it to us, that the firſt
Impetus's of the Cadent Body, although it be very heavy, are
moſt ſlack and ſlow. Lay a Grave Body upon ſome yielding mat­
ter, and let it continue upon it till it hath preſſed into it as far as
it can with its ſimple Gravity; it is manifeſt, that raiſing it a yard
or two, and then letting it fall upon the ſame matter, it ſhall
with its percuſſion make a new preſſure, and greater than that
made at firſt by its meer weight: and the effect ſhall be cauſed
by the falling Moveable conjoyned with the Velocity acquired in
the Fall: which impreſſion ſhall be greater and greater, accord­
ing as the Percuſſion ſhall come from a greater height; that is,
according as the Velocity of the Percutient ſhall be greater. We
1may therefore without miſtake conjecture the quantity of the Ve­
locity of a falling heavy Body; by the quality and quantity of
the Percuſſion. But tell me Sirs, that Beetle which being let fall
upon a Stake from an height of four yards, driveth it into the
ground, v. gr. four inches, comming from an height of two yards,
ſhall drive it much leſſe, and leſſe from an height of one, and
leſſe from a foot; and laſtly lifting it up an inch, what will it do
more than if without any blow it were laid upon it? Certainly
but very little, and the operation would be wholly impercep­
tible, if it were raiſed the thickneſſe of a leaf. And becauſe the
effect of the Percuſſion is regulated by the Velocity of the Percu­
tient, who will queſtion but that the Motion is very ſlow, and
the Velocity extreme ſmall, where its operation is impercep­
tible? See now of what power Truth is, ſince the ſame Experi­
ment that ſeemed at the firſt bluſh to hold forth one thing, be­
ing better conſidered, aſcertains us of the contrary. But without
having recourſe to that Experiment (which without doubt is moſt
perſwaſive) me-thinks that it is not hard to penetrate ſuch a
Truth as this by meer Diſcourſe. We have an heavy ſtone ſu­
ſtained in the Air at Reſt: let it be diſengaged from its uphol­
der, and ſet at liberty; and, as being more grave than the Air, it
goeth deſcending downwards, and that not with a Motion Equa­
ble, but ſlow in the beginning, and continually afterwards ac­
celerate: and ſeeing that the Velocity is Augmentable and Di­
miniſhable in infinitum, what Reaſon ſhall perſwade me, that that
Moveable departing from an infinite Tardity (for ſuch is Reſt)
entereth immediately into ten degrees of Velocity, rather than in
one of four, or in this more than in one of two, of one, of half
one, or of the hundredth part of one; and to be ſhort, in all
the infinite leſſer? Pray you hear me. I do not think that you
would ſcruple to grant me, that the acquiſt of the Degrees of Ve­
locity of the falling Stone may be made with the ſame Order as
is the Diminution and loſſe of the ſame degrees, when with an
impellent Virtue it is driven upwards to the ſame height: But if
that be ſo, I do not ſee how it can be ſuppoſed that in the diminu­
tion of the Velocity of the aſcendent Stone, ſpending it all, it
can come to the ſtate of Reſt before it hath paſſed thorow all the
degrees of Tardity.
SIMP. But if the greater and greater degrees of Tardity are
infinite, it ſhall never ſpend them all; ſo that the aſcendent
Grave will never attain to Reſt, but will move ad infinitum, ſtill
retarding: a thing which we ſee not to happen.
SALV. This would happen, Simplicius, in caſe the Moveable
ſhould ſtay for ſome time in each degree: but it paſſeth thorow
them, without ſtaying longer than an inſtant in any of them.
1And becauſe in every quantitative Time, though never ſo ſmall,
there are infinite Inſtants, therefore they are ſufficient to anſwer
to the infinite degrees of Velocity diminiſhed. And that the
aſcendent Grave Body perſiſts not for any quantitative Time in
one and the ſame degree of Velocity, may thus be made out:
Becauſe, a certain quantitative Time being aſſigned it in the firſt
inſtant of that Time, and likewiſe in the laſt, the Moveable
ſhould be found to have one and the ſame degree of Velocity, it
might by this ſecond degree be likewiſe driven upwards ſuch an­
other Space, like as from the firſt it was tranſported to the ſe­
cond; and by the ſame reaſon it would paſſe from the ſecond to
the third, and, in ſhort, would continue its Motion Uniform ad
infinitum.
SAGR. From this Diſcourſe, as I conceive, one might derive a
very appoſite Reaſon of the Queſtion controverted amongſt Philo.
ſophers, Touching what ſhould be the Cauſe of the acceleration
of the Natural Motion of Grave Moveables. For when I confider
in the Grave Body driven upwards, its continual Diminution of
that Virtue impreſſed upon it by the Projicient, which ſo long as
it was ſuperiour to that other contrary one of Gravity, forced it
upwards, this and that being come to an Equilibrium, the Move­
able ceaſeth to riſe any higher, and paſſeth thorow the ſtate of
Reſt, in which the Impetus impreſſed is not annihilated, but one­
ly that exceſſe is ſpent, which it before had above the Gravity of
the Moveable, whereby prevailing over the ſame, it did drive
it upwards. And the Diminution of this forrein Impetus continu­
ing, and conſequently the advantage beginning to be on the part
of the Gravity, the Deſcent alſo beginneth but ſlow, in regard
of the oppoſition of the Virtue impreſſed, a conſiderable part of
which ſtill remaineth in the Moveable: but becauſe it doth go
continually diminiſhing, and is ſtill with a greater and greater
proportion overcome by the Gravity, hence ariſeth the continual
Acceleration of the Motion.
SIMP. The conceit is witty, but more ſubtil than ſolid: for in
caſe it were concludent, it ſalveth onely thoſe Natural Motions
to which a Violent Motion preceded, in which part of the extern
Virtue ſtill remains in force: but where there is no ſuch remaining
impulſe, as where the Moveable departeth from a long Quieſ­
cence, the ſtrength of your whole Diſcourſe vaniſheth.
SAGR. I believe that you are in an Errour, and that this Di­
ſtinction of Caſes which you make, is needleſſe, or, to ſay bet­
ter, Null. Therefore tell me, whether may there be impreſſed
on the Project by the Projicient ſometimes much, and ſometimes
little Vertue; ſo as that it may be ſtricken upwards an hundred
yards, and alſo twenty, or four, or one?
1
SIMP. No doubt but there may.
SAGR. And no leſſe poſſible is it, that the ſaid Virtue impreſſed
ſhall ſo little ſeperate the Reſiſtance of the Gravity, as not to
raiſe the Project above an inch: and finally the Virtue of the
Projicient may be onely ſo much, as juſt to equalize and com­
penſate the Reſiſtance of the Gravity, ſo as that the Moveable
is not driven upwards, but onely ſuſtained. So that when you
hold a Stone in your hand, what elſe do you, but impreſſe on it
ſo much Virtue impelling upwards, as is the faculty of its Gra­
vity drawing downwards? And this your Virtue, do you not
continue to keep it impreſſed on the Stone all the time that you
hold it in your hand? What ſay you, is it diminiſhed by your
long holding it? And this ſuſtention which impedeth the Stones
deſcent, what doth it import, whether it be made by your hand,
or by a Table, or by a Rope, that ſuſpends it? Doubtleſſe no
thing at all. Conclude with your ſelf therefore, Simplicius, that
the precedence of a long, a ſhort, or a Momentary Reſt to the
Fall of the Stone, makes no alteration at all, ſo that the Stone
ſhould not alwaies depart affected with ſo much Virtue contrary
to Gravity, as did exactly ſuffice to have kept it in Reſt.
SALV. I do not think it a ſeaſonable time at preſent to enter
upon the Diſquiſition of the Cauſe of the Acceleration of Natu­
ral Motion: touching which ſundry Philoſophers have produced
ſundry opinions: ſome reducing it to the approximation unto
the Center others to the leſſe parts of the Medium ſucceſſively re­
maining to be perforated; others to a certain Extruſion of the
Ambient Medium, which in reuniting upon the back of the
Moveable, goeth driving and continually thruſting it; which
Fancies, and others of the like nature, it would be neceſſary to
examine, and with ſmall benefit to anſwer. It ſerveth our Au­
thours turn at the preſent, that we underſtand that he will de­
clare and demonſtrate to us ſome Paſſions of an Accelerate Mo­
tion (be the Cauſe of its Acceleration what it will) ſo as that the
Moments of its Velocity do go encreaſing, after its departure from
Reſt with that moſt ſimple proportion wherewith the Continua­
tion of the Time doth encreaſe: which is as much as to ſay, that
in equal Times there are made equal additaments of Velocity.
And if it ſhall be found, that the Accidents that ſhall hereafter
be demonſtrated, do hold true in the Motion of Naturally De­
ſcendent and Accelerate Grave Moveables, we may account,
that the aſſumed Definition taketh in that Motion of Grave Bo­
dies, and that it is true, that their Acceleration doth encreaſe ac­
cording as the Time and Duration of the Motion encreaſeth.
SAGR. By what as yet is ſet before my Intellectuals, it appears
to me that one might with (haply) more plainneſſe define, and yet
1never alter the Conceit; ſaying that, A Motion uniformly accele­
rate is that in which the Velocity goeth encreaſing according as
the Space encreaſeth that is paſſed thorow: So that, for example,
the degree of Velocity acquired by the Moveable in a deſcent of
four yards ſhould be double to that that it would have after it had
deſcended a Space of two, and this double to that acquired in the
Space of the firſt Yard. For I do not think that it can be doubted,
but that that Grave Moveable which falleth from an height of ſix
yards hath, and percuſſeth with an Impetus double to that which
it had when it had deſcended three yards, and triple to that which
it had at two, and ſextuple to that had in the Space of one.
SALV. I comfort my ſelf in that I have had ſuch a Companion
in my Errour: and I will tell you farther, that your Diſcourſe hath
ſo much of likelihood and probability in it, that our Author himſelf
did not deny unto me, when I propoſed it to him, that he likewiſe
had been for ſome time in the ſame miſtake. But that which I af­
terwards extreamly wondred at, was to ſee in four plain words,
diſcovered, not only the falfity, but impoſſibility of two Propoſi­
tions that carry with them ſo much of ſeeming truth, that having
propounded them to many, I never met with any one but did freely
admit them to be ſo.
SIMP. Certainly I ſhould be of the number, and that the De­
ſcendent Grave Moveable vires acquir at eundo, encreaſing its Ve­
locity at the rate of the Space, and that the Moment of the ſame
Percutient is double, coming from a double height, ſeem to me Pro­
poſitions to be granted without any hæſitation or controverſie.
SALV. And yet they are as falſe and impoſſible, as that Moti­
on is made in an inſtant. And hear a clear proof of the ſame. In
caſe the Velocities have the ſame proportion as the Spaces paſſed,
or to be paſſed, thoſe Spaces ſhall be paſſed in equal Times: if
therefore the Velocities with which the falling Moveable paſſeth
the Space of four yards, were double to the Velocities with which it
paſſeth the two firſt yards (like as the Space is double to the Space)
then the Times of thoſe Tranſitions are equal: but the ſame Move­
able's paſſing the four yards, and the two in one and the ſame Time,
hath place only in Inſtantaneous Motion. But we ſee, that the
falling grave Body maketh its Motion in Time, and paſſeth the two
yards in a leſſer than it doth the four. Therefore it is falſe that its
Velocity encreaſeth as its Space. The other Propoſition is demon­
ſtrated to be falſe with the ſame perſpicuity. For that which per­
cuſſeth being the ſame, the difference and Moment of the Percuſſton
cannot be determined but by the difference of Velocity; If there­
fore the percutient, coming from a double height, make a Percuſſi­
on with a double Moment, it is neceſſary that it ſtrike with a dou­
ble Velocity: But the double Velocity paſſeth the double Space in
1the ſame Time; and we ſee the Time of the Deſcent from the grea­
ter altitude to be longer.
SAGR. This is too great an Evidence, too great a Facility
wherewith you manifeſt abſtruce Concluſions: this extream eaſi­
neſs rendreth them of leſſe value than they were whilſt they lay hid
under contrary appearances. I believe that the Generality of men
little preſſe thoſe Notions which are eaſily obtained, in compari­
ſon of thoſe about which men make ſo long and inexplicable alter­
cations.
SALV. To thoſe which with great brevity and clarity ſhew the
fallacies of Propoſitions that have been commonly received for
true by the generality of people, it would be a very tolerable in­
jury to return them only ſlighting inſtead of thanks: but there is
much diſpleaſure and moleſtation in another certain affection
ſometimes found in ſome men, that pretending in the ſame Studies
at leaſt Parity with any whomſoever, do ſee that they have let
paſs ſuch and ſuch for true Concluſions, which afterwards by
another, with a ſhort and eaſie diſquiſition, have been detected and
convicted for falſe. I will not call that affection Envy, that is ac­
cuſtomed to convert in time to hatred and deſpite againſt the diſ­
coverers of ſuch Fallacies, but I will call it an itch, and a deſire to
be able rather to maintain their inveterate Errours, than to per­
mit the reception of new-diſcovered Truths. Which humour ſome­
times induceth them to write in contradiction of thoſe truths
which are but too perfectly known unto themſelves only to keep
the Reputation of others low in the opinion of the numerous and
ill-informed Vulgar. Of ſuch falſe Concluſions received for true,
and very eaſie to be confuted, I have heard no ſmall number from
our Academick, of ſome of which I have kept account.
SAGR. And you muſt not deprive us of them; but in due time
impart them to us, when a particular Meeting ſhall be appointed
for them. For the preſent, continuing the diſcourſe we are about,
I think that by this time we have eſtabliſhed the Definition of Mo­
tion uniformly Accelerate, treated of in the enſuing diſcourſes,
and it is this;
A Motion Equable, or Vniformly Accelerate, we call that which
departing from Reſt ſuperadds equal Moments of Velocity in
equal Times.
SALV. That Definition being confirmed, the Author asketh
and ſuppoſeth but one only Principle to be true, namely:
1
SVPPOSITION.
I ſuppoſe that the degrees of Velocity acquired by the
ſame Moveable upon Planes of different inclinations
are equal then, when the Elevations of the ſaid
Planes are equal.
By the Elevation of an inclined Plane he meaneth the Per­
pendicular, which from the higher term of the ſaid Plane
falleth upon the Horizontal Line produced along by the
lower term of the ſaid Plane inclined: as for better underſtanding;
the Line A B being parallel to the Horizon, upon which let the two
81[Figure 81]
Planes C A, and C D be inclined:
the Perpendicular C B falling up­
on the Horizontal Line B A the
Author calleth the Elevation
of the Planes C A and C D;
and ſuppoſeth that the degrees of
Velocity of the ſame Moveable
deſcending along the inclined Planes C A and C D, acqui­
red in the Terms A and D are equal, for that their Elevation is
the ſame C B. And ſo great alſo ought the degree of Velocity be
underſtood to be which the ſame Moveable falling from the Point
C would acquire in the term B.
SAGR. The truth is, this Suppoſition hath in it ſo much of pro­
bability, that it deſerveth to be granted without diſpute, alwaies
preſuppoſing that all accidental and extern Impediments are re­
moved, and that the Planes be very Solid and Terſe, and the Move­
able in Figure moſt perfectly Rotund, ſo that neither the Plane,
nor the Moveable have any unevenneſs. All Contraſts and Im­
pediments, I ſay, being removed, the light of Nature dictates to
me without any difficulty, that a Ball heavy and perfectly round
deſcending by the Lines C A, C D, and C B would come to the
terms A D, and B with equal Impetus's.
SALV. You argue very probably; but over and above the pro­
bability, I will by an Experiment ſo increaſe the likelihood, as that
it wants but little of being equal to a very neceſſary Demonſtrati­
on. Imagine this leafe of Paper to be a Wall erect at Right-angles
to the Horizon, and at a Nail, faſtned in the ſame, hang a Ball or
Plummet of Lead, weighing an ounce or two, ſuſpended by the
ſmall thread A B, two or three yards long, perpendicular to the
Horizon: and on the Wall draw an Horizontal Line D C, cutting
1the Perpendicular A B at Right angles, which A B muſt hang two
Inches, or thereabouts, from the Wall: Then transferring the
ſtring A B with the Ball into C, let go the ſaid Ball; which you will
82[Figure 82]
ſee firſt to deſcend
deſcribing C B D, and
to paſs ſo far beyond
the Term B, that run­
ning along the Arch
B D it will riſe almoſt
as high as the deſigned
Parallel C D, wanting
but a very ſmall mat­
ter of reaching to it,
the preciſe arrival thi­
ther being denied it by
the Impediment of the Air, and of the Thread. From which we
may truly conclude, that the Impetus acquired in the point B by
the Ball in its deſcent along the Arch C B, was ſo much as ſufficed
to carry it upwards along ſuch another Arch B D unto the ſame
height: having made, and often reiterated this Experiment, let
us drive into the Wall, along which the Perpendicular A B paſſeth,
another Nail, as in E or in F, which is to ſtand out five or ſix In­
ches; and this to the end that the thread A B, returning as before
to carry back the Ball C along the Arch C B, when it is come to
B, the Thread ſtopping at the Nail E may be conſtrained to move
along the Circumference B G, deſcribed about the Center E: by
which we ſhall ſee what that ſame Impetus is able to do, which be­
fore, being conceived in the ſame term B, carried the ſame Move­
able along the Arch B D unto the height of the Horizontal Line
C D. Now, Sirs, you ſhall with delight ſee the Ball carried unto
the Horizontal Line in the Point G; and the ſame will happen if
the ſtop be placed lower, as in F, where the Ball would deſcribe
the Arch B I, evermore terminating its aſcent exactly in the Line
C D: and in caſe the Check were ſo low that the overplus of the
thread beneath it cannot reach to the height of C D, (which would
happen if it were nearer to the point B than to the interſection of
A B with the Horizontal Line C D) then the thread would
whirle and twine about the Nail. This experiment leaveth no
place for our doubting of the truth of the Suppoſition: for the
two Arches C B and D B being equall, and ſcituate alike, the
acquiſt of Moment made along the Deſcent in the Arch C B, is
the ſame with that made along the Deſcent in the Arch D B. But
the Moment acquired in B, along the Arch C B, is able to carry the
ſame Moveable upwards along the Arch B D: Therefore the Mo­
ment acquired in the Deſcent D B is equall to that which driveth
1the ſame Moveable along the ſame Arch from B to D: So that ge­
nerally every Moment acquired along the Deſcent of an Arch is
equall to that which hath power to make the ſame Moveable re­
aſcend along the ſame Arch: But all the Moments that make the
Moveable aſcend along all the Arches B D, B G, B I are equal,
ſince they are made by one and the ſame Moment acquired along
the Deſcent C B, as Experience ſhews: Therefore all the Moments
that are acquired by the Deſcents along the Arches D B, G B, and
I B are equal.
SAGR. Your Diſcourſe is in my Judgment very Rational, and
the Experiment ſo appoſite and pertinent to verifie the Poſtulatum,
that it very well deſerveth to be admitted as if it were Demon­
ſtrated.
SALV. I will not conſent, Sagredus, that we take more to our
ſelves than we ought; and the rather for that we are chiefly to
make uſe of this Aſſumption in Motions made upon ſtreight and
not curved Superficies; in which the Acceleration proceedeth with
degrees very different from thoſe wherewith we ſuppoſe it to pro­
ceed in ſtreight Planes. Inſomuch, that although the Experiment
alledged ſhews us, that the deſcent along the Arch C B conferreth
on the Moveable ſuch a Moment, as that it is able to re-carry it
to the ſame height along any other Arch B C, B G, and B I, yet
we cannot with the like evidence ſhew, that the ſame would hap­
pen in caſe a moſt exact Ball were to deſcend by ſtreight Planes in­
clined according to the inclinations of the Chords of theſe ſame
Arches: yea, it is credible, that Angles being formed by the ſaid
Right Planes in the term B, the Ball deſcended along the Declivi­
ty according to the Chord C B, finding a ſtop in the Planes aſcend­
ing according to the Chords B D, B G, and B I, in juſtling againſt
them, would loſe of its Impetus, and could not be able in riſing to
attain the height of the Line C D. But the Obſtacle being remo­
ved, which prejudiceth the Experiment, I do believe, that the un­
derſtanding may conceive, that the Impetus (which in effect de­
riveth vigour from the quantity of the Deſcent) would be able to
remount the Moveable to the ſame height. Let us therefore take
this at preſent for a Poſtulatum or Petition, the abſolute truth of
which will come to be eſtabliſhed hereafter by ſeeing other Con­
cluſions raiſed upon this Hypotheſis to anſwer, and exactly jump
with the Experiment. The Author having ſuppoſed this only Prin­
ciple, he paſſeth to the Propoſitions, demonſtratively proving them;
of which the firſt is this;
1
THEOR. I. PROP. I.
The time in which a Space is paſſed by a Movea­
ble with a Motion Vniformly Accelerate, out of
Reſt, is equal to the Time in which the ſame
Space would be paſt by the ſame Moveable
with an Equable Motion, the degree of whoſe
Velocity is ſubduple to the greateſt and ulti
mate degree of the Velocity of the former Vni­
formly Accelerate Motion.
Let us by the extenſion A B repreſent the Time, in which the
Space C D is paſſed by a Moveable with a Motion Vniformly
Accelerate, out of Reſt in C: and let the greateſt and laſt de-
83[Figure 83]
gree of Velocity acquired in the Inſtants of the Time
A B be repreſented by E B; and conſtitute at plea­
ſure upon A B any number of parts, and thorow the
points of diviſion draw as many Lines, continued
out unto the Line A E, and equidiſtant to B E,
which will repreſent the encreaſe of the degrees of
Velocity after the firſt Inſtant A. Then divide B E
into two equall parts in F, and draw F G and A G
parallel to B A and B F: The Parallelogram A G
F B ſhall be equall to the Triangle A E B, its Side
G F dividing A E into two equall parts in I: For
if the Parallels of the Triangle A E B be continued
out unto I G F, we ſhall have the Aggregate of all
the Parallels contained in the Quadrilatural Figure
equal to the Aggregate of all the Parallels compre­
hended in the Triangle A E B; For thoſe in the Triangle I E F are equal
to thoſe contained in the Triangle G I A, and thoſe that are in the Tra­
pezium are in common. Now ſince all and ſingular the Inſtants of Time
do anſwer to all and ſingular the Points of the Line A B; and ſince the
Parallels contained in the Triangle A E B do repreſent the degrees of Ac­
celeration or encreaſing Velocity, and the Parallels contained in the Pa­
rallelogram do likewiſe repreſent as many degrees of Equable Motion or
unencreaſing Velocity: It appeareth, that as many Moments of Velocity
paſſed in the Accelerate Motion according to the encreaſing Parallels of the
Triangle A E B, as in the Equable Motion according to the Parallels of
the Parallelogram G B: Becauſe what is wanting in the firſt half of the
1Accelerate Motion of the Velocity of the Equable Motion (which defi­
cient Moments are repreſented by the Parallels of the Triangle A G I)
is made up by the moments repreſented by the Parallels of the Triangle
I E F. It is manifeſt, therefore, that thoſe Spaces are equal which are
in the ſame Time by two Moveables, one whereof is moved with a Mo­
tion uniformly Accelerated from Reſt, the other with a Motion Equable
according to the Moment ſubduple of that of the greateſt Velocity of the
Accelerated Motion: Which was to be demonſtrated.
THEOR. II. PROP. II.
If a Moveable deſcend out of Reſt with a Moti­
on uniformly Accelerate, the Spaces which it
paſſeth in any whatſoever Times are to each
other in a proportion Duplicate of the ſame
Times; that is, they are as the Squares of
them.
Let A B repreſent a length of Time beginning at the firſt Inſtant A;
and let A D and A E repreſent any two parts of the ſaid Time;
and let H I be a Line in which the Moveable out of H, (as the firſt
beginning of the Motion) deſcendeth uniformly accelerating; and let the
84[Figure 84]
Space H L be paſſed in the firſt Time A D; and let H M
be the Space that it ſhall deſcend in the Time A E. I ſay,
the Space M H is to the Space H L in duplicate propor­
tion of that which the Time E A hath to the Time A D:
Or, if you will, that the Spaces M H and H L are to one
another in the ſame proportion as the Squares E A and
A D. Draw the Line A C at any Angle with A B, and
from the points D and E draw the Parallels D O and
P E: of which D O will repreſent the greateſt degree
of Velocity acquired in the Inſtant D of the Time A D;
and P the greateſt degree of Velocity acquired in the In­
ſtant E of the Time A E. And becauſe we have de­
monſtrated in the laſt Propoſition concerning Spaces, that
thoſe are equal to one another, of which two Moveables
have paſt in the ſame Time, the one by a Moveable out
of Reſt with a Motion uniformly Accelerate, and the
other by the ſame Moveable with an Equable Motion,
whoſe Velocity is ſubduple to the greateſt acquired by the
Accelerate Motion: Therefore M H and H L are the Spaces that two
Lquable Motions, whoſe Velocities ſhould be as the half of P E, and
1half of O D, would paſſe in the Times E A and D A. If it be proved
therefore that theſe Spaces M H and L H are in duplicate proportion to
the Times E A and D A; We ſhall have done that which was intended.
But in the fourth Propoſition of the Firſt Book we have demonſtrated:
That the Spaces paſt by two Moveables with an Equable Motion are
to each other in a proportion compounded of the proportion of the Velo­
cities and of the proportion of the Times: But in this caſe the propor­
tion of the Velocities and the proportion of the Times is the ſame (for
as the half of P E is to the half of O D, or the whole P E to the whole
O D, ſo is A E to A D: Therefore the proportion of the Spaces paſ­
ſed is double to the proportion of the Times. Which was to be demon­
ſtrated.
Hence likewiſe it is manifeſt, that the proportion of the ſame Spaces
is double to the proportions of the greateſt degrees of Velocity: that is,
of the Lines P E and O D: becauſe P E is to O D, as E A to D A.
COROLARY I.
Hence it is manifeſt, that if there were many equal Times taken in or­
der from the firſt Inſtant or beginniug of the Motion, as ſuppoſe
A D, D E, E F, F G, in which the Spaces H L, L M, M N, N I
are paſſed, thoſe Spaces ſhall be to one another as the odd numbers
from an Vnite: ſcilicet, as 1, 3, 5, 7. For this is the Rate or pro­
portion of the exceſſes of the Squares of Lines that equally exceed
one another, and the exceſſe of which is equal to the least of them,
or, if you will, of Squares that follow one another, beginning ab
Unitate. Whilſt therefore the degree of Velocity is encreaſed ac­
cording to the ſimple Series of Numbers in equal Times, the Spaces
paſt in thoſe Times make their encreaſe according to the Series of
odd Numbers from an Vnite.
SAGR. Be pleaſed to ſtay your Reading, whilſt I do paraphraſe
touching a certain Conjecture that came into my mind
but even now; for the explanation of which, unto your under­
ſtanding and my own, I will deſcribe a ſhort Scheme: in which I
fanſie by the Line A I the continuation of the Time after the firſt
Inſtant, applying the Right Line A F unto A according to any
Angle: and joyning together the Terms I F, I divide the Time A I
in half at C, and then draw C B parallel to I F. And then conſide­
ring B C, as the greateſt degree of Velocity which beginning from
Reſt in the firſt Inſtant of the Time A goeth augmenting accord­
ing to the encreaſe of the Parallels to B C, drawn in the Triangle
A B C, (which is all one as to encreaſe according to the encreaſe
of the Time) I admit without diſpute, upon what hath been ſaid
already, That the Space paſt by the falling Moveable with the
1Velocity encreaſed in the manner aforeſaid would be equal to the
Space that the ſaid Moveable would paſſe, in caſe it were in the
ſame Time A C, moved with an Uniform Motion, whoſe degree of
Velocity ſhould be equal to E C, the half of B C. I now proceed
farther, and imagine the Moveable; having deſcended with an
Accelerate Motion, to have in the Inſtant
C the degree of Velocity B C: It is ma­
85[Figure 85]
nifeſt, that if it did continue to move
with the ſame degree of Velocity B C,
without farther Acceleration, it would
paſſe in the following Time C I, a Space
double to that which it paſſed in the equal
Time A C, with the degree of Uniform
Velocity E C, the half of the Degree B C.
But becauſe the Moveable deſcendeth
with a Velocity encreaſed alwaies Uni­
formly in all equal Times; it will add to
the degree C B in the following Time
C I, thoſe Tame Moments of Velocity
that encreaſe according to the Parallels of
the Triangle B F G, equal to the Triangle
A B C. So that adding to the degree of
Velocity G I, the half of the degree F G, the greateſt of thoſe ac­
quired in the Accelerate Motion, and regulated by the Parallels of
the Triangle B F G, we ſhall have the degree of Velocity I N, with
which, with an Uniform Motion, it would have moved in the
Time C I: Which degree I N, being triple the degree E C, pro­
veth that the Space paſſed in the ſecond Time C I ought to be tri­
ple to that of the firſt Time C A. And if we ſhould ſuppoſe to be
added to A I another equal part of Time I O, and the Triangle to
be enlarged unto A P O; it is manifeſt, that if the Motion ſhould
continue for all the Time I O with the degree of Velocity I F,
acquired in the Accelerate Motion in the Time A I, that degree
I F being Quadruple to E C, the Space paſſed would be Quadruple
to that paſſed in the equal firſt Time A C: But continuing the
encreaſe of the Uniform Acceleration in the Triangle F P Q like
to that of the Triangle A B C, which being reduced to equable
Motion addeth the degree equal to E C, Q R being added, equal
to E C, we ſhall have the whole Equable Velocity exerciſed in the
Time I O, quintuple to the Equable Velocity of the firſt Time A C,
and therefore the Space paſſed quintuple to that paſt in the firſt
Time A C. We ſee therefore, even by this familiar computation,
That the Spaces paſſed in equal Times by a Moveable which
departing from Reſt goeth acquiring Velocity, according to the
encreaſe of the Time, are to one another as the odd Numbers ab
1unitate 1, 3, 5: And that the Spaces paſſed being conjunctly taken,
that paſſed in the double Time is quadruple to that paſſed in the
ſubduple, that paſſed in the triple Time is nonuple; and, in a word,
that the Spaces paſſed are in duplicate proportion to their Times;
that is, as the Squares of the ſaid Times.
SIMP. I muſt confeſſe that I have taken more pleaſure in this
plain and clear diſcourſe of Sagredus, than in the to-me-more
obſcure Demonſtration of the Author: ſo that I am very well
ſatisfied, that the buſineſſe is to ſucceed as hath been ſaid, the
Definition of Uniformly Accelerate Motion being ſuppoſed, and
granted. But whether this be the Acceleration of which Nature
maketh uſe in the Motion of its deſcending Grave Bodies, I yet
make a queſtion: and therefore for information of me, and of
others like unto me, me thinks it would be ſeaſonable in this place
to produce ſome Experiment amongſt thoſe which were ſaid to be
many, which in ſundry Caſes agree with the Concluſions demon­
ſtrated.
SALV. You, like a true Artiſt, make a very reaſonable demand,
and ſo it is uſual and convenient to do in Sciences that apply
Mathematical Demonſtrations to Phyſical Concluſions, as we ſee
in the Profeſſors of Perſpection, Aſtronomy, Mechanicks, Muſick,
and others, who with Senſible Experiments confirm thoſe their
Principles that are as the foundations of all the following Structure:
and therefore I deſire that it may not be thought ſuperfluous, that
we diſcourſe with ſome prolixity upon this firſt and grand funda­
mental on which we lay the weight of the Immenſe Machine of
infinite Concluſions, of which we have but a very ſmall part ſet
down in this Book by our Author, who hath done enough to open
the way and door that hath been hitherto ſhut unto all Specula­
tive Wits. Touching Experiments, therefore, the Author hath
not omitted to make ſeveral; and to aſſure us, that the Accelerati­
on of natural-deſcending Graves hapneth in the aforeſaid propor­
tion, I have many times in his company ſet my ſelf to make a triall
thereof in the following Method.
In a priſme or Piece of Wood, about twelve yards long, and
half a yard broad one way, and three Inches the other, we made,
upon the narrow Side or edge a Groove of little more than an Inch
wide; we ſhot it with the Grooving Plane very ſtraight, and to
make it very ſmooth and ſleek, we glued upon it a piece of Vellum,
poliſhed and ſmoothed as exactly as can be poſſible: and in it we
have let a brazen Ball, very hard, round, and ſmooth, deſcend.
Having placed the ſaid Priſme Pendent, raiſing one of its ends
above the Horizontal Plane a yard or two at pleaſure, we have let
the Ball (as I ſaid) deſcend along the Grove, obſerving, in the
manner that I ſhall tell you preſently, the Time which it ſpent in
1runing it all; repeating the ſame obſervation again and again to
aſſure our ſelves of the Time, in which we never found any diffe­
rence, no not ſo much as the tenth part of one beat of the Pulſe.
Having done, and preciſely ordered this buſineſſe, we made the
ſame Ball to deſcend only the fourth part of the length of that
Grove: and having meaſured the time of its deſcent, we alwaies
found it to be punctually half the other. And then making trial of
other parts, examining one while the Time of the whole Length
with the Time of half the Length, or with that of 2/3, or of 3/4, or, in
brief, with any whatever other Diviſion, by Experiments repeated
near an hundred Times, we alwaies found the Spaces to be to one
another as the Squares of the Times. And this in all Inclinations
of the Plane, that is, of the Grove in which the Ball was made to
deſcend. In which we obſerved moreover, that the Times of the
Deſcents along ſundry Inclinations did retain the ſame proportion
to one another, exactly, which anon you will ſee aſſigned to them,
and demonſtrated by the Author. And as to the meaſuring of the
Time; we had a good big Bucket full of Water hanged on high,
which by a very ſmall hole, pierced in the bottom, ſpirted, or, as
we ſay, ſpin'd forth a ſmall thread of Water, which we received
with a ſmall cup all the while that the Ball was deſcending in the
Grove, and in its parts; and then weighing from time to time the
ſmall parcels of Water, in that manner gathered, in an exact pair
of ſcales, the differences and proportions of their Weights gave
juſtly the differences and proportions of the Times; and this with
ſuch exactneſſe, that, as I ſaid before, the trials being many
and many times repeated, they never differed any conſiderable
matter.
SIMP. I ſhould have received great ſatisfaction by being preſent
at thoſe Experiments: but being confident of your diligence in
making them, and veracity in relating them, I content my ſelf, and
admit them for true and certain.
SALV. We may, then, reaſſume our Reading, and go on.
COROLLARY II.
It is collected in the ſecond place, that if any two Spaces are ta­
ken from the beginning of the Motion, paſſed in any Times,
thoſe Times ſhall be unto each other as one of them is to a
Space that is the Mean proportional between them.
For taking two Spaces S T, and S V from the beginning of the Mo­
tion S, to which S X is a Mean-proportional, the Time of the deſcent
along S T, ſhall be to the Time of the deſcent along S V, as S T to S X;
or, if you will, the Time along S V ſhall be to the Time along S T,
186[Figure 86]
as VS is to SX. For it is demonſtrated, that Spaces
paſſed are in duplicate proportion to the Times, or, (which
is the ſame) are as the Squares of the Times: But the pro­
portion of the Space VS to the Space ST is double to the
proportion of V S to SX, or is the ſame that V S, and S X
ſquared have to one another: Therefore, the proportion of
the Times of the Motion by V S, and ST, is as the Spaces or
Lines V S to S X.
SCHOLIUM.
That which is demonſtrated in Motions that are made Perpendicu­
larly, may be underſtood alſo to hold true in the Motions made along
Planes of any whatever Inclination; for it is ſuppoſed, that in them
the degree of Acceleration encreaſeth in the ſame proportion; that
is, according to the encreaſe of the Time; or, if you will, according
to the ſimple and primary Series of Numbers.
SALV. Here I deſire Sagredus, that I alſo may be allowed, al­
beit perhaps with too much tediouſneſſe in the opinion of Simplici­
us, to defer for a little time the preſent Reading, untill I may have
explained what from that which hath been already ſaid and de­
monſtrated, and alſo from the knowledge of certain Mechanical
Concluſions heretofore learnt of our Academick, I now remember
to adjoyn for the greater confirmation of the truth of the Princi­
ple, which hath been examined by us even now with probable
Reaſons and Experiments: and, which is of more importance, for
the Geometrical proof of it, let me firſt demonſtrate one ſole Ele­
mental Lemma in the Contemplation of Impetus's.
SAGR. If our advantage ſhall be ſuch as you promiſeus, there
is no time that I would not moſt willingly ſpend in diſcourſing
about the confirmation and thorow eſtabliſhing theſe Sciences of
Motion: and as to my own particular, I not only grant you liber­
ty to ſatisfie your ſelf in this particular, but moreover entreat you
to gratifie, as ſoon as you can, the Curioſity which you have begot
in me touching the ſame: and I believe that Simplicius alſo is of the
ſame mind.
SIMP. I cannot deny what you ſay.
SALV. Seeing then that I have your permiſſion, I will in the
firſt place conſider, as an Effect well known, That
1
LEMMA.
That the Moments or Velocities of the ſame Moveable are different
upon different Inclinations of Planes, and the greateſt is by the
Line elevated perpendicularly above the Horizon, and by the
others inclined, the ſaid Velocity diminiſheth according as they
more and more depart from Perpendicularity, that is, as they in­
cline more obliquely: ſo that the Impetus, Talent, Energy, or, we
may ſay, Moment of deſcending is diminiſhed in the Moveable by
the ſubjected Plane, upon which the ſaid Moveable lyeth and
deſcendeth.
And the better to expreſs my ſelf, let the Line A B be perpen­
dicularly erected upon the Horizon A C: then ſuppoſe the
ſame to be declined in ſundry Inclinations towards the Horizon, as
in A D, A E, A F, &c. I ſay, that the greateſt and total Impetus
of the Grave Body in deſcending is along the Perpendicular B A,
and leſs than that along D A,
87[Figure 87]
and yet leſs along E A; and
ſucceſſively diminiſhing along
the more inclined F A, and fi­
nally is wholly extinct in the
Horizontal C A, where the
Moveable is indifferent either
to Motion or Reſt, and hath not
of it ſelf any Inclination to
move one way or other, nor yet
any Reſiſtance to its being mo­
ved: for as it is impoſſi­
ble that a Grave Body, or a
Compound thereof ſhould move naturally upwards, receding from
the Common Center, towards which all Grave Matters conſpire
to go, ſo it is impoſſible that it do ſpontaneouſly move, unleſs
with that Motion its particular Center of Gravity do acquire Proxi­
mity to the ſaid Common Center: ſo that upon the Horizontal
which here is underſtood to be a Superficies equidiſtant from the
ſaid Center, and therefore altogether void of Inclination, the Im­
petus or Moment of that ſame Moveable ſhall be nothing at all.
Having underſtood this mutation of Impetus, I am to explain that
which, in an old Treatiſe of the Mechanicks, written heretofore
in Padona by our Academick, only for the uſe of his Scholars, was
diffuſely and demonſtratively proved, upon the occaſion of con­
ſidering the Original and Nature of the admirable Inſtrument cal­
led the Screw, and it is, With what proportion that mutation of
1Impetus is made along ſeveral Inclinations or Declivities of
Planes.
As, for example, in the inclined Plane A F, drawing its Eleva­
tion above the Horizontal, that is, the Line F C, along the which
the Impetus of a Grave Body, and the Moment of Deſcent is the
greateſt; it is ſought what proportion this Moment hath to the
Moment of the ſame Moveable along the Declivity F A: Which
Proportion, I ſay, is Reciprocal to the ſaid Lengths. And this is
the Lemma that was to go before the Theorem, which I hope to be
able anon to Demonſtrate. Hence it is manifeſt, That the Impetus
of Deſcent of a Grave Body is as much as the Reſiſtance or leaſt
force that ſufficeth to arreſt and ſtay it. For this Force or Reſi­
ſtance, and its meaſure, I will make uſe of the Gravity of another
Moveable. Let us now upon the Plane F A put the Moveable G
tyed to a thread which ſliding over F hath faſtned at its other end
the Weight H: and let us conſider that the Space of the Deſcent
or Aſcent of the Weight H along the Perpendicular, is alwaies
equal to the whole Aſcent or Deſcent of the other Moveable G
along the ^{*} Declivity A F, but yet not to the Aſcent or Deſcent

along the Perpendicular, in which only the ſaid Moveable G (like
as every other Moveable) exerciſeth its Reſiſtance. Which is
manifeſt: for conſidering in the Triangle AFC the Motion of
the Moveable G, as for example, upwards from A to F, to be com­
poſed of the tranſverſe Horizontal Line A C, and of the Perpendi­
cular C F: And in regard, that as to the Horizontal Plane along
which the Moveable, as hath been ſaid, hath no Reſiſtance to mo­
ving (it not making by that Motion any loſs, nor yet acquiſt in
regard of its particular diſtance from the Common Center of Grave
Matters, which in the Horizon continueth ſtill the ſame) it remai­
neth that the Reſiſtance be only in reſpect of the Aſcent that it is to
make along the Perpendicular C F. Whilſt therefore the Grave
Moveable G, moving from A to F, hath only the Perpendicular
Space C F to reſiſt in its Aſcent, and whilſt the other Grave Move­
able H deſcendeth along the Perpendicular of neceſſity as far as
the whole Space F A, and that the ſaid proportion of Aſcent and
Deſcent maintains it ſelf alwaies the ſame, be the Motion of the
ſaid Moveables little or much (by reaſon they are tyed toge­
ther) we may confidently affirm, that in caſe there were an Equi­
librium, that is Reſt, to enſue betwixt the ſaid Moveables, the Mo­
ments, the Velocities, or their Propenſions to Motion, that is the
Spaces which they would paſs in the ſame Time ſhould anſwer re­
ciprocally to their Gravities, according to that which is demonſtra­
ted in all caſes of Mechanick Motions: ſo that it ſhall ſuffice to
impede the deſcent of G, if H be but ſo much leſs grave than it, as
in proportion the Space C F is leſſer than the Space F A. Therefore
1ſuppoſe that the Moveable G is to the Moveable H, as F A is to
F C; and then the Equilibrium ſhall follow, that is, the Moveables
H and G ſhall have equal Moments, and the Motion of the ſaid
Moveables ſhall ceaſe. And becauſe we ſee that the Impetus,
Energy, Moment, or Propenſion of a Moveable to Motion is the
ſame as is the Force or ſmalleſt Reſiſtance that ſufficeth to ſtop it;
and becauſe it hath been concluded, that the Grave Body H is ſuf.
ficient to arreſt the Motion of
88[Figure 88]
the Grave Body G: Therefore
the leſſer Weight H, which in
the Perpendicular F C imploy­
eth its total Moment, ſhall be
the preciſe meaſure of the par­
tial Moment that the greater
Weight G exerciſeth along the
inclined Plane F A: But the
meaſure of the total Moment of
the ſaid Grave Body G, is the
ſelf ſame, (ſince that to impede
the Perpendicular Deſcent of a
Grave Body there is required the oppoſition of ſuch another Grave
Body, which likewiſe is at liberty to move Perpendicularly:)
Therefore the partial Impetus or Moment of G along the inclined
Plane F A ſhall be to the grand and total Impetus of the ſame G
along the Perpendicular F C, as the Weight H to the Weight G:
that is, by Conſtruction, as the ſaid Perpendicular F C, the Eleva­
tion of the inclined Plane, is to the ſame inclined Plane F A:
Which is that that by the Lemma was propoſed to be demon­
ſtrated, and which by our Author, as we ſhall ſee, is ſuppoſed as
known in the ſecond part of the Sixth Propoſition of the preſent
Treatiſe.
* Or inclined
Plane.
SAGR. From this that you have already concluded I conceive
one may eaſily deduce, arguing ex æquali by perturbed Proportion,
that the Moments of the ſame Moveable, along Planes variouſly
inclined (as F A and F I) that have the ſame Elevation, are to each
other in Reciprocal proportion to the ſame Planes.
SALV. A moſt certain Concluſion. This being agreed on, we
will paſs in the next place to demonſtrate the Theoreme, namely,
that
1
THEOREM.
The degrees of Velocity of a Moveable deſcending with a Natural
Motion from the ſame height along Planes in any manner inclined
at the arrival to the Horizon are alwaies equal, Impediments be­
ing removed.
Here we are in the firſt place to advertiſe you, that it having
been proved, that in any Inclination of the Plane the Move­
able from its receſſion from Quieſſence goeth encreaſing its Ve­
locity, or quantity of its Impetus, with the proportion of the
Time (according to the Definition which the Author giveth of
Motion naturally Accelerate) whereupon, as he hath by the pre­
cedent Propoſition demonſtrated, the Spaces paſſed are in dupli­
cate proportion to the Times, and, conſequently, to the degrees
of Velocity: look what the Impetus's were in that which was firſt
moved, ſuch proportionally ſhall be the degrees of Velocity gai­
ned in the ſame Time; ſeeing that both theſe and thoſe encreaſe
with the ſame proportion in the ſame Time.
Now let the inclined Plane be A B, its elevation above the Ho
rizon the Perpendicular A C, and the Horizontal Plane C B: and
becauſe, as was even now concluded, the Impetus of a Moveable
along the Perpendicular A C is to the Impetus of the ſame along
the inclined Plane A B, as A B is to A C, let there be taken in the
inclined Plane A B, A D a third proportional to A B and A C:
The Impetus, therefore, along A C is to the Impetus along A B,
that is along A D, as A C is to
89[Figure 89]
A D: And therefore the Move­
able in the ſame Time that it
would paſs the Perpendicular
Space AC, ſhall likewiſe paſs the
Space A D, in the inclined Plane
A B, (the Moments being as
the Spaces:) And the degree of Velocity in C ſhall have the ſame
proportion to the degree of Velocity in D, as A C hath to A D:
But the degree of Velocity in B is to the ſame degree in D, as the
Time along A B is to the Time along AD, by the definition of
Accelerate Motion; And the Time along AB is to the Time along
A D, as the ſame A C, the Mean Proportional between B A and
A D, is to A D, by the laſt Corollary of the ſecond Propoſition:
Therefore the degrees of Velocity in B and in C have to the de­
gree in D, the ſame Proportion as A C hath to A D; and therefore
are equal: Which is the Theorem intended to be demonſtrated.
By this we may more concludingly prove the enſuing third
1Propoſition of the Author, in which he makes uſe of this Princi­
ple; and it is, That the Time along the inclined Plane, hath to the
Time along the Perpendicular, the ſame proportion as the ſaid In­
clined Plane and Perpendicular. For if we put the caſe that BA
be the Time along A B, the Time along A D ſhall be the Mean
between them, that is A C, by the ſecond Corollary of the ſecond
Propoſition: But if C A be the Time along A D, it ſhall likewiſe
be the Time along A C, by reaſon that A D and A C are paſt in
equal Times: And therefore in caſe B A be the Time along A B,
A C ſhall be the Time along A C: Therefore, as A B is to A C, ſo
is the Time along A B to the Time along A C.
By the ſame diſcourſe one ſhall prove, that the Time along A C
is to the Time along the inclined Plane A E, as A C is to A E:
Therefore, ex æquali, the Time along the inclined Plane A B is,
Directly, to the Time along the inclined Plane A E as A B to
A E, &c.
One might alſo by the ſame application of the Theorem, as Sa­
gredus ſhall very evidently ſee anon, immediately demonſtrate the
ſixth Propoſition of the Author: But let this Digreſſion ſuffice
for the preſent, which he perhaps thinketh too tedious, though in­
deed it is of ſome importance in theſe matters of Motion.
SAGR. You may ſay extreamly delightful, and moſt neceſſary
to the perfect underſtanding of that Principle.
SALV. I will go on, then, in my Reading of the Text.
THEOR. III. PROP. III.
If a Moveable departing from Reſt do move along
an Inclined Plane, and alſo along the Perpendi­
cular whoſe heights are the ſame, the Times of
their Motions ſhall be to one another as the
Lengths of the ſaid Plane and Perpendicular.
Let the inclined Plane be A C, and the Perpendicular A B,
whoſe heights are the ſame above the Horizon C B, to wit,
the ſelf ſame Line B A. I ſay, that the Time of the Deſcent
of the ſame Moveable upon the Plane A C, hath the ſame Proporti­
on to the Time of the Deſcent along the Perpendicular A B, as the
Length of the Plane A C hath to the Length of the ſaid Perpendi­
cular. For let any number of Lines D G, E I, F L, be drawn, Paral­
lel to the Horizon C B: It is manifeſt from the Aſſumption fore­
going, that the degrees of Velocity of the Moveable, departing from
A the beginning of Motion, acquired in the Points G and D are
1equal, their exceſſe or elevation above the Horizon being equal;
and ſo the degrees in the Points I and E; as alſo the degrees in L
and F. And if not only theſe Parallels, but many more were ſup­
poſed to be drawn from all the points imagined to be in the Line
A B, untill they meet the Line A C, the Mo-
90[Figure 90]
ments, or degrees of the Velocities along the
extreams [or ends] of every one of thoſe
Parallels, ſhall be alwaies equal to one ano­
ther: Therefore the two Spaces A C and A B
are paſt with the ſame degree of Velocity:
But it hath been demonſtrated, that if two
Spaces be paſſed by a Moveable with one
and the ſame degree of Velocity, the Times
of the Motions have the ſame proportion as
thoſe Spaces: Therefore the Time of the Motion along A C is to the
Time along A B, as the Length of the Plane A C to the length of the
Perdendicular A B. Which was to be demonſtrated.
SAGR. It ſeemeth to me, that the ſame might very clearly and
conciſely be concluded, it having firſt been proved that the ſum of
the Accelerate Motion of the Tranſitions along A C and A B, is
as much as the Equable Motion, whoſe degree of Velocity is ſub­
duple to the greateſt degree C B: Therefore the two Spaces AC
and A B being paſſed with the ſame Equable Motion, it hath been
ſhewn, by the Firſt Propoſition of the firſt, that the Times of the
Tranſitions ſhall be as the ſaid Spaces.
COROLLARY.
Hence is collected, that the Times of the Deſcents along Planes
of different Inclination, but of the ſame Elevation, are to
one another according to their Lengths.
For if we ſuppoſe another Plane A M, coming from A, and ter­
minated by the ſame Horizontal C B; it ſhall in like manner be
demonſtrated, that the Time of the Deſcent along A M, is to the
Time along A B, as the Line A M to A B: But as the Time A B is
to the Time along A C, ſo is the Line A B to A C: Therefore, ex
æquali, as A M is to A C, ſo is the Time along A M to the Time
along A C.
1
THEOR. IV. PROP. IV.
The Times of the Motions along equal Planes,
but unequally inclined, are to each other in
ſubduple proportion of the Elevations of thoſe
Planes Reciprocally taken.
Let there proceed from the term B two equal Planes, but une­
qually inclined, B A and B C, and let A E and C D be Hori­
zontal Lines, drawn as far as the Perpendicular B D: Let the
Elevation of the Plane B A be B E; and let the Elevation of the
Plane B C be B D: And let B I be a Mean Proportional between the
Elevations D B and B E: It is manifeſt
91[Figure 91]
that the proportion of D B to B I, is ſub­
duple the proportion of D B to B E. Now
I ſay, that the proportion of the Times
of the Deſcents or Motions along the
Planes B A and B C, are the ſame with
the proportion of D B to B I Reciprocal­
ly taken: So that to the Time B A the
Elevation of the other Plane B C, that is
B D be Homologal; and to the Time along
B C, B I be Homologal: Therefore it is
to be demonſtrated, That the Time along B A is to the Time along
B C, as D B is to B I. Let I S be drawn equidiſtant from D C. And
becauſe it hath been demonſtrated that the Time of the Deſcent
along B A, is to the Time of the Deſcent along the Perpendicular
B E, as the ſaid B A is to B E; and the Time along B E is to the
Time along B D, as B E is to B I; and the Time along B D is to the
Time along B C, as B D to B C, or as B I to B S: Therefore, ex æqua­
li, the Time along B A ſhall be to the Time along B C as B A to B S,
or as C B to BS: But C B is to B S, as D B to B I: Therefore the
Propoſition is manifeſt:
1
THEOR. V. PROP. V.
The proportion of the Times of the Deſcents
along Planes that have different Inclinations
and Lengths, and the Elivations unequal, is
compounded of the proportion of the Lengths
of thoſe Planes, and of the ſubduple proporti­
on of their Elevations Reciprocally taken.
Let A B and A C be Planes inclined after different manners,
whoſe Lengths are unequal, as alſo their Elevations. I ſay,
the proportion of the Time of the Deſcent along A C to the
Time along A B, is compounded of the proportion of the ſaid A C
to A B, and of the ſubduple proportion of their Elevation Recipro­
cally taken. For let the Perpendicular A D be drawn, with which
let the Horizontal Lines B G and C D interſect, and let A L be a
Mean-proportional between C A and A E; and from the point L let
a Parallel be drawn to the Horizon interſecting
92[Figure 92]
the Plane A C in F; and A F ſhall be a Mean
proportional between C A and A E. And becauſe
the Time along A C is to the Time along A E, as
the Line F A to A E; and the Time along A E is
to the Time along A B, as the ſaid A E to the ſaid
A B: It is manifeſt that the Time along A C is to
the Time along A B, as A F to A B. It remaineth,
therefore, to be demonſtrated, that the proportion
of A F to A B is compounded of the proportion of
C A to A B, and of the proportion of G A to A L;
which is the ſubduple proportion of the Elevati­
ons D A and A G Reciprocally taken. But that is manifeſt, C A
being put between F A and A B: For the proportion of F A to A C
is the ſame as that of L A to A D, or of G A to A L; which is ſub­
duple of the proportion of the Elevations G A and A D; and the
proportion of C A to A B is the proportion of the Lengths: Therefore
the Propoſition is manifeſt.
1
THEOR. VI. PROP. VI.
If from the higheſt or loweſt part of a Circle,
erect upon the Horizon, certain Planes be
drawn inclined towards the Circumference,
the Times of the Deſcents along the ſame
ſhall be equal.
Let the Circle be erect upon the Horizon G H, whoſe Diameter
recited upon the loweſt point, that is upon the contact with the
Horizon, let be F A, and from the higheſt point A let certain
Planes A B and A C incline towards the Circumference: I ſay that the
Times of the Deſcents along the ſame are equal. Let B D and C E be
two Perpendiculars let fall unto the Diameter; and let A I be a Mean­
Proportional between the Altitudes
93[Figure 93]
of the Planes E A and A D. And
becauſe the Rectangles F A E and
F A D are equal to the Squares of
A C and A B; And alſo becauſe
that as the Rectangle F A E, is to
the Rectangle F A D, ſo is E A to
A D. Therefore as the Square of
C A is to the Square of B A,
ſo is the Line E A to the Line
A D. But as the Line E A is to
D A, ſo is the Square of I A to the Square of A D: Therefore
the Squares of the Lines C A and A B are to each other as the Squares
of the Lines I A and A D: And therefore as the Line C A is to A B,
ſo is I A to A D: But in the precedent Propoſition it hath been demon­
ſtrated that the proportion of the Time of the Deſcent along A C to the
Time of the Deſcent by A B, is compounded of the proportions of C A
to A B, and of D A to A I, which is the ſame with the proportion of
B A to A C: Therefore the proportion of the Time of the Deſcent along
A C, to the Time of the Deſcent along A B, is compounded of the pro­
portions of C A to A B, and of B A to A C: Therefore the proporti­
on of thoſe Times is a proportion of equality: Therefore the Propoſition
is evident.
The ſame is another way demonſtrated from the Mechanicks: Name­
ly that in the enſuing Figure the Moveable paſſeth in equal Times along
C A and D A. For let B A be equal to the ſaid D A, ond let fall the
Perpendiculars B E and D F: It is manifeſt by the Elements of the
1Mechanicks: That the Moment of the Weight elevated upon the Plane
according to the Line A B C, is
to its total Moment, as B E to B A;
94[Figure 94]
And that the Moment of the ſame
Weight upon the Elevation A D,
is to its total Moment, as D F to
D A or B A: Therefore the Mo­
ment of the ſaid Weight upon the
Plane inclined according to D A,
is to the Moment upon the Plane
inclined according to A B C, as
the Line D F to the Line B E:
Therefore the Spaces which the
ſaid Weight ſhall paſſe in equal
Times along the Inclined Planes C A and D A, ſhall be to each other as
the Line B E to D F; by the ſecond Propoſition of the Firſt Book:
But as B E is to D F, ſo A C is demonſtrated to be to D A:
Therefore the ſame Moveable will in equal Times paſſe the Lines
C A and D A.
And that C A is to D A as B E is to D F, is thus demonſtrated.
Draw a Line from C to D; and by D and B draw the Lines
D G L, (cutting C A in the point I) and B H, Parallels to A F:
And the Angle A D I ſhall be equal to the Angle D C A, for that
the parts L A and A D of the Circumference ſubtending them, are
equal, and the Angle D A C common to them both: Therefore of
the equiangled Triangles C A D and D A I, the ſides about the
equal Angles ſhall be proportional: And as C A is to A D, ſo is
D A to A I, that is B A to A I, or H A to A G; that is, B E to
D F: Which was to be proved.
Or elſe the ſame ſhall be demonſtrated more ſpeedily thus.
Vnto the Horizon A B, let a Circle be erect, whoſe Diameter is
perpendicular to the Horizon: and
from the higheſt Term D let a Plane
95[Figure 95]
at pleaſure D F, be inclined to the
Circumference. I ſay that the De­
ſcent along the Plane D F, and the
Fall along the Diameter B C, will
be paſſed by the ſame Moveable in
equal Times. For let F G be drawn
parallel to the Horizon A B, which
ſhall be perpendicular to the Diameter
D C, and let a Line conjoyn F and
C: and becauſe the Time of the Fall
along D C, is to the Time of the Fall along D G, as the Mean
Proportional between C D and D G, is to the ſaid D G; and the
1Mean between C D and D G being D F, (for that the Angle D F C
in the Semicircle, is a Right Angle, and F G perpendicular to D C:)
Therefore the Time of the Fall along D C is to the Time of the Fall
along D G, as the Line F D to D G: But it hath been demonſtrated
that the Time of the Deſcent along D F, is to the Time of the Fall
along D G, as the ſame Line D F is to D G: The Times, therefore,
of the Deſcent along D F and Fall along D C, are to the Time of the
Fall along the ſaid D G in the ſame proportion: Therefore they are
equal. It will likewiſe be demonſtrated, if from the loweſt Term C,
one ſhould raiſe the Chord C E, and draw E H parallel to the Hori­
zon, and conjoyn E and D, that the Time of the Deſcent along E C
equals the Time of the Fall along the Diameter D C.
COROLLARY I.
Hence is collected that the Times of the Deſcents along all the
Chords drawn from the Terms C or D are equal to one
another.
COROLLARY II.
It is alſo collected that if the Perpendicular and inclined Plane
deſcend from the ſame point along which the Deſcents are
made in equal Times, they are in a Semicircle whoſe Dia­
meter is the ſaid Perpendicular.
COROLLARY III.
Hence it is collected that the Times of the Motions along inclined
Planes, are then equal, where the Elevations of equal parts of
thoſe Planes ſhall be to one another as their Longitudes.
For it hath been ſhewn that the Times C A and D A in the laſt Fi­
gure ſave one are equal, the Elevation of the part A B being equal
to A D, that is, that B E ſhall be to the Elevation D F, as C A
to D A.
SAGR. Pray you Sir be pleaſed to ſtay your Reading of what
followeth until that I have ſatisfied my ſelf in a Contemplation
that juſt now cometh into my mind, which if it be not a deluſi­
on, is not far from being a pleaſing divertiſement: as are all ſuch
that proceed from Nature or neceſſity.
It is manifeſt, that if from a point aſſigned in an Horizontal
Plane, one ſhall produce along the ſame Plane infinite right Lines
every way, upon each of which a point is underſtood to move with
an Equable Motion, all beginning to move in the ſame inſtant
1of Time from the aſſigned point, and the Velocities of them all
being equal, there ſhall conſequently be deſcribed by thoſe move­
able points Circumferences of Circles alwayes bigger and bigger,
all concentrick about the firſt point aſſigned: juſt in the ſame
manner as we ſee it done in the Undulations of ſtanding Water,
when a ſtone is dropt into it; the percuſſion of which ſerveth to
give the beginning to the Motion on every ſide, and remaineth
as the Center of all the Circles that happen to be deſigned ſucceſ­
ſively bigger and bigger by the ſaid Undulations. But if we ima­
gine a Plane erect unto the Horizon, and a point be noted in the
ſame on high, from which infinite Lines are drawn inclined, ac­
cording to all inclinations, along which we fancy grave Movea­
bles to deſcend, each with a Motion naturally Accelerate
with thoſe Velocities that agree with the ſeveral Inclinations;
ſuppoſing that thoſe deſcending Moveables were continually viſi­
ble, in what kind of Lines ſhould we ſee them continually diſpoſed?
Hence my wonder ariſeth, ſince that the precedent Demonſtrati­
ons aſſure me, that they ſhall all be alwayes ſeen in one and the
ſame Circumference of Circles ſucceſſively encreaſing, according
as the Moveables in deſcending go more and more ſucceſſively re­
ceding from the higheſt point in which their Fall began: And the
better to declare my ſelf, let the chiefeſt point A be marked, from
which Lines deſcend according to any Inclinations A F, A H, and
the Perpendicular A B, in which taking the points C and D, de­
ſcribe Circles about them that paſs by
96[Figure 96]
the point A, interſecting the inclined
Lines in the points F, H, B, and E, G,
I. It is manifeſt, by the fore-going
Demonſtrations, that Moveables de­
ſcendent along thoſe Lines departing
at the ſame Time from the term A,
one ſhall be in E, the other ſhall be in
G, and the other in I; and ſo con­
tinuing to deſcend they ſhall arrive
in the ſame moment of Time at F, H,
and B: and theſe and infinite others continuing to move along the
infinite differing Inclinations, they ſhall alwayes ſucceſſively arrive
at the ſelf-ſame Circumferences made bigger & bigger in infinitum.
From the two Species, therefore, of Motion of which Nature makes
uſe, ariſeth, with admirable harmonious variety, the generation of in­
ſinite Circles. She placeth the one as in her Seat, and original be­
ginning, in the Center of infinite concentrick Circles; the other
is conſtituted in the ſublime or higheſt Contact of infinite Circum­
ferences of Circles, all excentrick to one another: Thoſe proceed
from Motions all equal and Equable; Theſe from Motions all al­
1wayes Inequable to themſelves, and all unequal to one another,
that deſcend along the infinite different Inclinations. But we fur­
ther adde, that if from the two points aſſigned for the Emanations,
we ſhall ſuppoſe Lines to proceed, not onely along two Superfi­
cies Horizontal and Upright [or erect] but along all every ways
like as from thoſe, beginning at one ſole point, we paſſed to the
production of Circles from the leaſt to the greateſt, ſo beginning
from one ſole point we ſhall ſucceſſively produce inſinite Spheres,
or we may ſay one Sphere, that ſhall gradatim increaſe to infinite
bigneſſes: And this in two faſhions; that is, either with placing
the original in the Center, or elſe in the Circumference of thoſe
Spheres.
SALV. The Contemplation is really ingenuous, and adequate
to the Wit of Sagredus.
SIMP. Though I am at leaſt capable of the Speculation, ac­
cording to the two manners of the production of Circles and
Spheres, with the two different Natural Motions, howbeit I do
not perfectly underſtand the production depending on the Acce­
lerate Motion and its Demonſtration, yet notwithſtanding that
licence of aſſigning for the place of that Emanation as well the
loweſt Center, as the higheſt Spherical Superficies, maketh me to
think that its poſſible that ſome great Miſtery may be contained
in theſe true and admirable Concluſions: ſome Miſtery I ſay
touching the Creation of the Univerſe, which is held to be of
Spherical form, and concerning the Reſidence of the Firſt
Cauſe.
SALV. I am not unwilling to think the ſame: but ſuch pro­
found Speculations are to be expected from Sharper Wits than
ours. And it ſhould ſuffice us, that if we be but thoſe leſſe noble
Workmen that diſcover and draw forth of the Quarry the
Marbles, in which the Induſtrious Statuaries afterwards make
wonderful Images appear, that lay hid under rude and miſhaped
Cruſts. Now, if you pleaſe, we will go on.
THEOR. VII. PROP. VII.
If the Elevations of two Planes ſhall have a pro­
portion double to that of their Lengths, the
Motions in them from Reſt ſhall be finiſhed in
equal Times.
Let A E and A B be two unequal Planes, and unequally inclined,
and let their Elevations be F A and D A, and let F A have the
ſame proportion to D A, as A E hath to A B. I ſay that the Times
of the Motions along the Planes A E and A B, out of Reſt in A are
1equal. Draw Horizontal Parallels to the Line of Elevation E F and
B D, which cutteth A E in G. And be-
97[Figure 97]
cauſe the proportion of F A to A D, is
double the proportion of E A to A B; and
as F A to A D, ſo is E A to A G: There­
fore the proportion of E A to A G, is dou­
ble the proportion of E A to A B: There­
fore A B is a Mean-Proportional between
E A and A G: And becauſe the Time of the
Deſcent along A B, is to the Time of the De­
ſcent along A G, as A B to A G; and the
Time of the Deſcent along AG, is to the Time of the Deſcent along A E, as
A G is to the Mean-proportional between A G and A E, which is A B:
Therefore ex equali, the Time along A B is to the Time along A E, as A B
unto it ſelf: Therefore the Times are equal: Which was to be demonſtrated.
THEOR. VIII. PROP. VIII.
In Planes cut by the ſame Circle, erect to the
Horizon, in thoſe which meet with the end of
the erect Diameter, whether upper or lower,
the Times of the Motions are equal to the
Time of the Fall along the Diameter: and in
thoſe which fall ſhort of the Diameter, the
Times are ſhorter; and in thoſe which inter­
ſect the Diameter, they are longer.
Let A B be the Perpendicular Diameter of the Circle erect to the
Horizon. That the Times of the Motions along the Planes pro­
duced out of the Terms A and B unto the Circumference are equal,
hath already been demonſtrated: That the Time of the Deſcent along
the Plane D F, not reaching to the
98[Figure 98]
Diameter is ſborter, is demonſtrated
by drawing the Plane D B, which
ſhall be both longer and leſſe decli­
ning than D F. Therefore the Time
along D F is ſhorter than the Time
along D B, that is, along A B. And
that the Time of the Deſcent along
the Plane that interſecteth the Dia­
meter, as C O is longer, doth in the
ſame manner appear, for that it is
longer and leſſe declining than C B: Therefore the Propoſition is de­
monſtrated.
1
THEOR. IX. PROP. IX.
If two Planes be inclined at pleaſure from a point
in a Line parallel to the Horizon, and be inter­
ſected by a Line which may make Angles Al­
ternately equal to the Angles contained be­
tween the ſaid Planes and Horizontal Parallel,
the Motion along the parts cut off by the ſaid
Line, ſhall be performed in equal Times.
From off the point C of the Horizontal Line X, let any two Planes
be inclined at pleaſure C D and C E, and in any point of the
Line C D make the Angle C D F equal to the Angle X C E:
and let the Line D F cut the Plane C E in F, in ſuch a manner that
the Angles C D F and C F D may be equal to the Angles X C E, L C D
Alternately taken. I ſay, that
99[Figure 99]
the Times of the Deſcents along
C D and C F are equal. And
that (the Angle C D F being
ſuppoſed equal to the Angle
X C E) the Angle C F D is
equal to the Angle D C L, is
manifeſt. For the Common An­
gle D C F being taken from the
three Angles of the Triangle
C D F equal to two Right An­
gles, to which are equal all the Angles made with to the Line L X
at the point C, there remains in the Triangle two Angles C D F and
C F D, equal to the two Angles X C E and L C D: But it was ſup­
poſed that C D F is equal to the Angle X C E: Therefore the remaining
Angle C F D is equal to the remaining angle D C L. Let the Plane
C E be ſuppoſed equal to the Plane C D, and from the points D and
E raiſe the Perpendiculars D A and E B, unto the Horizontal Paral­
lel X L; and from C unto D F let fall the Perpendicular C G. And
becauſe the Angle C D G is equal to the Angle E C B; and becauſe
D G C and C B E are Right Angles; The Triangles C D G and
C B E ſhall be equiangled: And as D C is to C G, ſo let C E be
to E B: But D C is equal to C E: Therefore C G ſhall be equal to
E B. And inregard that of the Triangles D A C and C G F, the An­
gles C and A are equal to the Angles F and G: Therefore as C D is to
D A, ſo ſhall F C be to C G; and Alternately, as D C is to C F, ſo
1is D A to C G, or B E. The proportion therefore of the Elevations
of the Planes equal to C D and C E, is the ſame with the proportion
of the Longitudes D C and C E: Therefore, by the firſt Corollary of
the precedent Sixth Propoſition, the Times of the Dcſcent along the
ſame ſhall be equal: Which mas to be proved.
Take the ſame another way: Draw F S perpendicular to the
Horizontal Parallel A S. Becauſe the Triangle C S F is like to
the Triangle D G C, it ſhall be, that as S F is to F C, ſo is G C
to C D. And becauſe the Triangle C F G is like to the Triangle
D C A, it ſhall be, that as F C is to C G, ſo is C D to D A:
Therefore, ex æquali, as
S F is to C G, ſo is C G to
D A: Thorefore C G is a
100[Figure 100]
Mean-proportional between
S F and D A: And as DA
is to S F, ſo is the Square
D A unto the Square C G
Again, the Triangle A C D
being like to the Triangle
C G F, it ſhall be, that as
D A is to D C, ſo is G C
to C F: and, Alternately,
as D A is to G C, ſo is D C to C F; and as the Square of D A
is to the Square of C G, ſo is the Square of D C to the Square of
C F. But it hath been proved that the Square D A is to the
Square C G as the Line D A is to the Line F S: Therefore, as the
Square D C is to the Square C F, ſo is the Line D E to F S: There­
fore, by the ſeventh fore-going, in regard that the Elevations D A
and F S, of the Planes C D, and C F are in double proportion to
their Planes; the Times of the Motions along the ſame ſhall be
equal.
THEOR. X. PROP. X.
The Times of the Motions along ſeveral Inclina­
tions of Planes whoſe Elevations are equal,
are unto one another as the Lengths of thoſe
Planes, whether the Motions be made from
Reſt, or there hath proceeded a Motion from
the ſame height.
Let the Motions be made along A B C, and along A B D, until
they come to the Horizon D C, in ſuch ſort as that the Motion
along A B precedeth the Motions along B D and B C. I ſay,
that the Time of the Motion along B D, is to the Time along B C, as
1the Length B D is to B C. Let A F be drawn parallel to the Ho­
rizon, to which continue out D B, meeting it in F; and let F E be
a Mean-proportional between D F and F B; and draw E O parallel
to D C, and A O ſhall be a Mean-proportional between C A and
A B: But if we ſuppoſe the Time
along A B, to be as A B, the Time a-
101[Figure 101]
long F B ſhall be as F B. And the
Time along all A C, ſhall be as the
Mean-proportional A O; and along
all F D ſhall be F E: Wherefore the
Time along the remainder B C ſhall
be B O; and along the remainder
B D ſhall be B E. But as B E is to
B O, ſo is B D to B C: Therefore
the Times along B D and B C, after the Deſcent along A B and
F B, or which is the ſame, along the Common part A B, ſhall be to
one another as the Lengths B D and B C: But that the Time along
B D, is to the Time along B C, out of Reſt in B, as the Length
B D to B C, hath already been demonſtrated. Therefore the Times
of the Motions along different Planes whoſe Elevations are equal, are
to one another as the Lengths of the ſaid Planes, whether the Motion
be made along the ſame out of Reſt, or whether another Motion of
the ſame Altitude do precede thoſe Motions: Which was to be de­
monſtrated.
THEOR. XI. PROP. XI.
If a Plane, along which a Motion is made out of
Reſt, be divided at pleaſure, the Time of
the Motion along the firſt part, is to the Time
of the Motion along the ſecond, as the ſaid
firſt part is to the exceſſe whereby the ſame
part ſhall be exceeded by the Mean-Propor­
tional between the whole Plane and the ſame
firſt part.
Let the Motion be along the whole Plane A B, ex quiete in A,
which let be divided at pleaſure in C; and let A F be a Mean
proportional between the whole B A and the firſt part A C;
C F ſhall be the exceſſe of the Mean proportional F A above the part
A C. I ſay the Time of the Motion along A C is to the Time of the
following Motion along C B, as A C to C F. Which is manifeſt;
1For the Time along A C is to the Time along all
A B, as A C to the Mean-proportional A F: There-
102[Figure 102]
fore, by Diviſion, the Time along A C, ſhall be to
the Time along the remainder C B as A C to C F:
If therefore the Time along A C be ſuppoſed to be
the ſaid A C, the Time along C B ſhall be C F:
Which was the Propoſition.
But if the Motion be not made along the continu­
ate Plane A C B, but by the inflected Plane A C D
until it come to the Horizon B D, to which from F a Parallel is
drawn F E. It ſhall in like manner be
103[Figure 103]
demonſtrated, that the Time along
A C is to the Time along the reflected
Plane C D, as A C is to C E. For
the Time along A C is to the Time a­
long C B, as A C is to C F: But the
Time along C B, after A C hath been
demonſtrated to be to the Time along
C D, after the ſaid Deſoent along
A C, as C B is to C D; that is, as
C F to C E: Therefore, ex æquali, the Time along A C ſhall be to
the Time along C D, as the Line A C to C E.
THEOR. XII. PROP. XII.
If the Perpendicular and Plane Inclined at plea­
ſure, be cut between the ſame Horizontal
Lines, and Mean-Proportionals between
them and the parts of them contained betwixt
the common Section and upper Horizontal
Line be given; the Time of the Motion a­
long the Perpendicular ſhall have the ſame
proportion to the Time of the Motion along
the upper part of the Perpendicular, and af­
terwards along the lower part of the interſe­
cted Plane, as the Length of the whole Per­
pendicular hath to the Line compounded of
the Mean-Proportional given upon the Per­
pendicular, and of the exceſſe by which the
whole Plane exceeds its Mean-Proporttonal.
1
Let the Horizontal Lines be A F the upper, and C D the low­
er; between which let the Perpendicular A C, and inclined
Plane D F, be cut in B; and let A R be a Mean-Proportional
between the whole Perpendicular C A, and the upper part A B; and
let F S be a Mean-proportional between the whole Inclined Plane D F,
and the upper part B F. I ſay, that the Time of the Fall along the
whole Perpendicular A C hath the ſame proportion to the Time along
its upper part A B, with the lower of the Plane, that is, with B D,
as A C hath to the Mean-proporti­
onal of the Perpendicular, that is
104[Figure 104]
A R, with S D, which is the ex­
ceſſe of the whole Plane D F above
its Mean-proportional F S. Let a
Line be drawn from R to S, which
ſhall be parallel to the two Horizon­
tal Lines. And becauſe the Time of
the Fall along all A C, is to the
Time along the part A B, as C A is
to the Mean proportional A R, if we ſuppoſe A C to be the Time of
the Fall along A C, A R ſhall be the Time of the Fall along A B,
and R C that along the remainder B C. For if the Time along A C
be ſuppoſed, as was done, to be A C it ſelf the Time along F D ſhall
be F D; and in like manner D S may be concluded to be the Time a­
long B D, after F B, or after A B. The Time therefore along the
whole A C, is A R, with R C; And the Time along the inflected
Plane A B D, ſhall be A R, with S D: Which was to be proved.
The ſame happeneth, if inſtead of the Perpendicular, another
Plane were taken, as ſuppoſe N O; and the Demonstration is the
ſame.
PROBL I. PROP. XIII.
A Perpendicular being given, to Inflect a Plane
unto it, along which, when it hath the ſame
Elevation with the ſaid Perpendicular, it may
make a Motion after its Fall along the Per­
pendicular in the ſame Time, as along the
ſame Perpendicular ex quiete.
Let the Perpendicular given be A B, to which extended to C,
let the part B C be equal; and draw the Horizontal Lines
C E and A G. It is required from B to inflect a Plane reach­
ing to the Horizon C E, along which a Motion, after the Fall out
1of A, ſhall be made in the ſame Time, as along A B from Reſt in A. Let
C D be equal to C B, and drawing B D, let B E be applied equal to both
B D and D C. I ſay B E is the Plane required. Continue out E B to
meet the Horizontal Line A G in G;
105[Figure 105]
and let G F be a Mean-Proportional be­
tween the ſaid E G and G B. E F ſhall
be to F B, as E G is to G F; and the
Square E F ſhall be to the Square F B, as
the Square E G is to the Square G F;
that is as the Line E G to G B: But
E G is double to G B: Therefore the
Square of E F is double to the Square of F B: But alſo the Square of
D B is double to the Square of B C: Therefore, as the Line E F is to
F B, ſo is D B to B C: And by Compoſition and Permutation, as E B is
to the two D B and B C, ſo is B F to B C: But B E is equal to the two
D B and B C: Therefore B F is equal to the ſaid B C, or B A. If there­
fore A B be underſtood to be the Time of the Fall along A B, G B ſhall
be the Time along G B, and G F the Time along the whole G E: There­
fore B F ſhall be the Time along the remainder B E, after the Fall from
G, or from A, which was the Propoſition.
PROBL. II. PROP. XIV.
A Perpendicular and a Plane inclined to it being
given, to find a part in the upper Perpendicu­
lar which ſhall be paſt ex quiete in a Time
equal to that in which the inclined Plane is
paſt after the Fall along the part found in the
Perpendicular.
Let the Perpendicular be D B, and the Plane inclined to it A C. It is
required in the Perpendicular A D to find a part which ſhall be
paſt ex quiete in a Time equal to that in which the Plane A C is
paſt after the Fall along the ſaid part. Draw the Horizontal Line C B;
and as B A more twice A C is to A C, ſo let E A be to A R; And from
R let fall the Perpendicular R X unto D B. I ſay X is the point requi­
red. And becauſe as B A more twice A C is to A C, ſo is C A to A E,
by Diviſion it ſhall be that as B A more A C is to A C, ſo is C E to E A:
And becauſe as B A is to A C, ſo is E A to A R, by Compoſition it ſhall
be that as B A more A C is to A C, ſo is E R to R A: But as B A more
A C is to A C, ſo is C E to E A: Therefore, as C E is to E A, ſo is E R,
to R A, and both the Antecedents to both the Conſequents, that is, C R
1to R E: Therefore C R, R E, and R A are Proportionals. Farther­
more, becauſe as B A is to A C, ſo E A is ſuppoſed to be to A R, and,
106[Figure 106]
in regard of the likeneſſe of the Triangles,
as B A is to A C, ſo is X A to A R: There­
fore, as E A is to A R, ſo is X A to A R:
Therefore E A and X A are equal. Now if
we underſtand the Time along R A to be as
R A, the Time along R C ſhall be R E, the
Mean-Proportional between C R and R A:
And A E ſhall be the Time along A C after
R A or after X A: But the Time along X A
is X A, ſo long as R A is the Time along R
A: But it hath been proved that X A and
A E are equal: Therefore the Propoſition is proved.
PROBL. III. PROP. XV.
A Perpendicular and a Plane inflected to it being
given, to find a part in the Perpendicular ex­
tended downwards which ſhall be paſſed in the
ſame. Time as the inflected Plane after the Fall
along the given Perpendicular.
Let the Perpendicular be A B, and the Plane Inſlected to it B C. It
is required in the Perpendicular extended downwards to find a
part which from the Fall out of A ſhall be paſt in the ſame Time as
B C is paſſed from the ſame Fall out of A. Draw the Horizontal Line
A D, with which let C B meet extended to D; and let D E be a Mean­
proportional between C D and D B;
107[Figure 107]
and let B F be equal to B E; and let
A G be a third Proportional to B A and
A F. I ſay, B G is the Space that after
the Fall A B ſhall be paſt in the ſame
Time, as the Plane B C ſhall be paſt af­
ter the ſame Fall. For if we ſuppoſe
the Time along A B to be as A B, the
Time along D B ſhall be as D B: And
becauſe D E is the Mean-proportional
between B D and D C, the ſame D E
ſhall be the Time along the whole D C, and B E the Time along the Part
or Remainder B C ex quiete, in D, or ^{*} ex caſu A B: And it may in

like manner be proved, that B F is the Time along B G, after the ſame
Fall: But B F is equal to B E: Which was the Propoſition to be proved.
1
* From or after
the Fall A B.
THEOR. XIII. PROP. XVI.
If the parts of an inclined Plane and Perpendicu­
lar, the Times of whoſe Motions ex quiete are
equal, be joyned together at the ſame point, a
Moveable coming out of any ſublimer Height
ſhall ſooner paſſe the ſaid part of the inclined
Plane, than that part of the Perpendicular.
Let the Perpendicular be E B, and the Inclined Plane C E, joyned
at the ſame Point E, the Times of whoſe Motions from off Reſt in
E are equal, and in the Perpendicular continued out, let a ſublime
point A be taken at pleaſure, out of which the Moveables may be let
fall. I ſay, that the Inclined Plane E C ſhall be paſſed in a leſſe Time
than the Perpendicular E B, after the Fall A E. Draw a Line from C
to B, and having drawn the Horizontal Line A D continue out C E till
it meet the ſame in D; and let D F be a Mean-Proportional between
C D and D E; and let A G be a
108[Figure 108]
Mean-Proportional between B A and
A E; and draw F G and D G. And
becauſe the Time of the Motion along
E C and E B out of Reſt in E are
equal, the Angle C ſhall be a Right
Angle, by the ſecond Corollary of the
Sixth Propoſition; and A is a Right
Angle, and the Vertical Angles
at E are equal: Therefore the Tri­
angles A E D and C E B are equian­
gled, and the Sides about equal An­
gles are Proportionals: Therefore as
B E is to E C, ſo is D E to E A.
Therefore the Rectangle B E A is
equal to the Rectangle C E D: And
becauſe the Rectangle C D E ex­
ceedeth the Rectangle C E D, by the Square E D, and the Rectangle
B A E doth exceed the Rectangle B E A, by the Square E A: The
exceſſe of the Rectangle C D E above the Rectangle B A E, that is of
the Square F D above the Square A G ſhall be the ſame as the exceſſe
of the Square D E above the Square A E; which exceſs is the
Square D A: Therefore the Square F D is equal to the two Squares
G A and A D, to which the Square G D is alſo equal: Therefore the
1Line D F is equal to D G, and the Angle D G F is equal to the An­
gle D F G, and the Angle E G F is leſſc than the Angle E F G, and
the oppoſite Side E F leſſe than the Side E G. Now if we ſuppoſe
the Time of the Fall along A E to be as A E, the Time by D E ſhall
be as D E; and A G being a Mean-Proportional between B A and A E,
A G ſhall be the Time along the whole A B, and the part E G ſhall be
the Time along the Part E B ex quiete in A. And it may in like man­
ner be proved that E F is the Time along E C after the Deſcent D E, or
after the Fall A E: But E F is proved to be leſſer than E G: Therefore
the Propoſition is proved.
COROLLARY.
By this and the precedent it appears, that the Space that is paſ­
ſed along the Perpendicular after the Fall from above in the
ſame Time in which the Inclined Plane is paſt, is leſſe than
that which is paſt in the ſame Time as in the Inclined, no fall
from above preceding, yet greater than the ſaid Inclined
Plane.
For it having been proved, but now, that of the Moveables coming
from the ſublime Term A the Time of the Converſion along E C is
ſhorter than the Time of the Progreſſion along E B; It is manifeſt that
the Space that is paſt along E B in a Time equal to the Time along E C
is leſs than the whole Space E B. And that the ſame Space along the
Perpendicular is greater than E C is mani­
feſted by reaſſuming the Figure of the pre-
109[Figure 109]
cedent Propoſition, in which the part of the
Perpendicular B G hath been demonſtrated
to be paſſed in the ſame Time as B C after
the Fall A B: But that B G is greater than
B C is thus collected. Becauſe B E and F B
are equal, and B A leſſer than B D, F B,
hath greater proportion to B A, than E B
hath to B D: And, by Compoſition, F A
hath greater proportion to A B, than E D
to D B: But as F A is to A B, ſo is G F
to F B, (for A F is the Mean-Proportional
between B A and A G:) And in like man­
ner, as E D is to B D, ſo is C E to E B: Therefore G B hath greater
proportion to B F, than C B hath to B E: Therefore G B is greater
than B C.
1
PROBL. IV. PROP. XVII.
A Perpendicular and Plane Inflected to it being
given, to aſſign a part in the given Plane, in
which after the Fall along the Perpendicular
the Motion may be made in a Time equal to
that in which the Moveable ex quiete paſſeth
the Perpendicular given.
Let the Perpendicular be A B, and a Plane Inflected to it B E: It is
required in B E to aſſign a Space along which the Moveable af­
ter the Fall along A B may move in a Time equal to that in which
the ſaid Perpendicular A B is paſſed ex quiete. Let the Line A D be
parallel to the Horizon, with which let the Plane prolonged meet in D;
and ſuppoſe F B equal to B A; and as B D
is to D F, ſo let F D be to D E. I ſay, that
110[Figure 110]
the Time along B E after the Fall along A B
equalleth the Time along A B, out of Reſt
in A. For if we ſuppoſe A B to be the Time
along A B, D B ſhall be the Time along
D B. And becauſe, as B D is to D F, ſo is
F D to D E, D F ſhall be the Time along
the whole Plane D E, and B F along the
part B E out of D: But the Time along
B E after D B, is the ſame as after A B: Therefore the Time along B E
after A B ſhall be B F, that is, equal to the Time ex quiete in A:
Which was the Propoſition.
PROBL. V. PROP. XVIII.
Any Space in the Perpendicular being given from
the aſſigned beginning of Motion that is
paſſed in a Time given, and any other leſſer
Time being alſo given, to find another Space in
the ſaid Perpendicular that may be paſſed in
the given leſſer Time.
1
Let the Perpendicular be A D, in which let the Space aſſigned be
A B, whoſe Time from the beginning A let be A B: and let the
Horizon be C B E, and let a Time be given leſs than A B, to
which let B C be noted equal in the Horizon: It is required in the
ſaid Perpendicular to find a Space equal to the ſame A B that ſhall be
paſſed in the Time B C. Draw a Line from A to
111[Figure 111]
C. And becauſe B C is leſſe than B A, the Angle
B A C ſhall be leſſe than the Angle B C A. Let
C A E be made equal to it, and the Line A E meet
with the Horizon in the Point E, to which ſup­
poſe E D a Perpendicular, cutting the Perpendi­
cular in D, and let D F be cut equal to B A. I
ſay, that the ſaid F D is a part of the Perpendi­
cular along which the Lation from the beginning
of Motion in A, the Time B C given will be ſpent.
For if in the Right-angled Triangle A E D, a
Perpendicular to the oppoſite Side A D, be drawn
E B, A E ſhall be a Mean-Proportional betwixt
D A and A B, and B E a Mean-Proportional betwixt D B and B A,
or betwixt F A and A B (for F A is equal to D B.) And in regard
A B hath been ſuppoſed to be the Time along A B, A E, or E C ſhall be
the Time along the whole A D, and E B the Time along A F: There­
fore the part B C ſhall be the Time along the part F D: Which was
intended.
PROBL. VI. PROP. XIX.
Any Space in the Perpendicular paſſed from the
beginning of the Motion being given, and the
Time of the Fall being aſſigned, to find the
Time in which another Space. equal to the gi­
ven one, and taken in any part of the ſaid Per­
pendicular, ſhall be afterwards paſt by the
ſame Moveable.
In the Perpendicular A B let A C be any Space taken from the be­
ginning of the Motion in A, to which let D B be another equal Space
taken any where at pleaſure, and let the Time of the Motion along
A C be given, and let it be A C. It is required to ſind the Time of the
1Motion along D B after the Fall from A. About the whole A B de­
ſcribe a Semicircle A E B, and from
112[Figure 112]
C let fall C E, a Perpendicular to A
B, and draw a Line from A to E;
which ſhall be greater than E C.
Let E F be out equall to E C: I ſay,
that the remainder F A is the Time
of the Motion along D B. For be­
cauſe A E is a Mean-proportional be­
twixt B A and and A C, and A C
is the Time of the Fall along A C;
A E ſhall be the Time along the
Whole A B. And becauſe C E is a
Mean-proportional betwixt D A and
A C, (for D A is equal to B C)
C E, that is E F ſhall be the Time
along A D: Therefore the Remainder A F ſhall be the Time along the
Remainder B B: Which is the Propoſition.
COROLLARY.
Hence is gathered, that if the Time of any Space ex quiete be
as the ſaid Spaec, the Time thereof after another Space is ad­
ded ſhall be the exceſſe of the Mean-proportional betwixt
the Addition and Space taken together, and the ſaid Space
above the Mean-proportional betwixt the firſt Space and the
Addition.
As for example, it being ſuppoſed that the Time along
113[Figure 113]
A B, out of Reſt in A, be A B; A S being another Space
added, The Time along A B after S A ſhall be the exceſſe of
the Mean-proportional betwixt S B and B A above the
Mean-proportional betwixt B A and A S.
PROBL VII. PROP. XX.
Any Space and a part therein after the begining
of the Motion being given, to find another
part towards the end that ſhall be paſt in the
ſame Time as the firſt part given.
Let the Space be C B, and let the part in it given after the begin­
ing of the Motion in C be C D. It is required to find another
part towards the end B, which ſhall be paſt in the ſame Time as
1the given part C D. Take a Mean-proportional betwixt B C and C D,
to which ſuppoſe B A equal; and let C E be a third proportional be-
114[Figure 114]
tween B C and C A. I ſay, that E B is the Space that after
the Fall out of C ſhall be past in the ſame Time as the ſaid
C D is paſſed. For if we ſuppoſe the Time along C B
to be as C B; B A (that is the Mean-proportional betwixt
B C and C D) ſhall be the Time along C D. And becauſe
C A is the Mean proportional betwixt B C and C E, C A
ſhall be the Time along C E: But the whole B C is the
Time along the Whole C B: Therefore the part B A ſhall be
the Time along the part E B, after the Fall out of C: But
the ſaid B A was the Time along C D: Therefore C D and
E B ſhall be paſt in equal Times out of Reſt in C: Which
was to be done.
THEOR. XIV. PROP. XXI.
If along the Perpendicular a Fall be made ex quie­
te, in which from the begining of the Motion
a part is taken at pleaſure, paſſed in any Time,
after which an Inflex Motion followeth along
any Plane however Inclined, the Space which
along that Plane is paſſed in a Time equal to
the Time of the Fall already made along the
Perpendicular ſhall be to the Space then paſ­
ſed along the Perpendicular more than double,
and leſſe than triple.
From the Horizon A E let fall a Perpendicular A B, along which
from the begining A let a Fall be made, of which let a part A C
be taken at pleaſure; then out of C let any Plane G be inclined at
pleaſure: along which after the Fall along A C let the Motion be con­
tinued. I ſay, the Space paſſed by that Motion along C G in a Time
equall to the Time of the Fall along A C, is more than double, and leſs
than triple that ſame Space A C. For ſuppoſe C F equal to A C, and
extending out the Plane G C as far as the Horizon in E, and as C E
is to E F, ſo let F E be to E G. If therefore we ſuppoſe the Time of
1the Fall along A C to be as the Line A C; C E ſhall be the Time along
E C, and C F or C A the Time of the Motion along C G. Therefore
it is to be proved that the
115[Figure 115]
Space C G is more than
double, and leſſe than
triple the ſaid C A. For
in regard that as C E is
to E F, ſo is F E to E G;
therefore alſo ſo is C F to
F G. But E C is leſſe
than E F: Therefore C F
ſhall be leſſe than F G, and
G C more than double to
F C or A C. And moreover, in regard that F E is leſſe than double to
E C, (for E C is greater than C A or C F) G F ſhall alſo be leſſe
than double to F C, and G C leſſe than triple to C F or C A: Which
was to be demonſtrated.
And the ſame may be more generally propounded: for that which
hapneth in the Perpendicular and Inclined Plane, holdeth true alſo if
after the Motion a Plane ſomewhat inclined it be inflected along a more
inclining Plane, as is ſeen in the other Figure: And the Demonſtration
is the ſame.
PROBL. VIII. PROP. XXII.
Two unequall Times being given, and a Space
that is paſt ex quiete along the Perpendicular
in the ſhorteſt of thoſe given Times, to inflect
a Plane from the higheſt point of the Perpen­
dicular unto the Horizon, along which the
Moveable may deſcend in a Time equal to the
longeſt of thoſe Times given.
Let the unsqual Times be A the greater, and B the leſſer; and let
the Space that is paſt ex quiete along the Perpendicular in the
Time B, be C D. It is required from the Term C to inflect [or
116[Figure 116]
bend] a Plane untill it reach the Horizon that may be paſſed in the
1Time A. As B is to A, ſo let C D be to another Line, to which let C X
be equal that deſcendeth from C unto the Horizon: It is manifeſt that
the Plane C X is that along which the Moveable deſcendeth in the Gi­
ven Time A. For it hath been demonſtrated, that the Time along the
inclined Plane hath the ſame proportion to the Time along its ^{*} Eleva-

tion, as the Length of the Plane hath to the Length of its Elevation,.
The Time, therefore, along C X is to the Time along C D, as C X is to
C D, that is, as the Time A is to the Time B: But the Time B is that
in which the Perpendicular is paſt ex quiete: Therefore the Time A is
that in which the Plane C X is paſſed.
* Or Perpendi­
cular.
PROBL. IX. PROP. XXIII.
A Space paſt ex quiete along the Perpendicular in
any Time being given, to inflect a Plane from
the loweſt term of that Space, along which,
after the Fall along the Perpendicular, a Space
equal to any Space given may be paſſed in the
ſame Time: which nevertheleſſe is more than
double, and leſſe than triple the Space paſſed
along the Perpendicular.
Along the Perpendicular A S, in the Time A C, let the Space
A C be paſt ex quiete in A; to which let I R be more than
double, and leſſe than triple. It is required from the Terme C
to inflect a Plane, along which a Moveable after the Fall along A C
may in the ſame Time A C paſſe a Space equal to the ſaid I R. Let
R N, and N M be equal to A C: And look what proportion the part
I M hath to M N, the ſame ſhall the Line A C have to another, equal
to which draw C E from C to
117[Figure 117]
the Horizon A E, which con­
tinue out towards O, and take
C F, F G, and G O, equal to
the ſaid R N, N M, and M I.
I ſay, that the Time along the
inflected Plane C O, after the
Fall A G, is equal to the Time
A C out of Reſt in A. For in
regard that as O G is to G F,
ſo is F C to C E by Compoſition it ſhall be that as O F is to F G or F C,
ſo is F E to E C; and as one of the Antecedents is to one of the Con­
ſequents, ſo are all to all; that is, the whole O E is to E F as F E to
E C: Therefore O E, E F, and E C are Continual Proportionals:
1And ſince it was ſuppoſed that the Time along A C is as A C, C E ſhall
be the Time along E C; and E F the Time along the whole E O; and
the part C F that along the part C O: But C F is equal to the ſaid C A:
Therefore that is done which was required: For the Time C A is the
Time of the Fall along A C ex quiete in A; and C F (which is equal
to C A) is the Time along C O, after the Deſcent along E C, or after
the Fall along A C: Which was the Propoſition.
And here it is to be noted, that the ſame may happen if the preceding
Motion be not made along the Perpendicular, but along an Inclined Plane:
As in the following Figure, in which let the preceding Lation be made
along the inclined Plane A S beneath the Horizon A E: And the Demon­
ſtration is the very ſame.
SCHOLIUM.
If one obſerve well, it ſhall be manifeſt, that the leſſe the given
Line I R wanteth of being triple to the ſaid A C, the nearer
ſhall the Inflected Plane, along which the ſecond Motion is
to be made, which ſuppoſe to be C O, come to the Perpen­
dicular, along which in a Time equal to A C a Space ſhall
be paſſed triple to A C.
For in caſe I R were very near the triple of A C, I M ſhould be well­
near equal to M N: And if, as I M is to M N by Conſtruction, ſo
A C is to C E, then it is evident that the ſaid C E will be found but
little bigger than C A, and, which followeth of conſequence, the point E
ſhall be found very near the point A, and C O to containe a very acute
118[Figure 118]
Angle with C S, and
almoſt to concur both in
one Line. And on the
contrary, if the ſaid I R
were but a very little
more than double the
ſaid A C, I M ſhould
be a very ſhort Line.
Hence it may happen
alſo that A C may come
to be very ſhort in reſpect of C E which ſhall be very long, and ſhall ap­
proach very near the Horizontal Parallel drawn from C. And from
hence we may collect, that if in the preſent Figure after the Deſcent along
the inclined Plane A C, a Reflexion be made along the Horizontal Line,
as v. gr. C T, the Space along which the Moveable afterwards moved
in a Time equal to the Time of the Deſcent along A C would be exactly
double to the Space A C. And it appears that the like Diſcourſe may be
here applied: For it is apparent by what hath been ſaid, that ſince O E
1is to E F, as F E is to E C, that F C determineth the Time along C O:
And if a part of the Horizontal Line T C double to C A be divided in
two equal parts in V, the extenſion towards X ſhall be prolonged in in­
finitum, whilſt it ſeeks to meet with the prolonged Line A E: And the
proportion of the Infinite Line T X to the Infinite Line V X, ſhall be
no other than the proportion of the Infinite Line V X to the Infinite
Line X C.
We may conclude the ſelf-ſame thing another way by reaſſuming the
ſame Reaſoning that we uſed in the Demonſtration of the firſt Propoſi­
tion. For reſuming the Triangle A B C, repreſenting to us by its Pa­
rallels to the Baſe B C the Degrees of Velocity continually encreaſed ac­
cording to the encreaſes of the Time; from which, ſince they are infi­
nite, like as the Points are infinite in the Line A C, and the Inſtants
in any Time, ſhall reſult the Superficies of that ſame Triangle, if we
underſtand the Motion to continue for ſuch another Time, but no far­
ther with an Accelerate, but with an Equable Motion, according to the
greateſt degree of Velocity acquired, which degree is repreſented
by the Line B C. Of ſuch degrees ſhall be made up an Aggregate like to
a Parallelogram A D B C, which is the double of
119[Figure 119]
the Triangle A B C. Wherefore the Space which
with degrees like to thoſe ſhall be paſſed in the ſame
Time, ſhall be double to the Space paſt with the de­
grees of Velocity repreſented by the Triangle A B C:
But along the Horizontal Plane the Motion is Equa­
ble, for that there is no cauſe of Acceleration, or Re­
tardation: Therefore it may be concluded that the
Space C D, paſſed in a Time equall to the Time A C is double to the
Space A C: For this Motion is made ex quiete Accelerate according
to the Parallels of the Triangle; and that according to the Parallels
of the Parallelogram, which, becauſe they are infinite, are donble to
the infinite Parallels of the Triangle.
Moreover it may farther be obſerved, that what ever degree of
ſwiftneſs is to be found in the Moveable, is indelibly impreſſed upon it
of its own nature, all external cauſes of Acceleration or Retardation
being removed; which hapneth only in Horizontal Planes: for in de­
clining Planes there is cauſe of greater Acceleration, and in the riſing
Planes of greater Retardation. From whence in like manner it fol­
loweth that the Motion along the Horizontal Plane is alſo Perpetual:
for if it be Equable, it can neither be weakned nor retarded, nor much
leſſe deſtroyed. Farthermore, the degree of Celerity acquired by the
Moveable in a Natural Deſcent, being of its own Nature Indelible and
Penpetual, it is worthy conſideration, that if after the Deſcent along a
declining Plane a Reflexion be made along another Plane that is riſing,
in this latter there is cauſe of Retardation, for in theſe kind of Planes
1the ſaid Moveable doth naturally deſcend; whereupon there reſults a
mixture of certain contrary Affections, to wit, that degree of Celerity
acquired in the precedent Deſcent, which would of it ſelf carry the Move­
able uniformly in infinitum, and of Natural Propenſion to the Motion of
Deſcent according to that ſame proportion of Acceleration wherewith it
alwaies moveth. So that it will be but reaſonable, if, enquiring what
accidents happen when the Moveable after the Deſcent along any incli­
ned Plane is Reflected along ſome riſing Plane, we take that greateſt de­
gree acquired in the Deſcent to keep it ſelf perpetually the ſame in the
Aſcending Plane; But that there is ſuperadded to it in the Aſcent the
Natural Inclination downwards, that is the Motion from Reſt Accelerate
according to the received proportion: And leſt this ſhould, perchance, be
ſomewhat intricate to be underſtood, it ſhall be more clearly explained by a
Scheme.
Let the Deſcent therefore be ſuppoſed to be made along the Declining
Plane A B, from which let the Reflex Motion be continued along another
Riſing Plane B C: And in the firſt place let the Planes be equal, and
elevated at equal Angles to the Horizon G H. Now it is manifeſt, that
the Moveable ex quiete in A deſcending along A B acquireth degrees of
Velocity according to the increaſe of its Time, and that the degree in B
is the greateſt of thoſe acquired and by Nature immutably impreſſed, I
mean the Cauſes of new Acceleration or Retardation being removed:
of Acceleration, I ſay, if it ſhould paſſe any farther along the extended
Plane; and of Retardation, whilſt the Reflection is making along the
Acclivity B C: But along the Horizontal Plane G H the Equable Mo­
tion according to the de-
120[Figure 120]
gree of Velocity acquired
from A unto B would ex­
tend in infinitum. And
ſuch a Velocity would
that be which in a Time
equal to the Time of the
Deſcent along A B would paſſe a Space in double the Horizon to the ſaid
A B. Now let us ſuppoſe the ſame Moveable to be Equably moved with
the ſame degree of Swiftneſſe along the Plane B C, in ſuch ſort that alſo
in this Time equal to the Time of the Deſcent along A B a Space may be
paſſed a long B C extended double to the ſaid A B. And let us under­
ſtand that as ſoon as it beginneth to aſcend there naturally befalleth the
ſame that hapneth to it from A along the Plane A B, to wit, a certain
Deſcent ex quiete according to thoſe degrees of Acceleration, by vertue
of which, as it befalleth in A B, it may deſcend as much in the ſame
Time along the Reflected Plane as it doth along A B: It is manifeſt, that
by this ſame Mixture of the Equable Motion of Aſcent, and the Acce­
lerate of Deſcent the Moveable may be carried up to the Term C along
the Plane B C according to thoſe degrees of Velocity, which ſhall be
1equal. And that two points at pleaſure D and E being taken, equally
remote from the Angle B, the Tranſition along D B is made in a Time
equal to the Time of the Reflection along B E, we may collect from hence:
Draw D F, which ſhall be Parallel to B C; for it is manifeſt that the
Deſcent along A D is reflected along D F: And if after D the Move­
able paſſe along the Horizontal Plane D E, the Impetus in E ſhall be
the ſame as the Impetus in D: Therefore it will aſcend from E to C:
And therefore the degree of Velocity in D is equal to the degree in E.
From theſe things, therefore, we may rationally affirm, that, if a de­
ſcent be made along any inclined Plane, after which a Reflection may
follow along an elevated Plane, the Moveable may by the conceived
Impetus aſcend untill it attain the ſame beight, or Elevation from the
Horizon. As if a Deſcent be made along A B, the Moveable would
paſſe along the Reflected Plane B C, untill it arrive at the Horizon
A C D; and that not only when the Inclinations of the Planes are
equal, but alſo when they are unequal, as is the Plane B D: For it was
first ſuppoſed, that the degrees of Velocity are equal, which are acqui­
red upon Planes unequally inclined, ſo long as the Elevation of thoſe
Planes above the Horizon was the ſame: But, if there being the ſame
Inclination of the Planes E B and B D, the Deſcent along E B ſufficeth
to drive the Moveable along the Plane BD as far as D, ſeeing this Impulſe
121[Figure 121]
is made by the Impe­
tus of Velocity in the
point B; and if the
Impetus be the ſame
in B, whether the
Moveable deſcend a­
long A B, or along E B: It is manifeſt, that the Moveable ſhall be in
the ſame manner driven along B D, after the Deſcent along A B, and
after that along E B: But it will happen that the Time of the Aſcent
along B D ſhall be longer than along B C, like as the Deſcent along
E B is made in a longer time than along A B: But the Proportion of
thoſe Times was before demonſtrated to be the ſame as the Lengths of
thoſe Planes. Now it follows, that we ſeek the proportion of the Spaces
paſt in equal Times along Planes, whoſe Inclinations are different, but
their Elevations the ſame; that is, which are comprehended between
the ſame Horizontal Parallels. And this hapneth according to the fol­
lowing Propoſition.
1
THEOR. XV. PROP. XXIV.
There being given between the ſame Horizontal
Parallels a Perpendicular and a Plane eleva­
ted from its loweſt term, the Space that a
Moveable after the Fall along the Perpendi­
cular paſſeth along the Elevated Plane in a
Time equal to the Time of the Fall, is greater
than that Perpendicular, but leſſe than double
the ſame.
Between the ſame Horizontal Parallels B C and H G let there
be the Perpendicular A E; and let the Elevated Plane be E B,
along which after the Fall along the Perpendicular A E out of
the Term E let a Reflexion be made towards B. I ſay, that the Space,
along which the Moveable aſcendeth in a Time equal to the Time of the
Deſcent A E, is greater than A E, but leſſe than double the ſame A E.
Let E D be equal to A E, and as E B is to B D, ſo let D B be to B F. It
ſhall be proved, firſt that the point F is the Term at which the Moveable
with a Reflex Motion along E B arriveth in a Time equal to the Time
A E: And then, that E F is greater than E A, but leſſe than double the
ſame. If we ſuppoſe the Time of the Deſcent along A E to be as A E,
the Time of the Deſcent along B E, or Aſcent along E B ſhall be as the
ſame Line B E: And D B being a Mean-Proportional betwixt E B
and B F, and B E being the Time of Deſcent along the whole B E, B D
ſhall be the Time of the Deſcent along B F, and the Remaining part
D E the Time of the
122[Figure 122]
Deſcent along the Re­
maining part F E: But
the Time along F E ex
quiete in B, and the
Time of the Aſcent a­
long E F is the ſame, ſince that the Degree of Velocity in E was acqui­
red along the Deſcent B E, or A E: Therefore the ſame Time D E ſhall
be that in which the Moveable after the Fall out of A along A E,
with a Reflex Motion along E B ſhall reach to the Mark F: But it hath
been ſuppoſed that E D is equal to the ſaid A E: Which was firſt to be
proved. And becauſe that as the whole E B is to the whole B D, ſo is the
part taken away D B to the part taken away B F, therefore, as the whole
E B is to the whole B D, ſo ſhall the Remainder E D be to D F:
But E B is greater than B D: Therefore E D is greater than D F, and
E F leſſe than double to D E or A E: Which was to be proved.
1
And the ſame alſo hapneth if the precedent Motion be not made
along the Perpendicular, but along an Inclined Plane; and the Demon­
ſtration is the ſame, provided that the Reflex Plane be leſſe riſing, that is,
longer than the declining Plane.
THEOR. XVI. PROP. XXV.
If after the Deſcent along any Inclined Plane a
Motion follow along the Plane of the Hori­
zon, the Time of the Deſcent along the Incli­
ned Plane ſhall be to the Time of the Motion
along any Horizontal Line; as the double
Length of the Inclined Plane is to the Line ta­
ken in the Horizon.
Let the Horizontal Line be C B, the inclined Plane A B, and after
the Deſcent along A B let a Motion follow along the Horizon, in
which take any Space B D. I ſay, that the Time of the Deſcent
along A B to the Time of the Motion along B D is as the double of A B
to B D. For B C being ſuppoſed
the double of A B, it is manifeſt by
123[Figure 123]
what hath already been demonſtra­
ted that the Time of the Deſcent
along A B is equal to the Time of
the Motion along B C: But the
Time of the Motion along B C is to
the Time of the Motion along B D, as the Line C B is to the Line B D:
Therefore the Time of the Motion along A B is the Time along B D, as
the Double of A B is to B D: Which was to be proved.
PROBL X. PROP. XXVI.
A Perpendicular between two Horizontal Paral­
lel Lines, as alſo a Space greater than the ſaid
Perpendicular, but leſſe than double the ſame,
being given, to raiſe a Plane between the ſaid
Parallels from the loweſt Term of the Per­
pendicular, along which the Moveable may
with a Reflex Motion after the Fall along the
Perpendicular paſſe a Space equal to the Space
given, and in a Time equal to the Time of the
Fall along the Perpendicular.
1
Let A B be a Perpendicular between the Horizontal Parallels A O
and B C; and let F E be greater than B A, but leſſe than double
the ſame. It is required between the ſaid Parallels from the point
B to raiſe a Plane, along which the Moveable after the Fall from A to
B may with a Reflex Motion in a Time equal to the Time of the Fall
along A B paſſe a Space aſcending equal to the ſaid E F. Suppoſe E D
equall to A B, the Remaining Part D F ſhall be leſſe, for that the whole
E F is leſſe than double to A B: Let D I be equal to D F, and as E I is
to I D, ſo let D F be to another Space F X, and out of B let the Right-
124[Figure 124]
Line B O be reflected, equal to E X. I ſay, that the Plane along B O
is that along which after the Fall A B a Moveable in a Time equal
to the Time of the Fall along A B paſſeth aſcending a Space equal to
the given Space E F. Suppoſe B R and R S equal to the ſaid E D and
D F. And becauſe that as E I is to I D, ſo is D F to F X; therefore,
by Compoſition, as E D is to D I, ſo ſhall D X be to X F; that is, as
E D is to D F, ſo ſhall D X be to X F, and E X to X D; that is, as
B O is to O R, ſo ſhall R O be to O S: And if we ſuppoſe the Time
along A B to be A B, the Time along O B ſhall be the ſame O B, and
R O the Time along O S, and the Remaining Part B R the Time along
the Remaining Part S B, deſcending from O to B: But the Time of
the Deſcent along S B from Rest in O, is equal to the Time of the
Aſcent from B to S after the Fall A B: Therefore B O is the Plane ele­
vated from B, along which after the Fall along A B the Space B S
equal to the given Space E F is paſſed in the Time B R or B A: Which
was required to be done.
1
THEOR. XVII. PROP. XXVII.
If a Moveable deſcend along unequal Planes,
whoſe Elevation is the ſame, the Space that
ſhall be paſt along the lower part of the longeſt
in a Time equal to that in which the whole
ſhorter Plane is paſſed, is equal to the Space
that is compounded of the ſaid ſhorter Plane
and of the part to which that ſhorter Plane
hath the ſame Proportion that the longer
Plane hath to the Exceſſe by which the longeſt
exceedeth the ſhorteſt.
Let A C be the longer Plane, and A B the ſhorter, whoſe Elevation
A D is the ſame; and in the lower part of A C take the Space
C E, equal to the ſaid A B; and as C A is to A E, (that is to
the exceſſe of the Plane C A above A B) ſo let C E be to E F. I ſay,
that the Space F C is that which is paſt after the Deſcent out of A in
a Time equal to the Time of
125[Figure 125]
the Deſcent along A B. For
the whole C A, being to the
whole A E, as the part taken
away C E is to the part taken
away E F, therefore the re­
maining part E A ſhall be to
the remaining part A F, as the
whole C A is to the whole A E: Therefore the three Spaces C A,
A E, and A F are three Continual proportionals. And if the Time
along A B be ſuppoſed to be as A B, the Time along A C ſhall be as
A C, and the Time along A F ſhall be as A E, and along the remain­
ing part F C ſhall be as E C: But E C is equal to the ſaid A B: There­
fore the Propoſition is manifeſt.
THEOR. XVIII. PROP. XXVIII.
Let the Horizontal Line A G be Tangent to a Circle, and from the
point of Contact let A B be the Diameter, and A E B two Chords
at pleaſure: We are to aſſign the proportion of the Time of the
Fall along A B to the Time of the Deſcent along both the Chords
A E B. Let B E be continued out till it meet the Tangent in G, and
1let the Angle B A E be cut in two equal parts, and draw A F. I ſay,
that the Time along A B is to the Time along A E B, as A E is to A E F.
For in regard the Angle F A B is equal to the Angle F A E, and the An­
gle E A G to the Angle A B F, the whole Angle G A F ſhall be equal to
the two Angles F A B, and A B F;
to which alſo the Angle G F A
126[Figure 126]
is equal: Therefore the Line G F
is equal to G A. And becauſe the
Rectangle B G E is equal to the
Square of G A, it ſhall likewiſe
be equal to the Square of G F, and
the three Lines B G, G F, and
G E ſhall be proportionals. And
if we ſuppoſe A E to be the Time
along A E, G E ſhall be the Time
along G E, and G F the Time along the whole G B, and E F the Time
along E B, after the Deſcent out of G, or out of A, along A E: The Time,
therefore, along A E, or along A B ſhall be to the Time along A E B, as
A E is to A E F: Which was to be determined.
More briefly thus. Let G F be cut equal to G A: It is manifeſt
that G F is the Mean-proportional between B G, and G E. The reſt as
before.
PROBL. XI. PROP. XXIX.
Any Horizontal Space being given upon the
end of which a Perpendicular is erected,
in which a part is taken equal to half of the
Space given in the Horizontal a Moveable fal­
ling from that height, and turned along the
Horizon, ſhall paſſe the Horizontal Space to­
gether with the Perpendicular in a ſhorter
Time than any other Space of the Perpendi­
cular with the ſame Horizontal Space.
Let there be an Horizontal Space in which let any Space be given
B C, and on B let there be a Perpendicular erected, in which let
B A be the half of the foreſaid B C. I ſay, that the Time in which
a Moveable let fall out of A paſſeth both the Spaces A B and B C is the
ſhorteſt of all Times in which the ſaid Space B C with a part of the
Perpendicular, whether greater or leſſer than the part A B, ſhall be paſ­
ſed. Let a greater be taken, as in the ſirſt Figure, or leſſer, as in the
1ſecond, which let be E B. It is to be proved that the Time in which the
Spaces E B and B C are paſſed is longer than the Time in which A B
and B C are paſſed. Let the Time along A B be as A B; the ſame ſhall
be the Time of the Motion along the Horizontal Space B G; becauſe
B C is double to A B, and the Time along both the Spaces A B C ſhall
be double of O B A. Let B O
127[Figure 127]
be a Mean-proportional between
E B and B A. B O ſhall be the
Time of the Fall along E B.
Again, let the Horizontal Space
B D be double to the ſaid B E:
It is manifeſt that the Time of it
after the Fall E B is the ſame
B O. As D B is to B C, or as
E B is to B A, ſo let O B be to
B N: and in regard the Motion
along the Horizontal Plane is Equable, and O B being the Time along
B D after the Fall out of E, therefore N B ſhall be the Time along B C
after the Fall from the ſame Altitude E. Hence it is manifeſt, that O B,
together with B N is the Time along E B C; and becauſe the double of
B A is the Time along A B C; it remains to be proved, that O B, to­
gether with B N is more than double B A. Now becauſe O B is a Mean
between E B and B A, the proportion of E B to B A is double the pro­
portion of O B to B A: and, in regard that E B is to B A, as O B is to
B N, the proportion of O B to B N ſhall alſo be double the proportion of
O B to B A: But that proportion of O B to B N is compounded of the
proportions of O B to B A, and of A B to B N: therefore the proportion
of A B to B N is the ſame with that of O B to B A. Therefore B O,
B A, and B N are three continual Proportionals, and O B, together with
B N, are greater than double B A: Whereupon the Propoſition is ma­
nifeſt.
1
THEOR. XIX. PROP. XXX.
If a Perpendicular be let fall from any point of the
Horizontal Line, and out of another point in
the ſame Horizontal Line a Plane be drawn
forth untill it meet the Perpendicular, along
which a Moveable deſcendeth in the ſhorteſt
time unto the ſaid Perpendicular, this Plane
ſhall be that which cutteth off a part equall to
the diſtance of the aſſigned point from the end
of the Perpendicular.
Let the Perpendicular B D be let fall from the point B of the Ho­
rizontal Line A C, in which let there be any point C, and in the
Perpendicular let the Diſtance B E be ſuppoſed equal to the Di­
ſtance B C, and draw C E. I ſay, that of all Planes inclined out of
the point C till they meet the Perpendicular C E is that, along which
in the ſhorteſt of all Times the Deſcent
128[Figure 128]
is made unto the Perpendicular. For
let the Planes C F and C G be inclined
above and below, and draw I K a Tan­
gent unto the Semidiameter B C of the
deſcribed Circle in C, which ſhall be
equidiſtant from the Perpendicular;
and unto the ſaid C F let E K be Paral­
lel cutting the Circumference of the Cir­
cle in L: It is manifeſt that the Time of
the Deſcent along L E is equal to the
Time of the Deſcent along C E: But
the Time along K E is longer than along
L E: Therefore the Time along K E is
longer than that along C E: But the
Time along K E is equal to the Time a­
long C F, they being equal, and drawn
according to the ſame Inclination: Likewiſe ſince C G, and I E are
equal, and inclined according to the ſame Inclination, the Times of the
Motions along them ſhall be equal: But H E being ſhorter than I E, the
Time along it is alſo ſhorter than I E: Therefore the Time alſo along
C E, (which is equal to the Time along H E) ſhall be ſhorter than the
Time along I E: The Propoſition, therefore, is manifeſt.
1
THEOR. XX. PROP. XXXI.
If a Right-Line ſhall be in any manner inclined
upon the Horizontal Line, the Plane produced
from a given point in the Horizon untill it
meet with the Inclined Plane, along which
the Deſcent is made in the ſhorteſt of all
Times, is that which ſhall divide the Angle
contained between the two Perpendiculars
drawn from the given Point, the one unto the
Horizontal Line, the other to the Inclined
Line, into two equal parts.
Let C D be a Line inclined in any manner upon the Hori­
zontal Line A B, and let any point A be given in the Hori­
zon, and from it let A C be drawn Perpendicular to A B,
and A E Perpendicular to C D, and let the Line F A divide the
Angle C A E into two equal parts. I ſay, that of all Planes incli­
ned out of any point of the Line C D to the point A that ſame pro­
duced along F A is it along
129[Figure 129]
which the Deſcent is made in
the ſhorteſt of all Times. Let
F G be drawn Parallel to AE;
the alternate Angles G F A
and F A E ſhall be equal: But
E A F is equal to that other
F A G: Therefore of the Tri­
angle the Sides F G and G A
ſhall be equal. If therefore
about the Center G, at the di­
ſtance G A, a Circle be deſcri­
bed it ſhall paſſe by F, and ſhall
touch the Horizontal, and the Inclined Lines in the points A and F:
For the Angle G F C is a Right Angle, and likewiſe G F is equidiſtant
to A E: Whence it is manifeſt that all Lines produced from the point
A unto the inclined Plane do extend beyond the Circumference, and,
which followeth of conſequence, that the Motions along the ſame do
take up more Time than along F A. Which was to be demonſtrated.
1
LEMMA.
If two Circles touch one another within, the innermoſt of which
toucheth ſome Right Line, and the exteriour one cutteth it,
three Lines produced from the Contact of the Circles unto
three points of the Tangent Right-Line, that is, to the Con­
tact of the interiour Circle, and to the Sections of the exte­
riour ſhall contain equall Angles in the Contact of the
Circles.
Let two Circles touch one another in the point A, of which let the
Centers be B, that of the leſſer, and C that of the greater; and let
the interiour Circle touch any Line F G in the point H, and let the grea­
ter cut it in the points F and G, and connect the three Lines A F, A H,
and A G. I ſay, that the Angles by
130[Figure 130]
them contained F A H and G A H are
equal. Produce A H untill it meeteth
the Circumference in I, and from the
Centers draw B H and C I, and thorow
the ſaid Centers let B C be drawn,
which continued forth ſhall meet with
the Contact A, and with the Circum­
ferences of the Circles in O and N.
And becauſe the Angles I C N and
H O B are equal, for as much as either
of them is double to the Angle I A N,
the Lines B H and C I ſhall be Parallels: And becauſe B H drawn
from the Center to the Contact is Perpendicular to F G; C I ſhall alſo be
Perpendicular to the ſame, and the Arch F I equal to the Arch I G, and,
which followeth of conſequence, the Angle F A I to the Angle I A G:
Which was to be demonſtrated.
1
THEOR. XXI. PROP. XXXII.
If two points be taken in the Horizon, and any
Line ſhould be inclined from one of them to­
wards the other, out of which a Right-Line is
drawn unto the Inclined Line, cutting off a
part thereof equal to that which is included
between the points of the Horizon, the De­
ſcent along this laſt drawn ſhall be ſooner per­
formed, than along any other Right Lines pro­
duced from the ſame point unto the ſaid Incli­
ned Line. And along other Lines which are
on each hand of this by equal Angles a De­
ſcent ſhall be made in equal Times.
In the Horizon let there be two points A and B, and from B incline
the Right Line B C, in which from the Term B take B D equal to
the ſaid B A, and draw a Line from A to D. I ſay, that the De­
ſcent along A D is more ſwiftly made, than along any other whatſoever
drawn from the point A unto the inclined Line B C. For out of the
points A and D unto B A and
131[Figure 131]
B D draw the Perpendiculars
A E and D E, interſecting one
another in E: and foraſmuch as
in the equicrural Triangle A B D
the Angles B A D and B D A
are equal, the remainders to the
Right-Angles D A E and E D A
ſhall be equal. Therefore a Circle
deſcribed about the Center E at
the diſtance A E ſhall alſo paſſe
by D; and the Lines B A and
B D will touch it in the points A
and D. And ſince A is the end of the Perpendicular A E, the Deſcent
along A D ſhall be ſooner performed, than along any other produced from
the ſame Term A unto the Line B C beyond the Circumference of the
Circle: Which was firſt to be proved.
But if in the Perpendicular A E being prolonged any Center be taken as
F, and at the diſtance F A the Circle A G C be deſcribed cutting the
Tangent Line in the points G and C; drawing A G and A C they ſhall
make equal Angles with the middle Line A D by what hath been afore
1demonſtrated, and the Motions thorow them ſhall be performed in equal
Times ſeeing that they terminate in A unto the Circumference of the
Circle A G O from the higheſt point of it A.
PROBL. XII. PROP. XXXIII.
A Perpendicular and Plane inclined to it being
given, whoſe height is one and the ſame, as al­
ſo the higheſt term, to find a point in the Per­
pendicular above the common term, out of
which if a Moveable be demitted that ſhall
afterwards turn along the inclined Plane, the
ſaid Plane may be paſt in the ſame Time in
which the Perpendicular ex quiete would be
paſſed.
Let the Perpendicular and inclined Plane, whoſe Altitude is the
ſame, be A B and A C. It is required in the Perpendicular B A,
continued out from the point A to find a Point out of which a
Moveable deſcending may paſſe the Space A C in the ſame Time in
which it will paſſe the ſaid Perpendicular A B out of Reſt in A. Draw
D C E at Right-Angles to A C, and let C D be cut equal to A B, and
draw a Line from A to D: The Angle A D C ſhall be greater than the
Angles C A D: (for C A is greater than A B or C D:) Let the
Angle D A E be equal to the Angle A D E; and to A E let E F an in­
clined Plane be Perpen-
132[Figure 132]
dicular, and let both be­
ing prolonged meet in F,
and unto both A I and
A G ſuppoſe C F to be
equal, and by G draw
G H equidiſtant to the
Horizon. I ſay, that H
is the point which is
ſought. For ſuppoſing the
Time of the Fall along
the Perpendicular A B
to be A B, the Time along
A C ex quiete in A ſhall be the ſame A C. And becauſe in the Right­
angled Triangle A E F, from the Right Angle E unto the Baſe A F,
E C is a Perpendicular, A E ſhall be a Mean-Proportional betwixt F A
and A C, and C E a Mean betwixt A C and C F, that is, betwixt C A
and A I: and foraſmuch as the Time of A C out of A is A C, A E
1ſhall be the Time of the whole A F, and E C the Time of A I: And be­
cauſe in the Equicrural Triangle A E D the Side A E is equal to the
Side E D, E D ſhall be the Time along A F, and E C is the Time along
A I: Therefore C D, that is A B ſhall be the Time along A F ex qui­
ete in A; which is the ſame as if we ſaid, that A B is the Time along
A G out of G, or out of H: Which was to be done.
PROBL. XIII. PROP. XXXIV.
An inclined Plane and Perpendicular whoſe ſub­
lime term is the ſame being given, to find a
more ſublime point in the Perpendicular pro­
longed out of which a Moveable falling, and
being turned along the inclined Plane, may
paſſe them both in the ſame Time, as it doth
the ſole inclined Plane ex quiete in its ſuperi­
our Term.
Let the inclined Plane and Perpendicular be A B and A C, whoſe
Term A is the ſame. It is required in the Perpendicular prolonged
from A to find a ſublime point, out of which the Moveable deſcen­
ding, and being turned along the Plane A B, may paſſe the aſſigned part
of the Perpendicular and the Plane A B in the ſame Time, as it would the
ſole Plane A B out of Reſt in A.
133[Figure 133]
Let the Ho­
rizontal Line
be B C, and
let A N be
cut equal to
A C; and as
A B is to B N,
ſo let A L be
to L C: and
unto A L let
A I be equal,
and unto A C
and B I let C
E be a third
proportional,
marked in the
Perpendicular A C produced. I ſay, that C E is the Space acquired;
ſo that the Perpendicular being extended above A, and the part A X
equal to C E being taken, a Moveable out of X will paſſe both the
1Spaces X A B in the ſame Time as it would the ſole Space A B out of A.
Draw the Horizontal Line X R Parallel to B C, with which let B A
being prolonged meet in R, and then A B being continued out unto D
draw E D Parallel to C B, and upon A D deſcribe a Semicircle, and
from B, and Perpendicular to D A, erect B F till it meet with the Cir­
cumference. It is manifeſt that F B is a Mean-proportional betwixt
A B and B D, and that the Line drawn from F to A is a Mean-propor­
tional betwixt D A and A B. Suppoſe B S equal to B I, and F H equal
to F B: And becauſe, as A B is to B D, ſo is A C to C E, and becauſe
B F is a Mean-proportional betwixt A B and B D, and becauſe B I is a
Mean-proportional betwixt A C and C E; therefore as B A is to A C,
ſo is F B to B S. And becauſe as B A is to A C, or A N, ſo is F B to
B S, therefore, by Converſion of the proportion, B F is to F S, as A B is
to B N, that is, A L to L C; therefore the Rectangle under F B and
C L, is equal to the Rectangle under A L, and S F: But this Rectangle
A L, and S F, is the exceſſe of the Rectangle under A L and F B, or A I
and B F, over and above the Triangle A I and B S, or A I B; and the
Rectangle F B and L C is the exceſſe of the Rectangle A C and B F
over and above the Rectangle A L and B F: But the Rectangle A C and
B F is equal to the Rectangle A B I; (for as B A is to A C, ſo is F B to
B I:) The exceſſe, therefore, of the Rectangle A B I above the Rectan­
gle A I and B F, or A I and F H, is equal to the exceſſe of the Rectangle
A I and F H above the Rectangle A I B: Therefore twice the Rectan­
gle A I and F H is equal to the two Rectangles A B I and A I B; that
is twice A I B with the Square of B I. Let the Square A I be common
to both, and twice the Rectangle A I B with the two Squares A I, and
I B, (that is, the Square A B) ſhall be equal to twice the Rectangle
A I and F H, with the Square A I: Again, taking in commonly the
Square B F; the two Squares A B and B F, that is the ſole Square A F
ſhall be equal to twice the Rectangle A I and F H, with the two Squares
A I and F B, that is A I and F H: But the ſame Square A F is equal
to twice the Rectangle A H F, with the two Squares A H and H F:
Therefore twice the Rectangle A I and F H, with the Squares A I and
F H, are equal to twice the Rectangle A H F, with the Squares A H
and H F: And, the Common Square H F being taken away, twice the
Rectangle A I and F H, with the Square A I, ſhall be equal to twice the
Rectangle A H F, with the Square A H. And becauſe that in all the
Rectangles F H is the Common Side, the Line A H ſhall be equal to A I:
For if it ſhould be greater or leſſer, then the Rectangles F H A and the
Square H A would alſo be greater or leſſer than the Rectangles F H and
I A, and the Square I A: Contrary to what hath been demonſtrated.
Now if we ſuppoſe the Time of the Deſcent along A B to be as A B,
the Time along A C ſhall be as A C, and I B the Mean-proportional be­
twixt A C and C E ſhall be the Time along C E, or along X A from
Reſt in X: And becauſe betwixt D A and A B, or R B and B A the
1Mean-proportional is A F, and between A B and B D, that is, R A and
A B the Mean is B F, to which F H is equal; Therefore, exprædemon­
ſtratis, the exceſſe A H ſhall be the Time along A B ex quiete in R, or
after the Fall out of X; ſince the Time along the ſaid A B ex quiete in
A, ſhall be A B. Therefore the Time along X A is I B; and along A B
after R A, or after X A, is A I: Therefore the Time along X A B ſhall
be as A B, namely the ſelf-ſame with the Time along the ſole A B ex qui­
ete in A. Which was the Propoſition.
PROBL. XIV. PROP. XXXV.
An Inflected Line unto a given Perpendicular be­
ing aſſigned, to take part in the Inflected Line,
along which alone ex quiete a Motion may be
made in the ſame Time, as it would be along
the ſame together with the Perpendicular.
Let the Perpendicular be A B, and a Line inflected to it B C. It is
required in B C to take a part, along which alone out of Reſt a
Motion may be made in the ſame Time as it would along the ſame
together with the Perpendicular A B. Draw the Horizon A D, with
which let the Inclined Line C B prolonged meet in E; and ſuppoſe B F
equal to B A, and on the Center E at the diſtance E F deſcribe the Circle
F I G; and continue out F E unto the Circumference in G; and as G B
is to B F, ſo let B H be to H F; and let H I touch the Circle in I. Then
out of B erect B K
134[Figure 134]
Perpendicular to
F C, with which
let the Line E I L
meet in L; and laſt
of all let fall L M
Perpendicular to E
L, meeting B C in
M. I ſay, that along
the Line B M from
Rest in B a Motion
may be made in the
ſame Time, as it
would be ex quiete in A along both A B and B M. Let E N be made
equal to E L. And becauſe as G B is to B F, ſo is B H to H F; there­
fore, by Permutation as G B is to B H, ſo will B F be to F H; and, by
Diviſion, G H ſhall be to H B, as B H is to H F: Wherefore the Rect­
angle G H F ſhall be equal to the Square H B: But the ſaid Rectangle
is alſo equal to the Square H I: Therefore B H is equal to the ſame H I.
1And becauſe in the Quadrilateral Figure I L B H the Sides H B and
H I are equal, and the Angles B and I Right Angles, the Side B L ſhall
likewiſe be equal to the Side L I: But E I is equal to E F: Therefore the
whole Line L E, or N E is equal to the two Lines L B and E F: Let
the Common Line E F be taken away, and the remainder F N ſhall be
equal to L B: And F B was ſuppoſed equal to B A: Therefore L B ſhall
be equal to the two Lines A B and B N. Again, if we ſuppoſe the
Time along A B to be the ſaid A B, the Time along E B ſhall be equal to
E B; and the Time along the whole E M ſhall be E N, namely, the
Mean-proportional betwixt M E and E B: I berefore the Time of the
Deſcent of the remaining part B M after E B, or after A B, ſhall be the
ſaid B N: But it hath been ſuppoſed, that the Time along A B is A B:
Therefore the Time of the Fall along both A B and B M is A B N:
And becauſe the Time along E B ex quiete in E is E B, the Time along
B M ex quiete in B ſhall be the Mean-proportional between B E and
B M; and this is B L: The Time, therefore, along both A B M ex quiete
in A is A B N: And the Time along B M only ex quiete in B is B L:
But it was proved that B L is equal to the two A B and B N: Therefore
the Propoſition is manifeſt.
Otherwiſe with more expedition.
Let B C be the Inclined Plane, and B A the Perpendicular. Continue
out C B to E, and unto E C erect a Perpendicular at B, which being
prolonged ſuppoſe B H equal to the exceſſe of B E above B A; and to the
Angle B H E let the Angle H E L be equal; and let E L continued out
meet with B K in L; and from L erect the Perpendicular L M unto E L
meeting B C in M. I ſay, that
135[Figure 135]
B M is the Space acquired in
the Plane B C. For becauſe
the Angle M L E is a Right­
Angle, therefore B L ſhall be
a Mean-proportional betwixt
M B and B E; and L E a
Mean proportional betwixt M
E and E B; to which E L let
E N be cut equal: And the
three Lines N E, E L, and
L H ſhall be equal; and H B ſhall be the exceſſe of N E above B L: But
the ſaid H B is alſo the exceſſe of N E above N B and B A: Therefore
the two Lines N B and B A are equal to B L. And if we ſuppoſe E B
to be the Time along E B, B L ſhall be the Time along B M ex quiete in
B; and B N ſhall be the Time of the ſame B M after E B or after A B;
and A B ſhall be the Time along A B: Therefore the Times along A B M,
namely, A B N, are equal to the Times along the ſole Line B M ex quiete
in B: Which was intended.
1
LEMMAI.
Let D C be Perpendicular to the Diameter B A; and from the Term
B continue forth B E D at pleaſure, and draw a Line from F to B. I
ſay, that F B is a Mean-proportional be-
136[Figure 136]
twixt D B and B E. Draw a Line from E
to F, and by B draw the Tangent B G;
which ſhall be Parallel to the former C D:
Wherefore the Angle D B G ſhall be equal
to the Angle F D B, like as the ſame G B D
is equal alſo to the Angle E F B in the al­
tern Portion or Segment: Therefore the
Triangles F B D and F E B are alike: And,
as B D is to B F, ſo is F B to B E.
LEMMA II.
Let the Line A C be greater than D F; and let A B have greater
proportion to B C, than D E hath to E F. I ſay, that A B is greater
than D E. For becauſe A B hath to B C
137[Figure 137]
greater proportion than D E hath to D F,
therefore look what proportion A B hath to
B C, the ſame ſhall D E have to a Line leſ­
ſer than E F; let it have it to E G: And
becauſe A B to B C, is as D E, to E G, there­
fore, by Compoſition, and by converting the Proportion, as C A is to A B,
ſo is G D to D E: But C A is greater than G D: Therefore B A ſhall
be greater than D E.
LEMMA III.
138[Figure 138]
Let A C I B be the Quadrant of a Circle:
and to A C let B E be drawn from B Pa­
rallel: And out of any Center taken in the
ſame deſcribe the Circle B O E S, touching
A B in B, and cutting the Circumference of
the Quadrant in I; and draw a Line from
C to B, and another from C to I continued
out to S. I ſay, that the Line C I is alwaies
leſſe than C O. Draw a Line from A to I;
which toucheth the Circle B O E. And if
D I be drawn it ſhall be equal to D B: And
becauſé D B toucheth the Quadrant, the ſaid
D I ſhall likewiſe touch it; and ſhall be Per-
1pendicular to the Diameter A I: Wherefore alſo A I toucheth the Cir­
cle B O E in I. And, becauſe the Angle A I C is greater than the An­
gle A B C, as inſiſting on a larger Periphery: Therefore the Angle
S I N ſhall be alſo greater than the ſame A B C: Therefore the Portion
I E S is greater than the Portion B O; and the Line C S, nearer to the
Center, greater than C B: Therefore alſo C O is greater than C I;
for that S C is to C B, as O C is to C I.
And the ſame alſo would happen to be greater, if (as in the other
Figure) the Quadrant B I C were
139[Figure 139]
leſſer: For the Perpendicular D B
will cut the Circle C I B: Wherefore
D I alſo is equal to the ſaid D B; and
the Angle D I A ſhall be Obtuſe, and
therefore A I N will alſo cut B I N:
And becauſe the Angle A B C is leſſe
than the Angle A I C, which is equal
to S I N; and this now is leſſe than that
which would be made at the Contact in
I by the Line S I: Therefore the Porti­
on S E I is much greater than the Por­
tion B O: Wherefore, &c. Which was
to be demonſtrated.
THEOR. XXII. PROP. XXXVI.
If from the loweſt point of a Circle erect unto
the Horizon a Plane ſhould be elevated ſub­
tending a Circumference not greater than a
Quadrant, from whoſe Terms two other
Planes are Inflected to any point of the Cir­
cumference, the Deſcent along both the Infle­
cted Planes would be performed in a ſhorter
Time than along the former elevated Plane
alone, or than along but one of the other two,
namely, along the lower.
Let C B D be the Circumference not greater than a Quadrant of a
Circle erect unto the Horizon on the lower point C, in which let
C D be an elevated Plane; and let two Planes be inflected from the
Terms D and C to any point in the Circumference taken at pleaſure,
as B. I ſay, that the Time of the Deſcent along both thoſe Planes D B C
is ſhorter than the Time of the Deſcent along the ſole Plane D C, or
along the other only B C ex quiete in B. Let the Horizontal Line M D A
1be drawn by D, with which let C B prolonged meet in A; and let fall
the Perpendiculars D N and M C to M D, and B N to B D; and about
the Right-angled Triangle D B N deſcribe the Semicircle D F B N,
cutting D C in F; and let D O be a Mean-proportional betwixt C D
and D F; and A V a Mean-proportional betwixt C A and A B: And
let P S be the time in which the whole D C, or B C, ſhall be paſſed;
(for it is manifeſt that they ſhall be both paſt in the ſame Time;) And
look what proportion C D hath to D O, the ſame ſhall the Time S P
have to the Time P R: the Time P R ſhall be that in which a Movea­
ble out of D will paſſe D F; and R S that in which it ſhall paſſe the re­
mainder F C. And becauſe P S is alſo the Time in which the Movea­
ble out of B ſhall paſſe B C; if it be ſuppoſed that as B C is to C D, ſo is
S P to P T, P T ſhall be the Time of the Deſcent out of A to C: by
reaſon D C is a Mean-proportional betwixt A C and C B, by what was
before demonſtrated: Laſt of all, as C A is to A V, ſo let T P be to
140[Figure 140]
P G: P G ſhall be the Time,
in which thé Moveable out
of A deſcendeth to B. And
becauſe of the Circle D F N
the Diameter erect to the
Horizon is D N, the Lines
D F and D B ſhall be paſ­
ſed in equal Times. So that
if it ſhould be demonſtra­
ted that the Moveable would
ſooner paſſe B C after the
Deſcent D B, than F C after the Lation D F; we ſhould have our in­
tent. But the Moveable will with the ſame Celerity of Time paſſe B C
coming out of D along D B, as if it came out of A along A B: for that
in both the Deſcents D B and A B it acquireth equal Moments of Velo­
city: Therefore it ſhall reſt to be demonſtrated that the Time is ſhorter
in which B C is paſſed after A B, than that in which F C is paſt after
D F. But it hath been demonſtrated, that the Time in which B C is
paſſed after A B is G T; and the Time of F C after D F is R S. It is
to be proved therefore, that R S is greater than G T: Which is thus
done. Becauſe as S P is to P R, ſo is C D to D O, therefore, by Conver­
ſion of proportion, and by Inverſion, as R S is to S P, ſo is O C to C D:
and as S P is to P T, ſo is D C to C A: And, becauſe as T P is to PG,
ſo is C A to A V: Therefore alſo, by Converſion of the proportion, as
P T is to T G, ſo is A C to C V: therefore, ex equali, as R S is to G T,
ſo is O C to C V. But O C is greater than C V, as ſhall anon be de­
monſtrated: Therefore the Time R S is greater than the Time G T:
Which it was required to demonſtrate. And becauſe C F is greater than
C B, and F D leſſe than B A, therefore C D ſhall have greater propor­
tion to D F than C A to A B: And as C D is to D F, ſo is the Square
1C O to the Square O F; foraſmuch as C D, D O, and O F are Propor­
tionals: And as C A is to A B, ſo is the Square C V to the Square
V B: Therefore C O hath greater proportion to O F, than C V to V B:
Therefore, by the foregoing Lemma, C O is greater than C V. It is
manifeſt moreover, that the Time along D C is to the Time along
D B C, as D O C is to D O together with C V.
SCHOLIUM.
From theſe things that have been demonſtrated may evidently
be gathered, that the ſwifteſt of all Motions betwixt Term
and Term is not made along the ſhorteſt Line, that is by the
Right, but along a portion of a Circle.
For in the Quadrat B A E C, whoſe Side B C is erect to the Hori­
zon, let the Arch A C be divided into any number of equal parts,
A D, D E, E F, F G, G C; and let Right-lines be drawn from C to
the Points A, D, E, F, G, H; and alſo by Lines joyn A D, D E, E F,
F G. and G C. It is manifest, that the Motion along the two Lines
A D C is ſooner performed than along the
141[Figure 141]
ſole Line A C, or D C out of Reſt in D:
But out of Reſt in A, D C is ſooner paſt
than the two A D C: But along the two
D E C out of Reſt in A the Deſcent is
likewiſe ſooner made than along the ſole
C D: Therefore the Deſcent along the
three Lines A D E C ſhall be performed
ſooner than along the two A D C. And
in like manner the Deſcent along A D E
preceding, the Motion is more ſpeedily con­
ſummated along the two EFC than along the ſole FC: Therfore along the
four A D E F C the Motion is quicklier accompliſhed than along the
three A D E C: And ſo, in the laſt place, along the two F G C after the
precedent Deſcent along A D E F the Motion will be ſooner conſumma­
ted than along the ſole F C: Therefore along the five A D E F G C
the Deſcent ſhall be effected in a yet ſhorter Time than along the four
A D E F C: Whereupon the nearer by inſcribed Poligons we approach
the Circumference, the ſooner will the Motion be performed between the
two aſſigned points A C.
And that which is explained in a Quadrant, holdeth true likewiſe
in a Circumference leſſe than the Quadrant: and the Ratiocination is
the ſame.
1
PROBL.XV. PROP. XXXVII.
A Perpendicular and Inclined Plane of the ſame
Elevation being given, to find a part in the In­
clined Plane that is equal to the Perpendicu­
lar, and paſſed in the ſame Time as the ſaid
Perpendicular.
LET A B be the Perpendicular, and A C the Inclined Plane. It is
required in the Inclined to find a part equal to the Perpendicular
A B, that after Reſt in A may be paſſed in a Time equal to the
Time in which the Perpendicular is paſſed. Let A D be equal to A B,
and cut the Remainder B C in two equal parts in I; and as A C is to
142[Figure 142]
C I, ſo let C I be to another Line
A E; to which let D G be equal: It
is manifeſt that E G is equal to A D
and to A B. I ſay moreover, that
this ſame E G is the ſame that is
paſſed by the Moveable coming out
of Reſt in A in a Time equal to the
Time in which the Moveable fall eth along A B. For becauſe that as
A C is to C I, ſo is C I to A E, or I D to D G; Therefore by Converſion
of the proportion, as C A is to A I, ſo is D I to I G. And becauſe as the
whole C A is to the whole A I, ſo is the part taken away C I to the part
I G; therefore the Remaining part I A ſhall be to the Remainder A G,
as the whole C A is to the whole A I: Therefore A I is a Mean-propor­
tional betwixt C A and A G; and C I a Mean-proportional betwixt
C A and A E: If therefore we ſuppoſe the Time along A B to be as A B;
A C ſhall be the Time along A C, and C I or I D the Time along A E:
And becauſe A I is a Mean-proportional betwixt C A and A G; and
C A is the Time along the whole A C: Therefore A I ſhall be the Time
along. A G; and the Remainder I C that along the Remainder G C: But
D I was the Time along A E: Therefore D I and I C are the Times
along both the Spaces A E and C G: Therefore the Remainder D A ſhall
be the Time along E G, to wit, equal to the Time along A B. Which was
to be done.
COROLLARIE.
Hence it is manifeſt, that the Space required is an intermedial be­
tween the upper and lower parts that are paſt in equal
Times.
1
PROBL. XVI. PROP. XXXVIII.
Two Horizontal Planes cut by the Perpendicular
being given, to find a ſublime point in the Per­
pendicular, out of which Moveables falling
and being reflected along the Horizontal
Planes may in Times equal to the Times of
the Deſcents along the ſaid Horizontal Planes,
namely, along the upper and along the lower,
paſſe Spaces that have to each other any given
proportion of the leſſer to the greater.
LET the Planes C D and B E be interſected by the Perpendicular
A C B, and let the given proportion of the leſſe to the greater be
N to F G. It is required in the Perpendicular A B to find a point
on high, out of which a Moveable falling, and reflected along C D may
in a Time equal to the Time of its Fall, paſſe a Space, that ſhall have
unto the Space paſſed by the other Moveable coming out of the ſame ſub­
lime point in a Time equal to the Time of its Fall with a Reflex Motion
along the Plane B E the ſame proportion as the given Line N batb to
143[Figure 143]
F G. Let G H be
made equal to the
ſaid N; and as F H
is to H G, ſo let
B C be to C L. I ſay,
L is the ſublime
point required. For
taking C M double
to C L, draw L M
meeting the Plane
B E in O; B O
ſhall be double to
B L: And becauſe,
as F H is to H G, ſo is B C to C L; therefore, by Compoſition and In­
verſion, as H G, that is, N is to G F, ſo is C L to L B, that is, C M to
B O: But becauſe C M is double to L C; let the Space C M be that
which by the Moveable coming from L after the Fall L C is paſſed along
the Plane C D; and by the ſame reaſon B O is that which is paſſed after
the Fall L B in a Time equal to the Time of the Fall along L B; foraſ­
much as B O is double to B L: Therefore the Propoſition is manifeſt.
1
SAGR. Really me thinks that we may juſtly grant our Acade­
mian what he without arrogance aſſumed to himſelf in the begining
of this his Treatiſe of ſhewing us a New Science about a very old
Subject. And to ſee with what Facility and Perſpicuity he deduceth
from one ſole Principle the Demonſtrations of ſo many Propoſiti­
ons, maketh me not a little to wonder how this buſineſs eſcaped
unhandled by Archimedes, Apollonius, Euclid, and ſo many other
Illuſtrious Mathematicians and Phyloſophers: eſpecially ſince
there are found many great Volumns of Motion.
SALV. There is extant a ſmall Fragment of Euclid touching
Motion, but there are no marks to be ſeen therein of any ſteps that he
took towards the diſcovery of the Proportion of Acceleration, and
of its Varieties along different Inclinations. So that indeed one
may ſay, that never till now was the door opened to a new Con­
templation fraught with infinite and admirable Concluſions, which
in times to come may buſie other Wits.
SAGR. I verily believe, that as thoſe few Paſſions (I will ſay
for example) of the Circle demonſtrated by Euclid in the third of
his Elements are an introduction to innumerable others more ab­
ſtruce, ſo thoſe produced and demonſtrated in this ſhort Tractate,
when they ſhall come to the hands of other Speculative Wits, ſhall
be a manuduction unto infinite others mote admirable: and it is to
be believed that thus it will happen by reaſon of the Nobility of
the Argument above all others Phyſical.
This daies Conference hath been very long and laborious; in
which I have taſted more of the ſimple Propoſitions than of their
Demonſtrations; many of which, I believe, will coſt me more than
an hour a piece well to comprehend them: a task that I reſerve to
my ſelf to perform at leaſure, you leaving the Book in my hands ſo
ſoon as we ſhall have heard this part that remains about the Moti­
on of Projects: which ſhall, if you ſo pleaſe, be to morrow.
SALV. I ſhall not fail to be with you.
The End of the Third Dialogue.
1
GALILEUS,
HIS
DIALOGUES
OF
MOTION.
The Fourth Dialogue.
INTERLOCUTORS,
SALVIATUS, SAGREDUS, and SIMPLICIUS.
SALVIATUS.
Simplicius likewiſe cometh in the nick of time, therefore
without interpoſing any Reſt let us proceed to Motion;
and ſee here the Text of our Author.
OF THE MOTION OF
PROJECTS.
What accidents belong to Equable Motion, as alſo to the Na­
turally Accelerate along all whatever Inclinations of Planes,
we have conſidered above. In this Contemplation which we are now
entering upon, I will attempt to declare, and with ſolid Demonſtrations
1to eſtabliſh ſome of the principal Symptomes, and thoſe worthy of know­
ledge, which befall a Moveable whilſt it is moved with a Motion com­
pounded of a twofold Lation, to wit, of the Equable and Naturally­
Accelerate: and this is that Motion, which we call the Motion of Pro­
jects: whoſe Generation I constitute to be in this manner.
I fancy in my mind a certain Moveable projected or thrown along
an Horizontal Plane, all impediment ſecluded: Now it is manifeſt by
what we have elſewhere ſpoken at large, that that Motion will be Equa­
ble and Perpetual along the ſaid Plane, if the Plane be extended in in­
finitum: but if we ſuppoſe it terminate, and placed on high, the Move­
able, which I conceive to be endued with Gravity, being come to the end
of the Plane, proceeding forward, it addeth to the Equable and Indeli­
ble firſt Lation that propenſion downwards which it receiveth from its
Gravity, and from thence a certain Motion doth reſult compounded of
the Equable Horizontal, and of the Deſcending naturally. Accellerate
Lations: which I call Projection. Some of whoſe Accidents we will de­
monſtrate; the firſt of which ſhall be this.
THEOR.I. PROP.I.
A Project, when it is moved with a Motion compounded
of the Horizontal Equable, and of the Naturally­
Accelerate downwards, ſhall deſcribe a Semipara­
bolical Line in its Lation.
SAGR. It is requiſite, Salviatus, in favour of my ſelf, and, as I
believe, alſo of Simplicius, here to make a pauſe; for I
am not ſo far gone in Geometry as to have ſtudied Apol­
lonius, ſave only ſo far as to know that he treateth of theſe Para­
bola's, and of the other Conick Sections, without the knowledge
of which, and of their Paſſions, I do not think that one can under­
ſtand the Demonſtrations of other Propoſitions depending on
them. And becauſe already in the very firſt Propoſition it is pro­
poſed by the Author to prove the Line deſcribed by the Project to
be Parabolical, I imagine to my ſelf, that being to treat of none
but ſuch Lines, it is abſolutely neceſſary to have a perfect know­
ledge, if not of all the Paſſions of thoſe Figures that are demon­
ſtrated by Apollonius, at leaſt of thoſe that are neceſſary for the Sci­
ence in hand.
SALV. You undervalue your ſelf very much, to make ſtrange
of thoſe Notions, which but even now you admitted as very well
underſtood: I told you heretofore, that in the Treatiſe of Reſi­
ſtances we had need of the knowledge of certain Propoſitions of
1Apollonius, at which you made no ſeruple.
SAGR. It may be either that I knew them by chance, or that I
might for once gueſſe at, and take for granted ſo much as ſerved my
turn in that Tractate: but here where I imagine that we are to
hear all the Demonſtrations that concern thoſe Lines, it is not con­
venient, as we ſay, to ſwallow things whole, loſing our time and
pains.
SIMP. But as to what concerns me, although Sagredus were,
as I believe he is, well provided for his occaſions, the very firſt
Terms already are new to me: for though our Philoſophers have
handled this Argument of the Motion of Projects, I do not remem­
ber that they have confined themſelves to deſine what the Lines
are which they deſcribe, ſave only in general that they are alwaies
Curved Lines, except it be in Projections Perpendicularly upwards.
Therefore in caſe that little Geometry that I have learnt from Eu­
clid ſince the Time that we have had other Conferences, be not ſuf­
ficient to render me capable of the Notions requiſite for the under­
ſtanding of the following Demonſtrations, I muſt content my ſelf
with bare Propoſitions believed, but not underſtood.
SALV. But I will have you to know them by help of the Au­
thor of this Book himſelf, who when he heretofore granted me a
ſight of this his Work, becauſe I alſo at that time was not perfect
in the Books of Apollonius, took the pains to demonſtrate to me
two moſt principal Paſſions of the Parabola without any other Pre­
cognition, of which two, and no more, we ſhall ſtand in need in
the preſent Treatiſe; which are both likewiſe proved by Apollonius,
but after many others, which it would take up a long time to look
over, and I am deſirous that we may much ſhorten the Journey, ta­
king the firſt immediately from the pure and ſimple generation of
the ſaid Parabola, and from this alſo immediately ſhall be deduced
the Demonſtration of the ſecond. Coming therefore to the firſt;
Deſcribe the Right Cone, whoſe Baſe let be the Circle I B K C,
and Vertex the point L, in which, cut by a Plane parallel to the
144[Figure 144]
Side L K, ariſeth the Section B A C
called a Parabola; and let its Baſe
B C cut the Diameter I K of the
Circle I B K C at Right-Angles;
and let the Axis of the Parabola
A D be Parallel to the ſide L K;
and taking any point F in the Line
B F A, draw the Right-Line F E
parallel to B D. I ſay, that the Square
of B D hath to the Square of F E
the ſame proportion that the Axis
D A hath to the part A E. Let a Plane parallel to the Circle I B K C
1be ſuppoſed to paſſe by the Point E, which ſhall make in the Cone
a Circular Section, whoſe Diameter is G E H. And becauſe upon
the Diameter I K of the Circle I B K, B D is a Perpendicular, the
Square of B D ſhall be equal to the Rectangle made by the parts
I D and D K: And likewiſe in the upper Circle which is underſtood
to paſſe by the points G F H, the Square of the Line F E is equal
to the Rectangle of the parts G E H: Therefore the Square of B D
hath the ſame proportion to the Square of F E, that the Rectangle
I D K hath to the Rectangle G E H. And becauſe the Line E D is
Parallel to H K, E H ſhall be equal to D K, which alſo are Parallels:
And therefore the Rectangle I D K ſhall have the ſame proportion
to the Rectangle G E H, as I D hath to G E; that is, that D A hath
to A E: Therefore the Rectangle I D K to the Rectangle G E H,
that is, the Square B D to the Square F E, hath the ſame proportion
that the Axis D A hath to the part A E: Which was to be de­
monſtrated.
The other Propoſition, likewiſe neceſſary to the preſent Tract,
we will thus make out. Let us deſcribe the Parabola, of which let the
Axis C A be prolonged out unto D; and taking any point B, let the
Line B C be ſuppoſed to be continued out by the ſame Parallel un­
145[Figure 145]
to the Baſe of the ſaid Parabola;
and let D A be ſuppoſed equal
to the part of the Axis C A. I ſay,
that the Right-Line drawn by
the points D and B, falleth not
within the Parabola, but without,
ſo as that it only toucheth the
ſame in the ſaid point B: For, if
it be poſſible for it to fall within,
it cutteth it above, or being pro­
longed, it cutteth it below. And
in that Line let any point G be
taken, by which paſſeth the Right
Line F G E. And becauſe the
Square F E is greater than the
Square G E, the ſaid Square F E
ſhall have greater proportion to
the Square B C, than the ſaid Square G E hath to the ſaid B C. And
becauſe, by the precedent, the Square F E is to the Square B C as
E A is to A C; therefore E A hath greater proportion to A C, than
the Square G E hath to the Square B C; that is, than the Square
E D hath to the Square D C: (becauſe in the Triangle D G E as
G E is to the Parallel B C, ſo is E D to D C:) But the Line E A to
A C, that is, to A D hath the ſame proportion that four Rectangles
E A D hath to four Squares of A D, that is, to the Square C D,
1(which is equal to four Squares of A D:) Therefore four Rectan­
gles E A D ſhall have greater proportion to the Square C D, than
the Square E D hath to the Square D C: Therefore four Rectan­
gles E A D ſhall be greater than the Square E D: which is falſe,
for they are leſſe; becauſe the parts E A and A D of the Line E D
are not equal: Therefore the Line D B toucheth the Parabola in B,
and doth not cut it: Which was to be demonſtrated.
SIMP. You proceed in your Demonſtrations too ſublimely,
and ſtill, as far as I can perceive, ſuppoſe that the Propoſitions of
Euclid are as familiar and ready with me, as the firſt Axioms them­
ſelves, which is not ſo. And the impoſing upon me, juſt now, that
four Rectangles E A D are leſs than the Square D E becauſe the
parts E A and A D of the Line E D are not equal, doth not ſatisſie
me, but leaveth me in doubt.
SALV. The truth is, all the Mathematicians that are not vulgar
ſuppoſe that the Reader hath ready by heart the Elements of
Euclid: And here to ſupply your want, it ſhall ſuſfice to remember
you of a Propoſition in the ſecond Book, in which it is demonſtrated
that when a Line is cut into equal parts, and into unequal, the
Rectangle of the unequal parts is leſs than the Rectangle of the
equal, (that is, than the Square of the half) by ſo much as is the
Square of the Line comprized between the Sections. Whence it is
manifeſt, that the Square of the whole, which continueth four
Squares of the Half, is greater than four Rectangles of the unequal
parts. Now it is neceſſary that we bear in mind theſe two Propoſi­
tions which have been demonſtrated, taken from the Conick Ele­
ments, for the better underſtanding the things that follow in the
preſent Treatiſe: for of theſe two, and no more, the Author
makes uſe. Now we may reaſſume the Text to ſee in what manner
he doth demonſtrate his firſt Propoſition, in which he intendeth to
prove unto us, That the Line deſcribed by the Grave Moveable,
when it deſcends with a Motion compounded of the Equable
Horizontal, and of the Natural Deſcending is a Semiparabola.
Suppoſe the Horizontal Line or Plane A B placed on high; upon
[or along] which let the Moveable paſſe with an Equable Motion out
of A unto B: and the ſupport of the Plane failing in B let there be
derived upon the Moveable from its own Gravity a Motion naturally
downwards according to the Perpendicular B N. Let the Line B E be
ſuppoſed applyed unto the Plane A B right out, as if it were the Efflux
or meaſure of the Time, on which at pleaſure note any equal parts of
Time, B C, C D, D E: And out of the points B C D E ſuppoſe Per­
pendicular Lines to be let fall equidiſtant or parallel to B N: In the firſt
of which take any part C I, whoſe quadruple take in the following one
D F, nonuple E H, and ſo in the reſt that follow according to the propor-
1tion of the Squares of C B, D B, E B, or, if you will, in the doubled
proportion of the Lines. And if unto the Moveable moved beyond B
towards C with the Equable Lation we ſuppoſe the Perpendicular
Deſcent to be ſuperadded according to the quantity C I, in the Time
B C it ſhall be found conſtituted in the Term I. And proceeding farther,
146[Figure 146]
in the Time D B, namely,
in the double of B C, the
Space of the Deſcent down­
wards ſhall be quadruple to
the firſt Space C I: For
it hath beendemonſtrated in
the firſt Trastate, that the
Spaces paſſed by GraveBo­
dies with a Motion Natu­
rally Accelerate are in du­
plicate proportion of their Times. And it likewiſe followeth, that the
Space E H paſſed in the Time B E, ſhall be as G. So that it is manifeſtly
proved, that the Spaces E H, D F, C I, are to one another as the Squares
of the Lines E B, D B, C B. Now from the points I, F, and H draw
the Right Lines I O, F G, H L, Parallel to the ſaid E B; and each of
the Lines H L, F G, and I O ſhall be equal to each of the other Lines
E B, D B, and C B; as alſo each of thoſe B O, B G, and B L, ſhall be
equal to each of thoſe C I, D F, and E H: And the Square H L ſhall
be to the Square F G, as the Line L B to B G: And the Square F G
ſhall be to the Square I O, as G B to B O: Therefore the Points I, F,
and H are in one and the ſame Parabolical Line. And in like manner
it ſhall be demonſtrated, any equalparticles of Time of whatſoever Mag­
nitude being taken, that the place of the Moveable whoſe Motion is
compounded of the like Lations, is in the ſame Times to be found in the
ſame Parabolick Line: Therefore the Propoſition is manifeſt.
SALV. This Concluſion is gathered from the Converſion of the
firſt of thoſe two Propoſitions that went before, for the Parabola
being, for example, deſcribed by the points B H, if either of the
two F or I were not in the deſcribed Parabolick Line, it would be
within, or without; and by conſequence the Line F G would be
either greater or leſſer than that which ſhould determine in the Pa­
rabolick Line; Wherefore the Square of HL would have, not to
the Square of F G, but to another greater or leſſer, the ſame pro­
portion that the Line L B hath to BG, but it hath the ſame propor­
tion to the Square of F G: Therefore the point F is in the Parabo­
lick Line: And ſo all the reſt, &c.
SAGR. It cannot be denied but that the Diſcourſe is new, in­
genious and concludent, arguing ex ſuppoſitione, that is, ſuppoſing
that the Tranſverſe Motion doth continue alwaies Equable, and
1that the Natural Dcorſum do likewiſe keep its tenour of continu­
ally Accelerating according to a proportion double to the Times;
and that thoſe Motions and their Velocities in mingling be not al­
tered, diſturbed, and impeded, ſo that finally the Line of the Pro­
ject do not in the continuation of the Motion degenerate into an­
other kind; a thing which ſeemeth to me to be impoſſible. For, in
regard that the Axis of our Parabola, according to which we ſup­
poſe the Natural Motion of Graves to be made, being Perpendicu­
lar to the Horizon, doth terminate in the Center of the Earth; and
in regard that the Parabolical Line doth ſucceſſively enlarge from
its Axis, no Project would ever come to terminate in the Center, or
if it ſhould come thitherwards, as it ſeemeth neceſſary that it muſt,
the Line of the Project ſhould deſcribe another moſt different from
that of the Parabola.
SIMP. I add to theſe difficulties ſeveral others; one of which is
that we ſuppoſe, that the Horizontal Plane which hath neither accli­
vity or declivity is a Right Line; as if that ſuch a Line were in all
its parts equidiſtant from the Center, which is not true: for depart­
ing from its middle it goeth towards the extreams, alwaies more and
more receding from the Center, and therefore alwaies aſcending:
which of conſequence rendereth it Impoſſible that its Motion
ſhould be perpetual, or that it ſhould for any time continue Equa­
ble, and neceſſitates it to grow continually more and more weak.
Moreover, it is, in my Opinion, impoſſible to avoid the Impedi­
ment of the Medium, but that it will take away the Equability of
the Tranſverſe Motion, and the Rule of the Acceleration in falling
Grave Bodies. By all which difficulties it is rendred very improba­
ble that the things demonſtrated with ſuch inconſtant Suppoſi­
tions ſhould afterwards hold true in the practical Experiments.
SALV. All the Objections and Difficulties alledged are ſo
well grounded, that I eſteem it impoſſible to remove them; and
for my own part I admit them all, as alſo I believe the Author
himſelf would do. And I grant that the Concluſions thus demon­
ſtrated in Abſtract, do alter and prove falſe, and that ſo egregiouſ­
ly, in Concrete, that neither is the Tranſverſe Motion Equable,
nor is the Acceleration of the Natural in the proportion ſuppoſe,
nor is the Line of the Project Parabolical, &c. But yet on the
contrary, I deſire that you would not ſcruple to grant to this our
Author that which other famous Men have ſuppoſed, although
falſe. And the ſingle Authority of Archimedes may ſatisfie every
one: who in his Mechanicks, and in the firſt Quadrature of the
Parabola, taketh it as a true Principle, that the Beam of the Ballance
or Stilliard is a Right Line in all its points equidiſtant from the
Common Center of Grave Bodies, and that the Scale-ropes, to
which the Weights are hanged, are parallel to one another. Which
1Liberty of his hath been excuſed by ſome, for that in our practices
the Inſtruments we uſe, and the Diſtances which we take are ſo
ſmall in compariſon of our great remoteneſs from the Center of
the Terreſtrial Globe, that we may very well take a Minute of a
degree of the great Circle as if it were a Right Line, and two Per­
pendiculars that ſhould hang at its extreams as if they were Paral­
lels. For if we were in practical Operations to keep account of
ſuch like Minutes, we ſhould begin to reprove the Architects, who
with the Plumb Line ſuppoſe that they raiſe very high Towers
between Lines equidiſtant. And I here add, that we may ſay that
Archimedes, and others ſuppoſe in their Contemplations that they
were conſtituted remote at an infinite diſtance from the Center;
in which caſe their Aſſumptions were not falſe: And that therefore
they did conclude by Abſolute Demonſtration. Again, if we will
practice the demonſtrated Concluſions in terminate Diſtances, by
ſuppoſing an immenſe Diſtance, we ought to defalk from the
truth demonſtrated that which our Diſtance from the Center doth
import, not being really infinite, but yet ſuch as that it may be
termed Immenſe in compariſon of the Artifices that we make uſe
of, the greateſt of which will be the Ranges of Projects, and amongſt
theſe that only of Canon ſhot; which though it be great, yet ſhall
it not exceed four of thoſe Miles of which we are remote from the
Center well-nigh ſo many thouſands: and theſe coming to deter­
mine in the Surface of the Terreſtrial Globe may very well only in­
ſenſibly alter that Parabolick Figure, which we grant would be
extreamly transformed in going to determine in the Center. In
the next place as to the perturbation proceeding from the Impedi­
ment of the Medium, this is more conſiderable, and, by reaſon of
its ſo great multiplicity of Varieties, incapable of being brought
under any certain Rules, and reduced to a Science: for if we
ſhould propoſe to conſideration no more but the Impediment which
the Air procureth to the Motions conſidered by us, this alone ſhall
be found to diſturb all, and that infinite waies, according as we
infinite waies vary the Figures, Gravities, and Velocities of the
Moveables. For as to the Velocity, according as this ſhall be grea­
ter, the greater ſhall the oppoſition be that the Air makes againſt
them, which ſhall yet more impede the ſaid Moveable according as
they are leſs Grave: ſo that although the deſcending Grave Body
ought to go Accelerating in a duplicate proportion to the Duration
of its Motion, yet nevertheleſs, albeit the Moveable were very
Grave, in coming from very great heights, the Impediment of the
Air ſhall be ſo great, as that it will take from it all power of far­
ther encreaſing its Velocity, and will reduce it to an Uniform and
Equable Motion: And this Adequation ſhall be ſo much the ſooner
obtained, and in ſo much leſſer heights, by how much the Moveable
1ſhall be leſs Grave. That Motion alſo which along the Horizontal
Plane, all other Obſtacles being removed, ought to be Equable
and perpetual, ſhall come to be altered, and in the end arreſted by
the Impediment of the Air: and here likewiſe ſo much the ſooner,
by how much the Moveable ſhall be Lighter. Of which Accidents
of Gravity, of Velocity, and alſo of Figure, as being varied ſeve­
ral waies, there can no fixed Science be given. And therefore that
we may be able Scientifically to treat of this Matter it is requiſite
that we abſtract from them; and, having found and demonſtrated
the Concluſions abſtracted from the Impediments, that we make
uſe of them in practice with thoſe Limitations that Experience ſhall
from time to time ſhew us. And yet nevertheleſs the benefit ſhall
not be ſmall, becauſe ſuch Matters, and their Figures ſhall be made
choice of as are leſs ſubject to the Impediments of the Medium;
ſuch are the very Grave, the Rotund: and the Spaces, and the
Velocities for the moſt part will not be ſo great, but that their ex­
orbitances may with eaſie ^{*} Allowance be reduced to a certainty.

Yea more, in Projects practicable by us, that are of Grave Matters,
and of Round Figure, and alſo that are of Matters leſſe Grave,
and of Cylindrical Figure, as Arrows, ſhot from Slings or Bows,
the variation of their Motion from the exact Parabolical Figure
ſhall be altogether inſenſible. Nay, (and I will aſſume to my ſelf
a little more freedom) that in ^{*} Inſtruments that are practicable by

us, their ſmalneſs rendreth the extern and accidental Impediments,
of which that of the Medium is moſt conſiderable, to be but of
very ſmall note, I am able by two experiments to make manifeſt.
I will conſider the Motions made thorow the Air, for ſuch are thoſe
chiefly of which we ſpeak: againſt which the ſaid Air in two man­
ners exerciſeth its power. The one is by more impeding the Movea­
bles leſs Grave, than thoſe very Grave. The other is in more oppo­
ſing the greater than the leſs Velocity of the ſame Moveable. As
to the firſt; Experience ſhewing us that two Balls of equal
bigneſs, but in weight one ten or twelve times more Grave than the
other, as, for example, one of Lead and another of Oak would
be, deſcending from an height of 150, or 200 Yards, arrive to the
Earth with Velocity very little different, it aſſureth us that the Im­
pediment or Retardment of the Air in both is very ſmall: for if
the Ball of Lead departing from on high in the ſame Moment with
that of Wood, were but little retarded, and this much, the Lead at
its coming to the ground ſhould leave the Wood a very conſidera­
ble Space behind, ſince it is ten times more Grave; which never­
theleſs doth not happen: nay, its Anticipation ſhall not be ſo
much as the hundredth part of the whole height. And between a
Ball of Lead, and another of Stone which weighs a third part, or
half ſo much as it, the difference of the Times of their coming to
1the ground would be hardly obſervable. Now becauſe the Impe­
tus that a Ball of Lead acquireth in falling from an height of 200
Yards (which is ſo much that continuing it in an Equable Moti­
on it would in a like Time run 400 Yards) is very conſiderable in
compariſon of the Velocity that we confer with Bows or other Ma­
chines, upon our Projects (excepting the Impetus's that depend
on the Fire) we may without any notable Errour conclude and
account the Propoſitions to be abſolutely true that are demonſtra­
ted without any regard had to the alteration of the Medium. In
the next place as touching the other part, that is to ſhew, that the
Impediment that the ſaid Moveable receiveth from the Air whilſt
it moveth with great Velocity is not much greater than that which
oppoſeth it in moving ſlowly, the enſuing Experiment giveth us
full aſſurance of it. Suſpend by two threads both of the ſame
length, v. gr. four or five Yards, two equal Balls of Lead: and
having faſtned the ſaid threads on high, let both the Balls be re­
moved from the ſtate of Perpendicularity; but let the one be re­
moved 80. or more degrees, and the other not above 4 or 5: ſo
that one of them being left at liberty deſcendeth, and paſſing be­
yond the Perpendicular, deſcribeth very great Arches of 160, 150,
140, &c. degrees, diminiſhing them by little and little: but the
other ſwinging freely paſſeth little Arches of 10, 8, 6, &c. this
alſo diminiſhing them in like manner by little and little. Here I
ſay, in the firſt place, that the firſt Ball ſhall paſs its 180, 160, &c.
degrees in as much Time as the other doth its 10, 8, &c. From
whence it is manifeſt, that the Velocity of the firſt Ball ſhall be 16
and 18 times greater than the Velocity of the ſecond: ſo that in
caſe the greater Velocity were to be more impeded by the Air than

the leſſer, the Vibrations ſhould be more ^{*} rare in the greateſt
Arches of 180, or 160 degrees, &c. than in the leaſt of 10, 8, 4,
and alſo of 2, and of 1; but this is contradicted by Experience:
for if two Aſſiſtants ſhall ſet themſelves to count the Vibrations,
one the greateſt, the other the leaſt, they will find that they ſhall
number not only tens, but hundreds alſo, without diſagreeing one
ſingle Vibration, yea, or one ſole point. And this obſervati­
on joyntly aſſureth us of the two Propoſitions, namely, that the
greateſt and leaſt Vibrations are all made one after another under
equal Times, and that the Impediment and Retardment of the Air
operates no more in the ſwifteſt Motion, than in the ſloweſt:
contrary to that which before it ſeemed that we our ſelves alſo
would have judged for company.
* Tarra.
* Artifizii.
Or ſewer.
SAGR. Rather, becauſe it cannot be denied but that the Air
impedeth both thoſe and theſe, ſince they both continually grow
more languid, and at laſt ceaſe, it is requiſite to ſay that thoſe Re­
tardations are made with the ſame proportion in the one and in the
1other Operation. And then, the being to make greater Reſiſtance
at one time than at another, from what other doth it proceed, but
only from its being aſſailed at one time with a greater Impetus and
Velocity, and at another time with leſſer? And if this be ſo then the
ſame quantity of the Velocity of the Moveable is at once the Cauſe
and the Mealure of the quantity of the Reſiſtance. Therefore all
Motions, whether they be ſlow or ſwift, are retarded and impe­
ded in the ſame proportion: a Notion in my judgment not con­
temptible.
SALV. We may alſo in this ſecond caſe conclude, That the
Fallacies in the Concluſions, which are demonſtrated, abſtracting
from the extern Accidents, are in our Inſtruments of very ſmall
conſideration, in reſpect of the Motions of great Velocities of
which for the moſt part we ſpeak, and of the Diſtances which are
but very ſmall in relation to the Semidiameter and great Circles of
the Terreſtrial Globe.
SIMP. I would gladly hear the reaſon why you ſequeſtrate
the Projects from the Impetus of the Fire, that is, as I conceive from
the force of the Powder, from the other Projects made by Slings,
Bows, or Croſs-bows, touching their not being in the ſame manner
ſubject to the Acceleration and Impediment of the Air.
SALV. I am induced thereto by the exceſſive, and, as I may ſay,
Supernatural Fury or Impetuouſneſs with which thoſe Projects are
driven out: For indeed I think that the Velocity with which a Bul­
let is ſhot out of a Musket or Piece of Ordinance may without any
Hyperbole be called Supernatural. For one of thoſe Bullets de­
ſcending naturally thorow the Air from ſome immenſe height, its
Velocity, by reaſon of the Reſiſtance of the Air will not go in­
creaſing perpetually: but that which in Cadent Bodies of ſmall
Gravity is ſeen to happen in no very great ^{*} Space, I mean their

being reduced in the end to an Equable Motion, ſhall alſo happen
after a Deſcent of thouſands of yards, in a Ball of Iron or Lead:
and this determinate and ultimate Velocity may be ſaid to be the
greateſt that ſuch a Body can obtain or acquire thorow the Air:
which Velocity I account to be much leſſer than that which cometh
to be impreſſed on the ſame Ball by the fired Powder. And of this
a very appoſite Experiment may advertiſe us. At an height of an
hundred or more yards let off a Musket charged with a Leaden
Bullet perpendicularly downwards upon a Pavement of Stone; and
with the ſame Musket ſhoot againſt ſuch another Stone at the Di­
ſtance of a yard or two, and then ſee which of the two Bullets is
more flatted: for if that coming from on high be leſs ^{*} dented than

the other, it ſhall be a ſign that the Air hath impeded it, and dimi­
niſhed the Velocity conferred upon it by the Fire in the beginning
of the Motion: and that, conſequently, ſo great a Velocity the Air
1would not ſuffer it to gain coming from never ſo great an height:
for in caſe the Velocity impreſſed upon it by the Fire ſhould not
exceed that which it might acquire of its ſelf deſcending naturally,
the battery downwards ought rather to be more valid than leſs.
I have not made ſuch an Experiment, but incline to think that a
Musket or Cannon Bullet falling from never ſo great an height,
will not make that percuſſion which it maketh in a Wall at a Di­
ſtance of a few yards, that is of ſo few that the ſhort perforation,
or, if you will, Sciſſure to be made in the Air ſufficeth not to ob­
viate the exceſs of the ſupernatural impetuoſity impreſſed on it by
the Fire. This exceſſive Impetus of ſuch like forced ſhots may
cauſe ſome deformity in the Line of the Projection; making
the beginning of the Parabola leſs inclined or curved than the end.
But this can be but of little or no prejudice to our Author in
practical Operations: amongſt the which the principal is the com­
poſition of a Table for the Ranges, or Flights, which containeth
the diſtances of the Falls of Balls ſhot according to all Elevations.
And becauſe theſe kinds of Projections are made with Mortar­
Pieces, and with no great charge; in theſe the Impetus not being
ſupernatural, the Ranges deſcribe their Lines very exactly.
* Or Way.
* Or battered.
But for the preſent let us proceed forwards in the Treatiſe,
where the Author deſireth to lead us to the Contemplation and
Inveſtigation of the Impetus of the Moveable whilſt it moveth
with a Motion compounded of two. And firſt of that compoun­
ded of two Equable Motions; the one Horizontal, and the other
Perpendicular.
THEOR. II. PROP. II.
If any Moveable be moved with a twofold Equa­
ble Motion, that is, Horizontal and Perpen­
dicular, the Impetus or Moment of the Lation
compounded of both the Motions ſhall be po­
tentia equal to both the Moments of the firſt
Motions.
For let any Moveable be moved Equably with a double Lation,
and let the Mutations of the Perpendicular anſwer to the Space
A B, and let B C anſwer to the Horizontal Lation paſſed in
the ſame Time. Foraſmuch therefore as the Spa-
147[Figure 147]
ces A B, and B C are paſſed by the Equable Mo­
tion in the ſame Time, their Moments ſhall be to
cach other as the ſaid A B and B C. But the
Moveable which is moved according to theſe two Mutations ſhall de-
1ſcribe the Diagonal A C, and its Moment ſhall be as A C. But A C is
potentia equal to the ſaid A B and B C: therefore the Moment com­
pounded of both the Moments A B and B C, is potentia equal to them
both taken together: Which was to be demonſtrated.
SIMP. It is neceſſary that you eaſe me of one Scruple that
cometh into my mind, it ſeemeth to me that this which is now con­
cluded oppugneth another Propoſition of the former Tractate: in
which it is affirmed, That the Impetus of the Moveable coming
from A into B is equal to that coming from A into C; and now it is
concluded, that the Impetus in C is greater than that in B.
SALV. The Propoſitions, Simplicius, are both true, but very
different from one another. Here the Author ſpeaks of one ſole
Moveable moved with one ſole Motion, but compounded of two,
both Equable; and there he ſpeaks of two Moveables moved
with Motions Naturally Accelerated, one along the Perpendicular
A B, and the other along the Inclined Plane A C: and moreover,
the Times there are not ſuppoſed equal, but the Time along
the Inclined Plane A C is greater than the Time along the Perpen­
dicular A B: but in the Motion ſpoken of at preſent, the Motions
along A B, B C and A C are underſtood to be Equable, and made
in the ſame Time.
SIMP. Excuſe me, and go on, for I am ſatisfied.
SALV. The Author proceeds to ſhew us that which hapneth
concerning the Impetus of a Moveable moved in like manner with
one Motion compounded of two, that is to ſay, the one Horizon­
tal and Equable, and the other Perpendicular but Naturally-Acce­
lerate, of which in fine the Motion of the Project is compounded,
and by which the Parabolick Line is deſcribed; in each point of
which the Author endeavours to determine what the Impetus of the
Project is; for underſtanding of which he ſheweth us the manner,
or, if you will, Method of regulating and meaſuring that ſame Im­
petus upon the ſaid Line, along which the Motion of the Grave
Moveable deſcending with a Natural-Accelerate Motion departing
from Reſt is made, ſaying:
THEOR. III. PROP. III.
Let a Motion be made along the Line A B out of Reſt in A, and
take in ſome point C; and ſuppoſe the ſaid A C to be the Time or
Meaſure of the Time of the ſaid Fall along the Space A C, as alſo
the Meaſure of the Impetus or Moment in the Point C acquired by
the Deſcent along A C. Now let there be taken in the ſaid Line
A B any other Point, as ſuppoſe B, in which we are to determine of the
Impetus acquired by the Moveable along the Fall A B, in proportion to
1the Impetus, which it obtaineth in C, whoſe Meaſure is ſuppoſed to be
A C, Let A S be a Mean-proportional betwixt B A and A C. We will
demonſtrate that the Impetus in B is to the Impetus in C, as S A is to
A C. Let the Horizontal Line C D be double to the ſaid A C; and B E
double to B A. It appeareth by what hath been demonſtrated, That the
Cadent along A C being turned along the Horizon C D, and according
to the Impetus acquired in C, with an Equable Motion, ſhall paſs the
Space C D in a Time equal to that
in which the ſaid A C is paſſed
148[Figure 148]
with an Accelerate Motion; and
likewiſe that B E is paſſed in the
ſame time as A B: But the Time of
the Deſcent along A B is A S: There­
fore the Horizontal Line B E is
paſſed in A S. As the Time S A is
to the Time A C, ſo let E B be to
B L. And becauſe the Motion by
B E is Equable, the Space B L ſhall be paſſed in the Time A C ac­
cording to the Moment of Celerity in B: But in the ſame Time A C
the Space C D is paſſed, according to the Moment of Velocity in C:
the Moments of Velocity therefore are to one another as the Spaces
which according to the ſame Moments are paſſed in the ſame Time:
Therefore the Moment of Velocity in C is to the Moment of Celerity in
B, as D C is to B L. And becauſe as D C is to B E, ſo are their halfs,
to wit, C A to A B: but as E B is to B L, ſo is B A to A S: Therefore,
exæquali, as D C is to B L, ſo is C A to A S: that is, as the Moment
of Velocity in C is to the Moment of Velocity in B, ſo is C A to A S; that
is, the Time along C A to the Time along A B. I he manner of Meaſu­
ring the Impetus, or the Moment of Velocity upon a Line along which it
makes a Motion of Deſcent is therefore manifeſt; which Impetus
is indeed ſuppoſed to encreaſe according to the Proportion of the
Time.
But this, before we proceed any farther, is to be premoniſhed, that in
regard we are to ſpeak for the future of the Motion compounded of the
Equable Horizontal, and of the Naturally Accelerate downwards, (for
from this Mixtion reſults, and by it is deſigned the Line of the Project,
that is a Parabola;) it is neceſſary that we define ſome common meaſure
according to which we may meaſure the Velocity, Impetus, or Moment
of both the Motions. And ſeeing that of the Equable Motion the de­
grees of Velocity are innumerable, of which you may not take any
promiſcuouſly, but one certain one which may be be compared and con­
joyned with the Degree of Velocity naturally Accelerate. I can think of
no more eaſie way for the electing and determining of that, than by aſ­
ſuming another of the ſame kind. And that I may the better expreſs
my meaning; Let A C be Perpendicular to the Horizon C B; and A C
1to be the Altitude, and C B the Amplitude of the Semiparabola A B;
which is deſcribed by the Compoſition of two Lations; of which one is
that of the Moveable deſcending along A C with a Motion Naturally
Acceler ate ex quiete in A; the other is the Equable Tranſverſal Moti­
on according to the Horizontal Line A D. The Impetus acquired in C
along the Deſcent A C is determined by the quantity of the ſaid height
A C; for the Impetus of a Moveable
149[Figure 149]
falling from the ſame height is alwaies
one and the ſame: but in the Horizontal
Line one may aſſign not one, but innume­
rable Degrees of Velocities of Equable
Motions: out of which multitude that I
may ſingle out, and as it were point with
the finger to that which I make choice of,
I extend or prolong the Altitude C A in
ſublimi, in which, as was done before, I
will pitch upon A E; from which if I
conceive in my mind a Moveable to fall
ex quiete in E, it appeareth that its Im­
petus acquired in the Time A, is one with which I conceive the ſame
Moveable being turned along A D to be moved; and its degree of
Vclocity to be that, which in the Time of the Deſcent along E A paſſeth
a Space in the Horizon double to the ſaid E A. This Præmonition I
judged neceſſary.
It is moreover to be advertized that the Amplitude of the Semi­
parabola A B ſhall be called by me the Horizontal Line [or Plane]
C B.
The Altitude, to with A C, the Axis of the ſaid Parabola.
And the Line E A, by whoſe Deſcent the Horizontal Impetus is de­
termined, I call the Sublimity, or height.
Theſe things being declared and defined, I proceed to Demonſtra­
tion.
SAGR. Stay, I pray you, for here me thinks it is convenient to
adorn this Opinion of our Author with the conformity of it to
the Conceit of Plato about the determining the different Veloci­
ties of the Equable Motions of the Revolutions of the Cœleſtial
Bodies; who, having perhaps had a conjecture that no Moveable
could paſſe from Reſt into any determinate degree of Velocity in
which it ought afterwards to be perpetuated, unleſs by paſſing
thorow all the other leſſer degrees of Velocity, or, if you will,
greater degrees of Tardity, which interpoſe between the aſſigned
degree, and the higheſt degree of Tardity, that is of Reſt, ſaid that
God after he had created the Moveable Cœleſtial Bodies that he
might aſſign them thoſe Velocities wherewith they were afterwards
1to be perpetually moved with an Equable Circular Motion, made
them, they departing from Reſt, to move along determinate Spaces
with that Natural Motion in a Right Line, according to which we
ſenſibly ſee our Moveables to move from the ſtate of Reſt ſucceſ­
ſively Accelerating. And he addeth, that having made them to
acquire that degree in which it pleaſed him that they ſhould after­
wards be perpetually conſerved, he converted their Right or direct
Motion into Circular; which only is apt to conſerve it ſelf Equa­
ble, alwaies revolving without receding from, or approaching to
any prefixed term by them deſired. The Conceit is truly worthy
of Plato; and is the more to be eſteemed in that the grounds there­
of paſſed over in ſilence by him, and diſcovered by our Author by
taking off the Mask or Poetick Repreſentation, do ſhew it to be
in its native aſpect a true Hiſtory. And I think it very credible that
we having by the Doctrine of Aſtronomy ſufficiently competent
Knowledge of the Magnitudes of the Orbes of the Planets, and of
their Diſtances from the Center about which they move, as alſo
of their Velocities, our Author (to whom Plato's Conjecture was
not unknown) may ſometime for his curioſity have had ſome
thought of attempting to inveſtigate whether one might aſſign a
determinate Sublimity from which the Bodies of the Planets depar­
ting, as from a ſtate of Reſt, and moved for certain Spaces with a
Right and Naturally Accelerate Motion, afterwards converting
the Acquired Velocity into Equable Motions, they might be found
to correſpond with the greatneſs of their Orbes, and with the Times
of their Revolutions.
SALV. I think I do remember that he hath heretofore told me,
that he had once made the Computation, and alſo that he found
it exactly to anſwer the Obſervations; but that he had no mind to
ſpeak of them, doubting leſt the two many Novelties by him diſ­
covered, which had provoked the diſpleaſure of many againſt him,
might blow up new ſparks. But if any one ſhall have the like de­
ſire he may of himſelf by the Doctrine of the preſent Tract give
himſelf content. But let us purſue our buſineſs, which is to
ſhew;
PROBL. I. PROP. IV.
How in a Parabola given, deſcribed by the Pro­
ject, the Impetus of each ſeveral point may be
determined.
Let the Semiparabola be B E C, whoſe Amplitude is C D and Al­
titude D B, with which continued out on high the Tangent of the
Parabola C A meeteth in A; and along the Vertex B let B I be
1an Horizontal Line, and parallel to C D. And if the Amplitude C D
be equal to the whole Altitude D A, B I ſhall be equal to B A and B D.
And if the Time of the Fall along A B, and the Moment of Velocity
acquired in B along the Deſcent A B ex quiete in A be ſuppoſed to be
meaſured by the ſaid A B, then D C (that is twice B I) ſhall be the
Space which ſhall be paſſed by the Impetus A B turned along the Hori­
zontal Line in the ſame Time: But in the ſame Time falling along B D
out of Reſt in B, it ſhall paſs the Altitude B D: Therefore the Movea­
ble falling out of Reſt in A along A B,
being converted with the Impetus A B
150[Figure 150]
along the Horizontal Parallel ſhall
paſs a Space equal to D C. And the
Fall along B D ſupervening, it paſſeth
the Altitude B D, and deſcribes the
Parabola B C; whoſe Impetus in the
Term C is compounded of the Equable
Tranſverſal whoſe Moment is as A B,
and of another Moment acquired in the
Fall B D in the Term D or C; which
Moments are Equal. If therefore we
ſuppoſe A B to be the Meaſure of one of them, as ſuppoſe of the Equa­
ble Tranſverſal; and B I, which is equal to B D, to be the Meaſure of
the Impetus acquired in D or C; then the Subtenſe I A ſhall be the
quantity of the Moment compound of them both: Therefore it ſhall be
the quantity or Meaſure of the whole Moment which the Project deſcend­
ing along the Parabola B C ſhall acquire of Impetus in C. This pre­
miſed, take in the Parabola any point E, in which we are to determine
of the Impetus of the Project. Draw the Horizontal Parallel E F,
and let B G be a Mean-proportional between B D and B F. And foraſ­
much as A B or B D is ſuppoſed to be the Meaſure of the Time, and of
the Moment of the Velocity in the Fall B D ex quiete in B: B G ſhall
be the Time, or the Meaſure of the Time, and of the Impetus in F, coming
out of B. If therefore B O be ſuppoſed equal to B G, the Diagonal
drawn from A to O ſhall be the quantity of the Impetus in E; for
A B hath been ſuppoſed the determinator of the Time, and of the Impe­
tus in B, which turned along the Horizontal Parallel doth alwaies
continue the ſame: And B O determineth the Impetus in F or in E
along the Deſcent ex quiete in B in the Altitude B F: But theſe two
A B and B O are potentia equal to the Power A O. Therefore that is
manifeſt which was ſought.
SAGR. The Contemplation of the Compoſition of theſe diffe­
rent Impetus's, and of the quantity of that Impetus which reſults
from this mixture, is ſo new to me, that it leaveth my mind in no
ſmall confuſion. I do not ſpeak of the mixtion of two Motions
1Equable, though unequal to one another, made the one along the
Horizontal Line, and the other along the Perpendicular, for I very
well comprehend that there is made a Motion of theſe two poten­
tia equal to both the Compounding Motions, but my confuſion
ariſeth upon the mixing of the Equable-Horizontal and Perpendi­
cular-Naturally-Accelerate Motion. Therefore I could wiſh we
might toge ther a little better conſider this buſineſs.
SIMP. And I ſtand the more in need thereof in that I am not
yet ſo well ſatisfied in Mind as I ſhould be, in the Propoſitions that
are the firſt foundations of the others that follow upon them. I
will add, that alſo in the Mixtion of the two Motions Equable
Horizontal, and Perpendicular, I would better underſtand that
Potentia of their Compound. Now, Salviatus, you ſee what we
want and deſire.
SALV. Your deſire is very reaſonable: and I will eſſay whe­
ther my having had a longer time to think thereon may facilitate
your ſatisfaction. But you muſt bear with and excuſe me if in diſ­
courſing I ſhall repeat a great part of the things hitherto delivered
by our Author.
It is not poſſible for us to ſpeak poſitively touching Motions and
their Velocities or Impetus's, be they Equable, or be they Naturally
Accelerate, unleſs we firſt agree upon the Meaſure that we are to
uſe in the commenſuration of thoſe Velocities, as alſo of the Time.
As to the Meaſure of the Time, we have already that which is
commonly received by all of Hours, Prime-Minutes, and Se­
conds, &c. and as for the meaſuring of Time we have that com­
mon Meaſure received by all, ſo it is requiſite to aſſign another
Meaſure for the Velocities that is commonly underſtood and re­
ceived by every one; that is, which every where is the ſame. The
Author, as hath been declared, adjudged the Velocity of Naturally
deſcending Grave-Bodies to be fit for this purpoſe; the encreaſing
Velocities of which are the ſame in all parts of the World. So that
that ſame degree of Velocity which (for example) a Ball of Lead of
a pound acquireth in having, departing from Reſt, deſcended Per­
pendicularly as much as the height of a Pike, is alwaies, and in all
places the ſame, and therefore moſt commodious for explicating
the quantity of the Impetus that is derived from the Natural De­
ſcent. Now it remains to find a way to determine likewiſe the
Quantity of the Impetus in an Equable Motion in ſuch a manner,
that all thoſe which diſcourſe about it may form the ſame conceit
of its greatneſs and Velocity; ſo that one may not imagine it more
ſwift, and another leſs; whereupon afterwards in conjoyning and
mingling this Equable Motion imagined by them with the eſtabli­
ſhed Accelerate Motion ſeveral men may form ſeveral Conceits of
ſeveral greatneſſes of Impetus's. To determine and repreſent this
1Impetus, and particular Velocity our Author hath not found any
way more commodious, than the making uſe of the Impetus which
the Moveable from time to time acquires in the Naturally-Accele­
rate Motion, any acquired Moment of which being reduced into
an Equable Motion retaineth its Velocity preciſely limited, and
ſuch, that in ſuch another Time as that wherein it did Deſcend, it
paſſeth double the Space of the Height from whence it fell. But
becauſe this is the principal point in the buſineſs that we are upon,
it is good to make it to be perfectly underſtood by ſome particular
Example. Reaſſuming therefore the Velocity and Impetus acqui­
red by the Cadent Moveable, as we ſaid before, from the height
of a Pike, of which Velocity we will make uſe for a Meaſure of
other Velocities and Impetuſſes upon other occaſions, and ſuppo­
ſing, for example, that the Time of that Fall be four ſecond Mi­
nutes of an hour, to find by this ſame Meaſure how great the Im­
petus of the Moveable would be falling from any other height
greater, or leſſer, we ought not from the proportion that this other
height hath to the height of a Pike to argue and conclude the quan­
tity of the Impetus acquired in this ſecond height, thinking, for
example, that the Moveable falling from quadruple the height
hath acquired quadruple Velocity, for that it is falſe: for that the
Velocity of the Naturally-Accelerate Motion doth not increaſe or
decreaſe according to the proportion of the Spaces, but according
to that of the Times, than which that of the Spaces is greater in a
duplicate proportion, as was heretofore demonſtrated. Therefore
when in a Right Line we have aſſigned a part for the Meaſure of
the Velocity, and alſo of the Time, and of the Space in that Time
paſſed (for that for brevity ſake all theſe three Magnitudes are
often repreſented by one ſole Line,) to find the quantity of the
Time, and the degree of Velocity that the ſame Moveable would
have acquired in another Diſtance we ſhall obtain the ſame, not
immediataly by this ſecond Diſtance, but by the Line which ſhall
be a Mean-proportional betwixt the two Diſtances. But I will
better declare my ſelf by an Example. In the Line A C Perpendi­
cular to the Horizon let the part A B be underſtood to
be a Space paſſed by a Moveable naturally deſcending
151[Figure 151]
with an Accelerate Motion: the Time of which paſ­
ſage, in regard I may repreſent it by any Line, I will, for
brevity, imagine it to be as much as the ſame Line A B
and likewiſe for a Meaſure of the Impetus and Velocity
acquired by that Motion, I again take the ſame Line
A B; ſo that of all the Spaces that are in the progreſs of
the Diſcourſe to be conſidered the part A B may be the
Meaſure. Having all our pleaſure eſtabliſhed under one
ſole Magnitude A B theſe three Meaſures of different kinds of
1Quantities, that is to ſay, of Spaces, of Times, and of Impetus's, let
it be required to determine in the aſſigned Space, and at the height
A C, how much the Time of the Fall of the Moveable from A to
C is to be, and what the Impetus is that ſhall be found to have been
acquired in the ſaid Term C, in relation to the Time and to the
Impetus meaſured by A B. Both theſe queſtions ſhall be reſolved
taking A D the Mean-proportional betwixt the two Lines A C
and A B; affirming the Time of the Fall along the whole Space
A C to be as the Time A D is in relation to A B, aſſigned in the
beginning for the Quantity of the Time in the Fall A B. And like­
wiſe we will ſay that the Impetus, or degree of Velocity that the
Cadent Moveable ſhall obtain in the Term C, in relation to the
Impetus that it had in B, is as the ſame Line A D is in relation to
A B, being that the Velocity encreaſeth with the ſame proportion
as the Time doth: Which Concluſion although it was aſſumed as
a Poſtulatum, yet the Author was pleaſed to explain the Applicati­
on thereof above in the third Propoſition.
This point being well underſtood and proved, we come to the
Conſideration of the Impetus derived from two compound Moti­
ons: whereof let one be compounded of the Horizontal and alwaies
Equable, and of the Perpendicular unto the Horizon, and it alſo
Equable: but let the other be compounded of the Horizontal like­
wiſe alwaies Equable, and of the Perpendicular Naturally-Accele­
rate. If both ſhall be Equable, it hath been ſeen already that the
Impetus emerging from the compoſition of both is potentia equal to
both, as for more plainneſs we will thus Exemplifie. Let the Move­
able deſcending along the Perpendicular A B be ſuppoſed to have,
for example, three degrees of Equable Impetus, but being tranſ­
ported along A B towards C, let the ſaid Velocity and Impetus be
ſuppoſed four degrees, ſo that in the ſame Time that falling it would
paſs along the Perpendicular, v. gr. three yards,
152[Figure 152]
it would in the Horizontal paſs four, but in
that compounded of both the Velocities it
cometh in the ſame Timefrom the point A un­
to the Term C, deſcending all the way along the Diagonal Line
A C, which is not ſeven yards long, as that ſhould be which is com­
pounded of the two Lines A B, 3, and B C, 4, but is 5; which 5 is
potentia equal to the two others, 3 and 4: For having found the
Squares of 3 and 4, which are 9 and 16, and joyning theſe together,
they make 25 for the Square of A C, which is equal to the two
Squares of A B and B C: whereupon A C ſhall be as much as is the
Side, or, if you will, Root of the Square 25, which is 5. For a conſtant
and certain Rule therefore, when it is required to aſſign the
Quantity of the Impetus reſulting from two Impetus's given, the
one Horizontal, and the other Perpendicular, and both Equable,
1they are each of them to be ſquared, and their Squares being put
together the Root of the Aggregate is to be extracted, which ſhall
give us the quantity of the Impetus compounded of them both.
And thus in the foregoing example, that Moveable that by vertue
of the Perpendicular Motion would have percuſſed upon the Hori­
zon with three degrees of Force, and with only the Horizontal Mo­
tion would have percuſſed in C with four degrees, percuſſing with
both the Impetus's conjoyned, the blow ſhall be like to that of the
Percutient moved with five degrees of Velocity and Force. And
this ſame Percuſſion would be of the ſame Impetuoſity in all the
points of the Diagonal A C, for that the compounded Impetus's
are alwaies the ſame, never encreaſing or diminiſhing.
Let us now ſee what befalls in compounding the Equable Hori­
zontal Motion with another Perpendicular to the Horizon which
beginning from Reſt goeth Naturally Accelerating. It is already
manifeſt, that the Diagonal, which is the Line of the Motion com­
pounded of theſe two, is not a Right Line, but Semiparabolical,
as hath been demonſtrated; ^{*} in which the Impetus doth go con­

tinually encreaſing by means of the continual encreaſe of the Ve­
locity of the Perpendicular Motion: Wherefore, to determine what
the Impetus is in an aſſigned point of that Parabolical Diagonal, it
is requiſite firſt to aſſign the Quantity of the Uniform Horizontal
Impetus, and then to find what is the Impetus of the falling Movea­
ble in the point aſſigned: the which cannot be determined without
the conſideration of the Time ſpent from the beginning of the
Compoſition of the two Motions: which Conſideration of the
Time is not required in the Compoſition of Equable Motions, the
Velocities and Impetus's of which are alwaies the ſame: but here
where there is inſerted into the mixture a Motion which beginning
from extream Tardity goeth encreaſing in Velocity according to
the continuation of the Time, it is neceſſary that the quantity of
the Time do ſhew us the quantity of the degree of Velocity in the
aſſigned point: for, as to the reſt, the Impetus compounded of theſe
two (as in Uniform Motions) is potentia equal to both the others
compounding. But here again I will better explain my meaning by
an example. In A C the Perpendicular to the Horizon let any part
be taken A B; the which I will ſuppoſe to ſtand for the Meaſure
of the Space of the Natural Motion made along the ſaid Perpen­
dicular, and likewiſe let it be the Meaſure of the Time, and alſo of
the degree of Velocity, or, if you will, of the Impetus's. It is ma­
nifeſt in the firſt place, that if the Impetus of the Moveable in B
ex quiete in A ſhall be turned along B D parallel to the Horizon in
an Equable Motion, the quantity of its Velocity ſhall be ſuch that
in the Time A B it ſhall paſs a Space double to the Space A B, which
let be the Line B D. Then let B C be ſuppoſed equal to B A, and
1let C E be drawn parallel and equal to B D, and thus by the Points
B and E we ſhall deſcribe the Parabolick Line B E I. And becauſe
that in the Time A B with the Impetus A B the Horizontal Line B D
or C E is paſſed, double to A B, and in ſuch another Time the Per­
pendicular B C is paſſed with an acquiſt of Impetus in C equal to
the ſaid Horizontal Line; therefore the Moveable in ſuch another
Time as A B ſhall be found to have paſſed from B to E along the
Parabola B E with an Impetus compounded of two, each equal to
the Impetus A B. And becauſe one of them is Horizontal, and the
other Perpendicular, the Impetus compound of them ſhall be equal
in Power to them both, that is
153[Figure 153]
double to one of them. So that
ſuppoſing B F equal to B A, and
drawing the Diagonal A F, the
Impetus or the Percuſſion in E
ſhall be greater than the Percuſ­
ſion in B of the Moveable fal­
ling from the Height A, or than
the Percuſſion of the Horizon­
tal Impetus along B D, according
to the proportion of A F to
A B. But in caſe, ſtill retaining
B A for the Meaſure of the
Space of the Fall from Reſt in
A unto B, and for the Meaſure of the Time and of the Impetus of
the falling Moveable acquired in B, the Altitude B O ſhould not be
equal to, but greater than A B, taking B G to be a Mean-propor­
tional betwixt the ſaid A B and B O, the ſaid B G would be the
Meaſure of the Time and of the Impetus in O, acquired in O by the
Fall from the height B O; and the Space along the Horizontal
Line, which being paſſed with the Impetus A B in the Time A B
would be double to A B, ſhall, in the whole duration of the Time
B G, be ſo much the greater, by how much in proportion B G is
greater than B A. Suppoſing therefore L B equal to B G, and draw­
ing the Diagonal A L, it ſhall give us the quantity compounded of
the two Impetus's Horizontal and Perpendicular, by which the
Parabola is deſcribed; and of which the Horizontal and Equable is
that acquired in B by the fall of A B, and the other is that acquired
in O, or, if you will, in I by the Deſcent B O, whoſe Time, as alſo
the quantity of its Moment was B G. And in this Method we ſhall
inveſtigate the Impetus in the extream term of the Parabola, in caſe
its Altitude were leſſer than the Sublimity A B, taking the Mean­
proportional betwixt them both: which being ſet off upon the Ho­
rizontal Line in the place of B F, and the Diagonal drawn, as A F,
we ſhall hereby have the quantity of the Impetus in the extream
term of the Parabola.
1
* Or along
which.
And to what hath hitherto been propoſed touching Impetus's,
Blows, or if you pleaſe, Percuſſions of ſuch like Projects, it is ne­
ceſſary to add another very neceſſary Conſideration; and this it is:
That it doth not ſuffice to have regard to the Velocity only of the
Project for the determining rightly of the Force and Violence of the
Percuſſion, but it is requiſite likewiſe to examine apart the State
and Condition of that which receiveth the Percuſſion, in the effica­
cy of which it hath for many reſpects a great ſhare and intereſt.
And firſt there is no man but knows that the thing ſmitten doth ſo
much ſuffer violence from the Velocity of the Percutient by how
much it oppoſeth it, and either totally or partially checketh its
Motion: For if the Blow ſhall light upon ſuch an one as yieldeth to
the Velocity of the Percutient without any Reſiſtance, that Blow
ſhall be nullified: And he that runneth to hit his Enemy with his
Launce, if at the overtaking of him it ſhall fall out that he moveth,
giving back with the like Velocity, he ſhall make no thruſt, and the
Action ſhall be a meer touch without doing any harm.
But if the Percuſſion ſhall happen to be received upon an Object
which doth not wholly yield to the Percutient, but only partially,
the Percuſſion ſhall do hurt, though not with its whole Impetus, but
only with the exceſs of the Velocity of the ſaid Percutient above
the Velocity of the recoile and receſſion of the Object percuſſed:
ſo that, if v. g. the Percutient ſhall come with 10 degrees of Velo­
city upon the Percuſſed Body, which giving back in part retireth
with 4 degrees, the Impetus and Percuſſion ſhall be as if it were of
6 degrees. And laſtly, the Percuſſion ſhall be entire and perfect on
the part of the Percutient when the thing percuſſed yieldeth not,
but wholly oppoſeth and ſtoppeth the whole Motion of the Percu­
tient; if haply there can be ſuch a caſe. And I ſay on the part of
the Percutient, for when the Body percuſſed moveth with a contra­
ry Motion towards the Percutient, the Blow and Shock ſhall be
ſo much the more Impetuous by how much the two Velocities uni­
ted are greater than the ſole Velocity of the Percutient. More­
over, you are likewiſe to take notice, that the more or leſs yielding
may proceed not only from the quality of the Matter more or leſs
hard, as if it be of Iron, of Lead, or of Wooll, &c. but alſo from
the Poſition of the Body that receiveth the Percuſſion. Which Po­
ſition if it ſhall be ſuch as that the Motion of the Percutient hap­
neth to hit it at Right-Angles, the Impetus of the Percuſſion ſhall
be the greateſt: but if the Motion ſhall proceed obliquely, and, as
we ſay, aſlant, the Percuſſion ſhall be weaker; and that more, and
more according to its greater and greater Obliquity: for an Ob­
ject in that manner ſcituate, albeit of very ſolid matter, doth not
damp or arreſt the whole Impetus and Motion of the Percutient,
which ſlanting paſſeth farther, continuing at leaſt in ſome part to
1move along the Surface of the oppoſed Body Reſiſting. When
therefore we have even now determined of the greatneſs of the
Impetus of the Project in the end of the Parabolicall Line, it ought
to be underſtood to be meant of the Percuſſion received upon a
Line at Right Angles with the ſame Parabolick Line, or with the
Line that is Tangent to the Parabola in the foreſaid point: for
although that ſame Motion be compounded of an Horizontal and
a Perpendicular Motion, the Impetus is not at the greateſt either
upon the Horizontal Plane, or upon that erect to the Horizon, be­
ing received upon them both obliquely.
SAGR. Your ſpeaking of theſe Blows, and theſe Percuſſions
hath brought into my mind a Problem, or, if you will, Queſtion
in the Mechanicks, the ſolution whereof I could never find in any
Author, nor any thing that doth diminiſh my admiration, or ſo
much as in the leaſt afford my judgment ſatisfaction. And my
doubt and wonder lyeth in my not being able to comprehend
whence that Immenſe Force and Violence ſhould proceed, and on
what Principle it ſhould depend, which we ſee to conſiſt in Per­
cuſſion, in that with the ſimple ſtroke of an Hammer, that doth
not weigh above eight or ten pounds, we ſee ſuch Reſiſtances to be
overcome as would not yield to the weight of a Grave Body that
without Percuſſion hath an Impetus only by preſſing and bearing
upon it, albeit the weight of this be many hundreds of pounds
more. I would likewiſe find out a way to meaſure the Force of this
Percuſſion, which I do not think to be infinite, but rather hold
that it hath its Term in which it may be compared, and in the end
Regulated with other Forces of preſſing Gravities, either of Lea­
vers, or of Screws, or of other Mechanick Inſtruments, of whoſe
multiplication of Force I am thorowly ſatisfied.
SALV. You are not alone in the admirableneſs of the effect,
and the obſcurity of the cauſe of ſo ſtupendious an Accident. I
ruminated a long time upon it in vain, my ſtupifaction ſtill encrea­
ſing; till in the end meeting with our Academian, I received from
him a double ſatisfaction: firſt in hearing that he alſo had been a
long time at the ſame loſs; and next in underſtanding that after he
had at times ſpent many thouſands of hours in ſtudying and con­
templating thereon, he had light upon certain Notions far from
our firſt conceptions, and therefore new, and for their Novelty to
be admired. And becauſe that I already ſee that your Curioſity
would gladly hear thoſe Conceits which are Remote from common
Conjecture, I ſhall not ſtay for your entreaty, but I give you my
word that ſo ſoon as we ſhall have finiſhed the Reading of this
Treatiſe of Projects, I will ſet before you all thoſe Fancies, or, I
might ſay, Extravagancies that are yet left in my memory of the
Diſcourſes of the Academick. In the mean time let us proſecute
the Propoſitions of our Author.
1
PROBL. II. PROP. V.
In the Axis of a given Parabola prolonged to find
a ſublime point out of which the Moveable
falling ſhall deſcribe the ſaid Parabola.
Let the Parabola be A B, its Amplitude H B, and its prolonged
Axis H E; in which a Sublimity is to be found, out of which the
Moveable falling, and converting the Impetus conceived in A
along the Horizontal Line, deſcribeth the Parabola A B. Draw the
Horizontal Line A G, which ſhall be Parallel to B H, and ſuppoſing A F
equal to A H draw the Right Line F B, which toucheth the Parabola in
B, and cutteth the Horizontal Line A G in G; and unto F A and A G
let A E be a third Proportional. I ſay, that E is the ſublime Point re­
quired, out of which the Moveable falling ex quiete in E, and the Im­
petus conceived in A being converted along the Horizontal Line over­
taking the Impetus of the Deſcent
154[Figure 154]
in H ex quiete in A, deſcribeth the
Parabola A B. For if we ſuppoſe
E A to be the Meaſure of the Time
of the Fall from E to A, and of
the Impetus acquired in A, A G
(that is a Mean-proportional be­
tween E A and A F) ſhall be the
Time and the Impetus coming
from F to A, or from A to H. And
becauſe the Moveable coming out of
E in the Time E A with the Impetus acquired in A paſſeth in the Ho­
rizontal Lation with an Equable Motion the double of E A; There­
fore likewiſe moving with the ſame Impetus it ſhall in the Time A G
paſs the double of G A, to wit, the Mean-proportional B H (for the
Spaces paſſed with the ſame Equable Motion are to one another as the
Times of the ſaid Motions:) And along the Perpendicular A H ſhall
be paſſed with a Motion ex quiete in the ſame Time G A: Therefore
the Amplitude H B, and Altitude A H are paſſed by the Moveable in the
ſame Time: Therefore the Parabola A B ſhall be deſcribed by the
Deſcent of the Project coming from the Sublimity E: Which was re­
quired.
COROLLARY.
Hence it appeareth that the half of the Baſe or Amplitude of the
Semiparabola (which is the fourth part of the Amplitude of
the whole Parabola) is a Mean-proportional betwixt its Al­
titude and the Sublimity out of which the Moveable falling
deſcribeth it.
1
PROBL. III. PROP. VI.
The Sublimity and Altitude of a Semiparabola
being given to find its Amplitude.
Let A C be perpendicular to the
155[Figure 155]
Horizontal Line D C, in
which let the Altitude C B and
the Sublimity B A be given: It is
required in the Horizontal Line
D C to find the Amplitude of the
Semiparabola that is deſcribed out of
the Sublimity B A with the Alti­
tude B C. Take a Mean proportional
between C B and B A, to which let
C D be double, I ſay, that C D is
the Amplitude required. The which
is manifeſt by the precedent Propoſition.
THEOR. IV. PROP. VII.
In Projects which deſcribe Semiparabola's of the
ſame Amplitude, there is leſs Impetus required
in that which deſcribeth that whoſe Ampli­
tude is double to its Altitude, than in any
other.
For let the Semiparabola be B D, whoſe Amplitude C D is dou­
ble to its Altitude C B; and in its Axis extended on high let B A
be ſuppoſed equal to the Altitude B C; and draw a Line from
A to D which toucheth the Semiparabola in D, and ſhall cut the Hori­
zontal Line B E in E; and B E ſhall be equal to B C or to B A: It is
manifeſt that it is deſcribed by the Project whoſe Equable Horizontal
Impetus is ſuch as is that gained in B of a thing falling from Reſt in A,
and the Impetus of the Natural Motion downwards, ſuch as is that of
a thing coming to C ex quiete in B. Whence it is manifeſt, that the
Impetus compounded of them, and that ſtriketh in the Term D is as the
Diagonal A E, that is potentia equal to them both. Now let there be
another Semiparabola G D, whoſe Amplitude is the ſame C D, and the
Altitude C G leſs, or greater than the Altitude B C, and let H D touch
the ſame, cutting the Horizontal Line drawn by G in the point K; and
as H G is to G K, ſo let K G be to G L: by what hath been demonſtrated
G L ſhall be the Altitude from which the Project falling deſcribeth the
1Parabola G D. Let G M be a Mean-proportional betwixt A B and
G L; G M ſhall be the Time, and the Moment or Impetus in G of the
Project falling from L, (for it hath been ſuppoſed that A B is the Mea­
ſure of the Time and Impetus.) Again, let G N be a Mean-propor­
tional betwixt B C and C G: this G N ſhall be the Meaſure of the
Time and the
Impetus of the
156[Figure 156]
Project falling
from G to C.
If therefore a
Line be drawn
from M to N
it ſhall be the
the Meaſure of
the Impetus of
the Project a­
long the Para­
bola B D, ſcri­
king in the
term D. Which
Impetus, I ſay,
is greater than the Impetus of the Project along the Parabola B D,
whoſe quantity was A E. For becauſe G N is ſuppoſed the Mean-pro­
portional betwixt B C and C G, and B C is equal to B E, that is to H G;
(for they are each of them ſubduple to D C:) Therefore as C G is to
G N, ſo ſhall N G be to G K: and, as C G or H G is to G K, ſo ſhall the
Square N G be to the Square of G K: But as H G is to G K, ſo was
K G ſuppoſed to be to G L: Therefore as N G is to the Square G K, ſo
is K G to G L: But as K G is to G L, ſo is the Square K G unto the
Square G M, (for G M is the Mean between K G and G L:) Therefore
the three Squares N G, K G, and G M are continual proportionals: And
the two extream ones N G and G M taken together, that is the Square
M N is greater than double the Square K G, to which the Square A E
is double: Therefore the Square M N is greater than the Square A E:
and the Line M N greater than the Line A E: Which was to be de­
monſtrated.
CORROLLARY I.
Hence it appeareth, that on the contrary, in the Project out of D
along the Semiparabola D B, leſs Impetus is required than
along any other according to the greater or leſſer Elevation
of the Semiparabola B D, which is according to the Tan­
gent A D, containing half a Right-Angle upon the Hori­
zon.
1
COROLLARRY II.
And that being ſo, it followeth, that if Projections be made with
the ſame Impetus out of the Term D, according to ſeveral
Elevations, that ſhall be the greateſt Projection or Amplitude
of the Semiparabola or whole Parabola which followeth at
the Elevation of a ^{*} Semi-Right-Angle; and the reſt, made

according to greater or leſſer Angles, ſhall be greater or
leſſer.
* Or, at the Ele­
vation of 45 de­
grees.
SAGR. The ſtrength of Neceſſary Demonſtrations are full of
pleaſure and wonder; and ſuch are only the Mathematical. I un­
derſtood before upon truſt from the Relations of ſundry Gunners,
that of all the Ranges of a Cannon, or of a Mortar-piece, the grea­
teſt, ſcilicet that which carryeth the Ball fartheſt was that made at
the Elevation of a Semi-Right-Angle, which they call, of the Sixth
point of the Square: but the knowledge of the Cauſe whence it
hapneth infinitely ſurpaſſeth the bare Notion that I received upon
their atteſtation, and alſo from many repeated Experiments.
SALV. You ſay very right: and the knowledge of one ſingle
Effect acquired by its Cauſes openeth the Intellect to underſtand
and aſcertain our ſelves of other effects, without need of repairing
unto Experiments, juſt as it hapneth in the preſent Caſe; in which
having found by demonſtrative Diſcourſe the certainty of this,
That the greateſt of all Ranges is that of the Elevation of a Semi­
Right-Angle, the Author demonſtrates unto us that which poſſibly
hath not been obſerved by Experience: and that is, that of the
other Ranges thoſe are equal to one another whoſe Elevations ex­
ceed or fall ſhort by equal Angles of the Semi-right: ſo that the
Balls ſhot from the Horizon, one according to the Elevation of ſe­
ven Points, and the other of 5, ſhall light upon the Horizon at
equal Diſtances: and ſo the Ranges of 8 and of 4 points, of 9 and
of 3, &c. ſhall be equal. Now hear the Demonſtration of it.
THEOR. V. PROP. VIII.
The Amplitudes of Parabola's deſcribed by Pro­
jects expulſed with the ſame Impetus according
to the Elevations by Angles equidiſtant above,

and beneath from the ^{*} Semi-right, are equal to
each other.
1
* Or Angle of
45.
Of the Triangle M C B, about the Right-Angle C, let the Ho­
rizontal Line B C and the Perpendicular C M be equal; for
ſo the Angle M B C ſhall be Semi-right; and prolonging C M
to D, let there be conſtituted in B two equal Angles above and below
the Diagonal M B, viz. M B E, and M B D. It is to be demonſtrated
that the Amplitudes of the Parabola's deſcribed by the Projects be­
ing emitted [or ſhot off] with the ſame Impetus out of the Term B,
according to the Elevations of the Angles E B C and D B C, are equal.
For in regard that the extern Angle B M C, is equal to the two intern
M D B and M B D, the Angle M B C ſhall alſo be equal to them. And if
we ſuppoſe M B E inſtead of the Angle M B D,
the ſaid Angle M B C ſhall be equal to the two
157[Figure 157]
Angles M B E and B D C: And taking away
the common Angle M B E, the remaining An­
gle B D C ſhall be equal to the remaining An­
gle E B C: Therefore the Triangles D C B
and B C E are alike. Let the Right Lines
D C and E C be divided in the midſt in H and
F; and draw H I and F G parallel to the Ho­
rizontal Line C B; and as D H is to H I, ſo
let I H be to H L: the Triangle I H L ſhall be
like to the Triangle I H D, like to which alſo is E G F. And ſeeing
that I H and G F are equal (to wit, halves of the ſame B C:) There­
fore F E, that is F C, ſhall be equal to H L: And, adding the common
Line F H, C H ſhall be equal to F L. If therefore we underſtand the Se­
miparabola to be deſcribed along by H and B, whoſe Altitude ſhall be
H C, and Sublimity H L, its Amplitude ſhall be C B, which is double
to HI, that is, the Mean betwixt D H, or C H, and HL: And D B
ſhall be a Tangent to it, the Lines C H and H D being equal. And if,
again, we conceive the Parabola to be deſcribed along by F and B from
the Sublimity FL, with the Altitude F C, betwixt which the Mean­
proportional is F G, whoſe double is the Horizontal Line C B: C B, as
before, ſhall be its Amplitude; and E B a Tangent to it, ſince E F and
F C are equal: But the Angles D B C and E B C (ſcilicet, their Eleva­
tions) ſhall be equidiſtant from the Semi-Right Angle: Therefore the
Propoſition is demonſtrated.
THEOR. VI. PROP. IX.
The Amplitudes of Parabola's, whoſe Altitudes
and Sublimities anſwer to each other è contra­
rio, are equall.
1
Let the Altitude G F of the Parabola F H have the ſame proporti­
on to the Altitude C B of the Parabola B D, as the Sublimity B A
hath to the Sublimity F E. I ſay, that the Amplitude H G is equal
to the Amplitude D C. For ſince the firſt G F hath the ſame propor­
tion to the ſecond C B, as the third B A hath to the fourth F E; There­
fore, the Rectangle
158[Figure 158]
G F E of the firſt and
fourth, ſhall be equal to
the Rectangle C B A
of the ſecond and
third: Therefore the
Squares that are equal
to theſe Rectangles ſhall
be equal to one another:
But the Square of half of G H is equal to the Rectangle G F E; and
the Square of half of C D is equal to the Rectangle C B A: There­
fore theſe Squares, and their Sides, and the doubles of their Sides ſhall
be equal: But theſe are the Amplitudes G H and C D: Therefore the
Propoſition is manifeſt.
LEMMA pro ſequenti.
If a Right Line be cut according to any proportion, the Squares
of the Mean-proportionals between the whole and the two
parts are equal to the Square of the whole.
Let A B be cut according to any proportion in C. I ſay, that the
Squares of the Mean-proportional Lines between the whole A B and
the parts A C and C B, being taken together are equal to the Square of
the whole A B. And this appeareth, a Semi-
159[Figure 159]
circle being deſcribed upon the whole Line
B A, and from C a Perpendicular being ere­
cted C D, and Lines being drawn from D to
A, and from D to B. For D A is the Mean­
proportional betwixt A B and A C; and D B is the Mean-proporti­
onal between A B and B C: And the Squares of the Lines D A and
D B taken together are equal to the Square of the whole Line A B,
the Angle A D B in the Semicircle being a Right-Angle: Therefore
the Propoſition is manifest.
1
THEOR. VII. PROP. X.
The Impetus or Moment of any Semiparabola is
equal to the Moment of any Moveable falling
naturally along the Perpendicular to the Ho­
rizon that is equal to the Line compounded of
the Sublimity and of the Altitude of the Se­
miparabola.
Let the Semiparabola be A B, its Sublimity D A, and Altitude
A C, of which the Perpendicular D C is compounded. I ſay, that
the Impetus of the Semiparabola in B is equal to the Moment of
the Moveable Naturally falling from D to C. Suppoſe D C it ſelf to be
the Meaſure of the Time and of the Impetus; and take a Mean-pro­
portional betwixt C D and D A, to which let
160[Figure 160]
C F be equal; and withal let C E be a Mean­
proportional between D C and C A: Now C F
ſhall be the Meaſure of the Time and of the Mo­
ment of the Moveable ſalling along D A out of
Reſt in D; and C E ſhall be the Time and Mo­
ment of the Moveable falling along A C, out of
Reſt in A, and the Moment of the Diagonal E F
ſhall be that compounded of both the others, ſcil.
that of the Semiparabola in B. And becauſe
D C is cut according to any proportion in A, and becauſe C F and C E
are Mean-Proportionals between C D and the parts D A and A C; the
Squares of them taken together ſhall be equal to the Square of the
whole; by the Lemma aforegoing: But the Squares of them are alſo
equal to the Square of E F: Therefore D F is equal alſo to the Line D C:
Whence it is manifeſt that the Moments along D C, and along the Se­
miparabola A B, are equal in C and B: Which was required.
COROLLARY.
Hence it is manifeſt, that of all Parabola's whoſe Altitudes and
Sublimities being joyned together are equal, the Impetus's are
alſo equal.
1
PROBL. IV. PROP. XI.
The Impetus and Amplitude of a Semiparabola be­
ing given, to find its Altitude, and conſequently
its Sublimity.
Let the Impetus given be defined by the Perpendicular to the Ho­
rizon A B; and let the Amplitude along the Horizontal Line be
B C. It is required to find the Altitude and Sublimity of the
Parabola whoſe Impetus is A B, and Amplitude B C. It is manifeſt,
from what hath been already demonſtrated, that half the Amplitude B C
will be a Mean-proportional betwixt the Altitude and the Sublimity of
the ſaid Semiparabola, whoſe Impetus, by the precedent Propoſition, is
the ſame with the Impetus of the Moveable falling from Reſt in A along
the whole Perpendicular A B: Wherefore B A is ſo to be cut that the
Rectangle contained by its parts may be equal to the Square of half of
B C, which let be B D. Hence it appeareth
to be neceſſary that D B do not exceed the
161[Figure 161]
half of B A; for of Rectangles contained by
the parts the greateſt is when the whole
Line is cut into two equal parts. Therefore
let B A be divided into two equal parts in E.
And if B D be equal to B E the work is
done; and the Altitude of the Semipara­
bola ſhall be B E, and its Sublimity E A:
(and ſee here by the way that the Amplitude
of the Parabola of a Semi-right Elevation,
as was demonſtrated above, is the greateſt of
all thoſe deſcribed with the ſame Impetus.)
But let B D be leſs than the half of B A,
which is ſo to be cut that the Rectangle under the parts may be equal to
the Square B D. Upon E A deſcribe a Semicircle, upon which out of A
ſet off A F equal to B D, and draw a Line from F to E, to which cut
a part equal E G. Now the Rectangle B G A, together with the Square
E G, ſhall be equal to the Square E A; to which the two Squares A F
and F E are alſo equal: Therefore the equal Squares G E and F E be­
ing ſubſtracted, there remaineth the Rectangle B G A equal to the
Square A F, ſcilicet, to B D; and the Line B D is a Mean-proportional
betwixt B G and G A. Whence it appeareth, that of the Semipa­
rabola whoſe Amplitude is B C, and Impetus A B, the Altitude is
B G, and the Sublimity G A. And if we ſet off B I below equal to G A,
this ſhall be the Altitude, and I A the Sublimity of the Semiparabola
I C. From what hath been already demonſtrated we are able,
1
PROBL. V. PROP. XII.
To collect by Calculation of the Amplitudes of all
Semiparabola's that are deſcribed by Projects
expulſed with the ſame Impetus, and to make
Tables thereof.
It is obvious, from the things demonſtrated, that Parabola's are de­
ſcribed by Projects of the ſame Impetus then, when their Subli­
mities together with their Altitudes do make up equal Perpendicu­
lars upon the Horizon. Theſe Perpendiculars therefore are to be com­
prehended between the ſame Horizontal Parallels. Therefore let the
Horizontal Line C B be ſuppoſed equal to the Perpendicular B A, and
draw the Diagonal from A to C. The Angle A C B ſhall be Semi­
right, or 45 Degrees. And the Perpendicular B A being divided into
two equal parts in D, the Semiparabola D C ſhall be that which is de­
ſcribed from the Sublimity A D together with the Altitude D B: and
its Impetus in C ſhall be as great as that of the Moveable coming out of
Reſt in A along the Perpendicular A B is in B. And if A G be drawn
parallel to B C, the united Altitudes and Sublimities of all other re­
maining Semiparabola's whoſe future Impetus's are the ſame with thoſe
now mentioned muſt be bounded by the Space between the Parallels
162[Figure 162]
A G and B C. Farthermore, it having
been but now demonſtrated, that the Am­
plitudes of the Semiparabola's whoſe
Tangents are equidiſtant either above or
below from the Semi right Elevation are
equal, the Calculations that we frame
for the greater Elevations will likewiſe
ſerve for the leſſer. We chooſe moreover
a number of ten thouſand parts for the
greateſt Amplitude of the Projection of
the Semiparabola made at the Elevation
of 45 degrees: ſo much therefore the Line
B A, and the Amplitude of the Semipa­
rabola B C, are to be ſuppoſed. And we
make choice of the number 10000, becauſe we in our Calculation uſe
the Table of Tangents, in which this number agreeth with the Tangent
of 45 degrees. Now, to come to the buſineſs, let C E be drawn, contain­
ing the Angle E C B greater (Acute nevertheleſs,) than the Angle
A C B; and let the Semiparabola be deſcribed which is touched by the
Line E C, and whoſe Sublimity united with its Altitude is equal to
B A. In the Table of Tangents take the ſaid B E for the Tangent at the
1given Angle B C E, which divide into two equal parts at F. Then
find a third Proportional to B F and B C, (or to the half of B C,)
which ſhall of neceſſity be greater than F A; therefore let it be F O:
Of the Semiparabola, therefore, inſcribed in the Triangle E C B, ac­
cording to the Tangent C E, whoſe Amplitude is C B, the Altitude B F,
and the Sublimity F O is found: But the whole Line B O riſeth above
the Parallels A G and C B, whereas our work was to bound it between
them: For ſo both it and the Semiparabola D C ſhall be deſcribed by
the Projects out of C expelled with the ſame Impetus. Therefore we
are to ſeek another like to this, (for innumerable greater and ſmaller,
like to one another, may be deſcribed within the Angle B C E) to whoſe
united Sublimity and Altitude B A ſhall be equal. Therefore as O B is
to B A, ſo let the Amplitude B C be to C R: and C R ſhall be found,
ſcilicet the Amplitude of the Semiparabola according to the Elevation
of the Angle B C E, whoſe conjoyned Sublimity and Altitude is equal
to the Space contained between the Parallels G A and C B: Which
was required. The work, therefore, ſhall be after this manner.
Take the Tangent of the given Angle B C E, to the half of which
add the third Proportional of it, and half of B C, which let be F O:
Then as O B is to B A, ſo let B C be to another, which let be C R, to wit,
the Amplitude ſought. Let us give an Example.
Let the Angle E C B be 50 degrees, its Tangent ſhall be 11918,
whoſe half, to wit, B F, is 5959, and the half of B C is 5000, the third
proportional of theſe halves is 4195, which added to the ſaid B F
maketh 10154: for the ſaid B O. Again, as O B is to B A, that is as
10154 is to 10000, ſo is B E, that is 10000 (for each of them is the
Tangent of 45 degrees) to another: and that ſhall give us the required
Altitude R C 9848, of ſuch as B C (the greateſt Amplitude) is
10000. To theſe the Amplitudes of the whole Parabola's are double,
ſcilicet 19696 and 20000. And ſo much likewiſe is the Amplitude of
the Parabola according to the Elevation of 40 degrees, ſince it is equal­
ly diſtant from 45 degrees.
SAGR. For the perfect underſtanding of this Demonſtration I
muſt be informed how true it is, that the Third Proportional to
B F and B I, is (as the Author ſaith) neceſſarily greater than
F A.
SALV. That inference, as I conceive, may be deduced thus.
The Square of the Mean of three proportional Lines is equal to
the Rectangle of the other two: whence the Square of B I, or of
B D equal to it, ought to be equal to the Rectangle of the firſt F B
multiplied into the third to be found: which third is of neceſſity to
be greater than F A, becauſe the Rectangle of B F multiplied into
F A is leſs than the Square B D: and the Defect is as much as the
Square of D F, as Euclid demonſtrates in a Propoſition of his
1Second Book. You muſt alſo know, that the point F which divi­
deth the Tangent E B in the middle, will many other times fall
above the point A, and once alſo in the ſaid A: In which caſes it is
evident of it ſelf, that the third proportional to the half of the Tan­
gent, and to B I (which giveth the Sublimity) is all above A. But
the Author hath taken a Caſe in which it was not manifeſt that the
ſaid third Proportional is alwaies greater than F A: and which
therefore being ſet off above the point F paſſeth beyond the Paral­
lel A G. Now let us proceed.
It will not be unprofitable if by help of this Table we compoſe ano­
ther, ſhewing the Altitudes of the ſame Semiparabola's of Projects of
the ſame Impetus. And the Conſtruction of it is in this manner.
PROBL. VI. PROP. XIII.
From the given Amplitudes of Semiparabola's in
the following Table ſet down, keeping the
common Impeius with which every one of
them is deſcribed, to compute the Altitudes of
each ſeveral Semiparabola.
Let the Amplitude given be B C, and of the Impetus, which is
ſuppoſed to be alwaies the ſame, let the Meaſure be O B, to wit,
the Aggregate of the Altitude and Sublimity. The ſaid Altitude
is required to be found and diſtinguiſhed. Which ſhall then be done when
B O is ſo divided as that the Rectangle contained under its parts is
equal to the Square of half the Amplitude B C. Let that ſame divi­
ſion fall in F; and let both O B and B C be cut in the midſt at D and I.
163[Figure 163]
The Square I B, therefore, is equal to the
Rectangle B F O: And the Square D O is
equal to the ſame Rectangle together with the
Square F D. If therefore from the Square
D O we deduct the Square B I, which is equal
to the Rectangle B F O, there ſhall remain
the Square F D; to whoſe Side D F, B D be­
ing added it ſhall give the deſired Altitude
Altitude B F. And it is thus compounded
ex datis. From half of the Square B O known
ſubſtract the Square B I alſo known, of the remainder take the Square
Root, to which add D B known; and you ſhall have the Altitude ſought
B F. For example. The Altitude of the Parabola deſcribed at the
Elevation of 55 degrees is to be found. The Amplitude, by the follow­
ing Table is 9396, its half is 4698, the Square of that is 22071204,
1this ſubſtracted from the Square of the half B O, which is alwaies
the ſame, to wit, 2500000, the remainder is 2928796, whoſe Square
Root is 1710 very near, this added to the half of B O, to wit, 5000,
gives 67101, and ſo much is the Altitude B F. It will not be unprofi­
table, to give the Third Table, containing the Altitudes and Sublimi­
ties of Semiparabola's, whoſe Amplitude ſhall be alwaies the ſame.
SAGR. This I would very gladly ſee ſince by it I may come to
know the Difference of the Impetus's, and of the Forces that are
required for carrying the Project to the ſame Diſtance with Ranges
which are called at Random: which Difference I believe is very
great according to the different Elevations [or Mountures:] ſo that
if, for example, one would at the Elevation of 3 or 4 degrees, or of
87 or 88 make the Ball to fall where it did, being ſhot at the Ele­
vation of gr. 45. (where, as hath been ſhewn, the leaſt Impetus is
required) I believe that it would require a very much greater
Force.
SALV. You are in the right: and you will find that to do the
full execution in all the Elevations it is requiſite to make great Pro­
greſſions towards an infinite Impetus. Now let us ſee the Conſtru­
ction of the Table.
1

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1Degrees of Elevation.The Amplitudes of the Semipara-bola's, deſcribed with the ſame Impetus.Gr.Gr.451000046999444479976434899454249990241509848405197823952970438539612375495113655939635569272345791363358898932598829316086593061848129628290286380902764788026657660256674312467719123686944226966922170642820716157197258781873559217745300167550001576469414774383137840671279374611803420108130909822756883241978420796851736586139148710443886982893491Degrees of Elevation.The Altitudes of the Se-miparabola's, whoſe Impetus is the ſame.Gr.Gr.1346517321347534632848552345049569857650586861085160387150526207819453637992455465461030255671017365566873124325770331350658719014585597348156706075021676061764917855627796189556379391910606480782011706582142112856683462214026784742315276885972416856987152517867088302619227189402720617290452822047391442923517492403024997593303126537694153228107794933329677895673431287996363532898096983634568197553736218298063837938398513939628498904041328599244143028699514244778799724346548899874448278999984550009010000A Table containing the Altitudes and Subli-mities of the Semiparabola's, whoſe Am-plitudes are the ſame, that is to ſay, of 10000 parts, calculated to each Deg. of Elevation.Gr.Altit.Sublim.Gr.Altit.Sublim.187286533465177482821751424504753634662326295802485553450243497153149575243455437571425059594106652547573516174404876144071652639930068702355875366353765979231565546882363210881283675571413500119722572056741333721210632351857769932471311542170158800231231412462005659833230041113391866360860028871614341740561902027711715291635562940326581816241538963981325471917221452264102512438201820137366510722233121191913024661122022262220201237667117792122232123117786812375202024222611230691302519192523321072270132371819262439102537114521172127254798147215388162428265894047316354152829277290207417437141330288786597518660133931300883367620054124632312480017721657115433324776997823523106234337374137925723972353501714180283568813636336882813156079237376866358235577702383906639583402226133940496174844757252540419659598557150437414246575286715033494245025553879540526243466253628814318117444482851778928649987455000500090Infinite
PROBL. VII. PROP. XIV.
To find the Altitudes and Sublimities of Semipa­
rabola's whoſe Amplitudes ſhall be equal for
each degree of Elevation.
This we ſhall eaſily do. For ſuppoſing the Amplitude of the Semi­
par abola to be of 10000 parts, the half of the Tangent of each
degree of Elevation ſhews the Altitude. As for example, of the
Semiparabola whoſe Elevation is 30 degrees, and Amplitude, as is
ſuppoſed, 10000 parts, the Altitude ſhall be 2887, for ſo much, very
near, is the half of the Tangent. And having found the Altitude the
Sublimity is to be known in this manner. For aſmuch as it hath been
demonſtrated that the half of the Amplitude of a Semiparabola is the
Mean proportional betwixt the Altitude and Sublimity, and the Alti­
tude being already found, and the half of the Amplitude being alwaies
the ſame, to wit, 5000 parts, if we ſhall divide the Square thereof by
the Altitude found, the deſired Sublimity ſhall come forth. As in the
Example: The Altitude found was 2887; The Square of the 5000
parts is 25000000; which being divided by 2887, giveth 8659, ve­
ry near, for the Sublimity ſought.
SALV. Now here we ſee, in the ſirſt place, that the Conje­
cture is very true which was mentioned afore, that in different
Elevations the farther one goeth from the middlemoſt, whether it
be in the Higher, or in the Lower, ſo much greater Impetus and Vio­
lence is required to carry the Project to the ſame Diſtance. For the
Impetus lying in the mixture of the two Motions, Equable, Hori­
zontal, and Perpendicular Naturally-Accelerate, of which Impetus
the Aggregate of the Altitude and Sublimity is the Meaſure, we do
ſee in the propounded Table that that ſame Aggregate is leaſt in
the Elevation of gr. 45, in which the Altitude and Sublimity are
equal, ſcilicet each 5000, and their Aggregate 10000. But if we
ſhould look on any greater Elevation, as, for example, of gr. 50, we
ſhould ſind the Altitude to be 5959, and the Sublimity 4196, which
added together make 10155. And ſo much alſo we ſhould find the
Impetus of gr. 40 to be, this and that Elevation being equally re­
mote from the middlemoſt. Where we are to note, in the ſecond
place, that it is true, That equal Impetus's are ſought by two, and
two in the Elevations equidiſtant from the middlemoſt, with this
pretty variation over and above that the Altitudes and the Subli­
mities of the ^{*} ſuperiour Elevations anſwer alternally to the Sub­

limities and Altitudes of the Inferiour: ſo that whereas in the
1example propoſed, in the Elevation of gr. 50. the Altitude is 5959
and the Sublimity 4196, in the Elevation of gr. 40. it falls out on
the contrary that the Altitude is 4196, and the Sublimity 5959:
And the ſame happens in all others without any difference; ſave
only that for the avoyding of tediouſneſs in Calculations we have
kept no account of ſome fractions, which in ſo great ſums are of no
value, but may without any prejudice be omitted.
* i.e. Thoſe above
45 deg.
SAGR. I am obſerving that of the two Impetus's Horizontal and
Perpendicular in Projections, the more Sublime they are, they need
ſo much the leſs of the Horizontal, and the more of the Perpendi­
cular. Moreover in thoſe of ſmall Elevation, great muſt be the
Force of the Horizontal Impetus, which is to carry the Project in a
little Altitude. But although I comprehend very well that in the
Total Elevation of gr. 90, all the force in the world ſufficeth not
to drive the Project one ſingle Inch from the Perpendicular, but
that it muſt of neceſſity fall in the ſame place whence it was expel­
led; yet dare I not with the like certainty affirm that likewiſe in the
nullity of Elevation, that is in the Horizontal Line, the Project
cannot by any Force leſs than infinite, be driven to any di­
ſtance: So, as that, for example, a Culverin it ſelf ſhould not be
able to carry a Ball of Iron Horizontally, or, as they ſay, at Point
blank, that is at no point, which is when it hath no Elevation. I
ſay, in this caſe I ſtand in ſome doubt; and that I do not reſolute­
ly deny the thing, the reaſon depends on another Accident which
ſeems no leſs ſtrange, and yet I have a very neceſſary Demonſtrati­
on for it. And the Accident is this, the Impoſſibility of diſtending
a Rope, ſo, as that it may be ſtretched right out, and parallel to the
Horizon, but that it alwaies ſwayes and bendeth, nor is there any
Force that can ſtretch it otherwiſe.
SALV. So then, Sagredus, your wonder ceaſeth in this caſe of
the Rope becauſe you have the Demonſtration of it. But if we
ſhall well conſider the matter, it may be we ſhall find ſome corre­
ſpondence between the Accident of the Project and this of the
Rope. The Curvity of the Line of the Horizontal Projection ſeem­
eth to be derived from two Forces, of which one, (which is that of
the Projicient) driveth it Horizontally, and the other, (which
is the Gravity of the Project) draweth it downwards Perpendicu­
larly. Now ſo in the ſtretching of the Rope, there are the Forces
of thoſe that pull it Horizontally, and there is alſo the weight of
the Rope it ſelf, which naturally inclineth it downwards. Theſe
two effects are very much alike in the generation of them. And if
you allow the weight of the Rope ſo much ſtrength and power as to
be able to oppoſe and overcome any whatever Immenſe Force, that
would diſtend it right out, why will you deny the like to the weight
of the Bullet? But beſides, I ſhall tell you, and at once procure your
1wonder, and delight, that the Rope thus tentered, and ſtretcht little
or much, doth ſhape it ſelf into Lines that come very near to Para­
bolical, and the reſemblance is ſo great, that if you draw a Para­
bolical Line upon a plain Superficies that is erect unto the Horizon,
and holding it reverſed, that is with the Vertex downwards and
with the Baſe Parallel to the Horizon, you cauſe a Chain to be held
pendent, and ſuſtained at the extreams of the Baſe of the Deſcribed
Parabola, you ſhall ſee the ſaid Chain, as you ſlaken it more or leſs,
to incurvate and apply it ſelf to the ſame Parabola, and this ſame
Application ſhall be ſo much the more exact, when the deſcribed
Parabola is leſs curved, that is more diſtended: So that in Parabola's
deſcribed with Elevations under gr. 45, the Chain anſwereth the
Parabola almoſt to an hair.
SAGR. It ſeems then that with ſuch a Chain wrought into ſmall
Links one might in an inſtant trace out many Parabolick Lines up­
on a plain Superficies.
SALV. One might, and that alſo with no ſmall commodity, as I
ſhall tell you anon.
SIMP. But before you paſs any farther, I alſo would gladly be
aſcertained at leaſt in that Propoſition of which you ſay there is a
very neceſſary Demonſtration, I mean that of the Impoſſibility of
diſtending a Rope, by any whatever immenſe Force, right out and
equidiſtant from the Horizon.
SAGR. I will ſee if I remember the Demonſtration, for under­
ſtanding of which it is neceſſary, Simplicius, that you ſuppoſe for
true, that which in all Mechanick Inſtruments is confirmed, not on­
ly by Experience, but alſo by Demonſtration: and this it is, That
the Velocity of the Mover, though its Force be very ſmall, may
overcome the Reſiſtance, though very great, of a Reſiſter, which
muſt be moved ſlowly when ever the Velocity of the Mover hath
greater proportion to the Tardity of the Reſiſter, than the Reſi­
ſtance of that which is to be moved hath to the Force of the Mo­
ver.
SIMP. This I know very well, and it is demonſtrated by Ari­
ſtotle in his Mechanical Queſtions, and is manifeſtly ſeen in the Lea­
ver and in the Stiliard, in which the Roman which weigheth not
above 4 pounds, will lift up a weight of 400 in caſe the diſtance of
the ſaid Roman from the Center on which the Beam turneth be
more than an hundred times greater than the diſtance of that point
at which the great weight hangeth from the ſame Center: and this
cometh to paſs becauſe in the deſcent which the Roman maketh
paſſeth a Space above an hundred times greater than the Space
which the great weight mounteth in the ſame Time: Which is all
one as to ſay, that the little Roman moveth with a Velocity above
an hundred times greater than the Velocity of the great Weight.
1
SAGR. You argue very well, and make no ſeruple at all of
granting, that be the Force of the Mover never ſo ſmall it ſhall ſu­
perate any what ever great Reſiſtance at all times when that ſhall
more exceed in Velocity than this doth in Force and Gravity.
Now come we to the caſe of the Rope. And drawing a ſmall
Scheme be pleaſed to underſtand for once that this Line A B, reſt­
ing upon the two fixed and ſtanding points A and B, to have hang­
ing at its ends, as you ſee, two immenſe Weights C and D, which
drawing it with great Force make it to ſtand directly diſtended, it
being a ſimple Line without any gravity. And here I proceed, and
tell you, that if at the midſt of that which is the point E, you ſhould
hang any never ſo little a Weight, as is this H, the Line A B would
yield, and inclining towards the point F, and by conſequence
lengthening, will conſtrain the two great Weights C and D to
aſcend upwards: which I demonſtrate to you in this manner:
About the two points A and B as Centers I deſcribe two Quadrants
E F G, and E L M, and in regard that the two Semidiameters AI
and B L are equal to the two Semidiameters A E and E B, the exceſ­
ſes F I and F L ſhall be the quantity of the prolongations of the
parts A F and F B, above A E and E B; and of conſequence ſhall
164[Figure 164]
determine the Aſcents
of the Weights C and
D, in caſe that the
Weight H had had a
power to deſcend to F:
which might then be
in caſe the Line E F,
which is the quantity
of the Deſcent of the
ſaid Weight H, had
greater proportion to
the Line F I which de­
termineth the Aſcent of
the two Weights C &
D, than the pondero­
ſity of both thoſe Weights hath to the ponderoſity of the Weight
H. But this will neceſſarily happen, be the ponderoſity of the
Weights C and D never ſo great, and that of H never ſo ſmall; for
the exceſs of the Weights C and D above the Weight His not ſo
great, but that the exceſs of the Tangent E F above the part of the
Secant F I may bear a greater proportion. Which we will prove
thus: Let there be a Circle whoſe Diameter is G A I; and look
what proportion the ponderoſity of the Weights C and D have to
the ponderoſity of H, let the Line B O have the ſame proportion to
another, which let be C, than which let D be leſſer: So that B O
1ſhall have greater proportion to D, than to C. Unto O B and D
take a third proportional B E; and as O E is to E B, ſo let the Dia­
meter G I (prolonging it) be to I F: and from the Term F
draw the Tangent F N. And becauſe it hath been preſuppoſed,
that as O E is to E B, ſo is G I to I F: therefore, by Compoſition, as
O B is to B E, ſo is G F to F I: But betwixt O B and B E the Mean­
proportional is D; and betwixt G F and F I the Mean-proporti­
onal is N F: Therefore N F hath the ſame proportion to F I that
O B hath to D: which proportion is greater than that of the
Weights C and D to the Weight H. Therefore, the Deſcent or
Velocity of the Weight H having greater proportion to the Aſcent
or Velocity of the Weights C and D, than the ponderoſity of the
ſaid Weights C and D hath to the ponderoſity of the Weight H:
It is manifeſt, that the Weight H ſhall deſcend, that is, that the
Line A B ſhall depart from Horizontal Rectitude. And that which
befalleth the right Line A B deprived of Gravity in caſe any ſmall
Weight H cometh to be hanged at the ſame in E, happens alſo to
the ſaid Rope A B, ſuppoſed to be of ponderous Matter, without
the addition of any other Grave Body; for that the Weight of
the Matter it ſelf compounding the ſaid Rope AB is ſuſpended
thereat.
SIMP. You have fully ſatisfied me; therefore Salviatus may ac­
cording to his promiſe declare unto us, what the Commodity is that
may be drawn from ſuch like Chains, and after that relate unto us
thoſe Speculations which have been made by our Accademian
touching the Force of Percuſſion.
SALV. We are for this day ſufficiently employed in the Con­
templations already delivered, and the Time, which is pretty late,
would not be enough to carry us through the matters you mention;
therefore we ſhall defer our Conference till ſome more convenient
time.
SAGR. I concur with you in opinion, for that by ſundry diſ­
courſes that I have had with the Friends of our Academick I have
learnt that this Argument of the Force of Percuſſion is very ob­
ſcure, nor hath hitherto any one that hath treated thereof penetra­
ted its intricacies, full of darkneſs, and altogether remote from
mans firſt imaginations: and amongſt the Concluſions that I have
heard of, one runs in my mind that is very extravagant and odde,
namely, That the Force of Percuſſion is Interminate, if not Infi­
nite. We will therefore attend the leaſure of Salviatus. But for
the preſent, tell me what things are thoſe which are written at the
end of the Treatiſe of Projects?
SALV. Theſe are certain Propoſitions touching the Center of
Gravity of Solids, which our Academick found out in his youth,

conceiving that what ^{*} Frederico Comandino had writ touching the
1ſame was not altogether without Imperſection. He therefore
thought that with theſe Propoſitions, which here you ſee written,
he might ſupply that which is wanting in the Book of Comandine;
and he applyed himſelf to the ſame at the Inſtance of the moſt
Illuſtrious Lord Marqueſs Guid' Vbaldo dal Monte, the moſt ex­
cellent Mathematician of his Time, as his ſeveral Printed Works
do ſpeak him; and gave a Copy thereof to that Noble Lord with
thoughts to have purſued the ſame Argument in other Solids not
mentioned by Comandine: But he chanced after ſome Time to
meet with the ^{*} Book of Signore Luca Valerio, a moſt famous

Geometrician, and ſaw that he reſolveth all theſe matters with­
out omiſſion of any thing, he proceeded no farther, although his
Agreſſions were by methods very different from theſe of Signore
Valerio.
* Fredericus Co­
mandinus.
* De.
SAGR. It would be a favour, therefore, if, for this time, which
interpoſeth between this and our next Meeting, you would pleaſe
to leave the Book in my hands: for I ſhall all the while be read­
ing and ſtudying the Propoſitions that are conſequently therein
writ.
SALV. I ſhall very willingly obey your Command; and hope
that you will take pleaſure in theſe Propoſitions.
1
AN
APPENDIX,
In which is contained certain
THE OREMS and their DEMONSTRATIONS:
Formerly written by the ſame Author, touching the
CENTER of GRAVITY, of
SOLIDS.
POSTVLATVM.
We preſuppoſe equall Weights to be alike diſpo­
ſed in ſever all Ballances, if the Center of Gra­
vity of ſome of thoſe Compounds ſhall divide the Ballance
according to ſome proportion, and the Ballance ſhall
alſo divide their Center of Gravity according to the
ſame proportion.
LEMMA.
Let the line A B be cut in two equall parts in C,
whoſe half A C let be divided in E, ſo that as B E is to
E A, ſo may A E be to E C. I ſay that B E is double
165[Figure 165]
to E A. For as B E is to E
A, ſo is E A to E C: there­
fore by Compoſition and by Permutation of Proportion, as
B A is to A C, ſo is A E to E C: But as A E is to E C,
that is, B A to A C, ſo is B E to E A: Wherefore B
E is double to E A.
This ſuppoſed, we will Demonſtrate, That,
1
PROPOSITION.
If certain Magnitudes at any Rate equally exceed­
ing one another, and whoſe exceſs is equal to
the leaſt of them, be ſo diſpoſed in the Balance,
as that they hang at equal diſtances, to divide
the Center of Gravity of the whole Balance
ſo, that the part towards the leſſer Magnitudes
be double to the remainder.
In the ^{*} Ballance A B, therefore, let there be ſuſpended at equal di-

ſtances any number of Magnitudes, as hath been ſaid, F, G, H, K,
N; of which let the leaſt be N, and let the points of the Suſpenſions
be A, C, D, E, B, and let the Center of Gravity of all the Magnitudes
ſo diſpoſed be X. It is to be proved that the part of the Ballance B X
towards the leſſer Magnitudes is double to the remaining part X A.
* Or Beam.
Let the Ballance be divided in two equal parts in D, for it muſt ei­
ther fall in ſome point of the Suſpenſions, or elſe in the middle point be­
tween two of the points of the Suſpenſions: and let the remaining di­
ſtances of the Suſpenſions which fall between A and D, be all divided
into halves by the Points M and I; and let all the Magnitudes be divi-
166[Figure 166]
ded into parts equal to
N: Now the parts of F
ſhall be ſo many in num­
ber, as thoſe Magnitudes
be which are ſuſpended
at the Ballance, and the
parts of G one fewer,
and ſo of the reſt. Let
the parts of F therefore be N, O, R, S, T, and let thoſe of G be N, O,
R, S, thoſe of H alſo N, O, R, then let thoſe of K be N, O: and all the
Magnitudes in which are N ſhall be equal to F; and all the Magnitudes
in which are O ſhall be equal to G; and all the Magnitudes in which
are R ſhall be equal to H; and thoſe in which S ſhall be equal to K; and
the Magnitude T is equal to N. Becauſe therefore all the Magnitudes
in which are N are equal to one another, they ſhall equiponderate in
the point D, which divideth the Ballance into two equal parts; and for
the ſame cauſe all the Magnitudes in which are O do equiponderate in
I; and thoſe in which are R in C; and in which are S in M do equi­
ponderate; and T is ſuſpended in A. Therefore in the Ballance A D at
the equal diſtances D, I, C, M, A, there are Magnitudes ſuſpended ex­
ceeding one another equally, and whoſe exceſs is equal to the leaſt: and
the greateſt, which is compounded of all the N N hangeth at D, the
1leaſt which is T hangeth at A; and the reſt are ordinately diſpoſed.
And again there is another Ballance A B in which other Magnitudes
equal in number and Magnitude to the former are diſpoſed in the ſame
order. Wherefore the Ballances A B and A D are divided by the Cen­
ter of all the Magnitudes according to the ſame proportion: But the
Center of Gravity of the aforeſaid Magnitudes is X: Wherefore X
divideth the Ballances B A and A D according to the ſame proportion;
ſo that as B X is to X A, ſo is X A to X D: Wherefore B X is double
to X A, by the Lemma aforegoing: Which was to be proved.
PROPOSITION.
If in a Parabolical Conoid Figure be deſcribed,
and another circumſcribed by Cylinders of
equal Altitude; and the Axis of the ſaid Co­
noid be divided in ſuch proportion that the
part towards the Vertex be double to that to­
wards the Baſe; the Center of Gravity of the
inſcribed Figure of the Baſe portion ſhall be
neareſt to the ſaid point of diviſion; and the
Center of Gravity of the circumſcribed from
the Baſe of the Conoid ſhall be more remote:
and the diſtance of either of thoſe Centers
from that ſame point ſhall be equal to the Line
that is the ſixth part of the Altitude of one of
the Cylinders of which the Figures are com­
poſed.
Take therefore a Parabolical Conoid, and the Figures that have
been mentioned: let one of them be inſcribed, the other circum­
ſcribed; and let the Axis of the Conoid, which let be A E, be di­
vided in N, in ſuch proportion as that A N be double to N E. It is to
be proved that the Center of Gravity of the inſcribed Figure is in the
Line N E, but the Center of the circumſcribed in the Line A N. Let
the Plane of the Figures ſo diſpoſed be cut through the Axis, and let
the Section be that of the Parabola B A C: and let the Section of the
cutting Plane, and of the Baſe of the Conoid be the Line B C; and
let the Sections of the Cylinders be the Rectangular Figures; as ap­
peareth in the deſcription. Firſt, therefore, the Cylinder of the inſcri­
bed whoſe Axis is D E, hath the ſame proportion to the Cylinder whoſe
Axis is D Y, as the Quadrate I D hath to the Quadrate S Y; that is,
as D A hath to A Y: and the Cylinder whoſe Axis is D Y is potentia
1to the Cylinder Y Z as S Y to R Z, that is, as Y A to A Z: and, by the
ſame reaſon, the Cylinder whoſe Axis is Z Y is to that whoſe Axis is
Z V, as Z A is to A V. The ſaid Cylinders, therefore, are to one ano­
ther as the Lines D A, A Y; Z A, A V: But theſe are equally exceed­
ing to one another, and the exceſs is equal to the leaſt, ſo that A Z is
double to A V; and A Y is triple the
167[Figure 167]
ſame; and D A Quadruple. Thoſe
Cylinders, therefore, are certain Mag­
nitudes in order equally exceeding one
another, whoſe exceſs is equal to the
leaſt of them, and is the Line X M,
in which they are ſuſpended at equal
diſtances (for that each of the Cy­
linders hath its Center of Gravity in
the miaſt of the Axis.) Wherefore,
by what hath been above demonſtra­
ted, the Center of Gravity of the Mag­
nitude compounded of them all divi­
deth the Line X M ſo, that the part
towards X is double to the reſt. Divide it, therefore, and, let X α be
double α M: therefore is α the Center of Gravity of the inſcribed Fi­
gure. Divide A V in two equal parts in ε: ε X ſhall be double to
M E: But X α is double to α M: Wherefore ε E ſhall be triple E α. But
α E is triple E N: It is manifeſt, therefore, that E N is greater than
E X; and for that cauſe α, which is the Center of Gravity of the in­
ſcribed Figure, cometh nearer to the Baſe of the Conoid than N. And
becauſe that as A E is to E N, ſo is the part taken away ε E to the part
taken away E α: and the remaining part ſhall be to the remaming part,
that is, A ε to N α, as A E to E N. Therefore α N is the third part of
A ε, and the ſixt part of A V. And in the ſame manner the Cylinders of
the circumſcribed Figure may be demonſtrated to be equally exceeding
one another, and the exceſs to me equal to the least; and that they have
their Centers of Gravity at equal diſtances in the Line ε M. If therefore
ε M be divided in π, ſo as that ε π be double to the remaining part π M;
π ſhall be the Center of Gravity of the whole circumſcribed Magnitude.
And ſince ε π is double to π M; and A ε leſs than double EM: (for
that they are equal:) the whole A E ſhall be leſs than triple E π: Where­
fore E π ſhall be greater than E N. And, ſince ε M is triple to M π,
and M E with twice ε A is likewiſe triple to M E: the whole A E with
A ε ſhall be triple to E π: But A E is triple to E N: Wherefore the
remaining part A ε ſhall be triple to the remaining part π N. Therefore
N π is the ſixth part of A V. And theſe are the things that were to be
demonſtrated.
1
COROLLARY.
Hence it is manifeſt, that a Conoid may be inſcribed in a Para­
bolical Figure, and another circumſcribed, ſo, as that the
Centers of their Gravities may be diſtant from the point N
leſs than any Line given.
For if we aſſume a Line ſexcuple of the propoſed Line, and make the
Axis of the Cylinders, of which the Figures are compounded given
leſſer than this aſſumed Line, there ſhall fall Lines between the Centers
of Gravities of theſe Figures and the mark N that are leſs than the
Line propoſed.
The former Propoſition another way.
Let the Axis of the Conoid (which let be C D) be divided in
O, ſo, as that C O be double to O D. It is to be proved that the
Center of Gravity of the inſcribed Figure is in the Line O D;
and the Center of the circumſcribed in C O. Let the Plane of the Fi­
gures be cut through the Axis and C, as hath been ſaid. Becauſe there­
fore the Cylinders S N, T M, V I,
168[Figure 168]
X E are to one another as the Squares
of the Lines S D, T N, V M, X I;
and theſe are to one another as the
Lines N C, C M, C I, C E: but
theſe do exceed one another equally;
and the exceſs is equal to the leaſt, to
wit, C E: And the Cylinder T M is
equal to the Cylinder Q N; and the
Cylinder V I equal to P N; and X E
is equal to L N: Therefore the Cylin­
ders S N, Q N, P N, and L N do
equally exceed one another, and the
exceſs is equal to the leaſt of them,
namely, to the Cylinder L N. But
the exceſs of the Cylinder S N, above
the Cylinder Q N is a Ring whoſe
height is Q T; that is, N D; and
its breadth S que And the exceſs of the Cylinder Q N above P N, is a
Ring, whoſe breadth is Q P. And the exceſs of the Cylinder P N above
L N is a Ring, whoſe breadth is P L. Wherefore the ſaid Rings S Q,
Q P, P L, are equal to another, and to the Cylinder L N. Therefore the
Ring S T equalleth the Cylinder X E: the Ring Q V, which is double
to S T, equalleth the Cylinder V I; which likewiſe is double to the
1Cylinder X E: and for the ſame cauſe the Ring P X is equal to the
Cylinder T M; and the Cylinder L E ſhall be equal to the Cylinder S N.
In the Beam or Ballance, therefore, K F connecting the middle points of
the Right-lines E I and D N, and cut into equal parts in the points H
and G, are certain Magnitudes ſuſpended, to wit the Cylinders S N,
T M, V I, X E; and the Center of Gravity of the firſt Cylinder is K;
and of the ſecond H; of the third G; of the fourth F. And we have
another Ballance M K, which is the half of the ſaid F K, and a like
number of points diſtributed into equal parts, to wit, M H, H N, N K,
and on it other Magnitudes, equal in number and bigneſs to thoſe which
are on the Beam F K, and having the Centers of Gravity in the points
M, H, N, and K, and diſpoſed in the ſame order. For the Cylinder L E
hath its Center of Gravity in M; and is equal to the Cylinder S N that
hath its Center in K: And the Ring P X hath the Center H; and is
equal to the Cylinder T M, whoſe Center is H: And the Ring Q V ha­
ving the Center N is equal to the V I whoſe Center is G: And laſtly,
the Ring S T having the Center K, is equal to the Cylinder X E whoſe
Center is F. Therefore the Center of Gravity of the ſaid Magnitudes
divideth the Beam in the ſame proportion: But the Center of them is
one, and therefore ſome point common to both the Beams or Ballance,
which let be Y. Therefore F Y and Y K ſhall be as K Y and Y M. F Y
therefore is double to Y K: and C E being divided into two equal parts
in Z, Z F, ſhall be double to K D: and for that cauſe Z D triple to D Y:
But to the Right Line D O C D is triple: Therefore the Right Line
D O is greater than D Y: And for the like cauſe Y the Center of the
inſcribed Figure approacheth nearer the Baſe than the point O. And
becauſe as C D is to D O, ſo is the part taken away Z D to the part ta­
ken away D Y; the remaining part C Z ſhall be to the remaining part
Y O, as C D is to D O; that is Y O ſhall be the third part of C Z;
that is, the ſixth part of C E. Again we will, by the ſame reaſon, de­
monſtrate the Cylinders of the circumſcribed Figure to exceed one ano­
ther equally, and that the exceſs is equal to the leaſt, and that their
Centers of Gravity are conſtituted in equal diſtances upon the Beam
K Z: and likewiſe that the Rings equal to thoſe ſame Cylinders are in
like manner diſpoſed on another Beam K G, the half of the ſaid K Z,
and that therefore the Center of Gravity of the circumſcribed Figure,
which let be R, ſo divideth the Beam, as that Z R is to R K, as K R is to
R G. Therefore Z R ſhall be double to R K: But C Z is equal to the
Right Line K D, and not double to it. The whole C D ſhall be leſſer
than triple to D R: Wherefore the Right Line D R is greater than D O;
that is to ſay, the Center of the circumſcribed Figure recedeth from the
Baſe more than the point O. And becauſe Z K is triple to K R; and
K D with twice Z C is triple to K D; the whole C D with C Z ſhall be
triple to D R: But C D is triple to D O: Wherefore the remaining
part C Z ſhall be triple to the remaining part R O; that is, O R
1is the ſixth part of E C: Which was the Propoſition.
This being pre-demonſtrated, we will prove that
PROPOSITION.
The Center of Gravity of the Parabolick
Conoid doth ſo divide the Axis, as that the
part towards the Vertex is double to the re­
maining part towards the Baſe.
Let there be a Parabolick Conoid whoſe Axis let be A B divided in
N ſo as that A N be double to N B. It is to be proved that the Cen­
ter of Gravity of the Conoid is the point N. For if it be not N, it
ſhall be either above or below it. Firſt let it be below; and let it be X:
And ſet off upon ſome place by it ſelf the Line L O equal to N X; and let
L O be divided at pleaſure in S: and look what proportion B X and
O S both together have to O S, and the ſame ſhall the Conoid have to
the Solid R. And in the Conoid let Figures be deſcribed by Cylinders
having equal Altitudes, ſo, as that that which lyeth between the Center
of Gravity and the point N be leſs than L S: and let the exceſs of the
Conoid above it be leſs than the Solid R: and that this may be done is
clear. Take therefore the inſcribed, whoſe Center of Gravity let be I:
now I X ſhall be greater than S O: And becauſe that as X B with S O
is to S O, ſo is the Conoid to the Solid R: (and R is greater than the
exceſs by which the Conoid exceeds the inſcribed Figure:) the proporti­
on of the Conoid to the ſaid exceſs ſhall be greater than both B X and
O S unto S O: And, by Diviſion, the inſcribed Figure ſhall have grea­
ter proportion to the ſaid exceſs than B X to S O: But B X hath to
X I a proportion yet leſs than to S O: Therefore the inſcribed Figure
ſhall have much greater proportion to the reſt of the proportions than
B X to X I: Therefore what proportion the inſcribed Figure hath to
thereſt of the portions, the ſame ſhall a certain other Line have to X I:
which ſhall neceſſarily be greater than B X: Let it, therefore, be M X.
We have therefore the Center of Gravity of the Conoid X: But the
Center of Gravity of the Figure inſcribed in it is I: of the reſt of the
portions by which the Conoid exceeds the inſcribed Figure the Center of
Gravity ſhall be in the Line X M, and in it that point in which it ſhall
be ſo terminated, that look what proportion the inſcribed Figure hath
to the exceſs by which the Conoid exceeds it, the ſame it ſhall have to
X I: But it hath been proved, that this proportion is that which M X
hath to X I: Therefore M ſhall be the Center of Gravity of thoſe pro­
portions by which the Conoid exceeds the inſcribed Figure: Which
certainly cannot be. For if along by M a Plane be drawn equidiſtant to
the Baſe of the Conoid, all thoſe proportions ſhall be towards one and
1the ſame part, and not by it divided. Therefore the Center of Gravity
of the ſaid Conoid is not below the point N: Neither is it above. For,
if it may, let it be H: and again, as before, ſet the Line L O by it ſelf
equalto the ſaid H N, and divided at pleaſure in S: and the ſame pro­
portion that B N and S O both together have to S L, let the Conoid
have to R: and about the Conoid let a Figure be circumſcribed conſi­
ſting of Cylinders, as hath been ſaid: by which let it be exceeded a leſs
quantity than that of the Solid R: and let the Line betwixt the Center
of Gravity of the circumſcribed Figure and the point N be leſſer than
S O: the remainder V H ſhall be greater than S L. And becauſe that as
both B N and O S is to SL, ſo is the
169[Figure 169]
Conoid to R: (and R is greater
than the exceſs by which the circum­
ſcribed Figure exceeds the Conoid:)
Therefore B N and S O hath leſs pro­
portion to S L than the Conoid to the
ſaid exceſs. And B V is leſſer than
both B N and S O; and V H is grea­
ter than S L: much greater proporti­
on, therefore, hath the Conoid to the
ſaid proportions, than B V hath to
V H. Therefore whatever proporti­
on the Conoid hath to the ſaid pro­
portions, the ſame ſhall a Line greater
than B V have to V H. Let the ſame be M V: And becauſe the Center
of Gravity of the circumſcribed Figure is V, and the Center of the
Conoid is H. and ſince that as the Conoid to the reſt of the proportions,
ſois M V to V H, M ſhall be the Center of Gravity of the remaining
proportions: which likewiſe is impoſſible: Therefore the Center of
Gravity of the Conoid is not above the point N: But it hath been de­
monſtrated that neither is it beneath: It remains, therefore, that it ne­
ceſſarily be in the point N it ſelf. And the ſame might be demonſtrated
of Conoidal Plane cut upon an Axis not erect. The ſame in other terms,
as appears by what followeth:
PROPOSITION.
The Center of Gravity of the Parabolick Co­
noid falleth betwixt the Center of the cir­
cumſcribed Figure and the Center of the in­
ſcribed.
1
Let there be a Conoid whoſe Axis is A B, and the Center of the
circumſcribed Figure C, and the Center of the inſcribed O. I ſay
the Center of the Conoid is betwixt the points C and O. For if
not, it ſhall be either above them, or below them, or in one of them. Let
it be below, as in R. And becauſe R is the Center of Gravity of the
whole Conoid; and the Center of Gravity of the inſcribed Figure is O:
Therefore of the remaining proportions by which the Conoid exceeds
the inſcribed Figure the Center of Gravity ſhall be in the Line O R ex­
tended towards R, and in that point in which it is ſo determined, that,
what proportion the ſaid proportions have to the inſcribed Figure, the
ſame ſhall O R have to the Line falling betwixt R and that falling point.
Let this proportion be that of O R to R X. Therefore X falleth either
without the Conoid or within, or in its
170[Figure 170]
Baſe. That it falleth without, or in its
Baſe it is already manifeſt to be an abſur­
dity. Let it fall within: and becauſe X R
is to R O, as the inſcribed Figure is to
the exceſs by which the Conoid exceeds
it; the ſame proportion that B R hath to
R O, the ſame let the inſcribed Figure
have to the Solid K: Which neceſſarily
ſhall be leſſer than the ſaid exceſs. And let
another Figure be inſcribed which may be
exceeded by the Conoid a leſs quantity
than is K, whoſe Center of Gravity falleth betwixt O and C. Let it
be V. And, becauſe the firſt Figure is to K as B R to R O, and the ſe­
cond Figure, whoſe Center V is greater than the firſt, and exceeded
by the Conoid a leſs quantity than is K; what proportion the ſecond
Figure hath to the exceſs by which the Conoid exceeds it, the ſame
ſhall a Line greater than B R have to R V. But R is the Center of Gra­
vity of the Conoid; and the Center of the ſecond inſcribed Figure V:
The Center therefore of the remaining proportions ſhall be without
the Conoid beneath B: Which is impoſſible. And by the ſame means
we might demonſtrate the Center of Gravity of the ſaid Conoid not to
be in the Line C A. And that it is none of the points betwixt C and
O is manifeſt. For ſay, that there other Figures deſcribed, greater
ſomething than the inſcribed Figure whoſe Center is O, and leſs than
that circumſcribed Figure whoſe Center is C, the Center of the Conoid
would fall without the Center of theſe Figures: Which but now was
concluded to be impoſſible: It reſts therefore that it be betwixt the Cen­
ter of the circumſcribed and inſcribed Figure. And if ſo, it ſhall ne­
ceſſarily be in that point which divideth the Axis, ſo as that the part
towards the Vertex is double to the remainder; ſince N may circum­
ſcribe and inſcribe Figures, ſo, that thoſe Lines which fall between
1their Centers and the ſaid points, may be leſſer than any other Lines.
To expreſs the ſame in other terms, we have reduced it to an impoſſibi­
lity, that the Center of the Conoid ſhould not fall betwixt the Centers of
the inſcribed and circumſcribed Figures.
PROPOSITION.
Suppoſing three proportional Lines, and that
what proportion the leaſt hath to the exceſs
by which the greateſt exceeds the leaſt, the
ſame ſhould a Line given have to two thirds of
the exceſs by which the greateſt exceeds the
middlemoſt: and moreover, that what pro­
portion that compounded of the greateſt, and
of double the middlemoſt, hath unto that com­
pounded of the triple of the greateſt and mid­
dlemoſt, the ſame hath another Line given, to
the exceſs by which the greateſt exceeds the
middle one; both the given Lines taken toge­
ther ſhall be a third part of the greateſt of the
proportional Lines.
Let A B, B C, and B F, be three proportional Lines; and what
proportion B F hath to F A, the ſame let M S have to two thirds
of C A. And what proportion that compounded of A B and the
double of B C hath to that compounded of the triple of both A B and
B C, the ſame let another, to wit S N, have to A C. Becauſe therefore
that A B, B C, and C F,
171[Figure 171]
are proportionals, A G
and C F ſhall, for the ſame
reaſon, be likewiſe ſo.
Therefore, as A B is to
B C, ſo is A C to C F:
and as the triple of A B is to the triple of B C, ſo is A C to C F:
Therefore, what proportion the triple of A B with the triple of B C
hath to the triple of C B, the ſame ſhall A C have to a Line leſs than
C F. Let it be C O. Wherefore by Compoſition and by Converſion of
proportion, O A ſhall have to A C, the ſame proportion, as triple A B
with Sextuple B C, hath to triple A B with triple B C. But A C hath
to S N the ſame proportion, that triple A B with triple B C hath to A B
with double B C: Therefore, ex equali, O A to NS ſhall have the
ſame proportion, as triple A B with Sexcuple B C hath to A B with
1double B C: But triple A B with ſexcuple B C, are triple to A B with
double B C. Therefore A O is triple to S N.
Again, becauſe O C is to C A as triple C B is to triple A B with tri­
ple C B: and becauſe as C A is to A F, ſo is triple A B to triple B C:
Therefore, ex equali, by perturbed proportion, as O C is to C F, ſo ſhall
triple A B be to triple A B with treble B C: And, by Converſion of
proportion, as O F is to F C, ſo is triple B C to triple A B with triple
B C: And as C F is to F B, ſo is A C to C B, and triple A C to triple
C B: Therefore, ex equali, by Perturbation of proportion, as O F is
to F B, ſo is triple A C to the triple of both A B and A C together.
And becauſe F C and C A are in the ſame proportion as C B and B A;
it ſhall be that as F C is to C A, ſo ſhall B C be to B A. And, by Com­
poſition, as F A is to A C, ſo are both B A and B C to B A: and ſo the
triple to the triple: Therefore as F A is to A C, ſo the compound of tri­
ple B A and triple B C is to triple A B. Wherefore, as F A is to two
thirds of A C, ſo is the compound of triple B A and triple B C to two
thirds of triple B A; that is, to double B A: But as F A is to two thirds
of A C, ſo is F B to M S: Therefore, as F B is to M S, ſo is the compound
of triple B A and triple B C to double B A: But as O B is to F B, ſo
was Sexcuple A B to triple of both A B and B C: Therefore, ex equa­
li, O B ſhall have to M S the ſame proportion as Sexcuple A B hath to
double B A. Wherefore M S ſhall be the third part of O B: And it
hath been demonſtrated, that S N is the third part of A O: It is mani­
feſt therefore, that MN is a third part likewiſe of A B: And this is
that which was to be demonſtrated.
PROPOSITION.
Of any Fruſtum or Segment cut off from a Para­
bolick Conoid the Center of Gravity is in the
Right Line that is Axis of the Fruſtum; which
being divided into three equal parts the Cen­
ter of Gravity is in the middlemoſt and ſo di­
vides it, as that the part towards the leſſer Baſe
hath to the part towards the greater Baſe, the
ſame proportion that the greater Baſe hath to
the leſſer.
From the Conoid whoſe Axis is R B let there be cut off the Solid
whoſe Axis is B E; and let the cutting Plane be equidiſtaut to
the Baſe: and let it be cut in another Plane along the Axis erect
upon the Baſe, and let it be the Section of the Parabola V R C: R B
ſhall be the Diameter of the proportion, or the equidiſtant Diameter
1L M, V C: they ſhall be ordinately applyed. Divide therefore E B in­
to three equal parts, of which let the middlemoſt be Q Y: and divide
this ſo in the point I that Q I may have the ſame proportion to I Y, as
the Baſe whoſe Diameter is V C hath to the Baſe whoſe Diameter is
L M; that is, that the Square V C hath to Square L M. It is to be de­
monſtrated that I is the Center of Gravity of the Fruſtrum L M C.
Draw the Line N S, by the by, equall to B R: and let S X be equal to
E R: and unto N S and S X aſſume a third proportional S G: and as
N G is to G S, ſo let B Q be to I O. And it nothing matters whether
the point O fall above or below L M. And becauſe in the Section V R C
the Lines L M and V C are ordinately
172[Figure 172]
applyed, it ſhall be that as the Square
V C is to the Square L M, ſo is the Line
B R to R E: And as the Square V C is
to the Square L M, ſo is Q I to I Y: and
as B R is to R E, ſo is N S to S X: There­
fore Q I is to I Y, as R S is to S X. Where­
fore as G Y is to Y I, ſo ſhall both N S and
S X be to S X: and as E B is to Y I, ſo
ſhall the compound of triple N S and tri­
ple S X be to S X: But as E B is to B Y,
ſo is the compound of triple N S and S X
both together to the compound of N S and S X: Therefore, as E B is to
B I, ſo is the compound of triple N S and triple S X to the compound of
N S and double S X. Therefore N S, S X, and S G are three proporti­
onal Lines: And as S G is to G N, ſo is the aſſumed O I to two thirds
of E B; that is, to N X: And as the compound of N S and double
S X is to the compound of triple N S and triple S X, ſo is another aſſu­
med Line I B to B E; that is, to N X. By what therefore hath been
above demonſtrated, thoſe Lines taken together are a third part of N S;
that is, of R B: Therefore R B is triple to B O: Wherefore O ſhall
be the Center of Gravity of the Conoid v R C. And let it be the Cen­
ter of Gravity of the Fruſtrum L R M of the Conoid: Therefore the
Center of Gravity of V L M C is in the Line O B, and in that point
which ſo terminates it, that as V L M C of the Fruſtrum is to the
proportion L R M, ſo is the Line A O to that which intervenes betwixt
O and the ſaid point. And becauſe R O is two thirds of R B; and
R A two thirds of R E; the remaining part A O ſhall be two thirds
of the remaining part E B. And becauſe that as the Fruſtum V L M C
is to the proportion L R M, ſo is N G to G S: and as N G to G S, ſo is
two thirds of E B to O I: and two thirds of E B is equal to the Line
A O: it ſhall be that as the Fruſtum V L M O is to the proportion
L R M, ſo is A O to O I. It is manifeſt therefore that of the Fruſtum
V L M C the Center of Gravity is the point I, and ſo divideth the Axis,
[as?] that the part towards the leſſer Baſe is to the part towards the grea-
1ter, as the double of the greater Baſe together with the Leſſer is to the
double of the leſſer together with the greater. Which is the Propoſition
more elegantly expreſſed.
PROPOSITION.
If any number of Magnitudes ſo diſpoſed to one
another, as that the ſecond addeth unto the firſt
the double of the firſt, the third addeth unto
the ſecond the triple of the firſt, the fourth
addeth unto the third the quadruple of the
firſt, and ſo every one of the following ones
addeth unto the next unto it the magnitude of
the firſt multiplyed according to the number
which it ſhall hold in order; if, I ſay, theſe
Magnitudes be ſuſpended ordinarily on the
Ballance at equal diſtances; the Center of the
Equilibrium of all the compounding Magni­
tudes ſhall ſo divide the Beam, as that the part
towards the leſſer Magnitudes is triple to the
remainder.
Let the Beam be L T, and let ſuch Magnitudes as were ſpoken of
hang upon it; and let them be A, F, G, H, K; of which A is in
the firſt place ſuſpended at T. I ſay, that the Center of the Equi­
librium ſo cuts the Beam T L as that the part towards T is triple to the
reſt. Let T L be triple to L I; and S L triple to L P: and Q L to L N,
173[Figure 173]
and L P to L O: I P,
P N, N O, and O L
ſhall be equal. And
in F let a Magnitude
be placed double to A;
in G another trebble to
the ſame; in H ano­
ther Quadruple; and
ſo of the reſt: and let
thoſe Magnitudes be
taken in which there
is A; and let the ſame
be done in the Magni­
tudes F, G, H, K. And
becauſe in F the remaining Magnitude, to wit B, is equal to A; take it
1double in G, triple in H, &c. and let thoſe Magnitudes be taken in
which there is B: and in the ſame manner let thoſe be taken in which is
C, D, and E: now all thoſe in which there is A ſhall be equal to K: and
the compound of all the B B ſhall equal H; and the compound of C C
ſhall equal G; and the compound of all the D D ſhall equal F; and
E ſhall equal A. And becauſe T I is double to I L, I ſhall be the point
of the Equilibrium of the Magnitudes compoſed of all the A A: and
likewiſe ſince S P is double to P L, P ſhall be the point of the Equilibri­
um of the compost of B B: and for the ſame cauſe N ſhall be the point
of the Equilibrium of the compoſt of C C: and O of the compound
of D D: and L that of E. Therefore T L is a Beam on which at
equal diſtances certain Magnitudes K, H, G, F, A do hang. And again
L I is another Ballance, on which, at diſtances in like manner equal, do
hang ſuch a number of Magnitudes, and in the ſame order equal to the
former. For the compound of all the A A, which hang on I, is equal to
K hanging at L; and the compoſt of all B B, which is ſuſpended at P, is
equal to H hanging at P; and likewiſe the compound of C C, which
hangeth at N do equal G; and the compoſt of D, which hang on O,
are equal to F; and E, hanging on L, is equal to A. Wherefore the
Ballances are divided in the ſame proportion by the Center of the com­
pounds of the Magnitudes And the Center of the compound of, the ſaid
Magnitudes is one. Therefore the common point of the Right Line T L,
and of the Right Line L I ſhall be the Center, which let be X. Therefore
as T X is to X L, ſo ſhall L X be to X I; and the whole T L to the whole
L I. But T L is triple to L I: Wherefore T X ſhall alſo be triple to X L.
PROPOSITION.
If any number of Magnitudes be ſo taken, that the
ſecond addeth unto the firſt the triple of the
firſt, and the third addeth unto the ſecond the
quintuple of the firſt, and the fourth addeth
unto the third the ſeptuple of the firſt, and ſo
the reſt, every one encreaſing above the next to
it, and proceedeth ſtill to a new multiplex of
the firſt Magnitude according to the conſe­
quent odd numbers, like as the Squares of
Lines equally exceeding one another do pro­
ceed, whereof the exceſs is equal to the leaſt,
and if they be ſuſpended on a Ballance at equal
Diſtances, the Center of Equilibrium of all the
compound Magnitudes ſo divideth the Beam
1that the part towards the leſſer Magnitudes is
more than triple the remaining part; and alſo
one may take a diſtance that is to the ſame leſs
than triple.
In the Ballance B E let there be Magnitudes, ſuch as were ſpoken off,
from which let there be other Magnitudes taken away that were to
one another as they were diſpoſed in the precedent, and let it be of
the compound of all
the A A: the reſt
174[Figure 174]
in which are C
ſhall be diſtributed
in the ſame order,
but the greateſt de­
ficient. Let E D be
triple to D B; and
G F triple to F B.
D ſhall be the Center
of the Equilibrium
of the compound con­
ſiſting of all the A A;
and F that of the
compound of all the
C C. Wherefore the
Center of the com­
pound of both A A
and C C falleth be­
tween D and F. Let
it be O. It is there­
fore manifeſt that
E O is more than triple to O B; but G O leſs thantriple to the
ſame O B: Which was to be demonſtrated.
1
PROPOSITION.
If to any Cone or portion of a Cone a Eigure con­
ſiſting of Cylinders of equal heights be inſcri­
bed and another circumſcribed; and if its Axis
be ſo divided as that the part which lyeth be­
twixt the point of diviſion and the Vertex be
triple to the reſt; the Center of Gravity of
the inſcribed Figure ſhall be nearer to the Baſe
of the Cone than that point of diviſion: and
the Center of Gravity of the circumſcribed
ſhall be nearer to the Vertex than that ſame
point.
Take therefore a Cone, whoſe Axis is N M. Let it be divided
in S ſo, as that N S be triple to the remainder S M. I ſay, that
the Center of Gravity of any Figure inſcribed, as was ſaid, in
a Cone doth conſiſt in the Axis N M, and approacheth nearer to the Baſe
of the Cone than the point S: and that the Center of Gravity of the
Circumſcribed is likewiſe in the Axis N M, and nearer to the Vertex
than is S. Let a Figure therefore be ſuppoſed to be inſcribed by the Cy­
linders whoſe Axis M C, C B, B E, E A are equal. Firſt therefore
the Cylinder whoſe Axis is M C hath
175[Figure 175]
to the Cylinder whoſe Axis is C B the
ſame proportion as its Baſe hath to
the Baſe of the other (for their Alti­
tudes are equal.) But this propor­
tion is the ſame with that which the
Square C N hath to the Square N B.
And ſo we might prove, that the Cy­
linder whoſe Axis is C B hath to the
Cylinder whoſe Axis is B E the ſame
proportion, as the Square B N hath to
the Square N E: and the Cylinder
whoſe Axis is B E hath to the Cylin­
der whoſe Axis is E A the ſame pro­
portion that the Square E N hath to
the Square N A. But the Lines N C,
N B, E N, and N A equally exceed one
another, and their exceſs equalleth the
leaſt, that is N A. Therefore they are certain Magnitudes, to wit, in­
ſcribed Cylinders having conſequently to one another the ſame proporti­
on as the Squares of Lines that equally exceed one another, and the ex-
1ceſs of which is equal to the leaſt: and they are ſo diſpoſed on the Beam
T I that their ſeveral Centers of Gravity conſiſt in it, and that at equal
diſtances. Therefore by the things above demonſtrated it appeareth that
the Center of Gravity of all ſo compoſed Magnitudes do ſo divide the
Balance T I, that the part to wards T is more than triple to the remain­
der. Let this Center be O. T O therefore is more than triple to O I.
But T N is triple to I M. Therefore the whole M O will be leſs than a
fourth part of the whole M N, whoſe fourth part was ſuppoſed to be
M S. It is manifeſt, therefore, that the point O doth nearer approach
the Baſe of the Cone than S. And let the circumſcribed Figure be com­
poſed of the Cylinders whoſe Axis M C, C B, B E, E A and A N are
equal to each other, and, like as in thoſe inſcribed, let them be to one
another as the Squares of the Lines M N, N C, B N, N E, A N,
which equally exceed one another, and the exceſs is equal to the leaſt
A N. Wherefore, by the premiſes, the Center of Gravity of all the Cy­
linders ſo diſpoſed, which let be V, doth ſo divide the Beam R I, that the
part towards R, to wit R V, is more than triple to the remaining part
V I: but T V ſhall be leſs than triple to the ſame. But N T is triple to
all I M: Therefore all V M is more than the fourth part of all M N,
whoſe fourth part was ſuppoſed to be M S. Therefore the point V is
nearer to the Vertex than the Point S. Which was to be demonſtra­
ted.
PROPOSITION.
About a given Cone a Figure may be circumſcri­
bed and another inſcribed conſiſting of Cylin­
ders of equal height, ſo, as that the Line which
lyeth betwixt the Center of Gravity of the
circumſcribed, and the Center of Gravity of
the inſcribed, may be leſſer than any Line
given.
Let a Cone be given, whoſe Axis is A B; and let the Right Line
given be K. I ſay; Let there be placed by the Cylinder L
equal to that inſcribed in the Cone, having for its Altitude half
of the Axis A B: and let A B be divided in C, ſo as that A C be tri­
ple to C B: And as A C is to K, ſo let the Cylinder L be to the Solid X.
And about the Cone let there be a Figure circumſcribed of Cylin­
ders that have equal Altitude, and let another be inſcribed, ſo as that
the circumſcribed exceed the inſcribed a leſs quantity than the Solid X.
And let the Center of Gravity of the circumſcribed be E; which falls
above C: and let the Center of the inſcribed be S, falling beneath C.
1I ſay now, that the Line E S is leſſer than K. For if not, then let C A
be ſuppoſed equal to E O. Becauſe therefore O E hath to K the ſame
proportion that L hath to X; and the inſcribed Figure is not leſs than
the Cylinder L; and the exceſs with which the ſaid Figure is exceeded
by the circumſcribed is leſs than the Solid X: therefore the inſcribed
Figure ſhall have to the ſaid exceſs
176[Figure 176]
greater proportion than O E hath to
K: But the proportion of O E to K is
not leſs than that which O E hath to
E S with E S. Let it not be leſs than
K. Therefore the inſcribed Figure
hath to the exceſs of the circumſcri­
bed Figure above it greater propor­
tion than O E hath to E S. Therefore
as the inſcribed is to the ſaid exceſs,
ſo ſhall it be to the Line E S. Let E R
be a Line greater than E O; and the
Center of Gravity of the inſcribed
Figure is S; and the Center of the cir­
cumſcribed is E. It is manifeſt there­
fore, that the Center of Gravity of
the remaining proportions by which
the circumſcribed exceedeth the in
ſcribed is in the Line R E, and in that point by which it is ſo termina­
ted, that as the inſcribed Figure is to the ſaid proportions, ſo is the Line
included betwixt E and that point to the Line E S. And this propor­
tion hath R E to E S. Therefore the Center of Gravity of the remain­
ing proportions with which the circumſcribed Figure exceeds the in­
ſcribed ſhall be R, which is impoſſible. For the Plane drawn thorow
R equidiſtant to the Baſe of the Cone doth not cut thoſe proportions. It
is therefore falſe that the Line E S is not leſſer than K. It ſhall therefore
be leſs. The ſame alſo may be done in a manner not unlike this in Pyra­
mides, as ne could demonſtrate.
COROLLARY.
Hence it is manifeſt, that a given Cone may circumſcribe one
Figure and inſcribe another conſiſting of Cylinders of equal
Altitudes ſo, as that the Lines which are intercepted betwixt
their Centers of Gravity and the point which ſo divides the
Axis of the Cone, as that the part towards the Vertex is tri­
ple to the leſt, are leſs than any given Line.
For, ſince it hath been demonſtrated, that the ſaid point dividing the
Axis, as was ſaid, is alwaies found betwixt the Centers of Gravity
1of the Circumſcribed and inſcribed Figures: and that it's poſſible, that
there be a Line in the middle betwixt thoſe Centers that is leſs than any
Line aſſigned; it followeth that the ſame given Line be much leſs that
lyeth betwixt one of the ſaid Centers and the ſaid point that divides
the Axis.
PROPOSITION.
The Center of Gravity divideth the Axis of any
Cone or Pyramid ſo, that the part next the
Vertex is triple to the remainder.
Let there be a Cone whoſe Axis is A B. And in C let it be divided,
ſo that A C be triple to the remaining part C B. It is to be proved,
that C is the Center of Gravity of the Cone. For if it be not, the
Cone's Center ſhall be either above or below the point C. Let it be firſt
beneath, and let it be E. And draw the Line L P, by it ſelf, equal to
C E; which divided at pleaſure in N. And as both B E and P N to­
gether are to P N, ſo let the Cone be to the Solid X: and inſcribe in the
Cone a Solid Figure of Cylinders that have equal Baſes, whoſe Center
of Gravity is leſs diſtant from the point C than is the Line L N, and
the exceſs of the Cone above it leſs than the Solid X. And that this
may be done is manifeſt from what hath been already demonſtrated.
Now let the inſcribed Figure be ſuch as
177[Figure 177]
was required, whoſe Center of Gravity
let be I. The Line I E therefore ſhall be
greater than N P together with L P. Let
C E and I C leſs L N be equal: And be­
cauſe both together B E and N P is to N P
as the Cone to X: and the exceſs by which
the Cone exceeds the inſcribed Figure is
leſs than the Solid X: Therefore the Cone
ſhall have greater proportion to the ſaid
X S than both B E and N P to N P: and, by
Diviſion, the inſcribed Figure ſhall have
greater proportion to the exceſs by which
the Cone exceeds it, than B E to N P: But B E hath leſs proportion to
E I than to N P with I E. Let N P be greater. Then the inſcribed Fi­
gure hath to the exceſs of the Cone above it much greater proportion
than B E to E I. Therefore as the inſcribed Figure is to the ſaid exceſs,
ſo ſhall a Line bigger than B E be to E I. Let that Line be M E. Becauſe,
therefore, M E is to E I as the inſcribed Figure is to the exceſs of the
Cone above the ſaid Figure, and D is the Center of Gravity of the
Cone, and I the Center of Gravity of the inſcribed Figure: Therefore
1M ſhall be the Center of Gravity of the remaining proportions by which
the Cone exceeds the inſcribed Figure. Which is impoſſible. Therefore
the Center of Gravity of the Cone is not below the point C. Nor is it
above it. For if it may be, let it be R. And again aſſume L P cut at
pleaſure in N: And as both B C and N P together are to N L, ſo let the
Cone be to X. And let a Figure be, in like manner, circumſcribed about
the Cone, which exceeds the ſaid Cone a leſs quantity than the Solid X.
And let the Line which intercepts bet wixt its Center of Gravity and C,
be leſſer than N P. Now take the circumſcribed Figure, whoſe Center
let be O; the remainder O R ſhall be greater than the ſaid N L. And
becauſe, as both together B C and P N is to N L, ſo is the Cone to X:
And the exceſs by which the circumſcribed exceeds the Cone is leſſer
than X: And B O is leſſer than B C and P N together: And O R grea­
ter than L N: The Cone therefore ſhall have much greater proportion to
the remaining proportions by which it was exceeded by the circumſcribed
Figure, than B O to O R. Let it be as M O is to O R. M O ſhall
be greater than B C; and M ſhall be the Center of Gravity of the pro­
portions by which the Cone is exceeded by the circumſcribed Figure.
Which is inconvenient. Therefore the Center of Gravity of the Cone is
not above the point C. But neither is it below it; as hath been proved.
Therefore it ſhall be C it ſelf. And ſo in like manner may it be demon­
ſtrated in any Pyramid.
PROPOSITION.
If there were four Lines continual proportionals;
and as the leaſt of them were to the exceſs by
which the greateſt exceeds the leaſt, ſo a Line
taken at pleaſure ſhould be to 3/4 the exceſs by
which the greateſt exceeds the ſecond; and as
the Line equal to theſe (viz. to the greateſt,
double of the ſecond, and triple of the third)
is to the Line equal to the quadruple of the
fourth, the quadruple of the ſecond, and the
quadruple of the third, ſo ſhould another Line
taken be to the exceſs of the greateſt above the
ſecond: theſe two Lines taken together ſhall
be a fourth part of the greateſt of the propor­
tionals.
1
For let A B, B C, B D, and B E be four proportional Lines. And
as B E is to E A, ſo let F G be to 3/4 of A C. And as the Line equal
to A B and to double B C and to triple B D is to the Line equal
to the quadruples of A B, B C, and B D, ſo let H G be to A C. It is
to be proved, that H F is a fourth part of A B. Foraſmuch therefore
as A B, B C, B D, and B E
178[Figure 178]
are proportionals, A C,
C D, and D E ſhall be in
the ſame proportion: And
as the quadruple of the ſaid
A B, B C, and B D is to
A B with the double of B C and triple of B D, ſo is the quadruple of
A C, C D, and D E; that is, the quadruple of A E; to A C with the
double of C D, and triple of D E. And ſo is A C to H G. Therefore
as the triple of A E is to A C, with the double of C D and triple of
D E, ſo is 3/4 of A C to H G. And as the triple of A E is to the triple of
E B, ſo is 3/4 A C to G F: Therefore, by the Converſe of the twenty
fourth of the fifth, As triple A E is to A C with double C D and tri­
ple D B, ſo is 3/4 of A C to H F: And as the quadruple of A E is to A C
with the double of C D and triple of D B; that is, to A B with C B and
B D, ſo is A C to H F. And, by Permutation, as the quadruple of A E
is to A C, ſo is A B with C B and B D to H F. And as A C is to A E, ſo
is A B to A B with C B and B D. Therefore, ex æquali, by Perturbed
proportion, as quadruple A E is to A E, ſo is A B to H F. Wherefore it
is manifeſt that H F is the fourth part of A B.
PROPOSITION.
The Center of Gravity of the Fruſtum of any Py­
ramid or Cone, cut equidiſtant to the Plane
of the Baſe, is in the Axis, and doth ſo divide
the ſame, that the part towards the leſſer Baſe
is to the remainder, as the triple of the greater
Baſe, with the double of the mean Space be­
twixt the greater and leſſer Baſe, together
with the leſſer Baſe is to the triple of the leſſer
Baſe, together with the ſame double of the
mean Space, as alſo of the greater Baſe.
1
From a Cone or Pyramid whoſe Axis is A D, and equidiſtant to
the Plane of the Baſe, let a Fruſtum be cut whoſe Axis is V D.
And as the triple of the greateſt Baſe with the double of the
mean and leaſt is to the triple of the leaſt and double of the mean and
greateſt, ſo is \ O to O D. It is to be proved that the Center of Gra­
vity of the Fruſtum is in O. Let V M be the fourth part of V D.
Set the Line H X by the by, equal to A D: and let K X be equal to A V:
and unto H X K let X L be a third proportional, and X S a fourth.
And as H S is to S X, ſo let M D be to the Line taken from O towards
A: which let be O N. And becauſe the greater Baſe is in proportion
to that which is mean betwixt the
greater and leſſer as D A to A V; that
179[Figure 179]
is, as H X, to X K, but the ſaid
mean is to the leaſt as K X to X L;
the greater, mean, and leſſer Baſes
ſhall be in the ſame proportion as
H X, X K, and X L. Wherefore as
triple the greater Baſe, with double
the mean and leſſer, is to triple the
leaſt with double the mean and grea­
teſt; that is, as V O is to O D; ſo is
triple H X with double X K and X L
to triple X L, with double X K and
X H: And by Compoſition and Converting the proportion, O D ſhall
be to V D, as H X, with double X K and triple X L, to quadruple H X,
X K, and X L. There are, therefore, four proportional Lines, H X,
X K, X L, and X S: And as X S is to S H, ſo is the Line taken N O
to 3/4 of D V, to wit, to D M; that is, to 3/4 of H K: And as H X
with double X K and triple X L is to quadruple H X, X K and X L;
ſo is another Line taken O D to D V; that is, to H K. Therefore, by
the things demonſtrated, D N ſhall be the fourth part of H X; that
is, of A D. Wherefore the point N ſhall be the Center of Gravity
of the Cone or Pyramid whoſe Axis is A D. Let the Center of Gra­
vity of the Pyramid or Cone whoſe Axis is A V be I. It is therefore
manifeſt that the Center of Gravity of the Fruſtum is in the Line
I N inclining towards the part N, and in that point of it which with
the point N include a Line to which I M hath the ſame proportion that
the Fruſtum cut hath to the Pyramid or Cone whoſe Axis is A V.
It remaineth therefore to prove that I N hath the ſame proportion
to N O, that the Fruſtum hath to the Cone whoſe Axis is A V. But
as the Cone whoſe Axis is D A is to the Cone whoſe Axis is A V, ſo
is the Cube D A to the Cube D V; that is, the Cube H X to the
Cube X K: But this is the ſame proportion that H X hath to X S.
Wherefore, by Diviſion, as H S is to S X, ſo ſhall the Fruſtum whoſe
1Axis is D V be to the Cone or Pyramid whoſe Axis is V A. And as
H S is to S X, ſo alſo is M D to O N. Wherefore the Fruſtum is to the
Pyramid whoſe Axis is A V, as M D to N O. And becauſe A N
is 3/4 of A D; and A I is 3/4 of A V; the remainder I N ſhall be 3/4 of the
remainder V D. Wherefore I N ſhall be equal to M D.
And it hath been demonſtrated that M D is to N O,
as the Fruſtum to the Cone A V. It is mani­
feſt, therefore, that I N hath likewiſe
the ſame proportion to N O:
Wherefore the Propo­
ſition is manifeſt.
FINIS.
1
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1
GALILEUS,
HIS
MECHANICKS:
OF THE BENEFIT DERIVED
FROM THE SCIENCE OF MECHANICKS,
AND FROM ITS INSTRUMENTS.
I judged it extreamly neceſſary, before our
deſcending to the Speculation of Mecha­
nick Inſtruments, to conſider how I might,
as it were, ſet before your eyes in a gene­
ral Diſcourſe, the many benefits that are
derived from the ſaid Inſtruments: and
this I have thought my ſelf the more ob­
liged to do, for that (if I am not miſtaken)
I have ſeen the generality of Mechaniti­
ans deceive themſelves in going about to apply Machines to many
operations of their own nature impoſſible; by the ſucceſſe where­
of they have been diſappointed, and others likewiſe fruſtrate of
the hope which they had conceived upon the promiſe of thoſe pre­
ſumptuous undertakers: of which miſtakes I think I have found
the principall cauſe to be the belief and conſtant opinion theſe
1Artificers had, and ſtill have, that they are able with a ſmall force
to move and raiſe great weights; (in a certain manner with their
Machines cozening nature, whoſe Inſtinct, yea moſt poſitive con­
ſtitution it is, that no Reſiſtance can be overcome, but by a Force
more potent then it:) which conjecture how falſe it is, I hope by
the enſuing true and neceſſary Demonſtrations to evince.
In the mean time, ſince I have hinted, that the benefit and help
derived from Machines is not, to be able with leſſe Force, by help
of the Machine to move thoſe weights, which, without it, could
not be moved by the ſame Force: it would not be beſides the
purpoſe to declare what the Commodities be which are derived to
us from ſuch like faculties, for if no profit were to be hoped for,
all endeavours employed in the acquiſt thereof will be but loſt
labour.
Proceeding therefore according to the nature of theſe Studies,
let us firſt propoſe four things to be conſidered. Firſt, the weight
to be transferred from place to place; and ſecondly, the Force
and Power which ſhould move it; thirdly, the Diſtance between
the one and the other Term of the Motion; Fourthly, the Time
in which that mutation is to be made: which Time becometh the
ſame thing with the Dexterity, and Velocity of the Motion; we
determining that Motion to be more ſwift then another, which in
leſſe Time paſſeth an equal Diſtance.
Now, any determinate Reſiſtance and limited Force whatſoever
being aſſigned, and any Diſtance given, there is no doubt to be
made, but that the given Force may carry the given Weight to the
determinate Diſtance; for, although the Force were extream
ſmall, yet, by dividing the Weight into many ſmall parts, none
of which remain ſuperiour to the Force, and by transferring them
one by one, it ſhall at laſt have carried the whole Weight to the
aſſigned Term: and yet one cannot at the end of the Work with
Reaſon ſay, that that great Weight hath been moved, and tranſ­
ported by a Force leſſe then it ſelf, howbeit indeed it was done
by a Force, that many times reiterated that Motion, and that
Space, which ſhall have been meaſured but only once by the whole
Weight. From whence it appears, that the Velocity of the Force
hath been as many times Superiour to the Reſiſtance of the weight,
as the ſaid Weight was ſuperiour to the Force; for that in the
ſame Time that the moving Force hath many times meaſured the
intervall between the Terms of the Motion, the ſaid Moveable
happens to have paſt it onely once: nor therefore ought we to
affirm a great Reſiſtance to have been overcome by a ſmall Force,
contrary to the conſtitution of Nature. Then onely may we ſay
the Natural Conſtitution is overcome, when the leſſer Force tranſ­
fers the greater Reſiſtance, with a Velocity of Motion like to that
1wherewith it ſelf doth move; which we affirm abſolutely to be
impoſſible to be done with any Machine imaginable. But becauſe
it may ſometimes come to paſſe, that having but little Force, it is
required to move a great Weight all at once, without dividing it
in pieces, on this occaſion it will be neceiſary to have recourſe to
the Machine, by means whereof the propoſed Weight may be
transferred to the aſſigned Space by the Force given. But yet
this doth not hinder, but that the ſame Force is to move, meaſuring
that ſame Space, or another equall to it, as many ſeverall times as
it is exceeded by the ſaid Weight. So that in the end of the a­
ction we ſhall ſind that we have received from the Machine no
other benefit tnen only that of tranſporting the ſaid Weight with
the given Force to the Term given, all at once. Which Weight,
being divided into parts, would without any Machine have been
carried by the ſame Force, in the ſame Time, through the ſame
Intervall. And this ought to paſſe for one of the benefits taken
from the Mechanicks: for indeed it frequently happens, that be­
ing ſcanted in Force but not Time, we are put upon moving great
Weights unitedly or in groſſe: but he that ſhould hope, and at­
tempt to do the ſame by the help of Machines without increaſe of
Tardity in the Moveable, would certainly be deceived, and would
declare his ignorance of the uſe of Mechanick Inſtruments, and
the reaſon of their effects.
Another benefit is drawn from the Inſtruments, which depend­
eth on the place wherein the operation is to be made: for all In­
ſtruments cannot be made uſe of in all places with equall conve­
nience. And ſo we ſee (to explain our ſelves by an example) that
for drawing of Water out of a Well, we make uſe of onely a
Rope and a Bucket fitted to receive and hold Water, wherewith
we draw up a determinate quantity of Water, in a certain Time,
with our limited ſtrength: and he that ſhould think he could with
a Machine of whatſoever Force, with the ſame ſtrength, and in
the ſame Time, take up a great quantity of Water, is in a groſſe
Errour. And he ſhall find himſelf ſo much the more deceived,
the more he ſhall vary and multiply his Inventions: Yet never­
theleſſe we ſee Water drawn up with other Engines, as with a Pump
that drinks up Water in the Hold of Ships; where you muſt note
that the Pump was not imployed in thoſe Offices, for that it draws
up more Water in the ſame Time, and with the ſame ſtrength
then that which a bare Bucket would do, but becauſe in that place
the uſe of the Bucket or any ſuch like Veſſel could not effect what
is deſired, namely to keep the Hold of the Ship quite dry from e­
very little quantity of Water; which the Bucket cannot do, for
that it cannot dimerge and dive, where there is not a conſiderable
depth of Water. And thus we ſee the Holds of Ships by the
1ſaid Inſtrument kept dry, when Water cannot but onely oblique­
ly be drawn up, which the ordinary uſe of the Bucket would not
effect, which riſeth and deſcends with its Rope perpendicu­
larly.
The third is a greater benefit, haply, then all the reſt that are
derived from Mechanick Inſtruments, and reſpects the aſſiſtance
which is borrowed of ſome Force exanimate, as of the ſtream of a
River, or elſe animate, but of leſſe expence by far, then that which
would be neceſſary for maintaining humane ſtrength: as when to
turn Mills, we make uſe of the Current of a River, or the ſtrength
of a Horſe, to effect that, which would require the ſtrength of five
or fix Men. And this we may alſo advantage our ſelves in raiſing
Water, or making other violent Motions, which muſt have been
done by Men, if there were no other helps; becauſe with one ſole
Veſſel we may take Water, and raiſe, and empty it where occaſion
requires; but becauſe the Horſe, or ſuch other Mover wanteth
Reaſon, and thoſe Inſtruments which are requiſite for holding and
emptying the Veſſel in due time, returning again to fill it, and one­
ly is endued with Force, therefore it's neceſſary that the Mecha­
nitian ſupply the naturall defect of that Mover, furniſhing it with
ſuch devices and inventions, that with the ſole application of it's
Force the defired effect may follow. And therein is very great
advantage, not becauſe that a Wheel or other Machine can enable
one to tranſport the ſame Weight with leſſe Force, and greater
Dexterity, or a greater Space than an equall Force, without thoſe
Inſtruments, but having Judgment and proper Organs, could have
done; but becauſe that the ſtream of a River coſteth little or
nothing, and the charge of keeping of an Horſe or other Beaſt,
whoſe ſtrength is greater then that of eight, or it may be more
Men, is far leſſe then what ſo many Men would be kept
for.
Theſe then are the benefits that may be derived from Mecha­
nick Inſtruments, and not thoſe which ignorant Engineers dream
of, to their own diſgrace, and the abuſe of ſo many Princes,
whilſt they undertake impoſſible enterprizes; of which, both
by the little which hath been hinted, and by the much which
ſhall be demonſtrated in the Progreſſe of this Treatiſe, we ſhall
come to aſſure our ſelves, if we attentively heed that which ſhall
be ſpoken.
1
DEFINITIONS.
That which in all Demonſtrative Sciences is neceſſary to be
obſerved, we ought alſo to follow in this Diſcourſe, that is;
to propound the Definitions of the proper Terms of this
Art, and the primary Suppoſitions, from which, as from ſeeds full
of fecundity, may of conſequence ſpring and reſult the cauſes,
and true Demonſtrations, of the Nature of all the Mechanick
Engines which are uſed, for the moſt part about the Motions of
Grave Matters, therefore we will determine, firſt, what is GRA­
VITIE.
We call GRAVITIE then, That propenſion of moving
naturally downwards, which is found in ſolid Bodies, cauſed by
the greater or leſſe quantity of matter, whereof they are conſti­
tuted.
MOMENT is the propenſion of deſcending, cauſed not ſo
much by the Gravity of the moveable, as by the diſpoſure which
divers Grave Bodies have in relation to one another; by means of
whichMoment, we oft ſee a Body leſs Grave counterpoiſe another
of greater Gravity: as in the Stiliard, a great Weight is raiſed by
a very ſmall counterpoiſe, not through exceſs of Gravity, but
through the remoteneſſe from the point whereby the Beam is up­
held, which conjoyned to the Gravity of the leſſer weight adds
thereunto Moment, and Impetus of deſcending, wherewith the
Moment of the other greater Gravity may be exceeded. MO­
MENT then is that IMPETUS of deſcending, compounded
of Gravity, Poſition, and the like, whereby that propenfion may
be occaſioned
The CENTER of GRAVITY we define to be that point
in every Grave Body, about which conſiſt parts of equall Moment:
ſo that, imagining ſome Grave Body to be ſuſpended and ſuſtain­
ed by the ſaid point, the parts on the right hand will Equilibrate
thoſe on the left, the Anteriour, the Poſteriour, and thoſe above
thoſe below; ſo that be it in any whatſoever fite, and poſition,
provided it be ſuſpended by the ſaid CENTER, it ſhall ſtand
ſtill: and this is that point which would gladly unite with the
univerſall Center of Grave Bodies, namely withthat of the Earth,
if it might thorow ſome free Medium deſcend thither. From
whence we take theſe Suppoſitions.
1
SUPPOSITIONS.
Any Grave Body, (as to what belongeth to it's proper ver­
tue) moveth downwards, ſo that the Center of it's Gravity
never ſtrayeth out of that Right Line which is produced
from the ſaid Center placed in the firſt Term of the Motion unto
the univerſal Center of Grave Bodies. Which is a Suppoſition
very manifeſt, becauſe that ſingle Center being obliged to endea­
vour to unite with the common Center, it's neceſſary, unleſſe ſome
impediment intervene, that it go ſeeking it by the ſhorteſt Line,
which is the Right alone: And from hence may we ſecondarily
ſuppoſe
Every Grave Body putteth the greateſt ſtreſſe, and weigheth
moſt on the Center of it's Gravity, and to it, as to its proper ſeat,
all Impetus, all Ponderoſity, and, in ſome, all Moment hath re­
courſe.
We laſtly ſuppoſe the Center of the Gravity of two Bodies e­
qually Grave to be in the midſt of that Right Line which conjoyns
the ſaid two Centers; or that two equall weights, ſuſpended in
equall diſtence, ſhall have the point of Equilibrium in the common
Center, or meeting of thoſe equal Diſtances. As for Example,
the Diſtance C E being equall to the Diſtance E D, and there be­
ing by them two equall weights ſuſpended, A and B, we ſuppoſe
the point of Equilibrium to be in the point E, there being no
greater reaſon for inclining to
one, then to the other part. But
180[Figure 180]
here is to be noted, that the Di­
ſtances ought to be meaſured
with Perpendicular Lines, which
from the point of Suſpenſion E,
fall on the Right Lines, that from
the Center of the Gravity of the
Weights A and B, are drawn to
the common Center of things
Grave; and therefore if the Diſtance E D were tranſported into
E F, the weight B would not counterpoiſe the weight A, becauſe
drawing from the Centers of Gravity two Right Lines to the Cen­
ter of the Earth, we ſhall ſee that which cometh from the Center
of the Weight I, to be nearer to the Center E, then the other
produced from the Center of the weight A. Therefore our ſaying
that equal Weights are ſuſpended by [or at] equal Diſtances, is
to be underſtood to be meant when as the Right Lines that go from
their Centers & to ſeek out the common Center of Gravity, ſhall be
equidiſta nt from that Right Line, which is produced from the ſaid
1Term of thoſe Diſtances, that is from the point of Suſpenſion, to
the ſame Center of the Earrh.
Theſe things determined and ſuppoſed, we come to the explica­
tion of a Principle, the moſt common and materiall of the greater
part of Mechanick Inſtruments: demonſtrating, that unequall
Weights weigh equally when ſuſpended by [or at] unequal Diſtan­
ces, which have contrary proportion to that which thoſe weights
are found to have, See the Demonſtration in the beginning of the
ſecond Dialogue of Local-Motions.
Some Adveriiſements about what hath been ſaid.
Now being that Weights unequall come to acquire equall
Moment, by being alternately ſuſpended at Diſtances that
have the ſame proportion with them; I think it not fit to
over paſſe with ſilence another congruicy and probability, which
may confirm the ſame truth; for let the Ballance A B, be conſide­
red, as it is divided into unequal parts in the point C, and let the
Weights be of the ſame propor­
181[Figure 181]
tion that is between the Diſtan­
ces B C, and C A, alternately
ſuſpended by the points A, and
B: It is already manifeſt, that
the one will counterpoiſe the
other, and conſequently, that
were there added to one of them
a very ſmall Moment of Gravity, it would preponderate, raiſing
the other, ſo that an inſenſible Weight put to the Grave B, the
Ballance would move and deſcend from the point B towards E,
and the other extream A would aſcend into D, and in regard that
to weigh down B, every ſmall Gravity is ſufficient, therefore not
keeping any accompt of this inſenſible Moment, we will put no
difference between one Weights ſuſtaining, and one Weights
moving another. Now, let us conſider the Motion which the
Weight B makes, deſcending into E, and that which the other
A makes in aſcending into D, we ſhall without doubt find the
Space B E to be ſo much greater than the Space A D, as the Di­
ſtance B C is greater than C A, forming in the Center C two an­
gles D C A, and E C B, equall as being at the Cock, and conſe­
quently two Circumferences A D and B E alike; and to have the
ſame proportion to one another, as have the Semidiameters B C,
and C A, by which they are deſcribed: ſo that then the Velocity
of the Motion of the deſcending Grave B cometh to be ſo much
Superiour to the Velocity of the other aſcending Moveable A, as
the Gravity of this exceeds the Gravity of that; and it not being
1poſſible that the Weight A ſhould be raiſed to D, although ſlow­
ly, unleſſe the other Weight B do move to E ſwiftly, it will not
be ſtrange, or inconſiſtent with the Order of Nature, that the
Velocity of the Motion of the Grave B, do compenſate the greater
Reſiſtance of the Weight A, ſo long as it moveth ſlowly to D,
and the other deſcendeth ſwiftly to E, and ſo on the contrary,
the Weight A being placed in the point D, and the other B in
the point E, it will not be unreaſonable that that falling leaſurely
to A, ſhould be able to raiſe the other haſtily to B, recovering by
its Gravity what it had loſt by it's Tardity of Motion. And by
this Diſcourſe we may come to know how the Velocity of the
Motion is able to encreaſe Moment in the Moveable, according to
that ſame proportion by which the ſaid Velocity of the Motion is
augmented.
There is alſo another thing, before we proceed any farther, to
be confidered; and this is touching the Diſtances, whereat, or
wherein Weights do hang: for it much imports how we are to
underſtand Diſtances equall, and unequall; and, in ſum, in what
manner they ought to be mea­
182[Figure 182]
ſured: for that A B being the
Right Line, and two equall
Weights being ſuſpended at
the very ends thereof, the point
C being taken in the midſt of
the ſaid Line, there ſhall be an
Equilibrium upon the ſame:
And the reaſon is for that the
Diſtance C B is equal to C A.
But if elevating the Line C B, moving it about the point C, it
ſhall be transferred into CD, ſo that the Ballance ſtand according
to the two Lines A C, and C D, the two equall Weights hanging
at the Terms A and D, ſhall no longer weigh equally on that
point C, becauſe the diſtance of the Weight placed in D, is made
leſſe then it was when it hanged in B. For if we confider the Lines,
along [or by] which the ſaid Graves make their Impulſe, and
would deſcend, in caſe they were freely moved, there is no doubt
but that they would make or deſcribe the Lines A G, D F, B H:
Therefore the Weight hanging on the point D, maketh it's Moment
and Impetus according to the Line D F: but when it hanged in
B, it made Impetus in the Line B H: and becauſe the Line D F is
nearer to the Fulciment C, then is the Line B H Therefore we
are to underſtand that the Weights hanging on the points A and D,
are not equi-diſtant from the point C, as they be when they are
conſtituted according to their Right Line A C B: And laſtly,
we are to take notice, that the Diſtance is to be meaſured by
1Lines, which fall at Right Angles on thoſe whereon the Weights
hang, and would move, if ſo be they were permitted to deſcend
freely.
Of the BALLANCE and LEAVER.
Having underſtood by certain Demonſtration, one of the
firſt Principles, from which, as from a plentiſul Fountain,
many of the Mechanical Inſtruments are derived, we may
take occaſion without any difficulty to come to the knowledge of
the nature of them: and firſt ſpeaking of the Stiliard, an Inſtru­
ment of moſt ordinary uſe, with which divers Merchandizes are
weighed, ſuſtaining them, though very heavy, with a very ſmall
counterpoiſe, which is com­
monly called the Roman or
183[Figure 183]
Plummet, we ſhall prove that
there is no more to be done in
ſuch an operation, but to re­
duce into act and practice
what hath been above contemplated. For if we propoſe the Bal­
lance A B, whoſe Fulciment or Lanquet is in the point C, by
which, at the ſmall Diſtance C A, hangeth the heavy Weight D,
and if along the other greater C B, (which we call the Needle of
the Stiliard) we ſhould ſuppoſe the Roman F, though of but little
weight in compariſon of the Grave Body D to be ſlipped to and
fro, it ſhall be pofſible to place it ſo remotely from the Lanquet C,
that the ſame proportion may be found between the two Weights
D and F, as is between the Diſtances F C, and C A: and then ſhall
an Equilibrium ſucceed; unequall Weights hanging at Diſtances
alternately proportional to them.
Nor is this Inſtrument different from that other called Vectis,

and vulgarly the ^{*} Leaver, wherewith great Weights are moved
by ſmall Force; the application of which is according to the Fi­
gure prefixed; wherein the Leaver
is repreſented by the Bar of wood
or other ſolid matter, B C D, let
184[Figure 184]
the heavy Weight to be raiſed be
A, and let the ſteadfaſt ſupport
or Fulciment on which the Leaver
reſts and moves be ſuppoſed to be
E, and putting one end of the
Leaver under the Weight A, as
may be ſeen in the point C, en­
creaſing the Weight or Force at the other end D, it will be able
to lift up the Weight A, though not much, whenever the Force in
1D hath the ſame proportion to the Reſiſtance made by the Weight
A, in the point C: as the Diſtance B C hath to the Diſtance C D,
whereby it's clear, that the nearer the Fulciment E ſhall approach
to the Term B, encreaſing the proportion of the Diſtance D C to
the Diſtance C B, the more may one diminiſh the Force in D which
is to raiſe the Weight A. And here it is to be noted, which I ſhall
alſo in its place remember you of, that the benefit drawn from all
Mechanical Inſtruments, is not that which the vulgar Mechanitians
do perſwade us, to wit, ſuch, that there by Nature is overcome, and
in a certain manner deluded, a ſmall Force over-powring a very
great Reſiſtance with help of the Leaver; for we ſhall demonſtrate,
that without the help of the length of the Leaver, the ſame Force,
in the ſame Time, ſhall work the ſame effect. For taking the ſame
Leaver B C D, whoſe reſt or Fulci­
ment is in C, let the Diſtance C D
185[Figure 185]
be ſuppoſed, for example, to be
in quintuple proportion to the
Diſtance C B, & the ſaid Leaver to
be moved till it come to I C G: In
the Time that the Force ſhall have
paſſed the Space D I, the Weight
ſhall have been moved from B
to G: and becauſe the Diſtance
D C, was ſuppoſed quintuple to the other C B, it is manifeſt from
the things demonſtrated, that the Weight placed in B may be five
times greater then the moving Force ſuppoſed to be in D: but now,

if on the contrary, we take notice of the ^{*} Way paſſed by
the Force from D unto I, whilſt the Weight is moved from B unto
G, we ſhall find likewiſe the Way D I, to be quintuple to the Space
B G. Moreover if we take the Diſtance C L, equal to the Diſtance
C B, and place the ſame Force that was in D, in the point L, and
in the point B the fifth part onely of the Weight that was put there
at firſt, there is no queſtion, but that the Force in L being now
equal to this Weight in B, and the Diſtances L C and C B being
equall, the ſaid Force ſhall be able, being moved along the Space LM
to transfer the Weight equall to it ſelf, thorow the other equall
Space B G: which five times reiterating this ſame action, ſhall tranſ­
port all the parts of the ſaid Weight to the ſame Term G: But
the repeating of the Space L M, is certainly nothing more nor leſſe
then the onely once meaſuring the Space D I, quintuple to the
ſaid L M. Therefore the transferring of the Weight from B to G,
requireth no leſſe Force, nor leſſe Time, nor a ſhorter Way if it
wee placed in D, than it would need if the ſame were applied
in L: And, in ſhort, the benefit that is derived from the length of
the Leaver C D, is no other, ſave the enabling us to move that
1Body all at once, which would not have been moved by the ſame
Force, in the ſame Time, with an equall Motion, ſave onely in
pieces, without the help of the Leaver.
If of Iron, it is
called a Crow,
if of wood, a Bar
or Hand-ſpike.
Or Space.
Of the CAPSTEN and of the CRANE.
The Inſtruments which we are now about to declare, have
immediate dependence upon the Leaver, nay, are no other
but a perpetual Vectis or Leaver. For if we ſhall ſuppoſe the
Leaver B A C to be ſuſtained in
the point A, and the Weight G to
186[Figure 186]
hang at the point B, the Force be­
ing placed in C; It is manifeſt,
that transferring the Leaver unto
the points D A E, the Weight G
doth alter according to the Di­
ſtance B D, but cannot much far­
ther continue to raiſe it, ſo that
if it were required to elevate it yet
higher, it would be neceſſary to
ſtay it by ſome other Fulciment
in this Poſition, and to remit or return the Leaver to its former Po­
ſition B A C, and ſuſpending the Weight anew thereat, to raiſe it
once again to the like height B D; and in this manner repeating
the work, many times one ſhall come with an interrupted Motion
to effect the drawing up of the Weight, which for many reſpects
will not prove very beneficial: whereupon this difficulty hath bin
thought on, and remedied, by finding out a way how to unite to­
gether almoſt infinite Leavers, perpetuating the operation without
any interruption; and this hath been done by framing a Wheel
about the Center A, according to the Semidiameter A C, and an
Axis or Nave, about the ſame Center, of which let the Line A B
be the Semidiameter; and all this of very tough wood, or of other
ſtrong and ſolid matter, afterwards ſuſtaining the whole Machine
upon a Gudgeon or Pin of Iron planted in the point A, which
paſſeth quite thorow, where it is held faſt by two fixed Fulciments,
and the Rope D B G, at which the weight G hangeth, being be-laid
or wound about the Axis or Barrell, and applying another Rope
about the greater Wheel, at which let the other Grave I be hang­
ed: It is manifeſt, that the length C A having to the other A B
the ſelf-ſame proportion that the Weight G hath to the Weight I,
it may ſuſtain the Grave G, and with any little Moment more ſhall
move it: and becauſe the Axis turning round together with the
Wheel, the Ropes that ſuſtain the Weights are alwaies pendent and
contingent with the extream Circumferences of that Wheel and
1Axis, ſo that they ſhall conſtantly maintain alike Site and Poſition
in reſpect of the Diſtances B A and A C, the Motion ſhall be
perpetuated, the Weight I deſcending, and forcing the other G
to aſcend. Where we are to obſerve the neceſſity of be-laying
or winding the Rope about the Wheel, that ſo the Weight I may
hang according to the Line that is tangent to the ſaid Wheel: for
if one ſhould ſuſpend the ſaid Weight, ſo as that it did hang by the
point F, cutting the ſaid Wheel, as is ſeen along the Line F N M,
the Motion would ceaſe, the Moment of the Weight M being di­
miniſhed; which would weigh no more then if it did hang by the
point N: becauſe the Diſtance of its Suſpenſion from the Center
A, cometh to be determined by the Line A N, which falleth per­
pendicularly upon the Rope F M, and is no longer terminated by
the Semidiameter of the Wheel A F, which falleth at unequall
Angles upon the ſaid Line F M. A violence therefore being offered
in the Circumference of the Wheel by a Grave and Exanimate
Body that hath no other Impetus then that of Deſcending, it is
neceſſary that it be ſuſtained by a Line that is contingent with
the Wheel, and not by one that cutteth it. But if in the ſame
Circumference an Animate Force were employed, that had a Mo­
ment or Faculty of making an Impulſe on all ſides, the work might
be effected in any whatever place of the ſaid Circumference. And
thus being placed in F, it would draw up the Weight by turning
the Wheel about, pulling not according to the Line F M down­
wards, but ſide-waies according to the Contingent Line F L, which
maketh a Right Angle, with that which is drawn from the Center
A unto the point of Contact F: ſo, that if in this manner one do
meaſure the Diſtance from the Center A to the Force placed in
F, according to the Line A F perpendicular to F L, along which
the Impetus is made, a man ſhall not in any part have altered the
uſe of the ordinary Leaver. And we muſt note, that the ſame
would be poſſible to be done likewiſe with an Exanimate Force,
in caſe that a way were found out to cauſe that its Moment might
make Impulſe in the point F, drawing according to the Contingent
Line F L: which would be done by adjoyning beneath the Line F L
a turning Pulley, making the Rope wound about the Wheel to
paſſe along upon it, as it is ſeen to do by the Line F L X, ſuſpending
at the end thereof the Weight X equall to the other I, which ex­
erciſing its Force according to the Line F L, ſhall alwaies keep a
Diſtance from the Center A equall unto the Semidiameter of the
Wheel. And from what hath been declared we will gather for a
Concluſion, That in this Inſtrument the Force hath alwaies the
ſame proportion to the Weight, as the Semidiameter of the Axis
or Barrell hath to the Semidiameter of the Wheel.
1
From the Inſtrument laſt deſcribed, the other Inſtrument which
we call the Crane is not much different, as to form, nay, differeth
nothing, ſave in the way of applying or employing it: For that the
Capſten moveth and is conſtituted perpendicular to the Horizon,
and the Crane worketh with its Moment parallel to the ſame Ho­
187[Figure 187]
rizon. For if upon the Circle D A E we ſuppoſe an Axis to be
placed Column-wiſe, turning about the Center B, and about which
the Rope D H, faſtened to the Weight that is to be drawn, is be­
laid, and if the Bar F E B D be let into the ſaid Axis [by the Mor­
tace B] and the Force of a Man, of an Horſe, or of ſome other
Animal apt to draw, be applyed at its end F, which moving round,
paſſeth along the Circumference F G C, the Crane ſhall be framed
and finiſhed, ſo that by carrying round the Bar F B D, the Barrell
or Axis E A D ſhall turn about, and the Rope which is twined a­
bout it, ſhall conſtrain the Weight H to go forward: And becauſe
the point of the Fulciment about which the Motion is made, is the
point B, and the Moment keeps at a Diſtance from it according to
the Line B F, and the Reſiſtor at the Diſtance B D, the Leaver
F B D is formed, by vertue of which the Force acquireth Moment
equall to the Reſiſtance, if ſo be, that it be in proportion to it, as
the Line B D is to B F, that is, as the Semidiameter of the Axis to
the Semidiameter of the Circle, along whoſe Circumference the
Force moveth. And both in this, and in the other Inſtrument we
are to obſerve that which hath been frequently mentioned, that is,
That the benefit which is derived from theſe Machines, is not that
which the generality of the Vulgar promiſe themſelves from the
Mechanicks; namely, that being too hard for Nature, its poſſible
1with a Machine to overcome a Reſiſtance, though great, with a
ſmall Force, in regard, that we ſhall manifeſtly prove that the ſame
Force placed in F, might in the ſame Time conveigh the ſame
Weight, with the ſame Motion, unto the ſame Diſtance, without
any Machine at all: For ſuppoſing, for example, that the Reſiſtance
of the Grave H be ten times greater than the Force placed in F, it
188[Figure 188]
will be requiſite for the mo­
ving of the ſaid Reſiſtance,
that the Line F B be decuple
to B D; and conſequently,
that the Circumference of the
Circle F G C be alſo decuple
to the Circumference E A D:
and becauſe when the Force
ſhall be moved once along the
whole Circumference of the
Circle F G C, the Barrel EAD,
about which the Rope is be-laid which draweth the Weight, ſhall
likewiſe have given one onely turn; it is manifeſt, that the Weight
H ſhall not have been moved more than the tenth part of that way
which the Mover ſhall have gone. If therefore the Force that is to
move a Reſiſtance that is greater than it ſelf, for ſuch an aſſigned
Space by help of this Machine, muſt of neceſſity move ten times as
far, there is no doubt, but that dividing that Weight into ten parts,
each of them ſhall be equall to the Force, and conſequently, might
have been tranſported one at a Time, as great a Space as that
which it ſelf did move, ſo that making ten journeys, each equal to
the Circumference E A D, it ſhall not have gone any farther than
if it did move but once alone about the Circumference F G C;
and ſhall have conveighed the ſame Weight H to the ſame Di­
ſtance. The benefit therefore that is to be derived from theſe
Machines is, that they carry all the Weight together, but not with
leſſe Labour, or with greater Expedition, or a greater Way than
the ſame Force might have done conveying it by parcels.
Of PULLIES.
The Inſtruments, whoſe Natures are reducible unto the Bal­
lance, as to their Principle and Foundation, and others little
differing from them, have been already deſcribed; now for
the underſtanding of that which we have to ſay touching Pullies,
it is requiſite, that we conſider in the firſt place another way to uſe
the Leaver, which will conduce much towards the inveſtigation of
the Force of Pullies, and towards the underſtanding of other Me­
chanical Effects. The uſe of the Leaver above declared ſuppoſed
1the Weight to be at one extream, and the Force at the other, and
the Fulciment placed in ſome point between the extreams: but we
may make uſe of the Leaver another way, yet, placing, as we ſee,
the Fulciment in the extream A, the Force in the other extream C,
and ſuppoſing the Weight D to hang by ſome point in the midſt,
189[Figure 189]
as here we ſee by the point B, in
this example it's manifeſt, that if
the Weight did hang at a point
Equi-diſtant from the two ex­
treams A and C, as at the point F,
the labour of ſuſtaining it would
be equally divided betwixt the
two points A and C, ſo that half
the Weight would be felt by the
Force C, the other half being ſu­
ſtained by the Fulciment A: but if the Grave Body ſhall be hanged
at another place, as at B, we ſhall ſhew that the Force in C is ſuffi­
cient to ſuſtain the Weight in B, as it hath the ſame proportion
to it, that the Diſtance, A B hath to the Diſtance A C. For De­
monſtration of which, let us imagine the Line B A to be continued
right out unto G, and let the Diſtance B A be equall to A G, and
let the Weight hanging at G, be ſuppoſed equall to D: It is ma­
nifeſt, that by reaſon of the equality of the Weights D and E, and
of the Diſtances G A and A B, the Moment of the Weight E
ſhall equalize the Moment of the Weight D, and is ſufficient to
ſuſtain it: Therefore whatever Force ſhall have Moment equall to
that of the Weight E, and that ſhall be able to ſuſtain it, ſhall be
ſufficient likewiſe to ſuſtain the Weight D: But for ſuſtaining the
Weight E, let there be placed in the point C ſuch a Force, whoſe
Moment hath that proportion to the Weight E, that the Diſtance
G A hath to the Diſtance A C, it ſhall be ſufficient to ſuſtain it:
Therefore the ſame Force ſhall likewiſe be able to ſuſtain the
Weight D, whoſe Moment is equall to the of E: But look what
Proportion the Line G A hath to the Line A C; and A B alſo hath
the ſame to the ſaid A C, G A having been ſuppoſed equall to A B:
And becauſe the Weights E and D are equall, each of them ſhall
have the ſame proportion to the Force placed in C: Therefore the
Force in C is concluded to equall the Moment of the Weight D,
as often as it hath unto it the ſame proportion that the Diſtance B A
hath to the Diſtance C A. And by moving the Weight, with the
Leaver uſed in this manner, it is gathered in this alſo, as well as in
the other Inſtruments, that what is gained in Force is loſt in Velo­
city: for the Force C raiſing the Leaver, and transferring it to A I,
the Weight is moved the Space B H, which is as much leſſer than
the Space C I paſſed by the Force, as the Diſtance A B is leſſer
1than the Diſtance A C; that is, as the Force is leſſe than the
Weight.
Theſe Principles being declared, we will paſſe to the Contem­
plation of Pullies, the compoſition and ſtructure of which, together
with their uſe, ſhall be deſcribed by us. And firſt let us ſuppoſe the

^{*} Little Pulley A B C, made of Mettall or hard Wood, voluble a­
bout it's Axis which paſſeth thorow it's Center D, and about this
190[Figure 190]
Pulley let the Rope E A B C be put,
at one end of whichlet the Weight E
hang, and at the other let us ſuppoſe
the Force F. I ſay, that the Weight
being ſuſtained by a Force equall to
it ſelf in the upper Nut or Pulley
A B C, bringeth ſome benefit, as the
moving or ſuſtaining of the ſaid
Weight with the Force placed in F:
For if we ſhall underſtand, that from
the Center D, which is the place of the Fulciment, two Lines be
drawn out as far as the Circumference of the Pulley in the points
A and C, in which the pendent Cords touch the Circumference, we
ſhall have a Ballance of equal Arms which determine the Diſtance
of the two Suſpenſions from the Center and Fulciment D: Where­
upon it is manifeſt, that the Weight hanging at A cannot be ſuſtain­
ed by a leſſer Weight hanging at G, but by one equal to it; ſuch
is the nature of equal Weights hanging at equal Diſtances. And
although in moving downwards, the Force F cometh to turn about
the Pulley A B C, yet there followeth no alteration of the Alti­
tude or Reſpect, that the Weight and Force have unto the two
Diſtances A D and D C, nay, the Pulley encompaſſed becometh a
Ballance equal to A C, but perpetuall. Whence we may learn,
how childiſhly Ariſtotle deceiveth himſelf, who holds, that by making
the ſmall Pulley A B C bigger, one might draw up the Weight with
a leſſer Force; he conſidering that upon the enlargement of the
ſaid Pulley, the Diſtance D C encreaſed, but not conſidering that
there was as great an encreaſe of the other Diſtance of the Weight,
that is, the other Semidiameter D A. The benefit therefore that may
be drawn from the Inſtrument above ſaid, is nothing at all as to the
diminution of the labour: and if any one ſhould ask how it hap­
pens, that on many occaſions of raiſing Weights, this means is made
uſe of to help the Axis, as we ſee, for example, in drawing up the
Water of Wells; it is anſwered, that that is done, becauſe that
by this means the manner of employing the Force is found more
commodious: for being to pull downwards, the proper Gravity of
our Arms and other parts help us, whereas if we were to draw
the fame Weight upwards with a meer Rope, by the ſole ſtrength
1of the Members and Muſcles, and as we uſe to ſay, by Force of
Armes, beſides the extern Weight, we are to lift up the Weight of
our own Armes, in which greater pains is required. Conclude we,
therefore, that this upper Pulley doth not bring any Facility to the
Force ſimply conſidered, but onely to the manner of applying it:
but if we ſhall make uſe of the like Machine
191[Figure 191]
in another manner, as we are now about to
declare; we may raiſe the Weight with di­
minution of Forces: For let the Pulley
B D C be voluble about the Center E placed
in it's Frame B L C, at which hang the
Grave G; and let the Rope A B D C F
paſſe about the Pulley; of which let the end
A be faſtned to ſome fixed ſtay, and in the
other F let the Force be placed; which
moving to wards H ſhall raiſe the Machine
B L C, and conſequently the Weight G:
and in this operation I ſay, that the Force in
F is the half of the Weight ſuſtained by it.
For the ſaid Weight being kept to Rights by the two ^{*} Ropes A B

and F C, it is manifeſt, that the Labour is equally ſhared betwixt
the Force F and the Fulciment A: and more ſubtilly examining the
nature of this Inſtrument, if we but continue forth the Diameter
B E C, we ſhall ſee a Leaver to be made, at the midſt of which, that
is at the point E, the Grave doth hang, and the Fulciment cometh
to be at the end B, and the Force in the Term C: whereupon, by
what hath been above demonſtrated, the Force ſhall have the ſame
proportion to the Weight, that the Diſtance E B hath to the Di­
ſtance; Therefore it ſhall be the half of the ſaid Weight: And
becauſe the Force riſing towards A, the Pulley turneth round,
therefore that Reſpect or Conſtitution which the Fulciment B and
Center E, on which the Weight and Term C, in which the Force
is employed do depend, ſhall not change all the while; but yet in
the Circuinduction the Terms B and C happen to vary in number,
but not in vertue, others and others continually ſucceeding in their
place, whereby the Leaver B C cometh to be perpetuated. And
here (as hath been done in the other Inſtruments, and ſhall be in
thoſe that follow) we will not paſſe without conſidering how that
the journey that the Force maketh, is double to the Moment of the
Weight. For in caſe the Weight ſhall be moved ſo far, till that
the Line B C come to arrive with it's points B and C, at the points
A and F, it is neceſſary that the two equal Ropes be diſtended in
one ſole Line F H, and conſequently, when the Weight ſhall have
aſcended along the Intervall B A, the Force ſhall have been moved
twice as far, that is, from F unto H. Then conſidering that the
1Force in F, that it may raiſe the Weight, muſt move upwards, which
to exanimate Movers, as being for the moſt part Grave Bodies, is al­
192[Figure 192]
together impoſſible, or at leaſt more laborious,
than the making of the ſame Force down­
wards: Therefore to help this inconvenience,
a Remedy hath been found by adjoyning an­
other Nut or Pulley above, as in the adjacent
Figure is ſeen, where the Rope C E F hath
been made to paſs about the upper Pulley F G
upheld by the Hook L, ſo that the Rope paſſing
to H, and thither transferring the Force E, it
ſhall be able to move the Weight X by pulling
downwards, but not that it may be leſſer than
it was in E: For the Motions of the Force
F H, hanging at the equal Diſtances F D and
D G of the upper Pulley, do alwaies continue
equal; nor doth that upper Pulley (as hath
been ſhewn above) come to produce any di­
minution in the Labour. Moreover it having been neceſſary by
the addition of the upper Pulley to introduce the Appendix B, by
which it is ſuſtained, it will prove of ſome benefit to us to raiſe
the other A, to which one end of the Rope was faſtned, transferring
it to a Ring annexed to the lower part of the Frame of the upper
Pulley, as we ſee it done in M. Now finally, this Machine com­
pounded of upper and lower Pullies, is that which the Greeks call

Τποχίλιον.
*Called by ſome
a Nut.
* Or two ends of
the ſame Rope.
In Latine Tro­
chlea.
We have hitherto explained, how by help of Pullies one may
double the Force, it remaineth that with the greateſt brevity poſ­
ſible, we ſhew the way how to encreaſe it according to any Multi­
plicity. And firſt we will ſpeak of the Multiplicity according to
the even numbers, and then the odde: To ſhew how we may mul­
tiply the Force in a quadruple Proportion, we will propound the
following Speculation as the Soul of all that followeth.
Take two Leavers, A B, C D, with the Fulciments in the ex­
193[Figure 193]
treams A and C; and at the middles
of each of them let the Grave G hang,
ſuſtained by two Forces of equal Mo­
ment placed in B and D. I ſay, that
the Moment of each of them will
equal the Moment of the fourth part
of the Weight G. For the two For­
ces B and D bearing equally, it is
manifeſt, that the Force D hath not
contraſted with more then one half of the Weight G: But if the
Force D do by benefit of the Leaver D C ſuſtain the half of the
1Weight G hanging at F, it hath been already demonſtrated, that
the ſaid Force D hath to the Weight ſo by it ſuſtained, that ſame
proportion which the Diſtance F C hath to the Diſtance C D:
Which is ſubduple proportion: Therefore the Moment D is ſub­
duple to the Moment of half of the Weight G ſuſtained by it:
Wherefore it followeth, that it is the fourth part of the Moment
of the whole Weight. And in the ſame manner the ſame thing is
demonſtrated, of the Moment B; and it is but reaſonable, that the
Weight G being ſuſtained by the four points, A, B, C, D, each of
them ſhould feel an equall part of the Labour.
Let us come now to apply this Conſideration to Pullies, and let
the Weight X be ſuppoſed to hang at the two Pullies A B and D E
entwining about them, and about the uppermoſt Pulley G H, the
Rope, as we ſee, I D E H G A B, ſuſtaining the whole Machine in
the point K. Now I ſay, that placing the Force in L, it ſhall be able
to ſuſtain the Weight X, if ſo be, it be equal to the fourth part of
it. For if we do imagine the two Diameters D E and A B, and the
Weights hanging at the middle points F and C, we ſhall have two
Leavers like to thoſe before deſcribed, the Fulciments of which an­
ſwer to the points D and A. Whereupon the Force placed in B,
194[Figure 194]
or if you will, in L, ſhall be able to ſu­
ſtain the Weight X, being the fourth
part of it: And if we adde another Pul­
ley above the other two, making the
Rope or Cord to paſs along L M N, trans­
ferring the Force L into N, it ſhall be
able to bear the ſame Weight gravitating
downwards, the upper Pulley neither aug­
menting or diminiſhing the Force, as hath
been declared. And we will likewiſe
note, that to make the: Weight aſcend the

four Ropes B L, E H, D I, and A G
ought to paſs, whereupon the Mover will
be to begin, as much as thoſe Ropes are
long; and yet nevertheleſs the Weight
ſhall move but only as much as the length
of one of them: So that we may ſay by
way of advertiſement, and for confirma­
tion of what hatn been many times ſpo­
ken, namely, that look with what proportion the Labour of the

Mover is diminiſhed, the length of the Way, on the contrary, is
encreaſed with the ſame proportion
* Or four parts
of the ſame Rope
* The word Gy­
rilla ſignifieth a
Shiver, Rundle,
or ſmall Wheel
of a Pulley, tran­
ſlated by we
ſometimes Pul­
ley, ſometimes
Nut or Girill.
But if we would encreaſe the Force in ſexcuple proportion, it
will be requiſite that we adjoyn another ^{*} ſmall Pulley or Gyrill
to the inferiour Pulley which that you may the better underſtand
1we will ſet before you the preſent Contemplation. Suppoſe, there­
fore, that A B, C D, and E F are three Leavers; and that on the
middle points of them G, H, and I the Weight K doth hang in
common, ſo that every one of them ſhall ſuſtain the third part of
195[Figure 195]
it: And becauſe the Power in
B, ſuſtaining with the Leaver
B A thependent Weight in G,
hapneth to be the half of the
ſaid Weight, and it hath been
already ſaid, that it ſuſtaineth
the third part of the Weight
K: Therefore the Moment of
the Force B is equal to half of
the third part of the Weight K; that is, to the ſixth part of it:
And the ſame ſhall be demonſtrated of the other Forces D and F:
From whence we may eaſily gather, that putting three Gyrils or
Rundles into the inferiour Pulley, and two or three into the upper­
196[Figure 196]
moſt, we may multiply the Force accor­

ding to our ^{*} Senarius. And if we would
encreaſe it according to any other even
Number, the Gyrils of the Pulley below
muſt be multiplyed according to the half
of that Number, according to which the
Force is to be multiplyed, circumpoſing
the Rope about the Pulleys, ſo as that one
of the ends be faſtned to the upper Pul­
ley, and let the Force be in the other; as
in this Figure adjoyning may manifeſtly
be gathered.
* Or in Sexcuple
proportion.
Now paſſing to the Declaration of the
manner how to multiply the Force ac­
cording to the odd Numbers, and begin­
197[Figure 197]
ning at the triple proportion: firſt, let us
propoſe the preſent Contemplation, as
that, on the underſtanding of which the
knowledge of all the Work in hand
doth depend. Let therefore the Leaver
be A B, its Fulciment A, and from the
middle of it, that is, at the point C let
the Grave D be hanged; and let it be ſu­
ſtained by two equal Forces; and let one of them be applied to the
point C, and the other to the term B. I ſay, that each of thoſe Powers
have Moment equal to the third part of the Weight D. For the
Force in C ſuſtaineth a Weight equal to it ſelf, being placed in the
ſame Line in which the Weight D doth hang & Gravitate: But the
1Force in B ſuſtaineth a part of the Weight D double to it ſelf, its
Diſtance from the Fulciment A, that is, the Line B A being dou­
ble to the Diſtance A C at which the Grave hangeth: But becauſe
the two Forces in B and C are ſuppoſed to be equal to each other:
Therefore the part of the Weight D, which is ſuſtained by the
Force in B, is double to the part ſuſtained by the Force in C. If
therefore, of the Grave D two parts be made, the one double to
the remainder, the greater is ſuſtained by the Force in B, and the
leſſer by the Force in C: But this leſſer is the third part of the
Weight D: Therefore the Moment of the Force in C is equal to
the Moment of the third part of the Weight D; to which, of
conſequence, the Force B ſhall be equal, we having ſuppoſed it
equal to the other Force C: Wherefore our intention is manifell,
which we were to demonſtrate, how that each of the two Powers
C and B is equal to the third part of the Weight D. Which be­
ing demonſtrated, we will paſs forwards to the Pulleys, and will
deſcribe the inferiour Gyrils of A C B, voluble about the Center
G, and the Weight H hanging thereat, we will draw the other up­
per one E F, winding about them both the Rope D F E A C B I,
of which let the end D be faſtned to the inferiour Pulley, and to
198[Figure 198]
the other I let the Force be applyed:
Which, I ſay, ſuſtaining or moving the
Weight H, ſhall feele no more than the
third part of the Gravity of the ſame. For
conſidering the contrivance of this Ma­
chine, we ſhall find that the Diameter A B
ſupplieth the place of a Leaver, in whoſe
term B the Force I is applied, and in the
other A the Fuiciment is placed, at the mid­
dle G the Grave H is hanged, and another
Force D applied at the ſame place: ſo that

the Weight is faſtned to the ^{*} three Ropes
I B, F D, and E A, which with equal Labour
ſuſtain the Weight. Now, by what hath
already been contemplated, the two Forces
D and B being applied, one, to the midſt of the Leaver A B, and
the other to the extream term B, it is manifeſt, that each of them
holdeth no more but the third part of the Weight H: Therefore
the Power I, having a Moment equal to the third part of the
Weight H, ſhall be able to ſuſtain and move it: but yet the Way
of the Force in I ſhall be triple to the Way that the Weight ſhall
paſs; the ſaid Force being to diſtend it ſelf according to the
Length of the three Ropes I B, F D, and E A, of which one alone
meaſureth the Way of the Weight H.
1
* Or three parts
of one Rope.
Of the SCREW.
Amongſt the reſt of Mechanick Inſtruments for ſundry uſes
found out by the Wit of Man, the Screw doth, in my opi­
nion, both for Invention and for Utility, hold the firſt
place, as that which is appoſitely accommodated, and ſo contrived
not only to move, but alſo to ſtay and preſs with very great Force,
that taking up but little room, it worketh thoſe effects which other
Inſtruments cannot, unleſs they were reduced to a great Machine.
The Screw therefore being of moſt ingenious and commodious
contrivance, we ought deſervedly to be at ſome pains in explaining,
with all the plainneſs that is poſſible, the Original and Nature of
it. The which that we may do, we will begin at a Speculation,
which, though at firſt bluſh it may appear ſomewhat remote from
the conſideration of this Inſtrument, yet is the Baſis and Founda­
tion thereof.
No doubt, but that Natures operation in the Motions of Grave
Bodies is ſuch, that any whatever Body that hath a Gravity in it
hath a propenſion of moving, being at liberty, towards the Cen­

ter, and that not only ^{*} by the Right Line perpendicularly, but al­
ſo (when it cannot do otherwiſe) by any other Line, which ha­
ving ſome inclination towards the Center goeth more and more
abaſing. And thus we ſee the Water not only to fall downwards
along the Perpendicular from ſome eminent place, but alſo to run
about the Surface of the Earth along Lines though very little en­
clined; as we ſee in the Courſe of Rivers, the Waters of which, if ſo
be that the Bed have any the leaſt declivity, go freely declining
downwards. Which very effect, like as it is diſcerned in all Fluid
Bodies, would appear alſo in hard Bodies, if ſo be, that their Fi­
gure and other Accidental and Extern Impediments did not hinder
it. So that we, having a Superficies very well ſmoothed and poli­
ſhed, as for inſtance, that of a Looking-glaſs, and a Ball exactly
rotund and ſleek, either of Marble, or of Glaſs, or of any other
Matter apt to be poliſhed, this being placed upon that Superficies
ſhall trundle along, in caſe that this have any, though very ſmall,
inclination; and ſhall lie ſtill only upon that Superficies which is
exactly levelled and parallel to the Plane of the Horizon: as is
that, for example, of a Lake or ſtanding Water being frozen, up­
on which the ſaid Spherical Body would ſtand ſtill, but in a con­
dition of being moved by every ſmall Force. For we having ſup­
poſed that if that Plane did incline but an hairs breadth only, the
ſaid Ball would move along it ſpontaneouſly towards the part de­
clining, and on the oppoſite would have a Reſiſtance, nay, would
not be able without ſome Violence to move towards the part
1riſing or aſcending: it of neceſſity remaineth manifeſt, that in the
Superficies which is exactly equilibrated, the ſaid Ball remaineth in­
different and dubious between Motion and Reſt, ſo that every ſmall
Force is ſufficient to move it, as on the contrary, every ſmall Reſi­
ſtance, and no greater than that of the meer Air that environs it, is
able to hold it ſtill.
* Or along.
From whence we may take this Concluſion for indubitable, That
Crave Bodies, all Extern and Adventitious Impediments being re­
moved, may be moved along the Plane of the Horizon by any ne­
ver ſo ſmall Force: but when the ſame Grave is to be thrown along
an Aſcending Plane, then, it beginning to ſtrive againſt that aſcent,
having an inclination to the contrary Motion, there ſhall be requi­
red greater Violence, and ſtill greater the more Elevation that ſame
Plane ſhall have. As for example, the Moveable G, being poſited
upon the Line A B parallel to the Horizon, it ſhall, as hath been
ſaid, be indifferent on it either to Motion or Reſt, ſo that it may
be moved by a very ſmall Force: But if we ſhall have the Planes
Elevated, they ſhall not be driven along without Violence; which
199[Figure 199]
Violence will be required to be
greater to move it along the Line
A D, than along A C; and ſtill
greater along A E than along A D:
The which hapneth, becauſe it hath
greater Impetus of going down­
wards along A E than along A D,
and along A D than along A C. So
that we may likewiſe conclude
Grave Bodies to have greater Reſiſtance upon Planes differently
Elevared, to their being moved along the ſame, according as one
ſhall be more or leſs elevated than the other; and, in fine, that the
greateſt Reſiſtance of the ſame Grave to its being raiſed is in the
Perpendicular A F. But it will be neceſſary to declare exactly what
proportion the Force muſt have to the Weight, that it may be able
to carry it along ſeveral elevated Planes, before we proceed any
farther, to the end that we may perfectly underſtand all that which
remains to be ſpoken.
Letting, therefore, Perpendiculars fall from the points C, D,
and E unto the Horizontal Line A B, which let be C H, D I, and
E K: it ſhall be demonſtrated that the ſame Weight ſhall be mo­
ved along the Plane A C with leſſer Force than along the Perpendi­
cular A F, (where it is raiſed by a Force equal to it ſelf) accor­
ding to the proportion by which the Perpendicular C H is leſs than
A C: and that along the Plane A D, the Force hath the ſame pro­
portion to the Weight, that the Perpendicular I D hath to D A:
and, laſtly, that in the Plane A E the Force to the Weight obſer­
veth the proportion of E K and E A.
1
The preſent Speculation hath been attempted by Pappus Alex­
andrinus in Lib. 8. de Collection. Mathemat. but, if I be in the
right, he hath not hit the mark, and was overſeen in the Aſſumpti­
on that he maketh, where he ſuppoſeth that the Weight ought to
be moved along the Horizontal Line by a Force given; which is
falſe: there needing no ſenſible Force (removing the Accidental
Impediments, which in the Theory are not regarded) to move the
given Weight along the Horizon, ſo that he goeth about in vain
afterwards to ſeek with what Force it is to be moved along the
elevated Plane. It will be therefore better, the Force that moveth
the Weight upwards perpendicularly, (which equalizeth the Gra­
vity of that Weight which is to be moved) being given, to
ſeek the Force that moveth it along the Elevated Plane: Which
we will endeavour to do in a Method different from that of
Pappus.
Let us therefore ſuppoſe the Circle A I C, and in it the Diame­
ter A B C, and the Center B, and two Weights of equal Moment
in the extreams B and C; ſo that the Line A C being a Leaver,
or Ballance moveable about the Center B, the Weight C ſhall
come to be ſuſtained by the Weight A. But if we ſhall imagine
the Arm of the Ballance B C to be inclined downwards according
to the Line B F, but yet in ſuch a manner that the two Lines A B
and B F do continue ſolidly conjoyned in the point B, in this caſe
the Moment of the Weight C ſhall not be equal to the Moment
200[Figure 200]
of the Weight A, for that the Di­
ſtance of the point F from the Line
of Direction, which goeth accord­
ing to B I, from the Fulciment B un­
to the Center of the Earth, is dimi­
niſhed: But if from the point F we
erect a Perpendicular unto B C, as is
F K, the Moment of the Weight in
F ſhall be as if it did hang by the
Line K F, and look how much the
Diſtance K B is diminiſhed by the
Diſtance B A, ſo much is the Moment of the Weight F diminiſhed
by the Moment of the Weight A. And in this faſhion inclining
the Weight more, as for inſtance, according to B L, its Moment ſhall
ſtill diminiſh and ſhall be as if it did hang at the Diſtance B M, ac­
cording to the Line M L, in which point L it ſhall be ſuſtained by
a Weight placed in A, ſo much leſs than it ſelf, by how much the
Diſtance B A is greater than the Diſtance B M. See therefore that
the Weight placed in the extream of the Leaver B C, in inclining
downwards along the Circumference C F L I, cometh to diminiſh
its Moment and Impetus of going downwards from time to time,
1more and leſs, as it is more or leſs ſuſtained by the Lines B F and
B L: But the conſidering that this Grave deſcending, and ſuſtained
by the Semidiameters B F and B L is one while leſs, and another
while more conſtrained to paſs along the Circumference C F L, is
no other, than if we ſhould imagine the ſame Circumference
C F L I to be a Superſicies ſo curved, and put under the ſame
Moveable: ſo that bearing it ſelf thereon it were conſtrained to
deſcend along thereby; for if in the one and other manner the
Moveable deſcribeth the ſame Courſe or Way, it will nothing im­
port whether, if ſuſpended at the Center B, it is ſuſtained by the
Semidiameter of the Circle, or elſe, whether that Fulciment being
taken away, it proceed along the Circumference C F L I: So that
we may confidently affirm, that the Grave deſcending downwards
from the point C along the Circumference C F L I, its Moment
of Deſcent in the point C is total and entire, becauſe it is not in
any part ſuſtained by the Circumference: And there is not in that
firſt point C, any indiſpoſition to Motion different from that, which
being at liberty, it would make along the Perpendicular and Con­
tingent Line D C E: But if the Moveable ſhall be placed in the
point F, then its Gravity is in part ſuſtained, and its Moment of
Deſcent is diminiſhed by the Circular Path or Way that is placed
under it, in that proportion wherewith the Line B K is overcome
by B C: But if when the Moveable is in F, at the firſt inſtant of
ſuch its Motion, it be as if it were in the Plane elevated according
to the Contingent Line G F H, for that reaſon the inclination of the
Circumference in the point F differeth not from the inclination of
the Contingent Line F G any more ſave the inſenſible Angle of
the Contact. And in the ſame manner we ſhall find the Moment
of the ſaid Moveable to diminiſh in the point L, as the Line BM
is diminiſhed by B C; ſo that in the Plane contingent to the Circle
in the point L, as for inſtance, according to the Line N L O, the
Moment of Deſcent diminiſheth in the Moveable with the ſame
proportion. If therefore ^{*} upon the Plane HG the Moment of the

Moveable be diminiſhed by the total Impetus which it hath in its
Perpendicular D C E, according to the proportion of the Line K B
to the Line B C, and B F, being by the Solicitude of the Triangles
K B F and K F H the ſame proportion betwixt the Lines K F and
F H, as betwixt the ſaid K B and B F, we will conclude that the
proportion of the entire and abſolute Moment, that the Moveable
hath in the Perpendicular to the Horizon to that which it hath up­
on the Inclined Plane H F, hath the ſame proportion that the
Line H F hath to the Line F K; that is, that the Length of the
Inclined Plane hath to the Perpendicular which ſhall fall from it
unto the Horizon. So that paſſing to a more diſtinct Figure, ſuch
as this here preſent, the Moment of Deſcending which the Move­
1able hath upon the inclined Plane C A hath to its total Moment
wherewith it gravitates in the Perpendicular to the Horizon C P the
ſame proportion that the ſaid Line P C hath to C A. And if thus it
be, it is manifeſt, that like as the Force that ſuſtai­
neth the Weight in the Perpendiculation P C ought
201[Figure 201]
to be equal to the ſame, ſo for ſuſtaining it in the
inclined Plane C A, it will ſuffice that it be ſo much
leſſer, by how much the ſaid Perpendicular C P wan­
teth of the Line C A: and becauſe, as ſometimes we
ſce, it ſufficeth, that the Force for moving of the
Weight do inſenſibly ſuperate that which ſuſtaineth it, therefore
we will infer this univerſal Propoſition, [That upon an Elevated
Plane the Force hath to the Weight the ſame proportion, as the
Perpendicular let fall from the Plane unto the Horizon hath to the
Length of the ſaid Plane.]
* Or along
Returning now to our firſt Intention, which was to inveſtigate
the Nature of the Screw, we will conſider the Triangle A B C, of
which the Line A B is Horizontal, B C perpendicular to the ſaid
Horizon, and A C a Plane elevated; upon which the Moveable D
ſhall be drawn by a Force ſo much leſs than it, by how much the
Line B C is ſhorter than C A: But to elevate or raiſe the ſaid
Weight along the ſaid Plane A C, is as much as if the Triangle
C A B ſtanding ſtill, the Weight
202[Figure 202]
D be moved towards C, which is
the ſame, as if the ſame Weight
never removing from the Perpen­
dicular A E, the Triangle did
preſs forwards towards H. For if
it were in the Site F H G, the
Moveable would be found to
have mounted the height A I.
Now, in fine, the primary Form and Eſſence of the Screw is no­
thing elſe but ſuch a Triangle A C B, which being forced for­
wards, ſhall work it ſelf under the Grave Body to be raiſed, and
lifteth it up, as we ſay, by the ^{*} head and ſhoulders. And this was

its firſt Original: For its firſt Inventor (whoever he was) conſi­
dering how that the Triangle A B C going forwards raiſeth the
Weight D, he might have framed an Inſtrument like to the ſaid
Triangle, of a very ſolid Matter, which being thruſt forwards did
raiſe up the propoſed Weight: But afterwards conſidering better,
how that that ſame Machine might be reduced into a much leſſer
and more commodious Form, taking the ſame Triangle he twined
and wound it about the Cylinder A B C D in ſuch a faſhion, that
the height of the ſaid Triangle, that is the Line C B, did make the
Height of the Cylinder, and the Aſcending Plane did beget upon
1the ſaid Cylinder the Helical Line deſcribed by the Line AEFGH,
which we vulgarly call the Wale of the Screw, which was produ­
ced by the Line A C. And in this manner is the Inſtrument made,
which is by the Greeks called Κόχλος, and by us a Screw; which

winding about
cometh to work
203[Figure 203]
and inſinu­
ate with its
Wales under
the Weight, and
with facility rai­
ſeth it. And we
having demon­
ſtrated, That up­
on [or along]
the elevated Plane the Force hath the ſame proportion to the
Weight, that the perpendicular Altitude of the ſaid Plane hath to
its Length; ſo, ſuppoſing that the Force in the Screw A B C D is
multiplied according to the proportion by which the Length of the
whole Wale exceedeth the Altitude C B, from hence we come
to know that making the Screw with its Helix's more thick or cloſe
together, it becometh ſo much the more forceable, as being begot
by a Plane leſs elevated, and whoſe Length regards its own Per­
pendicular Altitude with greater proportion. But we will not
omit to advertiſe you, that deſiring to find the Force of a propo­
ſed Screw, it will not be needful that we meaſure the Length of
all its Wales, and the Altitude of the whole Cylinder, but it
will be enough if we ſhall but examine how many times the Di­
ſtance betwixt two ſingle and Contiguous terms do enter into one
ſole Turn of the ſame Wale, as for example, how many times
the Diſtance AF is contained in the Length of the Turn AEF:
For this is the ſame proportion that the Altitude CB hath to all
the Wale.
Levar in capo
ſignfieth to lift
on high by force
* Κόχλος, in La­
tine Cocblea, any
Screw winding
like the Shell of
a Snail.
If all that be underſtood which we have hitherto ſpoken touch­
ing the Nature of this Inſtrument, I do not doubt in the leaſt but
that all the other circumſtances may without difficulty be compre­
hended: as for inſtance, that inſteed of making the Weight to
mount upon the Screw if one accommodates its Nut with
the Helix incavated or made hollow, into which the Male Screw
that is the Wale entring, & then being turned round it raiſeth and
lifteth up the Nut or Male Screw together with the Weight which
was hanged thereat. Laſtly, we are not to paſs over that Conſidera­
tion with ſilence which at the beginning hath been ſaid to be neceſ­
ſary for us to have in all Mechanick Inſtruments, to wit, That
what is gained in Force by their aſſiſtance, is loſt again in Time,
1and in the Velocity: which peradventure, might not have ſeemed
to ſome ſo true and manifeſt in the preſent Contemplation; nay,
rather it ſeems, that in this caſe the Force is multiplied without the
Movers moving a longer way than the Moveable: In regard, that
if we ſhall in the Triangle A B C ſuppoſe the Line A B to be the
Plane of the Horizon, A C the elevated Plane, whoſe Altitude is
meaſured by the Perpendicular C B, a Moveable placed upon the
Plane A C, and the Cord E D F tyed to it, and a Force or Weight
applyed in F that hath to the
Gravity of the Weight E the
204[Figure 204]
ſame proportion that the Line
B C hath to C A; by what
hath been demonſtrated, the
Weight F ſhall deſcend
downwards, drawing the
Moveable E along the eleva­
ted Plane; nor ſhall the Move­
able E meaſure a greater Space
when it ſhall have paſſed the
whole Line A C, than that which the ſaid Grave F meaſureth in its
deſcent downwards. But here yet it muſt be advertiſed, that al­
though the Moveable E ſhall have paſſed the whole Line A C, in
the ſame Time that the other Grave F ſhall have been abaſed the
like Space, nevertheleſs the Grave E ſhall not have retired from the
common Center of things Grave more than the Space of the Per­
pendicular C B. but yet the Grave F deſcending Perpendicularly ſhall
be abaſed a Space equal to the whole Line A C. And becauſe Grave
Bodies make no Reſiſtance to Tranſverſal Motions, but only ſo
far as they happen to recede from the Center of the Earth; There­
fore the Moveable E in all the Motion A C being raiſed no more
than the length of the Line CB, but the other F being abaſed per­
pendicularly the quantity of all the Line A C: Therefore we may
deſervedly affirm that Way of the Force E maintaineth the ſame
proportion to the Force F that the Line A C hath to C B; that is,
the Weight E to the Weight F. It very much importeth, therefore,
to conſider by [or along] what Lines the Motions are made, eſpe­
cially in exanimate Grave Bodies, the Moments of which have their
total Vigour, and entire Reſiſtance in the Line Perpendicular to
the Horizon; and in the others tranſverſally Elevated and Inclined
they feel the more or leſs Vigour, Impetus, or Reſiſtance, the more
or leſs thoſe Inclinations approach unto the Perpendicular Inclina­
tion.
1
Of the SCREW of ARCHIMEDES
to draw Waier.
I Do not think it ſit in this place to paſs over with Silence the
Invention of Archimedes to raiſe Wa er with the Screw, which
is not only marvellous, but miraculous: for we ſhall find that
the Water aſcendeth in the Screw continually deſcending; and in
a given Time, with a given Force doth raiſe an unſpeakable quan­
tity therof. But before we proceed any farther, let us declare the uſe
of the Screw in making Water to riſe: And in the enſuing Figure,
let us conſider the Line I L O P Q
205[Figure 205]
R S H being wrapped or twined
about the Collumn M I K H,
which Line you are to ſuppoſe to
be a Chanel thorow which the
Water may run: If we ſhall put
the end I into the Water, making
the Screw to ſtand leaning, ſo as
the point L may be lower than
the firſt I, as the Diagram ſhew­
eth, and ſhall turn it round about
on the two Axes, T and V, the Water ſhall run thorow the Cha­
nel, till that in the end it ſhall diſcharge ſorth at the mouth H.
Now I ſay, that the Water, in its conveyance from the point I to
the point H, doth go all the way deſcending, although the point H
be higher than the point I. Which that it is ſo, we will declare
in this manner. We will deſcribe the Triangle A C B, which is
that of which the Screw H I is generated, in ſuch ſort that the
Chanel of the Screw is repreſented by the Line A C, whoſe
Aſcent and Elevation is determined by the Angle C A B; that is
to ſay, if ſo be, that that Angle ſhall be the third or fourth part of a
Right Angle, then the Elevation of the Chanel A C ſhall be ac­
cording to 1/3, or 1/4 of a Right Angle. And it is manifeſt; that the
Riſe of that ſame Chanel A C will be taken away debaſing the
point C as far as to B: for then the Chanel A C ſhall have no
Elevation. And debaſing the point C a little below B, the Water
will naturally run along the Chanel A C downwards from the
point A towards C. Let us therefore conclude, that the Angle A
being 1/3 of a Right Angle, the Chanel A C ſhall no longer have any
Riſe, debaſing it on the part C for 1/3 of a Right Angle.
Theſe things underſtood, let us infold the Triangle about the
Column, and let us make the Screw B A E F G, &c. which if it
ſhall be placed at Right Angles with the end B in the Water, turn­
ing it about, it ſhall not this way draw up the Water, the Chanel
about the Column being elevated, as may be ſeen by the part B A.
1But although the Column ſtand erect at Right-Angles, yet for all
that, the Riſe along the Screw, folded about the Column, is not of
a greater Elevation than of 1/3 of a Right Angle, it being generated
by the Elevation of the Chanel A C: Therefore if we incline the
Column but 1/3 of the
206[Figure 206]
ſaid Right Angle, and
a little more, as we ſee
I K H M, there is a
Tranſition and Moti­
on along the Chanel
I L: Therefore the
Water from the point
I to the point L ſhall
move deſcending, and
the Screw being turned
about, the other parts
of it ſhall ſucceſſively
diſpoſe or preſent
themſelves to the Wa­
ter in the ſame Poſition as the part I L: Whereupon the Water
ſhall go ſucceſſively deſcending, and in the end ſhall be found to
be aſcended from the point I to the point H. Which how admira­
ble a thing it is, I leave ſuch to judge who ſhall perfectly have un­
derſtood it. And by what hath been ſaid, we come to know, That
the Screw for raiſing of Water ought to be inclined a little more
than the quantity of the Angle of the Triangle by which the ſaid
Screw is deſcribed.
Of the Force of the
HAMMER, MALLET, or BEETLE.
The Inveſtigation of the cauſe of the Force of theſe Percuti­
ents is neceſſary for many Reaſons: and firſt, becauſe that
there appeareth in it much more matter of admiration than
is obſerved in any other Mechanick Inſtrument whatſoever. For
ſtriking with the Hammer upon a Nail, which is to be driven into
a very tough Poſt, or with the Beetle upon a Stake that is to pene­
trate into very ſtiffe ground, we ſee, that by the ſole vertue of the
blow of the Percutient both the one and the other is thruſt for­
wards: ſo that without that, only laying the Beetle upon the
Nail or Stake it will not move then, nay, more, although you
ſhould lay upon them a Weight very much heavier than the ſaid
Beetle. An effect truly admirable, and ſo much the more worthy
of Contemplation, in that, as I conceive, none of thoſe who have
1hitherto diſcourſed upon it, have ſaid any thing that hits the mark;
which we may take for a certain Sign and Argument of the Obſcu­
rity and difficulty of this Speculation. For Ariſtotle, or others,
who would reduce the cauſe of this admirable Effect unto the
length of the Manubrium, or Handle, may, in my judgement, be
made to ſee their miſtake in the effect of thoſe Inſtruments, which
having no Handle, yet percuſs, either in falling from on high
downwards, or by being thrown with Velocity ſidewaies. There­
fore it is requiſite, that we have recourſe to ſome other Principle, if
we would find out the truth of this buſineſs; the cauſe of which,
although it be of its own nature ſomewhat obſcure, and of diffi­
cult conſideration, yet nevertheleſs we will attempt with the grea­
teſt perſpicuity poſſible to render it clear and obvious, ſhewing, for
a cloſe of all, that the Principle and Original of this Effect is deri­
ved from no other Fountain than this, from which the reaſons of all
other Mechanick Effects do proceed: and this we will do, by ſetting
before your eyes that very thing which is ſeen to befall in every
other Mechanick Operation, ſcilicet, That the Force, the Reſiſtance,
and the Space by which the Motion is made, do go alternately
with ſuch proportion operating, and with ſuch a rate anſwering to
each other, that a Reſiſtance, equal to the Force, ſhall be moved by
the ſaid Force along an equal Space, with Velocity equal to that
with which it is moved. Likewiſe, That a Force that is leſs by half
than a Reſiſtance ſhall be able to move it, ſo that it be moved
with double Velocity, or, if you will, for a Diſtance twice as great
as that which the moved Reſiſtance ſhall paſs: and, in a word, it
hath been ſeen in all the other Inſtruments, that any, never ſo great,
Reſiſtance may be moved by every ſmall Force given, provided,
that the Space, along which the Reſiſtance ſhall move, have the
ſame proportion that is found to be betwixt the ſaid great Reſi­
ſtance and the Force: and that this is according to the neceſſary
Order and Conſtitution of Nature: So that inverting the Diſcourſe,
and Arguing the contrary way, what wonder ſhall it be, if that
Power that ſhall move a ſmall Reſiſtance a great way, ſhall carry
one an hundred times bigger an hundredth part of that Diſtance?
Certainly none at all: nay, it would be abſurd, yea, impoſſible
that it ſhould be otherwiſe. Let us therefore conſider, what the
Reſiſtance of the Beetle unto Motion may be in that point where
it is to ſtrike, and how far, if it do not ſtrike, it would be carryed
by the received Force beyond that point: and again, what Reſi­
ſtance to Motion there is in him who ſtriketh, and how much by
that ſame Percuſſion he is moved: and, having found that this
great Reſiſtance goeth forwards by a percuſſion ſo much leſs than
the Beetle driven by the Impetus of him that moveth it would do,
by how much that ſame great Reſiſtance is greater than that of
1the Beetle; we ſhall ceaſe to wonder at the Effect, which doth not
in the leaſt exceed the terms of Natural Conſtitutions, and of
what hath been ſpoken. Let us, for better underſtanding, give an
example thereof in particular Terms. There is a Beetle, which ha­
ving four degrees of Reſiſtance, is moved by ſuch a Force, that
being freed from it in that term where it maketh the Percuſſion, it
would, meeting with no ſtop, go ten Paces beyond it, and in that
term a great poſt being oppoſed to it, whoſe Reſiſtance to Moti­
on is as four thouſand, that is, a thouſand times greater than that of
the Beetle, (but yet is not immoveable) ſo that it without mea­
ſure or proportion exceeds the Reſiſtance of the Beetle, yet the
Percuſſion being made on it, it ſhall be driven forwards, though in­
deed no more but the thouſandth part of the ten Paces which the
Beetle ſhall be moved: and thus in an inverted method, changing
that which hath been ſpoken touching the other Mechanical Effects,
we may inveſtigate the reaſon of the Force of the Percutient. I
know that here ariſe difficulties and objections unto ſome, which
they will not eaſily be removed from, but we will freely remit them

to the ^{*} Problems Mechanical, which we ſhall adjoyn in the end of
this Diſcourſe.
* Theſe Pro­
blems he here
promiſeth were
never yet ex­
tant.
1
THE
BALLANCE
OF
Signeur GALILEO GALILEI;
In which, in immitation of Archimedes in the
Problem of the Crown, he ſheweth how to
find the proportion of the Alloy of
Mixt-Metals; and how to make
the ſaid Inſtrument.
As it is well known, by ſuch who take the pains to read
old Authors, that Archimedes detected the Cheat of
the Goldſmith in the Crown of ^{*} Hieron, ſo I think it

hitherto unknown what method this Great Philoſo­
pher obſerved in that Diſcovery: for the opinion, that he did per­
form it by putting the Crown into the Water, having firſt put in­

to it ſuch another Maſs of pure Gold, and another of Silver ſeve­
rally, and that from the differences in their making the Water
more or leſs riſe and run over, he came to know the Mixture or
Alloy of the Gold with the Silver, of which that Crown was
compounded; ſeems a thing (if I may ſpeak it) very groſs, and
far from exactneſs. And it will ſeem ſo much the more dull to
ſuch who have read and underſtood the exquiſite Inventions of ſo
Divine a Man amongſt the Memorials that are extant of him; by
which it is very manifeſt that all other Wits are inferiour to that
of Archimedes. Indeed I believe, that Fame divulging it abroad,
that Archimedes had diſcovered that ſame Fraud by means of the
Water, ſome Writer of thoſe Times committed the memory there­
of to Poſterity, and that this perſon, that he might add ſomething
to that little which he had heard by common Fame, did relate that
Archimedes had made uſe of the Water in that manner, as ſince
hath been by the generality of men believed.
* King of Sicily,
and Kinſman to
that Great Ma­
thematician.
Plutarch in Vit.
Marcel.
But in regard I know, that that method is altogether fallacious,
and falls ſhort of that exactneſs which is required in Mathematical
Matters, I have often thought in what manner, by help of the
Water, one might exactly find the Mixture of two Metals, and
in the end, after I had diligently peruſed that which Archimedes
demonſtrateth in his Books De inſidentibus aquæ, and thoſe others
1De æquiponder antium, there came into my thoughts a Rule which
exquiſitely reſolveth our Queſtion; which Rule I believe to be
the ſame that Archimedes made uſe of, ſeeing that beſides the
uſe that is to be made of the Water, the exactneſs of the Work
dependeth alſo upon certain Demonſtrations found by the ſaid
Archimedes.
The way is by help of a Ballance, whoſe Conſtruction and Uſe
ſhall be ſhewn by and by, after we ſhall have declared what is
neceſſary for the knowledge thereof. You muſt know there­
fore, that the Solid Bodies that ſink in the Water weigh ſo much
leſs in the Water than in the Air, as a Maſs of Water equal to
the ſaid Solid doth weigh in the Air: which hath been demon­
ſtrated by Archimedes. But, in regard his Demonſtration is very
mediate, becauſe I would not be over long, laying it aſide, I ſhall
declare the ſame another way. Let us conſider, therefore, that
putting into the Water v. g. a Maſs of Gold, if that Maſs were
of Water it would have no weight at all: For the Water moveth
neither upwards, nor downwards in the Water: It remains,
therefore, that the Maſs of Gold weigheth in the Water only ſo
much as the Gravity of the Gold exceeds the Gravity of the Wa­
ter. And the like is to be underſtood of other Metals. And be­
cauſe the Metals are different from each other in Gravity, their
Gravity in the Water ſhall diminiſh according to ſeveral proporti­
ons. As for example: Let us ſuppoſe that Gold weigheth twenty
times more than Water, it is manifeſt by that which hath been
ſpoken, that the Gold will weigh leſs in the Water than in the
Air by a twentieth part of its whole weight. Now, let us ſuppoſe
that Silver, as being leſs Grave than Gold, weigheth 12 times more
than Water: this then, being weighed in the Water, ſhall di­
miniſh in Gravity the twelfth part of its whole weight. Therefore
the Gravity of Gold in the Water decreaſeth leſs than that of
Silver; for that diminiſheth a twentieth part, and this a twelfth.
If therefore in an exquiſite Ballance we ſhall hang a Metal at the
one Arm, and at the other a Counterpoiſe that weigheth equally
with the ſaid Metal in the Water, leaving the Counterpoiſe in the
Air, to the end that it may equivalate and compenſate the Me­
tal, it will be neceſſary to hang it nearer the Perpendicular or
Cook. As for example, Let the Ballance be A B, its Perpendicu­
207[Figure 207]
lar C, and let a
Maſs of ſome
Metal be ſu­
ſpended at B,
counterpoiſedby
the Weight D: putting the Weight B into the Water, the
Weight D in A would weigh more: therefore that they may
1weigh equally it would be neceſſary to hang it nearer to the
Perpendicular C, as v. gr. in E: and look how many times the Di­
ſtance C A ſhall contain A E, ſo many times ſhall the Metal
weigh more than the Water. Let us therefore ſuppoſe that the
Weight in B be Gold, and that weighed in the Water it with­
draws the Counterpoiſe D into E; and then doing the ſame with
pure Silver, let us ſuppoſe that its Counterpoiſe, when afterwards
it is weighed in the Water, returneth to F: which point ſhall be
nearer to the point C, as Experience ſheweth, becauſe the Silver
is leſs grave than the Gold: And the Diſtance that is between
A and F ſhall have the ſame Difference with the Diſtance A E,
that the Gravity of the Gold hath with that of the Silver. But if
we have a Mixture of Gold and Silver, it is clear, that by reaſon it
participates of Silver, it ſhall weigh leſs than the pure Gold, and
by reaſon it participates of Gold, it ſhall weigh more than the
pure Silver: and therefore being weighed in the Air, and deſiring
that the ſame Counterpoiſe ſhould counterpoiſe it, when that
Mixture ſhall be put into the Water it will be neceſſary to draw
the ſaid Counterpoiſe more towards the Perpendicular C, than the
point E is, which is the term of the Gold; and more from C
than F is, which is the term of the pure Silver; Therefore it ſhall
fall between the points E and F: And the proportion into which
the Diſtance EF ſhall be divided, ſhall exactly give the proportion
of the two Metals which compound that Mixture. As for exam­
ple: Let us ſuppoſe the Mixture of Gold and Silver to be in B,
208[Figure 208]
counterpoiſed in
the Air by D,
which Counter­
poiſe when the
Compound Me­
tal is put into the Water returneth into G: I ſay now, that the
Gold and the Silver which compound this Mixture are to one ano­
ther in the ſame proportion, as the Diſtance F G is to the Diſtance
G E. But you muſt know that the Diſtance G F terminated in
the mark of the Silver, ſhall denote unto us the quantity of the
Gold, and the Diſtance G E, terminated in the mark of the Gold,
ſhall ſhew us the quantity of the Silver: inſomuch that if F G
ſhall prove double to G E, then that Mixture ſhall be two parts
Gold, and one part Silver: and in the ſame method proceeding in
the examination of other Mixtures, one ſhall exactly find the
quantity of the ſimple Metals.
To compoſe the Ballance, therefore, take a Rod at leaſt a yard
long, (and the longer it is, the exacter the Inſtrument ſhall be)
and divide it in the midſt, where place the Perpendicular: then
adjuſt the Arms that they may ſtand in Equilibrium, by filing or
1ſhaving that leſs which weigheth moſt; and upon one of the Arms
note the terms to which the Counterpoiſes of ſimple Metals return
when they ſhall be weighed in the Water: taking care to weigh the
pureſt Metals that can be found. This being done, it remaineth
that we find out a way, how we may with facility diſcover the
proportion, according to which, the Diſtances between the terms
of the ſimple and pure Metals are divided by the Marks of the
Mixt Metals: Which ſhall be effected in this manner.
We are to have two very ſmall Wires drawn thorow the ſame
drawing-Iron, one of Steel, the other of Braſs, and above the
terms of the ſimple Metals we muſt wind the Steel Wyer; as for
example: above the point E, the term of the pure Gold, we are
to wind the Steel Wyer, and under it the other Braſs Wyre, and
having made ten folds of the Steel Wyer, we muſt make ten
more with that of Braſs, and thus we are to continue to do with
ten of Steel, and ten of Braſs, until that the whole Space be­
tween the points E and F, the terms of the pure Metals, be full;
cauſing thoſe two terms to be alwaies viſible and perſpicuous:
and thus the Diſtance E F ſhall be divided into many equal parts,
and numbred by ten and ten. And if at any time we would know
the proportion that is between F G and G E, we muſt count the
Wyers F G, and the Wyers G E: and finding the Wyers F G
to be, for example, 40, and the Wyers G E, 21: we will ſay that
there is in the mixt Metal 40 parts of Gold, and 21 of Silver. But
here you muſt note, that there is ſome difficulty in the counting,
for thoſe Wyers being very ſmall, as it is requiſite for exactneſs
ſake, it is not poſſible with the eye to tell them, becauſe the
ſmalneſs of the Spaces dazleth & confoundeth the Sight. Therefore
to number them with facility, take a Bodkin as ſharp as a Needle
and ſet it into an handle, or a very fine pointed Pen-knife, with
which we may eaſily run over all the ſaid Wyers, and this way
partly by help of hearing, partly by the impediments the hand
ſhall feel at every Wyer, thoſe Wyers ſhall be counted;
the number of which, as I ſaid before, ſhall give us the exact
quantity of the ſunple Metals, of which the Mixt-Metal is com­
pounded: taking notice that the Simple anſwer alternately to the
Diſtances. As for example, in a Mixture of Gold and Silver,
the Wyers that ſhall be towards the term of Gold ſhall ſhew us
the quantity of the Silver: And the ſame is to be underſtood of
other Metals.
1
Annotations of Dominico Mantovani upon the Bal­
lance of Signore Galileo Galilei.
Firſt, I conceive that the difficulty of Numbring the Wyres
is removed by wrapping about the Ballance ten of Steel,
and then ten of Braſs, which being divided by tens, there
only remains that tenth part to be numbred, in which the term
of the Mixt Metal falleth. For although Signore Galileo, who is
Author of this Invention, makes mention of two Wyres, one of
Steel, the other of Braſs, yet he doth not ſay, that we are to
take ^{*} ten of the one, and ten of the other: which it may be

hapneth by the negligence of him that hath tranſcribed it; al­
though I muſt confeſs that the Copy which came to my hands was
of his own writing.
* Galileus ſaith it
expreſly in this
Copy which I fol­
low, but might
omit it in the Co­
py which came to
the hands of Man­
tovani.
Secondly, it is ſuppoſed in this Problem that the Compoſition
of two Metals do retain the ſame proportion of Maſs in the
Mixture as the two Simple Metals, of which it is compounded,
had at firſt. I mean, that the Simple Metals retain and keep in
the Compoſition (after that they are incorporated and commix­
ed) the ſame proportion in Maſs that the Simple Metals had
when they were ſeparated: Which in the Caſe of Signore Gali­
leo, touching the Commixtion of Gold and Silver, I do neither
deny, nor particularly confeſs. But if one would, for example,
unite 101 pounds of Copper with 21 pounds of Tin, to make
thereof 120 pounds of Bell-Metal, (I abate two pounds,
ſuppoſed to be waſted in the Melting) I do think that 120
pounds of Compound Metal will have a leſs Bulk than the 100
pounds of pure Copper, and the 20 pounds of Tin unmixt, that
is, before they were incorporated and melted into one Maſs, and
that the Compoſition is more grave in Specie than the ſingle Cop­
per, and the ſingle Braſs: and in the Caſe of Signore Galileo the
Compoſition of Gold and Silver is ſuppoſed to be lighter in Specie
than the pure Gold, and heavier in Specie than the pure Silver. Of
which it would be eaſie to make ſome ſuch like experiment, melt­
ing together, v. gr. 10 pounds of Lead with 5 pounds of Tin,
and obſerving whether thoſe 15 pounds, or whatever the Mixture
maketh, do give the difference betwixt the weight in the Water
to the weight in the Air, in the proportion that the 15 pounds of
the two Metals diſ-united gave before: I do not ſay, the ſame diffe­
rence, becauſe I pre ſuppoſe that they will waſte in melting down,
and that the Compound will be leſs than 15 pounds, therefore I
ſay in proportion.
Thirdly, He doth alſo ſuppoſe, that one ought to take the
1Simple Metals, that is, the Gold and the Silver, each of the ſame
weight as the Mixture, although he doth not ſay ſo; which may
be collected in that he marketh the ballance only betwixt the
Terms of the Gold and the Silver, which is the cauſe of the great
facility in reſolving the Problem by only counting the
Wyers.
One might take the pure Gold, and pure Silver of the ſame
weight, in reſpect of one another, but yet different from the
weight of the Mixture, that is, either more or leſs grave than the
Mixt Metal: and being equal in weight to one another they
might ſhew the proportion of the Maſs of the Gold to that of the
Silver; but yet with this difference, that the more grave will ſhew
the ſaid proportion more exactly than the ſmall and leſs grave.
But the Simple and pure Metals not being of the ſame weight as
the Compound, it will be neceſſary, having found the proportion
of the Maſs of the Gold to that of the Silver; to find by numbers
proportionally the exact quantity of each of the two Metals com­
pounding the Mixture.
A man may likewiſe uſe the quantity of the ſimple Metals ac­
cording to neceſſity and convenience, although of different
Weights, both as to each other, and to the Mixture, provided that
each of them be pure in its kind: but then we muſt after­
wards by numbers find the proportion of the Maſſes of the two
Simple ones of equal weight (which is ſoon done, taking them of
equal weight as was ſaid before) and then according to this pro­
portion to find, by means of the Weight, and of the Maſs of the
Compound Metal, the diſtinct quantity of each of the two Sim­
ple ones that make the Compoſition: of each of which Caſes
examples might be given. But to conclude, if the pure Gold,
and pure Silver, and the Mixt Metal ſhould be of equal Maſs,
they would be unequal in Weight, and it would not need to
weigh them in the Water, for being of equal Bulk, the differen­
ces of their Weights in the Air and in the Water would be alſo
equal: for the difference of the weight of any Body in the Air
to its weight in the Water, is alwaies equal to the Weight of ſo
much Water as equalleth the ſame Body in Maſs, by Archimedes
his fifth Propoſition, De ijs quæ vehuntur in aqua.
And laſt of all, the Simple and pure Metals may have the ſame
proportion in Gravity, mutually or reciprocally, as their Bodies
have in Bulk: In which caſe, as well the Maſs, found by help of
the weight in Water, or by any other meanes, as their Weight in
the Air ſhall ſhew the proportion of their Specifical Gravities; as
their Weights in the Water do when their Weights in the Air
are equal; but yet alternately weighed: that is to ſay, the Spe­
cifical Gravity of the Gold ſhall have ſuch proportion to the
1Specifical Gravity of the Silver, as the Maſs of the Silver hath to
the Maſs of the Gold; that is, as the difference betwixt the
Weight in Water and Weight in Air of the Silver, hath to the
difference betwixt the Weight in Water and Weight in Air of
the Gold.
With this ſame Ballance one may with facility meaſure the
Maſs or Magnitude of any Body, in any manner whatſoever Irre­
gular in manner following, namely:
We will have at hand a Solid Body of a ſubſtance more grave
in Specie than the Water; as for inſtance of Lead; or if it were
of Wood, or other matter more light in Specie than the Water,
it may be made heavier by faſtning unto it Lead, or ſome other
thing that makes it ſink in the Water, and let us take ſome
known Meaſure, and with it meaſure the Irregular Solid; as for
inſtance, the Roman Palm, the Geometrical Foot, or any other
known meaſure, or part of the ſame, as the half Foot, the quar­
ter of a Foot, or any ſuch like part known; then let it be weighed
in the Air, and ſuppoſe that it weigh 10 pounds; let the ſame
Meaſure be weighed in the Air, and ſuppoſe that it weigh 8
pounds: and ſubſtract 8 pounds, the Weight in the Water, from
10 pounds, the Weight in the Air, and there remaineth 2 pounds
for the Weight of a Body of Water equal in Magnitude to the
Meaſure known. Now, if we would meaſure a Statue of Mar­
ble, let it be weighed firſt in the Air, and then in the Water, and
ſubſtract the Weight in the Water from the Weight in the Air, and
the remainder ſhall be the weight of ſo much Water as equalleth
the Statue in Maſs; which being divided by the difference betwixt
the Weight in Water and the Weight in Air of the Meaſure known,
the Quotient will give how many times the Statue containeth the
ſame given Meaſure. As for example; if the Statue in Air weigh
100 pounds, and in the Water 80 pounds, 80 pounds being ſub­
ſtracted from 100 there reſteth 20 pounds for the Weight of ſo
much Water in Maſs as equalleth the Statue. But becauſe the
difference betwixt the Weight in Water, and the Weight in Air
equal in Magnitude to the Meaſure known, was ſuppoſed to be
2 pounds; divide 18 pounds by two pounds, and the Quotient
is 9, for the number of times that the propoſed Statue containeth
the given Meaſure. The ſame Method may be obſerved, if it
were required, to meaſure a Statue, or other Maſs of any kind of
Metal: only it muſt be advertiſed, that all the holes muſt be
ſtopt, that the Water may not enter into the Body of the Statue:
but he that deſireth only the Solid content of the Metal of the
ſaid Statue muſt open the holes, and with Tunnels fill the whole
cavity of the Statue with Water. And if the Statue were of a
Subſtance lighter in Specie than the Water; as, for example, of
1Wax, it will be requiſite to add unto the Statue ſome Counter­
poiſe, that maketh it ſink in the Water, and then to meaſure the
Counterpoiſe, as above, and to ſubſtract its meaſure from the
Compound Body, and there will remain the Meaſure of the
Statue of Wax. And laſtly, to make uſe of the ſaid Ballance,
inſtead of ſeeking the numbers of the pounds of the Differences
of the Weights of the Meaſure known, and of the Solid
to be meaſured in Water, and in Air, we may count the
Wyers of the Arm of the Ballance, which
being very ſmall will give the
Meaſure exactly.
FINIS.
1
DISCOURSES
OF THE
MECHANICKS:
A MANVSCRIPT of
Monſieur Des-Cartes.
The Explication.
Of Engines, by help of which we may raiſe a very great
weight with ſmall ſtrength.
The Invention of all theſe Engines de­
pends upon one ſole Principle, which is,
That the ſame Force that can lift up a
Weight, for example, of 100 pounds to
the height of one foot, can life up one of
200 pounds to the height of half a foot,
or one of 400 pounds to the height of a
fourth part of a foot, and ſo of the reſt,
be there never ſo much applyed to it: and
this Principle cannot be denied if we conſider, that the Effect
ought to be proportioned to the Action that is neceſſary for the
production of it; ſo that, if it be neceſſary to employ an Action by
which we may raiſe a Weight of 100 pounds to the height of two
foot, for to raiſe one ſuch to the height of one foot only this ſame
ought to weigh 200 pounds: for its the ſame thing to raiſe 100
pounds to the height of one foot, and again yet another 100
pounds to the height of one foot, as to raiſe one of 200 pounds to
the height of one foot, and the ſame, alſo, as to raiſe 100 pounds
to the height of two feet.
Now, the Engines which ſerve to make this Application of a
Force which acteth at a great Space upon a Weight which it cau­
1ſeth to be raiſed by a leſſer, are the Pulley, the Inclined Plane, the
Wedg, the Capſten, or Wheel, the Screw, the Leaver, and ſome
others, for if we will not apply or compare them one to another,
we cannot well number more, and if we will apply them we need
not inſtance in ſo many.
The PVLLEY, Trochlea.
Let A B C be a Chord put about the Pulley D, to which let
the Weight E be faſtned; and firſt, ſuppoſing that two
men ſuſtain or pull up equally each of them one of the
209[Figure 209]
ends of the ſaid Chord:
it is manifeſt, that if the
Weight weigheth 200
pounds, each of thoſe
men ſhal employ but the
half thereof, that is to ſay,
the Force that is requiſite
for ſuſtaining or raiſing
of 100 pounds, for each
of them ſhal bear but the
half of it.
Afterwards, let us ſup­
poſe that A, one of the
ends of this Chord, being
made faſt to ſome Nail,
the other C be again ſu­
ſtained by a Man; and it
is manifeſt, that this Man in C, needs not (no more than before)
for the ſuſtaining the Weight E, more Force than is requiſite for
the ſuſtaining of 100 pounds: becauſe the Nail at A doth the
ſame Office as the Man which we ſuppoſed there before. In fine,
let us ſuppoſe that this Man in C do pull the Chord to make the
Weight E to riſe, and it is manifeſt, that if he there employeth
the Force which is requiſite for the raiſing of 100 pounds to the
height of two feet, he ſhall raiſe this Weight E of 200 pounds to
the height of one foot: for the Chord A B C being doubled, as it
is, it muſt be pull'd two feet by the end C, to make the Weight E
riſe as much, as if two men did draw it, the one by the end A,
and the other by the end C, each of them the length of one foot
only.
There is alwaies one thing that hinders the exactneſs of the Cal­
culation, that is the ponderoſity of the Chord or Pulley, and the
difficulty that we meet with in making the Chord to ſlip, and in
bearing it: but this is very ſmall in compariſon of that which
1raiſeth it, and cannot be eſtimated ſave wthin a ſmall matter.
Moreover, it is neceſſary to obſerve, that it is nothing but the
redoubling of the Chord, and not the Pulley, that cauſeth this
Force: for if we faſten yet another Pulley towards A, about
which we paſs the Chord A B C H, there will be required no leſs
Force to draw H towards K, and ſo to lift up the Weight E, than
there was before to draw C towards G. But if to theſe two Pul­
leys we add yet another towards D, to which we faſten the Weight,
and in which we make the Chord to run or ſlip, juſt as we did in
the firſt, then we ſhall need no more Force to lift up this Weight
of 200 pounds than to lift up 50 pounds without the Pulley: be­
cauſe that in drawing four feet of Chord we lift it up but one
foot. And ſo in multiplying of the Pulleys one may raiſe the great­
eſt Weights with the leaſt Forces. It is requiſite alſo to obſerve,
that a little more Force is alwaies neceſſary for the raiſing of a
Weight than for the ſuſtaining of it: which is the reaſon why I
have ſpoken here diſtinctly of the one and of the other.
The Inclined PLANE.
If not having more Force than ſufficeth to raiſe 100 pounds, one
would nevertheleſs raiſe this Body F, that weigheth 200 pounds,
to the height of the Line B A, there needs no more but to draw
or rowl it along the Inclined Plane C A, which I ſuppoſe to be
twice as long as the Line
210[Figure 210]
A B, for by this means,
for to make it arrive at
the point A, we muſt
there employ the Force
that is neceſſary for the
raiſing 100 pounds twice
as high, and the more inclined this Plane ſhall be made, ſo much
the leſs Force ſhall there need to raiſe the Weight F. But yet there
is to be rebated from this Calculation the difficulty that there is
in moving the Body F, along the Plane A C, if that Plane were
laid down upon the Line B C, all the parts of which I ſuppoſe to
be equidiſtant from the Center of the Earth.
It is true, that this impediment being ſo much leſs as the Plane is
more united, more hard, more even, and more polite; it cannot
likewiſe be eſtimated but by gueſs, and it is not very conſide­
rable.
We need not neither much to regard that the Line B C being a
part of a Circle that hath the ſame Center with the Earth, the
Plane A C ought to be (though but very little) curved, and to
have the Figure of part of a Spiral, deſcribed between two Circles,
1which likewiſe have for their Center that of the Earth, for that it
is not any way ſenſible.
The WEDGE, Cuneus.
The Force of the Wedge A B C D is eaſily underſtood after
that which hath been ſpoken above of the Inclined Plane,
for the Force wherewith we ſtrike downwards acts as if it
were to make it move according to the Line B D; and the Wood,
or other thing and Body that it cleaveth, openeth not, or the
Weight that it raiſeth doth not riſe, ſave only according to the
211[Figure 211]
Line A C, inſomuch that the Force,
wherewith one driveth or ſtriketh this
Wedge, ought to have the ſame Pro­
portion to the Reſiſtance of this
Wood or Weight, that A C hath to
A B. Or elſe again, to be exact, it
would be convenient that B D were
a part of a Circle, and A D and
C D two portions of Spirals that had the ſame Center with the
Earth, and that the Wedge were of a Matter ſo perfectly hard
and polite, and of ſo ſmall weight, as that any little Force would
ſuffice to move it.
The CRANE, or the CAPSTEN,
Axis in Peritrochio.
We ſee alſo very eaſily, that the Force wherewith the Wheel
A or Cogg B is turned, which make the Axis or Cylinder C
to move, about which a Chord is rolled, to which the
Weight D, which we would raiſe, is faſtned, ought to have the
212[Figure 212]
ſame proportion to the ſaid
Weight, as the Circumference of
the Cylinder hath to the Cir­
cumference of a Circle which
that Force deſcribeth, or that the
Diameter of the one hath unto
the Diameter of the other; for
that the Circumferences have the
ſame proportion as the Diame­
ters: inſomuch that the Cylinder C, having no more but one foot
in Diameter, if the Wheel AB be ſix feet in its Diameter, and the
Weight D do weigh 600 pounds, it ſhall ſuffice that the Force in
B ſhall be capable to raiſe 100 pounds, and ſo of others. One may
1alſo inſtead of the Chord that rolleth about the Cylinder C, place
there a ſmall Wheel with teeth or Coggs, that may turn another
greater, and by that means multiply the power of the Force as
much as one ſhall pleaſe, without having any thing to deduct of
the ſame, ſave only the difficulty of moving the Machine, as in the
others.
The SCREW, Cochlea.
When once the Force of the Capſten and of the In­
clined Plane is underſtood, that of the Screw is eaſie
to be computed, for it is compoſed only of a Plane
much inclined, which windeth about a Cylinder: and if this Plane
be in ſuch manner Inclined, as that the Cylinder ought to make
v. gr. ten turns to advance forwards the length of a foot in the
Screw, and that the bigneſs of the Circumference of the Circle
213[Figure 213]
which the Force that turneth it
about doth deſcribe be of ten
feet; foraſmuch as ten times ten
are one hundred, one Man alone
ſhall be able to preſs as ſtrongly
with this Inſtrument, or Screw, as
one hundred without it, provided
alwaies, that we rebate the Force
that is required to the turning
of it.
Now I ſpeak here of Preſſing rather than of Raiſing, or Remo­
ving, in regard that it is about this moſt commonly that the Screw
is employed, but when we would make uſe of it for the raiſing of
Weights, inſtead of making it to advance into a Female Screw, we
joyn or apply unto it a Wheel of many Coggs, in ſuch ſort
made, that if v. gr. this Wheel have thirty Coggs, whilſt the Screw
maketh one entire turn, it ſhall not cauſe the Wheel to make more
than the thirtieth part of a turn, and if the Weight be faſtned to
a Chord that rowling about the Axis of this Wheel ſhall raiſe it but
one foot in the time that the Wheel makes one entire revolution,
and that the greatneſs of the Circumference of the Circle that is
deſcribed by the Force that turneth the Screw about be alſo of ten
ſeet, by reaſon that 10 times 30 make 300, one ſingle Man ſhall be
able to raiſe a Weight of that bigneſs with this Inſtrument, which
is called the Perpetual Screw, as would require 300 men with­
out it.
Provided, as before, that we thence deduct the difficulty that
we meet with in turning of it, which is not properly cauſed by the
Ponderoſity of the Weight, but by the Force or Matter of the In­
1ſtrument: which difficulty is more ſenſible in it than in thoſe afore­
going, foraſmuch as it hath greater Force.
The LEAVER, Vectis.
I Have deferred to ſpeak of the Leaver until the laſt, in regard
that it is of all Engines for raiſing of Weights, the moſt diffi­
cult to be explained.
Let us ſuppoſe that C H is a Leaver, in ſuch manner ſupported
at the point O, (by means of an Iron Pin that paſſeth thorow it
acroſs, or otherwiſe) that it may turn about on this point O, its
part C deſcribing the Semicircle A B C D E, and its part H the
214[Figure 214]
Semicircle F G H I K; and that
the Weight which we would
raiſe by help of it were in H,
and the Force in C, the Line
C O being ſuppoſed triple of
O H. Then let us conſider that
in the Time whilſt the Force
that moveth this Leaver deſcri­
beth the whole Semicircle
A B C D E, and acteth accord­
ing to the Line A B C D E, al­
though that the Weight deſcri­
beth likewiſe the Semicircle
F G H I K, yet it is not raiſed to
the length of this curved Line
F G H I K, but only to that of the Line F O K; inſomuch that the
Proportion that the Force which moveth this Weight ought to
have to its Ponderoſity ought not to be meaſured by that which is
between the two Diameters of theſe Circles, or between their two
Circumferences, as it hath been ſaid above of the Wheel, but ra­
ther by that which is betwixt the Circumference of the greater,
and the Diameter of the leſſer. Furthermore let us conſider, that
there is a neceſſity that this Force needeth not to be ſo great, at
ſuch time as it is near to A, or near to E, for the turning of the
Leaver, as then when it is near to B, or to D; nor ſo great when
it is near to B or D, as then when it is near to C: of which the rea­
ſon is, that the Weights do there mount leſs: as it is eaſie to un­
derſtand, if having ſuppoſed that the Line C O H is parallel to the
Horizon, and that A O F cutteth it at Right Angles, we take the
point G equidiſtant from the points F and H, and the point B equi­
diſtant from A and C; and that having drawn G S perpendicular
to F O, we obſerve that the Line F S (which ſheweth how much
the Weight mounteth in the Time that the Force operates along
1the Line A B) is much leſſer than the Line S O, which ſheweth
how much it mounteth in the Time that the Force opperates along
the Line B C.
And to meaſure exactly what his Force ought to be in each Point
of the curved Line A B C D E, it is requiſite to know that it ope­
rates there juſt in the ſame manner as if it drew the Weight along
a Plane Circularly Inclined, and that the Inclination of each of the
Points of this circular Plane were to be meaſured by that of the
right Line that toucheth the Circle in this Point. As for example,
when the Force is at the Point B, for to find the proportion that it
ought to have with the ponderoſity of the Weight which is at that
time at the Point G, it is neceſſary to draw the Contingent Line
G M, and to account that the ponderoſity of the Weight is to the
Force which is required to draw it along this Plane, and conſe­
quently to raiſe it, according to the Circle F G H, as the Line G M
is to SM Again, for as much as B O is triple of O G, the Force
in B needs to be to the Weight in G but as the third part of the
Line SM is unto the whole Line G M. In the ſelf ſame manner,
when the Force is at the Point D, to know how much the Weight
weigheth at I, it is neceſſary to draw the Contingent Line betwixt
I and P, and the right Line I N perpendicular upon the Horizon,
and from the Point P taken at diſcretion in the Line I P, provided
that it be below the Point I, you muſt draw P N parallel to the
ſame Horizon, to the end you may have the proportion that is be­
twixt the Line I P and the third part of the Line I N, for that which
betwixt the ponderoſity of the Weight, and the Force that ought to
be at the Point D for the moving of it: and ſo of others. Where,
nevertheleſs, you muſt except the Point H, at which the Contin­
gent Line being perpendicular upon the Horizon, the Weight can
be no other than triple the Force which ought to be in C for the
moving of it: in the Points F and K, at which the Contingent
Line being parallel unto the Horizon it ſelf, the leaſt Force that
one can aſſign is ſufficient to move the Weight. Moreover, that you
may be perfectly exact, you muſt obſerve that the Lines S G and
P N ought to be parts of a Circle that have for their Center that
of the Earth; and GM and I P parts of Spirals drawn between two
ſuch Circles; and, laſtly, that the right Lines S M and I N both
tending towards the Center of the Earth are not exactly Paral­
lels: and furthermore, that the Point H where I ſuppoſe the
Contingent Line to be perpendicular unto the Horizon ought
to be ſome ſmall matter nearer to the Point F than to K, at the
which F and K the Contingent Lines are Parallels unto the ſaid
Horizon.
This done, we may eaſily reſolve all the difficulties of the Ba­
lance, and ſhew, That then when it is moſt exact, and for inſtance,
1ſuppoſing it's Centre at O by which it is ſuſtained to be no more
but an indiviſible Point, like as I have ſuppoſed here for the Leaver,
if the Armes be declined one way or the other, that which ſhall be
the lowermoſt ought evermore to be adjudged the heavier; ſo that
the Centre of Gravity is not ſixed and immoveable in each ſeveral
Body, as the Ancients have ſuppoſed, which no perſon, that I
know of, hath hitherto obſerved.
But theſe laſt Conſiderations are of no moment in Practice, and
it would be good for thoſe who ſet themſelves to invent new
Machines, that they knew nothing more of this buſi­
neſſe than this little which I have now writ thereof,
for then they would not be in danger of decei­
ving themſelves in their Computation,
as they frequently do in ſuppoſing
other Principles.
FINIS.
215[Figure 215]
1
A
LETTER
OF
Monſieur Des-Cartes
TO THE
REVEREND FATHER
MARIN MERSENNE.
Reverend Father,
I Did think to have deferred writing unto you
yet eight or fifteen dayes, to the end I might
not trouble you too often with my Letters,
but I have received yours of the firſt of Sept.
which giveth me to underſtand that it is an
hard matter to admit the Principle which I
have ſuppoſed in my Examination of the
Geoſtatick Queſtion, and in regard that if it
be not true, all the reſt that I have inferred from it would be yet
leſſe true: I would not one onely day defer ſending you a more
particular Explication. It is requiſite above all things to conſider
that I did ſpeak of the Force that ſerveth to raiſe a Weight to ſome
heighth, the which Force hath evermore two Dimenſions, and not
of that which ſerveth in each point to ſuſtain it, which hath never
more than one Dimenſion, inſomuch that theſe two Forces differ
as much the one from the other, as a Superficies differs from a Line:
for the ſame Force which a Nail ought to have for the ſuſtaining of
a Weight of 100 pound one moment of time, doth alſo ſuffice for
to ſuſtain it the ſpace of a year, provided that it do not diminiſh,
but the ſame Quantity of this Force which ſerveth to raiſe the
Weight to the heighth of one foot, ſufficeth not (eadem numero)
to raiſe it two feet; and it is not more manifeſt that two and two
make four, than it's manifeſt that we are to employ double as much
therein.
Now, foraſmuch as that this is nothing but the ſame thing that
I have ſuppoſed for a Principle, I cannot gueſſe on what the Scruple
ſhould be grounded that men make of receiving it; but I ſhall in
1this place ſpeak of all ſuch as I ſuſpect, which for the moſt part
ariſe onely from this, that men are before-hand over-knowing in
the Mechanicks; that is to ſay, that they are pre-occupied with
Principles that others prove touching theſe matters, which not being
abſolutely true, they deceive the more, the more true they ſeem to
be.
The firſt thing wherewith a man may be pre-occupied in this
buſineſſe, is, that they many times confound the Conſideration of
216[Figure 216]
Space, with that of Time, or of the Ve­
locity, ſo that, for Example, in the
Leaver, or (which is the ſame) the Ba­
llance A B C D having ſuppoſed that
the Arm A B is double to B C, and the
Weight in C double to the Weight
in A, and alſo that they are in Equilibrium, inſtead of ſaying, that
that which cauſeth this Equilibrium is, that if the Weight C did
ſuſtain, or was raiſed up by the Weight A, it did not paſſe more
than half ſo much Space as it, they ſay that it did move ſlower by
the half: which is a fault ſo much the more prejudicial, in that it is
very difficult to be known: for it is not the difference of
217[Figure 217]
the Velocity that is the cauſe why theſe Weights are to be
one double to the other, but the difference of the Space, as
appeareth by this, that to raiſe, for Example, the Weight F
with the hand unto G, it is not neceſſary to employ a Force
that is preciſely double to that which one ſhould have
therein employed the firſt bout, to raiſe it twice as quick­
ly, but it is requiſite to employ therein either more or leſs
than the double, according to the different proportion that
this Velocity may have unto the Cauſes that reſiſt it.
Inſtead of requiring a Force juſt double for the raiſing of it with
the ſame Velocity twice as high, unto H, I ſay that it is juſt dou­
ble in counting (as two and two make four) that one and one make
two, for it is requiſite to employ a certain quantity of this Force
to raiſe the Weight from F to G, and again alſo, as much more of
the ſame Force to raiſe it from G to H.
For if I had had a mind to have joyned the Conſideration of the
Velocity with that of the Space, it had been neceſſary to have
aſſigned three Dimenſions to the Force, whereas I have aſſigned it
no more but two, on purpoſe to exclude it. And if I have teſtified
that there is ſo little of worth in any part of this ſmall Tract of the
Staticks, yet I de ſire that men ſhould know, that there is more in
this alone than in all the reſt: for it's impoſſible to ſay any thing
that is good and ſolid touching Velocity, without having rightly
explained what we are to underſtand by Gravity, as alſo the whole
Syſteme of the World. Now becauſe I would not under take it,
1I have thought good to omit this Conſideration, and in this manner
to ſingle out theſe others that I could explain without it: for
though there be no Motion but hath ſome Velocity, nevertheleſs
it is onely the Augmentations and Diminutions of this Velocity
that are conſiderable. And now that ſpeaking of the Motion of a
Body, we ſuppoſe that it is made according to the Velocity which
is moſt naturall to it, which is the ſame as if we did not conſider it
at all.
The other reaſon that may have hindred men from rightly un­
derſtanding my Principle is, that they have thought that they could
demonſtrate without it ſome of thoſe things which I demonſtrate
not without it: As, for example, touching the Pulley A B C, they
have thought that it was enough to know that the Nail in A did
218[Figure 218]
ſuſtain the half of the Weight B; to conclude
that the Hand in C had need but of half ſo much
Force to ſuſtain or raiſe the Weight, thus wound
about the Pulley, as it would need for to ſuſtain
or raiſe it without it. But howbeit that this ex­
plaineth very well, how the application of the
Force at C is made unto a Weight double to that
which it could raiſe without a Pulley, and that I
my ſelf did make uſe thereof, yet I deny that
this is ſimply, becauſe that that the Nail A ſu­
ſtaineth one part of the Weight B, that the Force
in C, which ſuſtaineth it, might be leſs than if it
had been ſo ſuſtained. For if that had been true, the Rope C E be­
ing wound about the Pulley D, the Force in E might by the ſame
reaſon be leſs than the Force in C: for that the Nail A doth not
ſuſtain the Weight leſs than it did before, and that there is alſo
another Nail that ſuſtains it, to wit, that to wich the Pulley D is
faſtned. Thus therefore, that we may not be miſtaken in this, that
the Nail A ſuſtaineth the half of the Weight B, we ought to con­
clude no more but this, that by this application the one of the Di­
menſions of the Force that ought to be in C
219[Figure 219]
to raiſe up this Weight is diminiſhed the one
half; and that the other, of conſequence, be­
cometh double, in ſuch ſort that if the Line
F G repreſent the Force that is required for
the ſuſtaining the Weight B in a point, with­
out the help of any Machine, and the
Quadrangle G H that which is required for
the raiſing of it to the height of a foot, the
ſupport of the Nail A diminiſheth the Di­
menſion which is repreſented by the Line F G the one half, and the
redoubling of the Rope A B C maketh the other Dimenſion to
1double, which is repreſented by the Line FH; and ſo the Force
that ought to be in C for the raiſing of the Weight B to the height
of one foot is repreſented by the Quadrangle IK; and, as we know
in Geometry, that a Line being added to, or taken from a Superfi­
cies, neither augmenteth, nor diminiſheth it in the leaſt, ſo the
Force where with the Nail A ſuſtains the Weight B, having but one
ſole Dimenſion, cannot cauſe that the Force in C, conſidered ac­
cording to its two Dimenſions, ought to be leſs for the raiſing in
like manner the Weight E, than for the raiſing it without any
Pulley.
The third thing which may make men imagine ſome Obſcurity
in my Principle is, that they, it may be, have not had regard to all
the words by which I explain it; for I do not ſay ſimply that the
Force that can raiſe a Weight of 50 pounds to the height of four
feet can raiſe one of 200 pounds to the height of one foot; but I
ſay that it may do it, if ſo be that it be applyed to it: now it is
impoſſible to apply the ſame thereto, but by the means of ſome Ma­
chine, or other Invention that ſhall cauſe this Weight to aſcend
but one, in the time whilſt the Force paſſeth the whole length
of four feet, and ſo that it do transform the Quandrangle, by
which the Force is repreſented that is required to raiſe this
Weight of 400 pounds to the height of one foot into another
that is equall and like to that which repreſents the Force that is
required for to raiſe a Weight of 50 pounds to the height of four
feet.
In fine, it may be that men may have thought the worſe of my
Principle, becauſe they have imagined that I have alledged the Ex­
amples of the Pulley, of the Inclined Plane, and of the Leaver, to
the end that I might better perſwarde the truth thereof, as if it had
been dubious, or elſe that I had ſo ill diſcourſed as to offer to aſſume
from thence a Principle, which ought of it felf to be ſo clear, as not
to need any proof by things that are ſo difficult to comprehend as
that; it may be, they have never been well demonſtrated by any
man: but neither have I made uſe of them, ſave only with a deſign
to ſhew that this Principle extends it ſelf to all matters of which
one treateth in the Staticks: or, rather, I have made uſe of this oc­
caſion for to inſert them into my Treatiſe, for that I conceived
that it would have been too dry and barren if I had therein ſpo­
ken of nothing elſe but of this Queſtion, that is of no uſe, as of
that of the Geoſtaticks, which I purpoſed to examine.
Now one may perceive, by what hath already been ſaid, how
the Forces of the Leaver and Pulley are demonſtrated by my
Principle ſo well, that there only remains the Inclined Plane, of
which you ſhall clearly ſee the Demonſtration by this Figure; in
which G F repreſents the firſt Dimenſion of the Force that the
1Rectangle F H deſcribeth whilſt it draweth the Weight D along
the Plane B A, by the means of a Chord parallel to this Plane, and
paſſing about the Pulley E, in ſuch ſort, that H G, that is the height
of this Rectangle, is equal to B A, along which the Weight D is to
move, whilſt it mounteth to the height of the Line C A. And N O
repreſents the firſt Dimenſion of ſuch another Force, that is de­
ſcribed by the Rectan­
gle N P, in the time that
220[Figure 220]
it is raiſing the Weight
L to M. And I ſuppoſe
that L M is equal to B A,
or double to C A; and
that N O is to F G, as
O P is to G H. This
done, I conſider that at
ſuch time as the Weight
D is moved from B to­
wards A, one may ima­
gine its Motion to be
compoſed of two others, of which the one carrieth it from B R to­
wards C A, (to which operation there is no Force required, as all
thoſe ſuppoſe who treat of the Mechanicks) and the other raiſeth
it from B C towards R A, for which alone the Force is required:
inſomuch that it needs neither more nor leſs Force to move it
along the Inclined Plane B A, than along the Perpendicular C A.
For I ſuppoſe that the unevenneſſes, &c. of the Plane do not
at all hinder it, like as it is alwaies ſuppoſed in treating of this
matter.
So then the whole Force F H is employed only about the raiſing
of D to the height of C A: and foraſmuch as it is exactly equal to
the Force N P, that is required for the raiſing of L to the Height
of L M, double to C A, I conclude by my Principle that the
Weight D is double to the Weight L. For in regard that it is
neceſſary to employ as much Force for the one as for the other,
there is as much to be raiſed in the one as in the other; and no
more knowledge is required than to count unto two for the
knowing that it is alike facile to raiſe 200 pounds from C to A,
as to raiſe 100 pounds from L to M: ſince that L M is double
to C A.
You tell me, moreover, that I ought more particularly to ex­
plain the nature of the Spiral Line that repreſenteth the Plane
equally enclined, which hath many qualities that render it ſuffi­
ciently knowable.
1
For if A be the Center of the Earth,
221[Figure 221]
and A N B C D the Spiral Line, having
drawn the Right Lines A B, A D, and the
like, there is the ſame proportion betwixt
the Curved Line A N B and the Right Line
AB, as is betwixt the Curved Line A N B C,
and the Right Line A C; or betwixt
A N B C D and A D: and ſo of the
reſt.
And if one draw the Tangents D E, C F,
and B G, the Angles A D E, A C F, A B G, &c.
ſhall be equal. As for the reſt I will, &c.----
Reverend Father,
Your very humble Servant
DES-CARTES.
1
A
LETTER
OF
Monſieur de Robberval
TO
Monſieur de Fermates,
Counſellour of THOULOUSE,
Containing certain Propoſitions in the
MECHANICKS.
MONSIEUR,
I have, according to my promiſe, ſent you the
Demonſtration of the Fundamental Propoſi­
tion of our Mechanicks, in which I follow the
common method of explaining, in the firſt
place, the Definitions and Principles of which
we make uſe.
We in general call that Quality a Force or
Power, by means of which any thing whatever
doth tend or aſpire into another place than that in which it is, be it
downwards, upwards, or ſide waies, whether this Quality naturally
belongeth to the Body, or be communicated to it from without.
From which definition it followeth, that all Weights are a ſpecies
of Force, in regard that it is a Quality, by means whereof Bodies
do tend downwards. We often alſo aſſign the name of Force to
that very thing to which the Force belongeth, as a ponderous Bo­
dy is called a Weight, but with this pre-caution, that this is in re­
ference to the true Force, the which augmenting or diminiſhing
ſhall be called a greater or leſſer Force, albeit that the thing to
which it belongeth do remain alwaies the ſame.
If a Force be ſuſpended or faſtned to a Flexible Line that is
without Gravity, and that is made faſt by one end unto ſome Ful­
ciment or ſtay, in ſuch ſort as that it ſuſtain the Force, drawing
1without impediment by this Line, the Force and the Line ſhall
take ſome certain poſition in which they ſhall reſt, and the Line
ſhall of neceſſity be ſtreight, let that Line be termed the Pendant,
or Line of Direction of the Force. And let the Point by which it is
faſtned to the Fulciment be called the Point of Suſpenſion: which
may ſometimes be the Arm of a Leaver or Ballance; and then let
the Line drawn from the Center of the Fulciment of the Leaver
or Ballance to the Point of Suſpenſion be named the Diſtance or
the Arm of the Force: which we ſuppoſe to be a Line fixed, and
conſidered without Gravity. Moreover, let the Angle comprehen­
ded betwixt the Arm of the Force and the Line of Direction be
termed the Angle of the Direction of the Force.
AXIOM I.
After theſe Definitions we lay down for a Principle, that in the
Leaver, and in the Ballance, Equal Forces drawing by Arms
that are equal, and at equall Angles of Direction, do draw equal­
ly. And if in this Poſition they draw one againſt the other they
ſhall make an Equilibrium: but if they draw together, or towards
the ſame part, the Effect ſhall be double.
If the Forces being equal, and the Augles of Direction alſo
equal, the Arms be unequal, the Force that ſhall be ſuſpended at
the greater Arm ſhall work the greater Effect.
As in this Figure, the Center of the Ballance or Leaver being A,
222[Figure 222]
if the Arms A B and A C are equal,
as alſo the Angles A B D, and A C E,
the equal Forces D and E ſhall
draw equally, and make an Equili­
brium. So likewiſe the Arm A F be­
ing equal to A B, the Angle A F G
to the Angle A B D, and the Force
G to D, theſe two Forces ^{*} G and D

draw equally; and in regard that
they draw both one way, the Effect
ſhall be double.
* In the M. S.
Copy it is C and
D.
In the ſame manner the Forces G and E ſhall make an Equilibri­
um; as alſo I and L ſhall counterpoiſe, if (being equal) the Arms
A K and A H, and the Angles A H T, and A K L be equal.
The ſame ſhall befall in the Forces P and R, if all things be
diſpoſed as before. And in this caſe we make no other diſtinction
betwixt Weights and other Forces ſave only this, that Weights all
tend towards the Center of Grave Bodies, and Forces may be un­
derſtood to tend all towards all parts of the Univerſe, with ſo
much greater or leſſer Impetus than Weights. So that Weights and
1their parts do draw by Lines of Direction, which all concur in one
and the ſame Point; and Forces and their parts may be underſtood
to draw in ſuch ſort that all the Lines of Direction are parallel to
each other.
AXIOM II.
In the ſecond place, we ſuppoſe that a Force and its Line of Di­
rection abiding alwaies in the ſame poſition, as alſo the Center
of the Ballance or Leaver, be the Arm what it will that is drawn
from the Center of the Ballance to the Line of Direction, the
Force drawing alwaies in the ſame faſhion, will alwaies produce
the ſame Effect.
As, in this ſecond Figure, the Center of the Ballance being A,
the Force B, and the Line of Direction
223[Figure 223]
B F prolonged, as occaſion ſhall re­
quire, in which the Arms A G, A C, and
A F do determine, in this poſition let
the Line B F be faſtned to the Arm
A F, or A C, or to another Arm drawn
from the Center A to the Line of Di­
rection ^{*} B F: we ſuppoſe that this

Force B ſhall alwaies work the ſame
Effect upon the Ballance. And if
drawing by the Arm A C it make an
Equilibrium with the Force D drawing by the Arm A E, when
ever it ſhall draw by the Arms A F or A G, it ſhall likewiſe make
an Equilibrium with the Force D drawing by the Arm A E. This
Principle although it be not expreſly found in Authors, yet it is
tacitly ſuppoſed by all thoſe that have writ on this Argument, and
Experience conſtantly confirmeth it.
* In the Original
it is writ, but by
the miſtake of
the Tranſcriber,
a la ligue de di­
rection A F.
AXIOM III.
If the Arms of a Ballance or Leaver are directly placed the one to
the other, and that being equal they ſuſtain equal Forces, of which
the Angles of Direction are Right An­
224[Figure 224]
gles, theſe Forces do alwaies weigh
equally upon the Center of the Bal­
lance, whether that they be near to the
ſame Center, or far diſtant, or both
conjoyned in the Center it ſelf; as in
this Figure the Ballance being E D,
the Center A, the equal Arms A D
and A E, let us ſuſtain equal Forces H and I, of which the Angles
1of Direction A D H and A E I are Right Angles, we ſuppoſe that
theſe two Forces I and H weigh alike upon the Center A as if they
were nearer to the Center, at the equal Diſtances A B and A C,
and we alſo ſuppoſe the ſame if theſe very Forces were ſuſpended
both together in A, the Angles of Directions being ſtill Right
Angles.
PROPOSITION I.
Theſe Principles agreed upon, we will eaſily demonſtrate,
in Imitation of Archimedes, that upon a ſtraight Balance
the Forces, of which and of all their parts the Lines of Dire­
ction are parallel to one another, and perpendicular to the Balance,
ſhall couuterpoiſe and make an Equilibrium, when the ſaid Forces
ſhall be to one another in Reciprocal proportion of their Arms,
which we think to be ſo manifeſt to you, that we thence ſhall de­
rive the Demonſtration of this Univerſal Propoſition to which we
haſten.
PROPOS. II.
In every Balance or Leaver, if the proportion of the Forces is
reciprocal to that of the Perpendicular Lines drawn from the
Center or Point of the Fulciment unto the Lines of Direction
of the Forces, drawing the one againſt the other, they ſhall make
an Equilibrium, and drawing on one and the ſame ſide, they ſhall
have a like Effect, that is to ſay, that they ſhall have as much Force
the one as the other, to move the Balance.
In this Figure let the Center of the Balance be A, the Arm A B,
bigger than A C, and firſt let the Lines of Direction B D, and E C
be perpendicular to the Arms A B and A C, by which Lines the
Forces D and E (which may be made of Weights if one will) do
draw; and that there is the ſame rate
225[Figure 225]
of the Force D to the Force E as there
is betwixt the Arm A C to the Arm
A B: the Forces drawing one againſt
the other, I ſay, that they will make an
Equilibrium upon the Balance C A B.
For let the Arm C A be prolonged
unto F, ſo as that AF may be equal to
A B: and let C A F be conſidered as a
ſtreight Balance, of which let the Center be A: and let there be
ſuppoſed two Forces G and H, of which and of all their parts the
Lines of Direction are parallel to the Line C E, and that the
Force G be equal to the Force D, and H to E, the one, to wit G,
1drawing upon the Arm A F, and the other, to wit H, upon the Arm
A C: now, by the firſt Propoſition, G and H ſhall make an Equili­
brium upon the Balance C A F: But, by the firſt Principle, the Force
D upon the Arm A B worketh the ſame effect as the Force G on
the Arm A F: Therefore the Force D upon the Arm A B maketh
an Equilibrium with the Force H upon A C: And the Force H
drawing in the ſame manner upon the Arm A C as the Force E, by
the ſame firſt Axiom, the Force D upon the Arm A B ſhall make an
Equilibrium with the Force E upon the Arm A C.
Now, in the following Figure, let the Center of the Balance be
A, the Arms A B and A C, the Lines of Direction B D and C E
which are not Perpendicular to the Arms, and the Forces D and E
drawing likewiſe by the Lines of Direction, upon which Perpen­
diculars are erected unto the Center A, that is A F upon B D, and
A G upon E C, and that as A F is to A G, ſo is the Force E to the
Force D: which Forces draw one
226[Figure 226]
againſt the other: I ſay, that they will
make an Equilibrium upon the Balance
C A B: For let the Lines A F and A G
be underſtood to be the two Arms of
a Balance G A F, upon which the For­
ces D and E do draw by the Lines of
Direction F D and G E: Theſe Forces
ſhall make an Equilibrium, by the firſt
part of this ſecond Propoſition; but, by the ſecond Axiom, the Force
D upon the Arm A F hath the ſame Effect as upon the Arm A B:
Therefore the Force D upon the Arm A B maketh an Equilibrium
with the Force E upon the Arm A C.
There are many Caſes, according to the Series of Perpendicu­
lars, but it will be eaſie for you to ſee that they have all but one
and the ſame Demonſtration.
It is alſo eaſie to demonſtrate, that if the Forces draw both on
one ſide they ſhall make the ſame Effect one as another, and that
the Effect of two together ſhall be double to that of one alone.
OF THE
GEOSTATICKS.
The Principle which you demand for the Geoſtaticks is,
That if two equal Weights are conjoyned by a right
Line fixed and void of Gravity, and that being ſo di­
ſpoſed they may deſcend freely, they will never reſt till
that the middle of the Line, that is the Center of Gravitation of
the Ancients, unites it ſelf to the common Center of Grave Bodies.
1
This Principle ſeems at the firſt very plauſible, but when
the Queſtion concerneth a Principle, you know what Conditions
are required to it, that it may be received, the principal of which are
wanting in the Principle now in controverſie: ſcil. that we do not
know what is the radical Cauſe why Grave Bodies deſcend; and
whence the Original of this Gravity ariſeth: as alſo that we are to­
tally ignorant of that which would arrive at the Center whither
Grave Bodies do tend, nor to other places without the Surface of the
Earth, of which, in regard we inhabit upon it, we have ſome Expe­
riments upon which we ground our Principles.
For it may be, that Gravity is a Quality that reſides in the Body
it ſelf that falleth; it may be that it is in another that attracteth
that which deſcends, as in the Earth: It may be, and it is very likely
that it is a Natural Attraction, or a Natural Deſire of two Bodies to
unite together, as in the Iron and Loadſtone, which are ſuch, that
if the Loadſtone be ſtaid, the Iron, if nothing hinder it, will go find
it out; and if the Iron be ſtaid the Loadſtone will go towards it;
and if they be both at liberty, they will reciprocally approach one
another, yet after ſuch a faſhion, that the ſtrongeſt of the two
will move the leaſt way.
If the firſt be true, according to the common opinion, we ſee not
how your Principle can ſubſiſt, for Common Senſe tells us, that in
whatever place a Weight is, it alwaies weigheth alike, having ever­
more the ſame Quality that maketh it to weigh, and that then a Bo­
dy will repoſe at the Common Center of things Grave when the
parts of the Body which ſhall be on each part of the ſaid Center
ſhall be of equal Ponderoſity to counterpoiſe one another, without
having any regard whether they be little or much removed from the
Center. Since therefore that of theſe three poſſible Cauſes of Gra­
vitation, we know not which is the right, nay, that we are not cer­
tain that it is any of them, it being poſſibly that there is a fourth
from which one may draw Concluſions very different, it ſeemeth to
me impoſſible for us to lay down other Principles in this bufineſs
than thoſe of which we are aſſured by a continual Experience, and
a ſound Judgment. As for our parts, we call thoſe Bodies equally
or unequally Grave which have an equal or unequal Force of mo­
ving towards the Common Center: and a Body is ſaid to have the
ſame Weight when it alwaies hath this ſame Force: but if this
Force augmenteth or diminiſheth, then, although it be the ſame Bo­
dy, we conſider it no longer as the ſame Weight: Now ſince that
this hapneth to Bodies that recede or approach to the Common
Center, this is it which we deſire to know, but finding nothing that
giveth me content upon this Subject, I will leave the Queſtion un­
determined and undeſcribed.
>FINIS.
1
ARCHIMEDES
HIS TRACT
De Incidentibus Humido,
OR OF THE
NATATION OF BODIES VPON,
OR SVBMERSION IN,
THE
WATER
OR OTHER LIQUIDS.
IN TWO BOOKS.
Tranſlated from the Original Greek,
Firſt into Latine, and afterwards into Italian, by NICOLO
TARTAGLIA, and by him familiarly demon­
ſtrated by way of Dialogue, with Richard Wentworth,
a Noble Engliſh Gentleman, and his Friend.
Together with the Learned Commentaries of Federico
Commandino, who hath Reſtored ſuch of the Demonſtrations
as, thorow the Injury of Time, were obliterated.
Now compared with the ORIGINAL, and Engliſhed
By THOMAS SALVSBVRY, Eſque
LONDON, Printed by W. Leybourn, 1662.
1
[Empty page]
1
ARCHIMEDES
HIS TRACT
De
INCIDENTIBUS HUMIDO,
OR OF
The Natation of Bodies upon, or Submerſion in,
the Water, or other Liquids.
1
BOOK I.
RICARDO.
Dear Companion, I have peruſed your Induſtrious Invention,
in which I find not any thing that will not certainly hold
true; but, truth is, there are many of your Concluſions
of which I underſtand uot the Cauſe, and therefore, if it
be not a trouble to you, I would deſire you to declare them
to me, for, indeed, nothing pleaſeth me, if the Cauſe
thereof be hid from me.
NICOLO. My obligations unto you are ſo many and
great, Honoured Campanion, that no requeſt of yours ought
to be troubleſome to me, and therefore tell me what thoſe Perticulars are of which
you know not the Cauſe, for I ſhall endeavour with the utmoſt of my power and
underſtanding to ſatisfie you in all your demands.
RIC. In the firſt Direction of the firſt Book of that your Induſtrious Invention
you conclude, That it is impoſſible that the Water ſhould wholly receive into it
any material Solid Body that is lighter than it ſeif (as to ſpeciæ) nay, you ſay, That
there will alwaies a part of the Body ſtay or remain above the Waters Surface
(that is uncovered by it;) and, That as the whole Solid Body put into the Water
is in proportion to that part of it that ſhall be immerged, or received, into the Wa­
ter, ſo ſhall the Gravity of the Water be to the Gravity (in ſpeciæ) of that ſame
material Body: And that thoſe Solid Bodies, that are by nature more Grave than the
Water, being put into the Water, ſhall preſently make the ſaid Water give place;
and, That they do not only wholly enter or ſubmerge in the ſame, but go continu­
ally deſcending untill they arrive at the Bottom; and, That they ſink to the Bot­
tom ſo much faſter, by how much they are more Grave than the Water. And,
again, That thoſe which are preciſely of the ſame Gravity with the Water, being
put into the ſame, are of neceſſity wholly received into, or immerged by it, but
yet retained in the Surface of the ſaid Water, and much leſs will the Water con­
ſent that it do deſcend to the Bottom: and, now, albeit that all theſe things are
manifeſt to Senſe and Experience, yet nevertheleſs would I be very glad, if it be
poſſible, that you would demonſtrate to me the moſt apt and proper Cauſe of
theſe Effects.
1
NIC. The Cauſe of all theſe Effects is aſſigned by Archimedes, the Siracuſan, in

that Book De Incidentibus (^{*}) Aquæ, by me publiſhed in Latine, and dedicated to
your ſelf, as I alſo ſaid in the beginning of that my Induſtrions Invention.
* Aquæ, tanſlated
by me Humido, as
the more Compre­
henſive word, for
his Doctrine holds
true in all Liquids
as well as in Wa­
ter, ſoil. in Wine,
Oyl, Milk, &c.
RIC. I have ſeen that ſame Archimedes, and have very well underſtood thoſe
two Books in which he treateth De Centro Gravitatis æquerepentibus, or of the
Center of Gravity in Figures plain, or parallel to the Horizon; and likewiſe thoſe
De Quadratura Parabolæ, or, of Squaring the Parabola; but ^{*}that in which he treat­
eth of Solids that Swim upon, or ſink in Liquids, is ſo obſcure, that, to ſpeak the
truth, there are many things in it which I do not underſtand, and therefore before

we proceed any farther, I ſhould take it for a favour if you would declare it to me
in your Vulgar Tongue, beginning with his firſt Suppoſition, which ſpeaketh in this
manner.
* He ſpeaks of but
one Book, Tartag­
lia having tranſla­
ted no more.
SVPPOSITION I.
It is ſuppoſed that the Liquid is of ſuch a nature, that
its parts being equi-jacent and contiguous, the leſs
preſſed are repulſed by the more preſſed. And
that each of its parts is preſſed or repulſed by the
Liquor that lyeth over it, perpendicularly, if the
Liquid be deſcending into any place, or preſſed any
whither by another.
NIC. Every Science, Art, or Doctrine (as you know, Honoured Companion,)
hath its firſt undemonſtrable Principles, by which (they being
granted or ſuppoſed) the ſaid Science is proved, maintained, or de­
monſtrated. And of theſe Principles, ſome are called Petitions,
and others Demands, or Suppoſitions. I ſay, therefore, that the Science or Doctrine
of thoſe Material Solids that Swim or Sink in Liquids, hath only two undemon­
ſtrable Suppoſitions, one of which is that above alledged, the which in compliance
with your deſire I have ſet down in our Vulgar Tongue.
RIC. Before you proceed any farther tell me, how we are to underſtand the
parts of a Liquid to be Equijacent.
NIC. When they are equidiſtant from the Center of the World, or of the
Earth (which is the ſame, although ^{*} ſome hold that the Centers of the Earth
and Worldare different.)
RIC. I underſtand you not unleſs you give me ſome Example thereof in
Figure.
* The Coperni­
cans.
NIC. To exemplifie this particular, Let us ſuppoſe a quantity of Liquor (as
for inſtance of Water) to be upon the Earth; then let us with the Imagination
cut the whole Earth together with that Water into two equal parts, in ſuch a
manner as that the ſaid Section may paſs ^{*} by the Center of the Earth: And let
us ſuppoſe that one part of the Superficies of that Section, as well of the Water
as of the Earth, be the Superficies A B, and that the Center of the Earth be the
point K. This being done, let us in our Imagination deſcribe a Circle upon the

ſaid Center K, of ſuch a bigneſs as that the Circumference may paſs by the Super­
ficies of the Section of the Water: Now let this Circumference be E F G: and
let many Lines be drawn from the point K to the ſaid Circumference, cutting the
ſame, as KE, KHO, KFQ KLP, KM. Now I ſay, that all theſe parts of
the ſaid Water, terminated in that Circumference, are Equijacent, as being all
1equidiſtant from the point K, the Center of the World, which parts are G M,
M L, L F, F H, H E.
* Or through.
RIC. I underſtand you very well, as to this particular: But tell me a little; he
ſaith that each of the parts of the Liquid is preſſed or repulſed by the Liquid that
is above it, according to the Perpendicular: I know not what that Liquid is that
lieth upon a part of another Perpendicularly.
NIC. Imagining a Line that cometh from the Center of the Earth penetrating
thorow ſome Water, each part of the Water that is in that Line he ſuppoſeth to
be preſſed or repulſed by the Water that lieth above it in that ſame Line, and that
that repulſe is made according to the ſame Line, (that is, directly towards the
Center of the World) which Line is called a Perpendicular; becauſe every
Right-Line that departeth from any point, and goeth directly towards the Worlds
Center is called a Perpendicular. And that you may the better underſtand me, let
227[Figure 227]
us imagine
the Line KHO,
and in that
let us imagine
ſeveral parts,
as ſuppoſe RS,
S T, T V, V H,
H O. I ſay,
that he ſup­
poſeth that
the part V H
is preſſed by
that placed a­
bove it, H O,
according to
the Line OK;
the which
O K, as hath been ſaid above, is called the Perpendicular paſſing thorow thoſe two
parts. In like manner, I ſay that the part T V is expulſed by the part V H, ac­
cording to the ſaid Line O K: and ſo the part S T to be preſſed by T V, according
to the ſaid Perpendicular O K, and R S by S T. And this you are to underſtand
in all the other Lines that were protracted from the ſaid Point K, penetrating the
ſaid Water, As for Example, in K G, K M, K L, K F, K E, and infinite others of the
like kind.
RIC. Indeed, Dear Companion, this your Explanation hath given megreat ſa­
tisfaction; for, in my Judgment, it ſeemeth that all the difficulty of this Suppoſition
conſiſts in theſe two particulars which you have declared to me.
NIC. It doth ſo; for having underſtood that the parts E H, H F, F L, L M, and
MG, determining in the Circumference of the ſaid Circle are equijacent, it is an
eaſie matter to underſtand the foreſaid Suppoſition in Order, which ſaith, That it is
ſuppoſed that the Liquid is of ſuch a nature, that the part thereof leſs preſſed or thrust is re­
pulſed by the more thruſt or preſſed. As for example, if the part E H were by chance
more thruſt, crowded, or preſſed from above downwards by the Liquid, or ſome
other matter that was over it, than the part H F, contiguous to it, it is ſuppoſed
that the ſaid part H F, leſs preſſed, would be repulſed by the ſaid part E H. And
thus we ought to underſtand of the other parts equijacent, in caſe that they be
contiguous, and not ſevered. That each of the parts thereof is preſſed and repul.
ſed by the Liquid that lieth over it Perpendicularly, is manifeſt by that which was
ſaid above, to wit, that it ſhould be repulſed, in caſe the Liquid be deſcending into
any place, and thruſt, or driven any whither by another.
RIC. I underſtand this Suppoſition very well, but yet me thinks that before
the Suppoſition, the Author ought to have defined thoſe two particulars, which
you firſt declared to me, that is, how we are to underſtand the parts of the Liquid
equijacent, and likewiſe the Perpendicular.
1
NIC. You ſay truth.
RIC. I have another queſtion to aske you, which is this, Why the Author
uſeth the word Liquid, or Humid, inſtead of Water.
NIC. It may be for two of theſe two Cauſes; the one is, that Water being the
principal of all Liquids, therefore ſaying Humidum he is to be underſtood to mean
the chief Liquid, that is Water: The other, becauſe that all the Propoſitions of
this Book of his, do not only hold true in Water, but alſo in every other Liquid,
as in Wine, Oyl, and the like: and therefore the Author might have uſed the word
Humidum, as being a word more general than Aqua.
RIC. This I underſtand, therefore let us come to the firſt Propoſition, which, as
you know, in the Original ſpeaks in this manner.
PROP. I. THEOR. I.
If any Superficies ſhall be cut by a Plane thorough any
Point, and the Section be alwaies the Circumference
of a Circle, whoſe Center is the ſaid Point: that Su­
perficies ſhall be Spherical.
Let any Superficies be cut at pleaſure by a Plane thorow the
Point K; and let the Section alwaies deſcribe the Circumfe­
rence of a Circle that hath for its Center the Point K: I ſay,
that that ſame Superficies is Sphærical. For were it poſſible that the
ſaid Superficies were not Sphærical, then all the Lines drawn
through the ſaid Point K unto that Superficies would not be equal,
Let therefore A and B be two
Points in the ſaid Superficies, ſo that
228[Figure 228]
drawing the two Lines K A and
K B, let them, if poſſible, be une­
qual: Then by theſe two Lines let
a Plane be drawn cutting the ſaid
Superficies, and let the Section in
the Superficies make the Line
D A B G: Now this Line D A B G
is, by our pre-ſuppoſal, a Circle, and
the Center thereof is the Point K, for ſuch the ſaid Superficies was
ſuppoſed to be. Therefore the two Lines K A and K B are equal:
But they were alſo ſuppoſed to be unequal; which is impoſſible:
It followeth therefore, of neceſſity, that the ſaid Superficies be
Sphærical, that is, the Superficies of a Sphære.
RIC. I underſtand you very well; now let us proceed to the ſecond Propoſition,
which, you know, runs thus.
1
PROP. II. THEOR. II.
The Superficies of every Liquid that is conſiſtant and
ſetled ſhall be of a Sphærical Figure, which Figure
ſhall have the ſame Center with the Earth.
Let us ſuppoſe a Liquid that is of ſuch a conſiſtance as that it
is not moved, and that its Superficies be cut by a Plane along
by the Center of the Earth, and let the Center of the Earth
be the Point K: and let the Section of the Superficies be the Line
A B G D. I ſay that the Line A B G D is the Circumference of a
229[Figure 229]
Circle, and that the Center
thereof is the Point K And
if it be poſſible that it may
not be the Circumference
of a Circle, the Right­

Lines drawn ^{*} by the Point
K to the ſaid Line A B G D
ſhall not be equal. There­
fore let a Right-Line be
taken greater than ſome of thoſe produced from the Point K unto
the ſaid Line A B G D, and leſſer than ſome other; and upon the
Point K let a Circle be deſcribed at the length of that Line,
Now the Circumference of this Circle ſhall fall part without the
ſaid Line A B G D, and part within: it having been preſuppoſed
that its Semidiameter is greater than ſome of thoſe Lines that may
be drawn from the ſaid Point K unto the ſaid Line A B G D, and
leſſer than ſome other. Let the Circumference of the deſcribed
Circle be R B G H, and from B to K draw the Right-Line B K: and
drawn alſo the two Lines K R, and K E L which make a Right­
Angle in the Point K: and upon the Center K deſcribe the Circum­
ference X O P in the Plane and in the Liquid. The parts, there­
fore, of the Liquid that are ^{*} according to the Circumference

X O P, for the reaſons alledged upon the firſt Suppoſition, are equi­
jacent, or equipoſited, and contiguous to each other; and both
theſe parts are preſt or thruſt, according to the ſecond part of the
Suppoſition, by the Liquor which is above them. And becauſe the
two Angles E K B and B K R are ſuppoſed equal [by the 26. of 3.
of Euclid,] the two Circumferences or Arches B E and B R ſhall
be equal (foraſmuch as R B G H was a Circle deſcribed for ſatis­
faction of the Oponent, and K its Center:) And in like manner
the whole Triangle B E K ſhall be equal to the whole Triangle
B R K. And becauſe alſo the Triangle O P K for the ſame reaſon
1ſhall be equal to the Triangle O X K; Therefore (by common
Notion) ſubſtracting thoſe two ſmall Triangles O P K and O X K
from the two others B E K and B R K, the two Remainders ſhall
be equal: one of which Remainders ſhall be the Quadrangle
B E O P, and the other B R X O. And becauſe the whole Quadran­
gle B E O P is full of Liquor, and of the Quadrangle B R X O,
the part B A X O only is full, and the reſidue B R A is wholly void
of Water: It followeth, therefore, that the Quadrangle B E O P
is more ponderous than the Quadrangle B R X O. And if the ſaid
Quadrangle B E O P be more Grave than the Quadrangle
B R X O, much more ſhall the Quadrangle B L O P exceed in Gra­
vity the ſaid Quadrangle B R X O: whence it followeth, that the
part O P is more preſſed than the part O X. But, by the firſt part
of the Suppoſition, the part leſs preſſed ſhould be repulſed by the
part more preſſed: Therefore the part O X muſt be repulſed by
the part O P: But it was preſuppoſed that the Liquid did not
move: Wherefore it would follow that the leſs preſſed would not
be repulſed by the more preſſed: And therefore it followeth of
neceſſity that the Line A B G D is the Circumference of a Circle,
and that the Center of it is the point K. And in like manner ſhall
it be demonſtrated, if the Surface of the Liquid be cut by a Plane
thorow the Center of the Earth, that the Section ſhall be the Cir­
cumference of a Circle, and that the Center of the ſame ſhall be
that very Point which is Center of the Earth. It is therefore mani­
feſt that the Superficies of a Liquid that is conſiſtant and ſetled
ſhall have the Figure of a Sphære, the Center of which ſhall be
the ſame with that of the Earth, by the firſt Propoſition; for it is
ſuch that being ever cut thorow the ſame Point, the Section or Di­
viſion deſcribes the Circumference of a Circle which hath for Cen­
ter the ſelf-ſame Point that is Center of the Earth: Which was to
be demonſtrated.
* O: through.
* i.e. Parallel.
RIC. I do thorowly underſtand theſe your Reaſons, and ſince there is in them
no umbrage of Doubting, let us proceed to his third Propoſition.
PROP. III. THEOR. III.
Solid Magnitudes that being of equal Maſs with the
Liquid are alſo equal to it in Gravity, being demit-

ted into the [^{*} ſetled] Liquid do ſo ſubmerge in the
ſame as that they lie or appear not at all above the
Surface of the Liquid, nor yet do they ſink to the
Bottom.
1
* I add the word
ſetled, as neceſſary
in making the Ex­
periment.
NIC. In this Propoſition it is affirmed that thoſe Solid Magnitules that hap­
pen to be equal in ſpecifical Gravity with the Liquid being lefeat liber­
ty in the ſaid Liquid do ſo ſubmerge in the ſame, as that they lie or ap­
pear not at all above the Surface of the Liquid, nor yet do they go or ſink to the
Bottom.
For ſuppoſing, on the contrary, that it were poſſible for one of
thoſe Solids being placed in the Liquid to lie in part without the
Liquid, that is above its Surface, (alwaies provided that the ſaid
Liquid be ſetled and undiſturbed,) let us imagine any Plane pro­
duced thorow the Center of the Earth, thorow the Liquid, and
thorow that Solid Body: and let us imagine that the Section of the
Liquid is the Superficies A B G D, and the Section of the Solid
Body that is within it the Superſicies E Z H T, and let us ſuppoſe
the Center of the Earth to be the Point K: and let the part of the
ſaid Solid ſubmerged in the Liquid be B G H T, and let that above
be B E Z G: and let the Solid Body be ſuppoſed to be comprized in
a Pyramid that hath its Parallelogram Baſe in the upper Surface of
the Liquid, and its Summity or Vertex in the Center of the Earth:
which Pyramid let us alſo ſuppoſe to be cut or divided by the ſame
Plane in which is the Circumference A B G D, and let the Sections
230[Figure 230]
of the Planes of the ſaid
Pyramid be K L and
K M: and in the Liquid
about the Center K let
there be deſcribed a Su­
perficies of another
Sphære below E Z H T,
which let be X O P;
and let this be cut by
the Superficies of the Plane: And let there be another Pyramid ta­
ken or ſuppoſed equal and like to that which compriſeth the ſaid
Solid Body, and contiguous and conjunct with the ſame; and let
the Sections of its Superficies be K M and K N: and let us ſuppoſe
another Solid to be taken or imagined, of Liquor, contained in that
ſame Pyramid, which let be R S C Y, equal and like to the partial
Solid B H G T, which is immerged in the ſaid Liquid: But the
part of the Liquid which in the firſt Pyramid is under the Super­
ficies X O, and that, which in the other Pyramid is under the Su­
perficies O P, are equijacent or equipoſited and contiguous, but
are not preſſed equally; for that which is under the Superficies
X O is preſſed by the Solid T H E Z, and by the Liquor that is
contained between the two Spherical Superficies X O and L M
and the Planes of the Pyramid, but that which proceeds accord­
ing to F O is preſſed by the Solid R S C Y, and by the Liquid
1contained between the Sphærical Superficies that proceed accord­
ing to P O and M N and the Planes of the Pyramid; and the Gra­
vity of the Liquid, which is according to M N O P, ſhall be leſſer
than that which is according to L M X O; becauſe that Solid of
Liquor which proceeds according to R S C Y is leſs than the Solid
E Z H T (having been ſuppoſed to be equal in quantity to only
the part H B G T of that:) And the ſaid Solid E Z H T hath been
ſuppoſed to be equally grave with the Liquid: Therefore the Gra­
vity of the Liquid compriſed betwixt the two Sphærical Superfi­
cies L M and X O, and betwixt the ſides L X and M O of the
231[Figure 231]
Pyramid, together with
the whole Solid EZHT,
ſhall exceed the Gravity
of the Liquid compri­
ſed betwixt the other
two Sphærical Superfi­
cies M N and O P, and
the Sides M O and N P
of the Pyramid, toge­
ther with the Solid of Liquor R S C Y by the quantity of the Gra­
vity of the part E B Z G, ſuppoſed to remain above the Surface of
the Liquid: And therefore it is manifeſt that the part which pro­
ceedeth according to the Circumference O P is preſſed, driven, and
repulſed, according to the Suppoſition, by that which proceeds ac­
cording to the Circumference X O, by which means the Liquid
would not be ſetled and ſtill: But we did preſuppoſe that it was
ſetled, namely ſo, as to be without motion: It followeth, therefore,
that the ſaid Solid cannot in any part of it exceed or lie above the
Superficies of the Liquid: And alſo that being dimerged in the Li­
quid it cannot deſcend to the Bottom, for that all the parts of the
Liquid equijacent, or diſpoſed equally, are equally preſſed, becauſe
the Solid is equally grave with the Liquid, by what we preſuppoſed.
RIC. I do underſtand your Argumentation, but I underſtand not that Phraſe
Solid Magnitudes.
NIC. I will declare this Term unto you. Magnitude is a general Word that
reſpecteth all the Species of Continual Quantity; and the Species of Continual
Quantity are three, that is, the Line, the Superficies, and the Body; which Body
is alſo called a Solid, as having in it ſelf Length, Breadth, and Thickneſs, or Depth:
and therefore that none might equivocate or take that Term Magnitudes to be
meant of Lines, or Superficies, but only of Solid Magnitudes, that is, Bodies, he
did ſpecifie it by that manner of expreſſion, as was ſaid. The truth is, that he
might have expreſt that Propoſition in this manner: Solids (or Bodies) which being
of equal Gravity with an equal Maſs of the Liquid, &c. And this Propoſition would have
been more cleer and intelligible, for it is as ſignificant to ſay, a Solid, or, a Body, as
to ſay, a Solid Magnitude: therefore wonder not if for the future I uſe theſe three
kinds of words indifferently.
RIC. You have ſufficiently ſatisfied me, wherefore that we may loſe no time
let us go forwards to the fourth Propoſition.
1
PROP. IV. THEOR. IV.
Solid Magnitudes that are lighter than the Liquid,
being demitted into the ſetled Liquid, will not total­
ly ſubmerge in the ſame, but ſome part thereof will
lie or ſtay above the Surface of the Liquid.
NIC. In this fourth Propoſition it is concluded, that every Body or Solid that is
lighter (as to Specifical Gravity) than the Liquid, being put into the
Liquid, will not totally ſubmerge in the ſame, but that ſome part of it
will ſtay and appear without the Liquid, that is above its Surface.
For ſuppoſing, on the contrary, that it were poſſible for a Solid
more light than the Liquid, being demitted in the Liquid to ſub­
merge totally in the ſame, that is, ſo as that no part thereof re­
maineth above, or without the ſaid Liquid, (evermore ſuppoſing
that the Liquid be ſo conſtituted as that it be not moved,) let us
imagine any Plane produced thorow the Center of the Earth, tho­
row the Liquid, and thorow that Solid Body: and that the Surface
of the Liquid is cut by this Plane according to the Circumference
A B G, and the Solid Body according to the Figure R; and let the
Center of the Earth be K. And let there be imagined a Pyramid
232[Figure 232]
that compriſeth the Figure
R, as was done in the pre.
cedent, that hath its Ver­
tex in the Point K, and let
the Superficies of that
Pyramid be cut by the
Superficies of the Plane
A B G, according to A K
and K B. And let us ima­
gine another Pyramid equal and like to this, and let its Superficies
be cut by the Superficies A B G according to K B and K G; and let
the Superficies of another Sphære be deſcribed in the Liquid, upon
the Center K, and beneath the Solid R; and let that be cut by the
ſame Plane according to X O P. And, laſtly, let us ſuppoſe ano­
ther Solid taken ^{*} from the Liquid, in this ſecond Pyramid, which

let be H, equal to the Solid R. Now the parts of the Liquid, name­
ly, that which is under the Spherical Superficies that proceeds ac­
cording to the Superficies or Circumference X O, in the firſt Py­
ramid, and that which is under the Spherical Superficies that pro­
ceeds according to the Circumference O P, in the ſecond Pyramid,
are equijacent, and contiguous, but are not preſſed equally; for
1that of the firſt Pyramid is preſſed by the Solid R, and by the Liquid
which that containeth, that is, that which is in the place of the Py­
ramid according to A B O X: but that part which, in the other Py­
ramid, is preſſed by the Solid H, ſuppoſed to be of the ſame Li­
quid, and by the Liquid which that containeth, that is, that which
is in the place of the ſaid Pyramid according to P O B G: and the
Gravity of the Solid R is leſs than the Gravity of the Liquid
H, for that theſe two Magnitudes were ſuppoſed to be equal in
Maſs, and the Solid R was ſuppoſed to be lighter than the Liquid:
and the Maſſes of the two Pyramids of Liquor that containeth theſe

two Solids R and H are equal ^{*} by what was preſuppoſed: There­
fore the part of the Liquid that is under the Superficies that pro­
ceeds according to the Circumference O P is more preſſed; and,
therefore, by the Suppoſition, it ſhall repulſe that part which is leſs
preſſed, whereby the ſaid Liquid will not be ſetled: But it was be­
fore ſuppoſed that it was ſetled: Therefore that Solid R ſhall not
totally ſubmerge, but ſome part thereof will remain without the
Liquid, that is, above its Surface, Which was the Propoſition.
* That is a Maſs of
the Liquid.
* For that the Py­
ramids were ſuppo­
ſed equal.
RIC. I have very well underſtood you, therefore let us come to the fifth Pro­
poſition, which, as you know, doth thus ſpeak.
PROP. V. THEOR. V.
Solid Magnitudes that are lighter than the Liquid,
being demitted in the (ſetled) Liquid, will ſo far
ſubmerge, till that a Maſs of Liquor, equal to the
Part ſubmerged, doth in Gravity equalize the
whole Magnitude.
NIC. It having, in the precedent, been demonſtrared that Solids lighter than
the Liquid, being demitted in the Liquid, alwaies a part of them remains
without the Liquid, that is above its Surface; In this fifth Propoſition it is
aſſerted, that ſo much of ſuch a Solid ſhall ſubmerge, as that a Maſs of the
Liquid equal to the part ſubmerged, ſhall have equal Gravity with the whole
Solid.
And to demonſtrate this, let us aſſume all the ſame Schemes
as before, in Propoſition 3. and likewiſe let the Liquid be ſet­
led, and let the Solid E Z H T be lighter than the Liquid.
Now if the ſaid Liquid be ſetled, the parts of it that are equija­
cent are equally preſſed: Therefore the Liquid that is beneath
1the Superficies that proceed according to the Circumferences X O
and P O are equally preſſed; whereby the Gravity preſſed is equal.
233[Figure 233]
But the Gravity of the
Liquid which is in the

firſt Pyramid ^{*} without
the Solid B H T G, is
equal to the Gravity of
the Liquid which is in
the other Pyramid with­
out the Liquid R S C Y:
It is manifeſt, therefore,
that the Gravity of the Solid E Z H T, is equal to the Gravity of
the Liquid R S C Y: Therefore it is manifeſt that a Maſs of Liquor
equal in Maſs to the part of the Solid ſubmerged is equal in Gra­
vity to the whole Solid.
* Without, i.e. that
being deducted.
RIC. This was a pretty Demonſtration, and becauſe I very well underſtand
it, let us loſe no time, but proceed to the ſixth Propoſition, ſpeaking thus.
PROP. VI. THEOR. VI.
Solid Magnitudes lighter than the Liquid being thruſt
into the Liquid, are repulſed upwards with a Force
as great as is the exceſs of the Gravity of a Maſs
of Liquor equal to the Magnitude above the Gra­
vity of the ſaid Magnitude.
NIC. This ſixth Propoſition ſaith, that the Solids lighter than the Liquid
demitted, thruſt, or trodden by Force underneath the Liquids Sur­
face, are returned or driven upwards with ſo much Force, by
how much a quantity of the Liquid equal to the. Solid ſhall
exceed the ſaid Solid in Gravity.
And to delucidate this Propoſition, let the Solid A be lighter
than the Liquid, and let us ſuppoſe that the Gravity of the ſaid
Solid A is B: and let the Gravity of a Liquid, equal in Maſs to A,
be B G. I ſay, that the Solid A depreſſed or demitted with Force
into the ſaid Liquid, ſhall be returned and repulſed upwards with
a Force equal to the Gravity G. And to demonſtrate this Propo­
ſition, take the Solid D, equal in Gravity to the ſaid G. Now
the Solid compounded of the two Solids A and D will be lighter
than the Liquid: for the Gravity of the Solid compounded of
them both is BG, and the Gravity of as much Liquor as equal­
leth in greatneſs the Solid A, is greater than the ſaid Gravity BG,
1for that B G is the Gravity of the Liquid equal in Maſs unto it:
Therefore the Solid compounded of thoſe two Solids A and D
being dimerged, it ſhall, by the precedent, ſo much of it ſubmerge,
as that a quantity of the Liquid equal to the ſaid ſubmerged part
ſhall have equal Gravity with the ſaid compounded Solid. And
234[Figure 234]
for an example of that Propoſition let the Su­
perficies of any Liquid be that which pro­
ceedeth according to the Circumference
A B G D: Becauſe now a Maſs or quantity
of Liquor as big as the Maſs A hath equal
Gravity with the whole compounded Solid
A D: It is manifeſt that the ſubmerged part
thereof ſhall be the Maſs A: and the remain­
der, namely, the part D, ſhall be wholly a­
top, that is, above the Surface of the Liquid.
It is therefore evident, that the part A hath ſo much virtue or
Force to return upwards, that is, to riſe from below above the Li­
quid, as that which is upon it, to wit, the part D, hath to preſs it
downwards, for that neither part is repulſed by the other: But D
preſſeth downwards with a Gravity equal to G, it having been ſup­
poſed that the Gravity of that part D was equal to G: Therefore
that is manifeſt which was to be demonſtrated.
RIC. This was a fine Demonſtration, and from this I perceive that you colle­
cted your Induſtrious Invention; and eſpecially that part of it which you inſert in
the firſt Book for the recovering of a Ship ſunk: and, indeed, I have many Que­
ſtions to ask you about that, but I will not now interrupt the Diſcourſe in hand, but
deſire that we may go on to the ſeventh Propoſition, the purport whereof is this.
PROP. VII. THEOR. VII.
Solid Magnitudes beavier than the Liquid, being de­
mitted into the [ſetled] Liquid, are boren down­
wards as far as they can deſcend: and ſhall be lighter
in the Liquid by the Gravity of a Liquid Maſs of
the ſame bigneſs with the Solid Magnitude.
NIC. This ſeventh Propoſition hath two parts to be demonſtrated.
The firſt is, That all Solids heavier than the Liquid, being demit­
ted into the Liquid, are boren by their Gravities downwards as far
as they can deſcend, that is untill they arrive at the Bottom. Which
firſt part is manifeſt, becauſe the Parts of the Liquid, which ſtill lie
under that Solid, are more preſſed than the others equijacent,
becauſe that that Solid is ſuppoſed more grave than the Liquid.
1But now that that Solid is lighter in the Liquid than out of it, as
is affirmed in the ſecond part, ſhall be demonſtrated in this man­
ner. Take a Solid, as ſuppoſe A, that is more grave than the Li­
quid, and ſuppoſe the Gravity of that ſame Solid A to be BG.
And of a Maſs of Liquor of the ſame bigneſs with the Solid A, ſup­
poſe the Gravity to be B: It is to be demonſtrated that the Solid
A, immerged in the Liquid, ſhall have a Gravity equal to G. And
to demonſtrate this, let us imagine another Solid, as ſuppoſe D,
more light than the Liquid, but of ſuch a quality as that its Gravi­
ty is equal to B: and let this D be of ſuch a Magnitude, that a
Maſs of Liquor equal to it hath its Gravity equal to the Gravity
B G. Now theſe two Solids D and A being compounded toge­
ther, all that Solid compounded of theſe two ſhall be equally
Grave with the Water: becauſe the Gravity of theſe two Solids
together ſhall be equal to theſe two Gravities, that is, to B G, and
235[Figure 235]
to B; and the Gravity of a Liquid that hath its
Maſs equal to theſe two Solids A and D, ſhall be
equal to theſe two Gravities B G and B. Let
theſe two Solids, therefore, be put in the Liquid,

and they ſhall ^{*} remain in the Surface of that Li­
quid, (that is, they ſhall not be drawn or driven
upwards, nor yet downwards:) For if the Solid
A be more grave than the Liquid, it ſhall be
drawn or born by its Gravity downwards to­
wards the Bottom, with as much Force as by the Solid D it is thruſt
upwards: And becauſe the Solid D is lighter than the Liquid, it
ſhall raiſe it upward with a Force as great as the Gravity G: Be­
cauſe it hath been demonſtrated, in the ſixth Propoſition, That So­
lid Magnitudes that are lighter than the Water, being demitted in
the ſame, are repulſed or driven upwards with a Force ſo much the
greater by how much a Liquid of equal Maſs with the Solid is more
Grave than the ſaid Solid: But the Liquid which is equal in Maſs
with the Solid D, is more grave than the ſaid Solid D, by the Gra­
vity G: Therefore it is manifeſt, that the Solid A is preſſed or
born downwards towards the Centre of the World, with a Force
as great as the Gravity G: Which was to be demonſtrated.
* Or, according to
Commandine, ſhall
be equall in Gravi­
ty to the Liquid,
neither moving up­
wards or down­
wards.
RIC. This hath been an ingenuous Demonſtration; and in regard I do ſuffici­
ently underſtand it, that we may loſe no time, we will proceed to the ſecond Suppo­
ſition, which, as I need not tell you, ſpeaks thus.
1
SVPPOSITION II.
It is ſuppoſed that thoſe Solids which are moved up­
wards, do all aſcend according to the Perpendicular
which is produced thorow their Centre of Gravity.
COMMANDINE.
And thoſe which are moved downwards, deſcend, likewiſe, according to the Perpendicular
that is produced thorow their Centre of Gravity, which he pretermitted either as known,
or as to be collected from what went before.
NIC. For underſtanding of this ſecond Suppoſition, it is requiſite to take notice
that every Solid that is lighter than the Liquid being by violence, or by ſome other
occaſion, ſubmerged in the Liquid, and then left at liberty, it ſhall, by that which
hath been proved in the ſixth Propoſition, be thruſt or born up wards by the Liquid,
and that impulſe or thruſting is ſuppoſed to be directly according to the Perpendi­
cular that is produced thorow the Centre of Gravity of that Solid; which Per­
pendicular, if you well remember, is that which is drawn in the Imagination
from the Centre of the World, or of the Earth, unto the Centre of Gravity of
that Body, or Solid.
RIC. How may one find the Centre of Gravity of a Solid?
NIC. This he ſheweth in that Book, intituled De Centris Gravium, vel de Æqui­
ponderantibus; and therefore repair thither and you ſhall be ſatisfied, for to declare
it to you in this place would cauſe very great confuſion.
RIC. I underſtand you: ſome other time we will talk of this, becauſe I have
a mind at preſent to proceed to the laſt Propoſition, the Expoſition of which ſeemeth
to me very confuſed, and, as I conceive, the Author hath not therein ſhewn all
the Subject of that Propoſition in general, but only a part: which Propoſition
ſpeaketh, as you know, in this form.
PROP. VIII. THEOR. VIII.
A
If any Solid Magnitude, lighter than the Liquid, that
hath the Figure of a Portion of a Sphære, ſhall be

demitted into the Liquid in ſuch a manner as that
the Baſe of the Portion touch not the Liquid, the
Figure ſhall ſtand erectly, ſo, as that the Axis of
the ſaid Portion ſhall be according to the Perpen­
dicular. And if the Figure ſhall be inclined to any
ſide, ſo, as that the Baſe of the Portion touch the
Liquid, it ſhall not continue ſo inclined as it was de­
mitted, but ſhall return to its uprightneſs.
1
B
For the declaration of this Propoſition, let a Solid Magnitude
that hath the Figure of a portion of a Sphære, as hath been ſaid,
be imagined to be de­
236[Figure 236]
mitted into the Liquid; and
alſo, let a Plain be ſuppoſed
to be produced thorow the
Axis of that portion, and
thorow the Center of the
Earth: and let the Section
of the Surface of the Liquid
be the Circumference A B
C D, and of the Figure, the
Circumference E F H, & let
E H be a right line, and F T
the Axis of the Portion. If now
it were poſſible, for ſatisfact­
ion of the Adverſary, Let
it be ſuppoſed that the ſaid Axis were not according to the (a) Per­

pendicular; we are then to demonſtrate, that the Figure will not
continue as it was conſtituted by the Adverſary, but that it will re­
turn, as hath been ſaid, unto its former poſition, that is, that the
Axis F T ſhall be according to the Perpendicular. It is manifeſt, by
the Corollary of the 1. of 3. Euclide, that the Center of the Sphære
is in the Line F T, foraſmuch as that is the Axis of that Figure.
And in regard that the Por­
237[Figure 237]
tion of a Sphære, may be
greater or leſſer than an He­
miſphære, and may alſo be
an Hemiſphære, let the Cen­
tre of the Sphære, in the He­
miſphære, be the Point T,
and in the leſſer Portion the
Point P, and in the greater,
the Point K, and let the Cen­
tre of the Earth be the Point
L. And ſpeaking, firſt, of
that greater Portion which
hath its Baſe out of, or a­
bove, the Liquid, thorew the Points K and L, draw the Line KL
cutting the Circumference E F H in the Point N, Now, becauſe

every Portion of a Sphære, hath its Axis in the Line, that from the
Centre of the Sphære is drawn perpendicular unto its Baſe, and hath
its Centre of Gravity in the Axis; therefore that Portion of the Fi­
gure which is within the Liquid, which is compounded of two
1tions of a Sphære, ſhall have its Axis in the Perpendicular, that is
drawn through the point K; and its Centre of Gravity, for the ſame
reaſon, ſhall be in the Line N K: let us ſuppoſe it to be the Point R:

But the Centre of Gravity of the whole Portion is in the Line F T,
betwixt the Point R and
238[Figure 238]
the Point F; let us ſuppoſe
it to be the Point X: The re­
mainder, therefore, of that

Figure elivated above the
Surface of the Liquid, hath
its Centre of Gravity in
the Line R X produced or
continued right out in the
Part towards X, taken ſo,
that the part prolonged may
have the ſame proportion to
X R, that the Gravity of
that Portion that is demer­
ged in the Liquid hath to
the Gravity of that Figure which is above the Liquid; let us ſuppoſe

that ^{*} that Centre of the ſaid Figure be the Point S: and thorow that

ſame Centre S draw the Perpendicular L S. Now the Gravity of the Fi­
gure that is above the Liquid ſhall preſſe from above downwards ac­
cording to the Perpendicular S L; & the Gravity of the Portion that
is ſubmerged in the Liquid, ſhall preſſe from below upwards, accor­
ding to the Perpendicular R L. Therefore that Figure will not conti­
nue according to our Adverſaries Propoſall, but thoſe parts of the
ſaid Figure which are towards E, ſhall be born or drawn downwards,
& thoſe which are towards H ſhall be born or driven upwards, and
this ſhall be ſo long untill that the Axis F T comes to be according
to the Perpendicular.
(a) Perpendicular
is taken kere, as
in all other places,
by this Author for
the Line K L
drawn thorow the
Centre and Cir­
cumference of the
Earth.
C
D
E
* i. e, The Center
of Gravity.
F
And this ſame Demonſtration is in the ſame manner verified in
the other Portions. As, firſt, in the Hæmiſphere that lieth with its
whole Baſe above or without the Liquid, the Centre of the Sphære
hath been ſuppoſed to be the Point T; and therefore, imagining T
to be in the place, in which, in the other above mentioned, the
Point R was, arguing in all things elſe as you did in that, you ſhall
find that the Figure which is above the Liquid ſhall preſs from
above downwards according to the Perpendicular S L; and the
Portion that is ſubmerged in the Liquid ſhall preſs from below up­
wards according to the Perpendicular R L. And therefore it ſhall
follow, as in the other, namely, that the parts of the whole Figure
which are towards E, ſhall be born or preſſed downwards, and thoſe

that are towards H, ſhall be born or driven upwards: and this ſhall
be ſo long untill that the Axis F T come to ſtand ^{*} P
1ly. The like ſhall alſo hold true in the Portion of the Sphære
leſs than an Hemiſphere that lieth with its whole Baſe above the
Liquid.
* Or according
to the Perpendi­
cular.
COMMANDINE.
The Demonſtration of this Propoſition is defaced by the Injury of Time, which we have re­
ſtored, ſo far as by the Figures that remain, one may collect the Meaning of Archimedes,
for we thought it not good to alter them: and what was wanting to their declaration and ex­
planation we have ſupplyed in our Commentaries, as we have alſo determined to do in the ſe­
cond Propoſition of the ſecond Book.
If any Solid Magnitude lighter than the Liquid.] Theſe words, light-

er than the Liquid, are added by us, and are not to be found in the Tranſiation; for of theſe
kind of Magnitudes doth Archimedes ſpeak in this Propoſition.
A
Shall be demitted into the Liquid in ſuch a manner as that the

Baſe of the Portion touch not the Liquid.] That is, ſhall be ſo demitted into
the Liquid as that the Baſe ſhall be upwards, and the Vertex downwards, which he oppoſeth
to that which he ſaith in the Propoſition following; Be demitted into the Liquid, ſo, as
that its Baſe be wholly within the Liquid; For theſe words ſignifie the Portion demit­
ted the contrary way, as namely, with the Vertex upwards and the Baſe downwards. The
ſame manner of ſpeech is frequently uſed in the ſecond Book; which treateth of the Portions
of Rectangle Conoids.
B
Now becauſe every Portion of a Sphære hath its Axis in the Line

that from the Center of the Sphære is drawn perpendicular to its
Baſe.] For draw a Line from B to C, and let K L cut the Circumference A B C D in the
Point G, and the Right Line B C in M:
239[Figure 239]
and becauſe the two Circles A B C D, and
E F H do cut one another in the Points
B and C, the Right Line that conjoyneth
their Centers, namely, K L, doth cut the
Line B C in two equall parts, and at
Right Angles; as in our Commentaries
upon Prolomeys Planiſphære we do
prove: But of the Portion of the Circle
B N C the Diameter is M N; and of the
Portion B G C the Diameter is M G;

for the (a) Right Lines which are drawn
on both ſides parallel to B C do make

Right Angles with N G; and (b) for
that cauſe are thereby cut in two equall
parts: Therefore the Axis of the Portion
of the Sphære B N C is N M; and the
Axis of the Portion B G C is M G:
from whence it followeth that the Axis of
the Portion demerged in the Liquid is
in the Line K L, namely N G. And ſince the Center of Gravity of any Portion of a Sphære is
in the Axis, as we have demonstrated in our Book De Centro Gravitatis Solidorum, the
Centre of Gravity of the Magnitude compounded of both the Portions B N C & B G C, that is,
of the Portion demerged in the Water, is in the Line N G that doth conjoyn the Centers of Gra­
vity of thoſe Portions of Sphæres. For ſuppoſe, if poſſible, that it be out of the Line N G, as
in Q, and let the Center of the Gravity of the Portion B N C, be V, and draw V que Becauſe
therefore from the Portion demerged in the Liquid the Portion of the Sphære B N C, not ha­
ving the ſame Center of Gravity, is cut off, the Center of Gravity of the Remainder of the
Portion B G C ſhall, by the 8 of the firſt Book of Archimedes, De Centro Gravitatis
1Planotum, be in the Line V Q prolonged: But that is impoſſible; for it is in the Axis
G: It followeth, therefore, that the Center of Gravity of the Portion demerged in
Liquid be in the Line N K: which we propounded to be proved.
C
(a) By 29. of the
firſt of Encl.
(b) By 3. of the
third.
But the Centre of Gravity of the whole Portion is in the Line

T, betwixt the Point R and the Point F; let us ſuppoſe it to be
the Point X.] Let the Sphære becompleated, ſo as that there be added of that Portion
the Axis T Y, and the Center of Gravity Z. And becauſe that from the whole Sphære,
whoſe Centre of Gravity is K, as we have alſo demonſtrated in the (c) Book before named, the
is cut off the Portion E Y H, having the Centre of Gravity Z; the Centre of the remaind

of the Portion E F H ſhall be in the Line Z K prolonged: And therefore it muſt of neceſſity
fall betwixt K and F.
D
(c) By 8 of the
firſt of Archimedes.
E
The remainder, therefore, of the Figure, elevated above the Sur­
face of the Liquid, hath its Center of Gravity in the Line R X
prolonged.] By the ſame 8 of the firſt Book of Archimedes, de Centro Gravita­
tis Planorum.
Now the Gravity of the Figure that is above the Liquid ſhall
preſs from above downwards according to S L; and the Gravit
of the Portion that is ſubmerged in the Liquid ſhall preſs from be
low upwards, according to the Perpendicular R L.] By the ſecond Sup­
poſition of this. For the Magnitude that is demerged in the Liquid is moved upwards with as
much Force along R L, as that which is above the Liquid is moved downwards along S L; as
may be ſhewn by Propoſition 6. of this. And becauſe they are moved along ſeverall other Lines,
neither cauſeth the others being leſs moved; the which it continually doth when the Portion
is ſet according to the Perpendicular: For then the Centers of Gravity of both the Magnitudes
do concur in one and the ſame Perpendicular, namely, in the Axis of the Portion: and look
with what force or Impetus that which is in the Lipuid tendeth upwards, and with the like
doth that which is above or without the Liquid tend downwards along the ſame Line: And

therefore, in regard that the one doth not ^{*} exceed the other, the Portion ſhall no longer move
but ſhall ſtay and reſt allwayes in one and the ſame Poſition, unleſs ſome extrinſick Cauſe
chance to intervene.
F
* Or overcome.
PROP. IX. THEOR. IX.
* In ſome Greek
Coppies this is no
diſtinct Propoſi­
tion, but all
Commentators,
do divide it
from the Prece­
dent, as having a
diſtinct demon­
ſtration in the
Originall.
^{*} But if the Figure, lighter than the Liquid, be demit­
ted into the Liquid, ſo, as that its Baſe be wholly
within the ſaid Liquid, it ſhall continue in ſuch
manner erect, as that its Axis ſhall ſtand according
to the Perpendicular.
For ſuppoſe, ſuch a Magnitude as that aforenamed to be de
mitted into the Liquid; and imagine a Plane to be produced
thorow the Axis of the Portion, and thorow the Center of the
Earth: And let the Section of the Surface of the Liquid, be the Cir­
cumference A B C D, and of the Figure the Circumference E F H
And let E H be a Right Line, and F T the Axis of the Portion. If
now it were poſſible, for ſatisfaction of the Adverſary, let it be
ſuppoſed that the ſaid Axis were not according to the Perpendicu­
lar: we are now to demonſtrate that the Figure will not ſo
1nue, but will return to be according to the
240[Figure 240]
Perpendieular. It is manifeſt that the Gen­
tre of the Sphære is in the Line F T. And
again, foraſmuch as the Portion of a Sphære
may be greater or leſſer than an Hemiſ­
phære, and may alſo be an Hemiſphære, let
the Centre of the Sphære in the Hemiſ­
phære be the Point T, & in the leſſer Por­
tion the Point P, and in the Greater the

Point R. And ſpeaking firſt of that greater
Portion which hath its Baſe within the
Liquid, thorow R and L, the Earths Cen­
241[Figure 241]
tre, draw the line RL. The Portion that is
above the Liquid, hath its Axis in the Per­
pendicular paſſing thorow R; and by
what hath been ſaid before, its Centre of
Gravity ſhall be in the Line N R; let it
be the Point R: But the Centre of Gra­
vity of the whole Portion is in the line F
T, betwixt R and F; let it be X: The re­
mainder therefore of that Figure, which is
within the Liquid ſhall have its Centre in
the Right Line R X prolonged in the part
242[Figure 242]
towards X, taken ſo, that the part pro­
longed may have the ſame Proportion to
X R, that the Gravity of the Portion that
is above the Liquid hath to the Gravity
of the Figure that is within the Liquid.
Let O be the Centre of that ſame Figure:
and thorow O draw the Perpendicular L
O. Now the Gravity of the Portion that
is above the Liquid ſhall preſs according
to the Right Line R L downwards; and
the Gravity of the Figure that is in the
Liquid according to the Right Line O L upwards: There the Figure
ſhall not continue; but the parts of it towards H ſhall move down­
wards, and thoſe towards E upwards: &
243[Figure 243]
this ſhall ever be, ſo long as F T is accord­
ing to the Perpendicular.
A
COMMANDINE.
The Portion that is above the Liquid

hath its Axis in the Perpendicular paſſing
thorow K.] For draw B C cutting the Line N K in
M; and let N K out the Circumference A B C D in G. In
the ſame manner as before me will demonſtrate, that the Axis
1of the Portion of the Sphære is N M; and of the Portion B G C the Axis is G M: Wherefore
the Centre of Gravity of them both ſhall be in the Line N M: And becauſe that from the Por­
tion B N C the Portion B G C, not having the ſame Centre of Gravity, is cut off, the Centre
of Gravity of the remainder of the Magnitude that is above the Surface of the Liquid ſhall be
in the Line N K; namely, in the Line which conjoyneth the Centres of Gravity of the ſaid
Portions by the foreſaid 8 of Archimedis de Centro Gravitatis Planorum.
A
NIC. Truth is, that in ſome of theſe Figures C is put for X, and ſo it was in
the Greek Copy that I followed.
RIC. This Demoſtration is very difficult, to my thinking; but I believe that
it is becauſe I have not in memory the Propoſitions of that Book entituled De Cen­
tris Gravium.
NIC. It is ſo.
RIC. We will take a more convenient time to diſcourſe of that, and now return

to ſpeak of the two laſt Propoſitions. And I ſay that the Figures incerted in the
demonſtration would in my opinion, have been better and more intelligble unto
me, drawing the Axis according to its proper Poſition; that is in the half Arch of
theſe Figures, and then, to ſecond the Objection of the Adverſary, to ſuppoſe
that the ſaid Figures ſtood ſomewhat Obliquely, to the end that the ſaid Axis, if it
were poſſible, did not ſtand according to the Perpendicular ſo often mentioned,
which doing, the Propoſition would be proved in the ſame manner as before:
and this way would be more naturall and clear.
A
B
NIC. You are in the right, but becauſe thus they were in the Greek Copy,
I thought not fit to alter them, although unto the better.
RIC. Companion, you have thorowly ſatisfied me in all that in the beginning
of our Diſcourſe I asked of you, to morrow, God permitting, we will treat of
ſome other ingenious Novelties.
THE TRANSLATOR.
I ſay that the Figures, &c. would have been more intelligible to

me, drawing the Axis Z T according to its proper Poſition, that
is in the half Arch of theſe Figures.] And in this conſideration I have followed
the Schemes of Commandine, who being the Reſtorer of the Demonſtrations of theſe two laſt
Propoſitions, hath well conſidered what Ricardo here propoſeth, and therefore hath drawn the
ſaid Axis (which in the Manuſcripts that he had by him is lettered F T, and not as in that of
Tartaylia Z T,) according to that its proper Poſition.
A
But becauſe thus they were in the Greek Copy, I thought not

fit to alter them although unto the better.] The Schemes of thoſe Manu-
244[Figure 244]
ſcripts that Tartaylia had ſeen were more imperfect then thoſe
in Commandines Copies; but for variety ſake, take here one
of Tartaylia, it being that of the Portion of a Sphære, equall
to an Hemiſphære, with its Axis oblique, and its Baſe dimitted
into the Liquid, and Lettered as in this Edition.
B
Now Courteous Readers, I hope that you may, amidſt the
great Obſcurity of the Originall in the Demonſtrations of theſe
two laſt Propoſitions, be able from the joynt light of theſe two Famous Commentators of our
more famous Author, to diſcern the truth of the Doctrine affirmed, namely, That Solids of the
Figure of Portions of Sphæres demitted into the Liquid with their Baſes upwards ſhall ſtand
erectly, that is, with their Axis according to the Perpendicular drawn from the Centre of the
Earth unto its Circumference: And that if the ſaid Portions be demitted with their Baſes
oblique and touching the Liquid in one Point, they ſhall not rest in that Obliquity, but ſhall
return to Rectitude: And that laſtly, if theſe Portions be demitted with their Baſes downwards,
they ſhall continue erect with their Axis according to the Perpendicular aforeſaid: ſo that no
more remains to be done, but that weſet before you the 2 Books of this our Admirable Author.
1
ARCHIMEDES,
HIS TRACT
DE
INSIDENTIBUS HUMIDO,
OR,
Of the NATATION of BODIES Upon, or
Submerſion In the WATER, or other LIQUIDS.
BOOK II.
PROP. I. THEOR. I.
If any Magnitude lighter than the Liquid be demitted
into the ſaid Liquid, it ſhall have the ſame proporti­
on in Gravity to a Liquid of equal Maſſe, that the
part of the Magnitude demerged hath unto the
whole Magnitude.
For let any Solid Magnitude, as for in­
ſtance F A, lighter than the Liquid, be de­
merged in the Liquid, which let be F A:
And let the part thereof immerged be A,
and the part above the Liquid F, It is to
be demonſtrated that the Magnitude F A
hath the ſame proportion in Gravity to a
Liquid of Equall Maſſe that A hath to F
A. Take any Liquid Magnitude, as ſup­
poſe N I, of equall Maſſe with F A; and let F be equall to N, and
A to I: and let the Gravity of the whole Magnitude F A be B, and
let that of the Magnitude N I be O,
and let that of I be R. Now the
245[Figure 245]
Magnitude F A hath the ſame pro­
portion unto N I that the Gravity B
hath to the Gravity O R: But for
aſmuch as the Magnitude F A demit­
ted into the Liquid is lighter than
the ſaid Liquid, it is manifeſt that a Maſſe of the Liquid, I, equall
to the part of the Magnitude demerged, A, hath equall Gravity

with the whole Magnitnde, F A: For this was (a) above demon­
ſtrated: But B is the Gravity of the Magnitude F A, and R of I:
1Therefore B and R are equall. And becauſe that of the Magni­
tude FA the Gravity is B: Therefore of the Liquid Body N I the
Gravity is O R. As F A is to N I, ſo is B to O R, or, ſo is R to
O R: But as R is to O R, ſo is I to N I, and A to F A: Therefore

I is to N I, as F A to N I: And as I to N I ſo is (b) A to F A.
Therefore F A is to N I, as A is to F A: Which was to be demon­
ſtrated.
(a) By 5. of the
firſt of this.
(b) By 11. of the
fifth of Eucl.
PROP. II. THEOR. II.
A
^{*} The Right Portion of a Right angled Conoide, when it
ſhall have its Axis leſſe than ſeſquialter ejus quæ ad
Axem (or of its Semi-parameter) having any what
ever proportion to the Liquid in Gravity, being de­
mitted into the Liquid ſo as that its Baſe touch not
the ſaid Liquid, and being ſet ſtooping, it ſhall not
remain ſtooping, but ſhall be restored to uprightneſſe.
I ſay that the ſaid Portion ſhall ſtand upright when
the Plane that cuts it ſhall be parallel unto the Sur­
face of the Liquid.
Let there be a Portion of a Rightangled Conoid, as hath been
ſaid; and let it lye ſtooping or inclining: It is to be demon­
ſtrated that it will not ſo continue but ſhall be reſtored to re­
ctitude. For let it be cut through the Axis by a plane erect upon
the Surface of the Liquid, and let the Section of the Portion be
A PO L, the Section of a Rightangled Cone, and let the Axis
246[Figure 246]
of the Portion and Diameter of the
Section be N O: And let the Sect­
ion of the Surface of the Liquid be
I S. If now the Portion be not
erect, then neither ſhall A L be Pa­
rallel to I S: Wherefore N O will
not be at Right Angles with I S.

Draw therefore K ω, touching the Section of the Cone I, in the
Point P [that is parallel to I S: and from the Point P unto I S

draw P F parallel unto O N, ^{*} which ſhall be the Diameter of the
Section I P O S, and the Axis of the Portion demerged in the Li­

quid. In the next place take the Centres of Gravity: ^{*} and of
the Solid Magnitude A P O L, let the Centre of Gravity be R; and

of I P O S let the Centre be B: ^{*} and draw a Line from B to R
prolonged unto G; which let be the Centre of Gravity of the
1remaining Figure I S L A. Becauſe now that N O is Seſquialter
of R O, but leſs than Seſquialter ejus quæ uſque ad Axem (or of its
Semi-parameter;) ^{*} R O ſhall be leſſe than quæ uſque ad Axem (or

than the Semi-parameter;) ^{*} whereupon the Angle R P ω ſhall be

acute. For ſince the Line quæ uſque ad Axem (or Semi-parameter)
is greater than R O, that Line which is drawn from the Point R,
and perpendicular to K ω, namely RT, meeteth with the line F P
without the Section, and for that cauſe muſt of neceſſity fall be­
tween the Points P and ω; Therefore if Lines be drawn through
B and G, parallel unto R T, they ſhall contain Right Angles with
the Surface of the Liquid: ^{*} and the part that is within the Li­

quid ſhall move upwards according to the Perpendicular that is
drawn thorow B, parallel to R T, and the part that is above the Li­
quid ſhall move downwards according to that which is drawn tho­
row G; and the Solid A P O L ſhall not abide in this Poſition; for
that the parts towards A will move upwards, and thoſe towards
B downwards; Wherefore N O ſhall be conſtituted according to
the Perpendicular.]
* Supplied by Fe­
derico Comman­
dino.
B
C
D
E
F
G
COMMANDINE.
The Demonſtration of this propoſition hath been much deſired; which we have (in like man­
ner as the 8 Prop. of the firſt Book) reſtored according to Archimedes his own Schemes, and
illustrated it with Commentaries.
The Right Portion of a Rightangled Conoid, when it ſhall

have its Axis leſſe than Seſquialter ejus quæ uſque ad Axem (or of
its Semi-parameter] In the Tranſlation of Nicolo Tartaglia it is falſlyread great­
er then Seſquialter, and ſo its rendered in the following Propoſition; but it is the Right
Portion of a Concid cut by a Plane at Right Angles, or erect, unto the Axis: and we ſay
that Conoids are then conſtituted erect when the cutting Plane, that is to ſay, the Plane of the
Baſe, ſhall be parallel to the Surface of the Liquid.
A
Which ſhall be the Diameter of the Section I P O S, and the

Axis of the Portion demerged in the Liquid.] By the 46 of the firſt of
the Conicks of Apollonious, or by the Corol­
lary of the 51 of the ſame.
B
247[Figure 247]
And of the Solid Magnitude A P

O L, let the Centre of Gravity be R;
and of I P O S let the Centre be B.]
For the Centre of Gravity of the Portion of a Right­
angled Conoid is in its Axis, which it ſo divideth
as that the part thereof terminating in the vertex,
be double to the other part terminating in the Baſe; as
in our Book De Centro Gravitatis Solidorum Propo. 29. we have demonſtrated. And
ſince the Centre of Gravity of the Portion A P O L is R, O R ſhall be double to RN and there­
fore N O ſhall be Seſquialter of O R. And for the ſame reaſon, B the Centre of Gravity of the Por­
tion I P O S is in the Axis P F, ſo dividing it as that P B is double to B F;
C
And draw a Line from B to R prolonged unto G; which let

be the Centre of Gravity of the remaining Eigure I S L A.]
1For if, the Line B R being prolonged unto G, G R hath the ſame proportion to R B as the Por­
tion of the Conoid I P O S hath to the remaining Figure that lyeth above the Surface of the
Liquid, the Toine G ſhall be its Centre of Gravity; by the 8 of the ſecond of Archimedes
de Centro Gravitatis Planorum, vel de Æquiponderantibus.
D
E
R O ſhall be leſs than quæ uſque ad Axem (or than the Semi­
parameter.] By the 10 Propofit. of Euclids fifth Book of Elements. The Line quæ
uſque ad Axem, (or the Semi-parameter) according to Archimedes, is the half of that
juxta quam poſſunt, quæ á Sectione ducuntur, (or of the Parameter;) as appeareth
by the 4 Propoſit of his Book De Conoidibus & Shpæroidibus: and for what reaſon it is
ſo called, we have declared in the Commentaries upon him by us publiſhed.
F
Whereupon the Angle R P ω ſhall be acute.] Let the Line N O be
continued out to H, that ſo RH may be equall to
the Semi-parameter. If now from the Point H
248[Figure 248]
a Line be drawn at Right Angles to N H, it ſhall
meet with FP without the Section; for being
drawn thorow O parallel to A L, it ſhall fall
without the Section, by the 17 of our ſirst Book of
Conicks; Therefore let it meet in V: and
becauſe F P is parallel to the Diameter, and H
V perpendicular to the ſame Diameter, and R H
equall to the Semi-parameter, the Line drawn
from the Point R to V ſhall make Right Angles
with that Line which the Section toucheth in the Point P: that is with K ω, as ſhall anon be
demonstrated: Wherefore the Perpendidulat R T falleth betwixt A and ω; and the Argle R
P ω ſhall be an Acute Angle.
Let A B C be the Section of a Rightangled Cone, or a Parabola,
and its Diameter B D; and let the Line E F touch the
ſame in the Point G: and in the Diameter B D take the Line
H K equall to the Semi-parameter: and thorow G, G L be­
ing drawn parallel to the Diameter, draw KM from the
Point K at Right Angles to B D cutting G L in M: I ſay
that the Line prolonged thorow Hand Mis perpendicular to
E F, which it cutteth in N.
For from the Point G draw the Line G O at Right Angles to E F cutting the Diameter in
O: and again from the ſame Point draw G P perpendicular to the Diameter: and let the
ſaid Diameter prolonged cut the Line E F in que P B ſhall be equall to B Q, by the 35 of

our firſt Book of Conick Sections, (a) and G
249[Figure 249]
P a Mean-proportion all betmixt Q P and PO;

(b) and therefore the Square of G P ſhall be e­
quall to the Rectangle of O P Q: But it is alſo
equall to the Rectangle comprehended under P B
and the Line juxta quam poſſunt, or the Par­
ameter, by the 11 of our firſt Book of Conicks:

(c) Therefore, look what proportion Q P hath to
P B, and the ſame hath the Parameter unto P O:
But Q P is double unto P B, for that P B and B
Q are equall, as hath been ſaid: And therefore
the Parameter ſhall be double to the ſaid P O:
and by the ſame Reaſon P O is equall to that which we call the Semi-parameter, that is, to K H:

But (d) P G is equall to K M, and (e) the Angle O P G to the Angle H K M; for they are both

Right Angles: And therefore O G alſo is equall to H M, and the Angle P O G unto the
1250[Figure 250]
Angle K H M: Therefore (f) O G and H N are parallel,

and the (g) Angle H N F equall to the Angle O G F; for
that G O being Perpendicular to E F, H N ſhall alſo be per-

pandicnlar to the ſame: Which was to be demon ſtrated.
(a) By Cor. of 8. of
6. of Euclide.
(b) By 17. of the
6.
(c) By 14. of the
6.
(d) By 33. of the
1.
(e) By 4. of the 1.
(f) By 28. of the
1.
(g) By 29. of th
1
And the part which is within the Liquid

doth move upwards according to the Per­
pendicular that is drawn thorow B parallel
to R T.] The reaſon why this moveth upwards, and that
other downwards, along the Perpendicular Line, hath been ſhewn above in the 8 of the firſt
Book of this; ſo that we have judged it needleſſe to repeat it either in this, or in the reſt
that follow.
G
THE TRANSLATOR.
In the Antient Parabola (namely that aſſumed in a Rightangled
Cone) the Line juxta quam Poſſunt quæ in Sectione ordinatim du­
cuntur (which I, following Mydorgius, do call the Parameter) is (a)

double to that quæ ducta eſt à Vertice Sectionis uſque ad Axem, or in
Archimedes phraſe, τᾱς υσ́χρι τοῡ ἄξον<34>; which I for that cauſe, and
for want of a better word, name the Semiparameter: but in Modern
Parabola's it is greater or leſſer then double. Now that throughout this
Book Archimedes ſpeaketh of the Parabola in a Rectangled Cone, is mani­
feſt both by the firſt words of each Propoſition, & by this that no Parabola
hath its Parameter double to the Line quæ eſt a Sectione ad Axem, ſave
that which is taken in a Rightangled Cone. And in any other Parabola, for
the Line τᾱς μσ́χριτοῡ ἄεον<34> or quæ uſque ad Axem to uſurpe the Word Se­
miparameter would be neither proper nor true: but in this caſe it may paſs
(a) Rîvalt. in Ar­
chimed. de Cunoid
& Sphæroid. Prop.
3. Lem. 1.
PROP. III. THEOR. III.
The Right Portion of a Rightangled Conoid, when it
ſhall have its Axis leſſe than ſeſquialter of the Se­
mi-parameter, the Axis having any what ever pro­
portion to the Liquid in Gravity, being demitted into
the Liquid ſo as that its Baſe be wholly within the
ſaid Liquid, and being ſet inclining, it ſhall not re­
main inclined, but ſhall be ſo reſtored, as that its Ax­
is do ſtand upright, or according to the Perpendicular.
Let any Portion be demitted into the Liquid, as was ſaid; and
let its Baſe be in the Liquid;
251[Figure 251]
and let it be cut thorow the
Axis, by a Plain erect upon the Sur­
face of the Liquid, and let the Se­
ction be A P O L, the Section of a
Right angled Cone: and let the Axis
of the Portion and Diameter of the
1Section of the Portion be A P O L, the Section of a Rightangled
Cone; and let the Axis of the Portion and Diameter of the Section
be N O, and the Section of the Surface of the Liquid I S. If now
the Portion be not erect, then N O ſhall not be at equall Angles with
I S. Draw R ω touching the Section of the Rightangled Conoid
in P, and parallel to I S: and from the Point P and parall to O N
draw P F: and take the Centers of Gravity; and of the Solid A
P O L let the Centre be R; and of that which lyeth within the
Liquid let the Centre be B; and draw a Line from B to R pro­
longing it to G, that G may be the Centre of Gravity of the Solid
that is above the Liquid. And becauſe N O is ſeſquialter of R
O, and is greater than ſeſquialter of the Semi-Parameter; it is ma­

nifeſt that (a) R O is greater than the
252[Figure 252]
Semi-parameter. ^{*}Let therefore R

H be equall to the Semi-Parameter,

^{*} and O H double to H M. Foraſ­
much therefore as N O is ſeſquialter

of R O, and M O of O H, (b) the
Remainder N M ſhall be ſeſquialter
of the Remainder R H: Therefore
the Axis is greater than ſeſquialter
of the Semi parameter by the quan­
tity of the Line M O. And let it be
ſuppoſed that the Portion hath not leſſe proportion in Gravity unto
the Liquid of equall Maſſe, than the Square that is made of the
Exceſſe by which the Axis is greater than ſeſquialter of the Semi­
parameter hath to the Square made of the Axis: It is therefore ma­
nifeſt that the Portion hath not leſſe proportion in Gravity to the
Liquid than the Square of the Line M O hath to the Square of N
O: But look what proportion the Portion hath to the Liquid in
Gravity, the ſame hath the Portion ſubmerged to the whole Solid:
for this hath been demonſtrated (c) above: ^{*}And look what pro­

portion the ſubmerged Portion hath to the whole Portion, the

ſame hath the Square of P F unto the Square of N O: For it hath
been demonſtrated in (d) Lib. de Conoidibus, that if from a Right­

angled Conoid two Portions be cut by Planes in any faſhion pro­
duced, theſe Portions ſhall have the ſame Proportion to each
other as the Squares of their Axes: The Square of P F, therefore,
hath not leſſe proportion to the Square of N O than the Square of
M O hath to the Square of N O: ^{*}Wherefore P F is not leſſe than

M O, ^{*}nor B P than H O. ^{*}If therefore, a Right Line be drawn

from H at Right Angles unto N O, it ſhall meet with B P, and ſhall

fall betwixt B and P; let it fall in T: (e) And becauſe P F is

parallel to the Diameter, and H T is perpendicular unto the ſame
Diameter, and R H equall to the Semi-parameter; a Line drawn
from R to T and prolonged, maketh Right Angles with the Line
1contingent unto the Section in the Point P: Wherefore it alſo
maketh Right Angles with the Surface of the Liquid: and that
part of the Conoidall Solid which is within the Liquid ſhall move
upwards according to the Perpendicular drawn thorow B parallel
to R T; and that part which is above the Liquid ſhall move down­
wards according to that drawn thorow G, parallel to the ſaid R T:
And thus it ſhall continue to do ſo long untill that the Conoid be
reſtored to uprightneſſe, or to ſtand according to the Perpendicular.
(a) By 10. of the
fifth.
A
B
(b) By 19. of the
fifth.
C
(c) By 1. of this
ſecond Book.
(d) By 6. De Co­
noilibus & Sphæ­
roidibus of Archi­
medes.
D
E
F
(e) By 2. of this
ſecond Book.
COMMANDINE.
A
Let therefore R H be equall to the Semi-parameter.] So it is to be
read, and not R M, as Tartaglia's Tranſlation hath is; which may be made appear from
that which followeth.
B
And O H double to H M.] In the Tranſlation aforenamed it is falſly render­
ed, O N double to R M.
C
And look what proportion the Submerged Portion hath to the whole
Portion, the ſame hath the Square of P F unto the Square of N O.]
This place we have reſtored in our Tranſlation, at the requeſt of ſome friends: But it is demon­
ſtrated by Archimedes in Libro de Conoidibus & Sphæroidibus, Propo. 26.
D
Wherefore P F is not leſſe than M O.] For by 10 of the fifth it followeth
that the Square of P F is not leſſe than the Square of M O: and therefore neither ſhall the
Line P F be leße than the Line M O, by 22 of the
253[Figure 253]

ſixth.
E
(a) By 14. of the
ſixth.
Nor B P than H O,] For as P F is to
P B, ſo is M O to H O: and, by Permutation, as

P F is to M O, ſo is B P to H O; But P F is not
leſſe than M O as hath bin proved; (a) Therefore
neither ſhall B P be leſſe than H O.
F
If therefore a Right Line be drawn
from H at Right Angles unto N O, it
ſhall meet with B P, and ſhall fall be­
twixt B and P.] This Place was corrupt in the
Tranſlation of Tartaglia: But it is thus demonstra­
ted. In regard that P F is not leſſe than O M, nor P B than O H, if we ſuppoſe P F equall to
O M, P B ſhall be likewiſe equall to O H: Wherefore the Line drawn thorow O, parallel to A L
ſhall fall without the Section, by 17 of the firſt of our Treatiſe of Conicks; And in regard that
B P prolonged doth meet it beneath P; Therefore the Perpendicular drawn thorow H doth
alſo meet with the ſame beneath B, and it doth of neceſſity fall betwixt B and P: But the
ſame is much more to follow, if we ſuppoſe P F to be greater than O M.
1
PROP. V. THEOR. V.
The Right Portion of a Right-Angled Conoid lighter
than the Liquid, when it ſhall have its Axis great­
er than Seſquialter of the Semi-parameter, if it have
not greater proportion in Gravity to the Liquid [of
equal Maſs] than the Exceſſe by which the Square
made of the Axis is greater than the Square made
of the Exceſſe by which the Axis is greater than
ſeſquialter of the Semi-Parameter hath to the
Square made of the Axis being demitted into the Li­
quid, ſo as that its Baſe be wholly within the Liquid,
and being ſet inclining, it ſhall not remain ſo inclined,
but ſhall turn about till that its Axis ſhall be accor­
ding to the Perpendicular.
For let any Portion be demitted into the Liquid, as hath been
ſaid; and let its Baſe be wholly within the Liquid, And being
cut thorow its Axis by a Plain erect upon the Surface of the
Liquid; its Section ſhall be the Section
254[Figure 254]
of a Rightangled Cone: Let it be
A P O L, and let the Axis of the Por­
tion and Diameter of the Section be
N O; and the Section of the Surface of
the Liquid I S. And becauſe the Axis
is not according to the Perpendicu­
lar, N O will not be at equall angles
with I S. Draw K ω touching the Se­
ction A P O L in P, and parallel unto
I S: and thorow P, draw P F parallel unto N O: and take the
Centres of Gravity; and of the Solid A P O L let the Centre be
R; and of that which lyeth above the Liquid let the Centre be B;
and draw a Line from B to R, prolonging it to G; which let be the
Centre of Gravity of the Solid demerged within the Liquid: and
moreover, take R H equall to the Semi-parameter, and let O H be
double to H M; and do in the reſt as hath been ſaid (a) above.

Now foraſmuch as it was ſuppoſed that the Portion hath not greater
proportion in Gravity to the Liquid, than the Exceſſe by which
the Square N O is greater than the Square M O, hath to the ſaid
Square N O: And in regard that whatever proportion in Gravity
1the Portion hath to the Liquid of equall Maſſe, the ſame hath the
Magnitude of the Portion ſubmerged unto the whole Portion; as
hath been demonſtrated in the firſt Propoſition; The Magnitude
ſubmerged, therefore, ſhall not have greater proportion to the

whole (b) Portion, than that which hath been mentioned: ^{*}And
therefore the whole Portion hath not greater proportion unto that

which is above the Liquid, than the Square N O hath to the Square

M O: But the (c) whole Portion hath the ſame proportion unto
that which is above the Liquid that the Square N O hath to the
Square P F: Therefore the Square N O hath not greater propor­

tion unto the Square P F, than it hath unto the Square M O: ^{*}And
hence it followeth that P F is not leſſe than O M, nor P B than O

H: ^{*} A Line, therefore, drawn from H at Right Angles unto N O
ſhall meet with B P betwixt P and B: Let it be in T: And be­
cauſe that in the Section of the Rectangled Cone P F is parallel unto
the Diameter N O; and H T perpendicular unto the ſaid Diame­
ter; and R H equall to the Semi-parameter: It is manifeſt that
R T prolonged doth make Right Angles with K P ω: And there­
fore doth alſo make Right Angles with I S: Therefore R T is per­
pendicular unto the Surface of the Liquid; And if thorow the
Points B and G Lines be drawn parallel unto R T, they ſhall be
perpendicular unto the Liquids Surface. The Portion, therefore,
which is above the Liquid ſhall move downwards in the Liquid ac­
cording to the Perpendicular drawn thorow B; and that part
which is within the Liquid ſhall move upwards according to the
Perpendicular drawn thorow G; and the Solid Portion A P O L
ſhall not continue ſo inclined, [as it was at its demerſion], but ſhall
move within the Liquid untill ſuch time that N O do ſtand accor­
ding to the Perpendicular.
(a) In 4. Prop. of
this.
(a) By 11. of the
fifth.
A
(b) By 26. of the
Book De Conoid.
& Sphæroid.
B
C
COMMANDINE.
A
And therefore the whole Portion hath not greater proportion
unto that which is above the Liquid, than the Square N O hath to
the Square M O.] For in regard that the Magnitude of the Portion demerged
within the Liquid hath not greater proportion unto the whole Portion than the Exceſſe by which
the Square N O is greater than the Square M O hath to the ſaid Square N O; Converting of
the Proportion, by the 26. of the fifth of Euclid, of Campanus his Tranſlation, the whole
Portion ſhall not have leſſer proportion unto the Magnitude ſubmerged, than the Square N O
hath unto the Exceſſe by which N O is greater than the Square M O. Let a Portion be taken;
and let that part of it which is above the Liquid be the firſt Magnitude; the part of it which
is ſubmerged the ſecond: and let the third Magnitude be the Square M O; and let the Exceſſe
by which the Square N O is greater than the Square M O be the fourth. Now of theſe Mag­
nitudes, the proportion of the firſt and ſecond, unto the ſecond, is not leſſe than that of the third &
fourth unto the fourth: For the Square M O together with the Exceſſe by which the Square
N O exceedeth the Square M O is equall unto the ſaid Square N O: Wherefore, by Converſi­
on of Proportion, by 30 of the ſaid fifth Book, the proportion of the firſt and ſecond unto the
firſt, ſhall not be greater than that of the third and fourth unto the third: And, for the ſame
1the proportion of the whole Portion unto that part thereof which is above the Liquid ſhall not be
greater than that of the Square N O unto the Square M O: Which was to be demonſtrated.
And hence it followeth that P F is not leſſe than O M, nor P B

than O H.] This followeth by the 10 and 14 of the fifth, and by the 22 of the ſixth of
Euclid, as hath been ſaid above.
B
A Line, therefore, drawn from Hat Right Angles unto N O ſhall

meet with P B betwixt P and B.] Why this ſo falleth out, we will ſhew in the
next.
C
PROP. VI. THEOR. VI.
The Right Portion of a Rightangled Conoid lighter
than the Liquid, when it ſhall have its Axis greater
than ſeſquialter of the Semi-parameter, but leſſe than
to be unto the Semi-parameter in proportion as fifteen
to fower, being demitted into the Liquid ſo as that
its Baſe do touch the Liquid, it ſhall never stand ſo
enclined as that its Baſe toucheth the Liquid in one
Point only.
Let there be a Portion, as was ſaid; and demit it into the Li­
quid in ſuch faſhion as that its Baſe do touch the Liquid in
one only Point: It is to be demonſtrated that the ſaid Portion

ſhall not continue ſo, but ſhall turn about in ſuch manner as that
its Baſe do in no wiſe touch the Surface of the Liquid. For let it be
cut thorow its Axis by a Plane erect
255[Figure 255]
upon the Liquids Surface: and let
the Section of the Superficies of the
Portion be A P O L, the Section of
a Rightangled Cone; and the Sect­
ion of the Surface of the Liquid be
A S; and the Axis of the Portion
and Diameter of the Section N O:
and let it be cut in F, ſo as that O
F be double to F N; and in ω ſo, as that N O may be to F ω in the
ſame proportion as fifteen to four; and at Right Angles to N O
draw ω Now becauſe N O hath greater proportion unto F ω than
unto the Semi-parameter, let the Semi-parameter be equall to F B:

and draw P C parallel unto A S, and touching the Section A P O L
in P; and P I parallel unto N O; and firſt let P I cut Kω in H. For­

aſmuch, therefore, as in the Portion A P O L, contained betwixt
the Right Line and the Section of the Rightangled Cone, K ω is
parallel to A L, and P I parallel unto the Diameter, and cut by the
1ſaid K ω in H, and A S is parallel unto the Line that toucheth in
P; It is neceſſary that P I hath unto P H either the ſame proportion
that N ω hath to ω O, or greater; for this hath already been de­
monſtrated: But N ω is ſeſquialter of ω O; and P I, therefore, is
either Seſquialter of H P, or more than ſeſquialter: Wherefore

P H is to H I either double, or leſſe than double. Let P T be
double to T I: the Centre of Gravity of the part which is within
the Liquid ſhall be the Point T. Therefore draw a Line from T
to F prolonging it; and let the Centre of
256[Figure 256]
Gravity of the part which is above the Liquid
be G: and from the Point B at Right Angles
unto N O draw B R. And ſeeing that P I is
parallel unto the Diameter N O, and B R
perpendicular unto the ſaid Diameter, and F
B equall to the Semi-parameter; It is mani­
feſt that the Line drawn thorow the Points
F and R being prolonged, maketh equall
Angles with that which toucheth the Section
A P O L in the Point P: and therefore doth alſo make Right An­
gles with A S, and with the Surface of the Liquid: and the Lines
drawn thorow T and G parallel unto F R ſhall be alſo perpendicu­
lar to the Surface of the Liquid: and of the Solid Magnitude A P
O L, the part which is within the Liquid moveth upwards according
to the Perpendicular drawn thorow T; and the part which is above
the Liquid moveth downwards according to that drawn thorow G:

The Solid A P O L, therefore, ſhall turn about, and its Baſe ſhall
not in the leaſt touch the Surface of the Liquid, And if P I do not
cut the Line K ω, as in the ſecond Figure, it is manifeſt that the
Point T, which is the Centre of Gravity of the ſubmerged Portion,
falleth betwixt P and I: And for the other particulars remaining,
they are demonſtrated like as before.
A
B
C
D
E
COMMANDINE.
A
It is to be demonſtrated that the ſaid Portion ſhall not continue
ſo, but ſhall turn about in ſuch manner as that its Baſe do in no wiſe
touch the Surface of the Liquid.] Theſe words are added by us, as having been
omitted by Tartaglia.
Now becauſe N O hath greater proportion to F ω than unto

the Semi parameter.] For the Diameter of the Portion N O hath unto F ω the
ſame proportion as fifteen to fower: But it was ſuppoſed to have leſſe proportion unto the
Semi-parameter than fifteen to fower: Wherefore N O hath greater proportion unto F ω
than unto the Semi-parameter: And therefore (a) the Semi-parameter ſhall be greater

than the ſaid F ω.
B
(a) By 10. of the
fifth.
Foraſmuch, therefore, as in the Portion A P O L, contained, be­

twixt the Right Line and the Section of the Rightangled Cone K
ω is parallel to A L, and P I parallel unto the Diameter, and cut by
1the ſaid K ω in H, and A S is parallel unto the Line that toucheth
in P; It is neceſſary that P I hath unto P H either the ſame propor­
tion that N ω hath to ω O, or greater; for this hath already been
demonſtrated.] Where this is demonſtrated either by Archimedes himſelf, or by
any other, doth not appear; touching which we will here inſert a Demonſtration, after that
we have explained ſome things that pertaine thereto.
C
LEMMA I.
Let the Lines A B and A C contain the Angle B A C; and from
the point D, taken in the Line A C, draw D E and D F at
pleaſure unto A B: and in the ſame Line any Points G and L
being taken, draw G H & L M parallel to D E, & G K and
L N parallel unto F D: Then from the Points D & G as farre
as to the Line M L draw D O P, cutting G H in O, and G Q
parallel unto B A. I ſay that the Lines that lye betwixt the Pa­
rallels unto F D have unto thoſe that lye betwixt the Par­
allels unto D E (namely K N to G Q or to O P; F K to D O;
and F N to D P) the ſame mutuall proportion: that is to ſay,
the ſame that A F hath to A E.
For in regard that the Triangles A F D, A K G, and A N L
257[Figure 257]
are alike, and E F D, H K G, and M N L are alſo alike: There-

fore, (a) as A F is to F D, ſo ſhall A K be to K G; and as F D is to
F E, ſo ſhall K G be to K H: Wherefore, ex equali, as A F is to F
E, ſo ſhall A K be to K H: And, by Converſion of proportion, as
A F is to A E, ſo ſhall A K be to K H. It is in the ſame manner
proved that, as A F is to A E, ſo ſhall A N be to A M. Now A

N being to A M, as A K is to A H; The (b) Remainder K N ſhall
be unto the Remainder H M, that is unto G Q, or unto O P, as
A N is to A M; that is, as A F is to A E: Again, A K is to
A H, as A F is to A E; Therefore the Remainder F K ſhall be to
the Remainder E H, namely to D O, as A F is to A E. We might in
like manner demonstrate that ſo is F N to D P: Which is that that
was required to be demonstrated.
(a) By 4. of the
ſixth.
(b) By 5. of the
fifth.
LEMMA II.
In the ſame Line A B let there be two Points R and S, ſo diſpo­
ſed, that A S may have the ſame Proportion to A R that
A F hath to A E; and thorow R draw R T parallel to E D,
and thorow S draw S T parallel to F D, ſo, as that it may
meet with R T in the Point T. I ſay that the Point T fall­
eth in the Line A C.
1258[Figure 258]
For if it be poſſible, let it fall ſhort of it: and let R T be pro­
longed as farre as to A C in V: and then thorow V draw V X pa­
rallel to F D. Now, by the thing we have last demonſtrated, A X
ſhall have the ſame proportion unto A R, as A F hath to A E.
But A S hath alſo the ſame proportion to A R: Wherefore (a)

A S is equall to A X, the part to the whole, which is impoſſi­
ble. The ſame abſurdity will follow if we ſuppoſe the Toint
T to fall beyond the Line A C: It is therefore neceſſary that
it do fall in the ſaid A C. Which we propounded to be demonstrated.
(a) By 9. of the
fifth.
LEMMA III.
Let there be a Parabola, whoſe Diameter

let be A B; and let the Right Lines A C and B D be ^{*} con­
tingent to it, A C in the Point C, and B D in B: And two
Lines being drawn thorow C, the one C E, parallel unto
the Diameter; the other C F, parallel to B D; take any
Point in the Diameter, as G; and as F B is to B G, ſo let B
G be to B H: and thorow G and H draw G K L, and H E
M, parallel unto B D; and thorow M draw M N O parallel
to A C, and cutting the Diameter in O: and the Line N P
being drawn thorow N unto the Diameter let it be parallel
to B D. I ſay that H O is double to G B.
* Or touch it.
For the Line M N O cutteth the Diameter either in G, or in other Points: and if it do
cut it in G, one and the ſame Point ſhall be noted by the two letters G and O. Therfore F C,
P N, and H E M being Parallels, and A C being Parallels to M N O, they ſhall make the
259[Figure 259]
Triangles A F C, O P N and O H M like to

each other: Wherefore (a) O H ſhall be to
H M, as A F to FC: and ^{*} Permutando,

O H ſhall be to A F, as H M to F C: But
the Square H M is to the Square G L as the Line
H B is to the Line B G, by 20. of our firſt Book
of Conicks; and the Square G L is unto the
Square F C, as the Line G B is to the Line B F:
and the Lines H B, B G and B F are thereupon

Proportionals: Therefore the (b) Squares
H M, G L and F C and there Sides, ſhall alſo be
Proportionals: And, therefore, as the (c)
Square H M is to the Square G L, ſo is the Line

H M to the Line F C: But as H M is to F C, ſo
is O H to A F; and as the Square H M is to
the Square G L, ſo is the Line H B to B G; that
is, B G to B F: From whence it followeth that
O H is to A F, as B G to B F: And Permu­
tando, O H is to B G, as A F to F B; But A F is double to F B: Therefore A B and B F
are equall, by 35. of our firſt Book of Conicks: And therefore N O is double to G B:
Which was to be demonſtrated.
1
(a) By 4. of the
ſixth.
* Or permitting.
(b) By 22. of the
ſixth.
(c) By Cor. of 20.
of the ſixth.
LEMMA IV.
The ſame things aſſumed again, and M Q being drawn from the
Point M unto the Diameter, let it touch the Section in the
Point M. I ſay that H Q hath to Q O, the ſame proportion
that G H hath to C N.
For make H R equall to G F; and ſeeing that
260[Figure 260]
the Triangles A F C and O P N are alike, and
P N equall to F C, we might in like manner de­
monſtrate P O and F A to be equall to each other:
Wherefore P O ſhall be double to F B: But H O
is double to G B: Therefore the Remainder P H
is alſo double to the Remainder F G; that is, to
R H: And therefore is followeth that P R, R H
and F G are equall to one another; as alſo that
R G and P F are equall: For P G is common to
both R P and G F. Since therefore, that H B is
to B G, as G B is to B F, by Converſion of Pro­
portion, B H ſhall be to H G, as B G is to G F:
But Q H is to H B, as H O to B G. For by 35
of our firſt Book of Conicks, in regard that Q
M toucheth the Section in the Point M, H B and
B Q ſhall be equall, and Q H double to H B:
Therefore, ex æquali, Q H ſhall be to H G, as
H O to G F; that is, to H R: and, Permu­
tando, Q H ſhall be to H O, as H G to H R: again, by Converſion, H Q ſhall be to Q
O, as H G to G R; that is, to P F; and, by the ſame reaſon, to C N: Whichwas to be de­
monſtrated.
Theſe things therefore being explained, we come now to that
which was propounded. I ſay, therefore, firſt that N C hath
to C K the ſame proportion that H G hath to G B.
For ſince that H Q is to Q O, as H G to C N;
261[Figure 261]
that is, to A O, equall to the ſaid C N: The Re­
mainder G Q ſhall be to the Remainder Q A, as
H Q to Q O: and, for the ſame cauſe, the Lines
A C and G L prolonged, by the things that wee
have above demonstrated, ſhall interſect or meet
in the Line Q M. Again, G Q is to Q A,
as H Q to Q O: that is, as H G to F P; as

(a) was bnt now demonstrated, But unto (b) G

Q two Lines taken together, Q B that is H B, and
B G are equall: and to Q A H F is equall; for
if from the equall Magnitudes H B and B Q there
be taken the equall Magnitudes F B and B A, the
Re mainder ſhall be equall; Therefore taking H
G from the two Lines H B and B G, there ſhall re­
main a Magnitude double to B G; that is, O H:
and P F taken from F H, the Remainder is H P:
Wherefore (c) O H is to H P, as G Q to Q A:

But as G Q is to Q A, ſo is H Q to Q O;
1
that is, H G to N C: and as (d) O H is to H P, ſo is G B to C K; For O H is double
to G B, and H P alſo double to G F; that is, to C K; Therefore H G hath the ſame propor­
tion to N C, that G B hath to C K: And Permutando, N C hath to C K the ſame proportion
that H G hath to G B.
(a) By 2. Lemma.
(b) By 4. Lemma.
(b) By 19. of the
fifth.
(d) By 15. of the
fifth.
Then take ſome other Point at pleaſure in the Section, which
let be S: and thorow S draw two Lines, the one S T paral­
lel to D B, and cutting the Diameter in the Point T; the
other S V parallel to A C, and cutting C E in V. I ſay
that V C hath greater proportion to C K, than T G hath
to G B.
For prolong V S unto the Line Q M in X; and from the Point X draw X Y unto the
Diameter parallel to B D: G T ſhall be leſſe than G Y, in regard that V S is leße than V X:
And, by the firſt Lemma, Y G ſhall be to V C, as H G to N C; that is, as G B to C K, which
was demonſtrated but now: And, Permutando, Y G ſhall be to G B, as V C to C K: But
T G, for that it is leſſe than Y G, hath leſſe proportion to G B, than Y G hath to the ſame;
Therefore V C hath greater proportion to C K. than T G hath to G B: Which was to be de­
monſtrated. Therefore a Poſition given G K, there ſhall be in the Section one only Point, to
wit M, from which two Lines M E H and M N O being drawn, N C ſhall have the ſame pro­
portion to C K, that H G hath to G B; For if they be drawn from any other, that which fall­
eth betwixt A C, and the Line parallel unto it ſhall alwayes have greater proportion to C K,
than that which falleth betwixt G K and the Line parallel unto it hath to G B. That, there­
fore, is manifeſt which was affirmed by Archimedes, to wit, that the Line P I hath unto P H,
either the ſame proportion that N ω hath to ω O, or greater.
D
Wherefore P H is to H I either double, or leſſe than double.]
If leſſe than double, let P T be double to T I: The Centre of Gravity of that part of the
Portion that is within the Liquid ſhall be the
262[Figure 262]
Point T: But if P H be double to H I, H ſhall
be the Centre of Gravity; And draw H F, and
prolong it unto the Centre of that part of the Por­
tion which is above the Liquid, namely, unto G,
and the reſt is demonſtrated as before. And the
ſame is to be underſtood in the Propoſition that
followeth.
The Solid A P O L, therefore,
ſhall turn about, and its Baſe ſhall
not in the leaſt touch the Surface
of the Liquid.] In Tartaglia's Tranſlation it is rendered ut Baſis ipſius non tangent
ſuperficiem humidi ſecundum unum ſignum; but we have choſen to read ut Baſis ipſius
nullo modo humidi ſuperficiem contingent, both here, and in the following Propoſitions,
becauſe the Greekes frequently uſe ὡδὲεἶς, ὡδὲ pro ὠδεὶσ & οὐδὶν: ſo that οὐδἔσινουδείς, nullus
eſt; οὐδὑπ̓ἑρὸς à nullo, and ſo of others of the like nature.
1
PROP. VII. THE OR. VII.
The Right Portion of a Rightangled Conoid lighter
than the Liquid, when it ſhall have its Axis greater
than Seſquialter of the Semi-parameter, but leſſe
than to be unto the ſaid Semi-parameter in proportion
as fiſteen to fower, being demitted into the Liquid ſo
as that its Baſe be wholly within the Liquid, it ſhall
never ſtand ſo as that its Baſe do touch the Surface
of the Liquid, but ſo, that it be wholly within the
Liquid, and ſhall not in the leaſt touch its Surface.
Let there be a Portion as hath been ſaid; and let it be de­
mitted into the Liquid, as we have ſuppoſed, ſo as that its
Baſe do touch the Surface in one Point only: It is to be de­
monſtrated that the ſame ſhall not ſo
263[Figure 263]
continue, but ſhall turn about in
ſuch manner as that its Baſe do in no
wiſe touch the Surface of the Liquid.
For let it be cut thorow its Axis by
a Plane erect upon the Liquids Sur­
face: and let the Section be A P O L,
the Section of a Rightangled
Cone; the Section of the Liquids
Surface S L; and the Axis of the
Portion and Diameter of the Section P F: and let P F be cut in
R, ſo, as that R P may be double to R F, and in ω ſo as that P F
may be to R ω as fifteen to fower: and draw ω K at Right Angles

to P F: (a) R ω ſhall be leſſe than the Semi-parameter. There­
fore let R H be ſuppoſed equall to the Semi-parameter: and
draw C O touching the Section in O and parallel unto S L; and
let N O be parallel unto P F; and firſt let N O cut K ω in the Point
I, as in the former Schemes: It ſhall be demonſtrated that N O is
to O I either ſeſquialter, or greater than ſeſquialter. Let O I be
leſſe than double to I N; and let O B be double to B N: and let
them be diſpoſed like as before. We might likewiſe demonſtrate
that if a Line be drawn thorow R and T it will make Right Angles
with the Line C O, and with the Surface of the Liquid: Where­
fore Lines being drawn from the Points B and G parallels unto
R T, they alſo ſhall be Perpendiculars to the Surface of the Liquid:
The Portion therefore which is above the Liquid ſhall move
1264[Figure 264]
wards according to that ſame Perpendicular
which paſſeth thorow B; and the Portion
which is within the Liquid ſhall move up­
wards acording to that paſſing thorow G:
From whence it is manifeſt that the Solid
ſhall turn about in ſuch manner, as that
its Baſe ſhall in no wiſe touch the Surface
of the Liquid; for that now when it touch­
eth but in one Point only, it moveth down­
wards on the part towards L. And though
N O ſhould not cut ω K, yet ſhall the ſame hold true.
(a) By 10 of the
fifth.
PROP. VIII. THE OR. VIII.
The Right Portion of a Rightangled Conoid, when it
ſhall have its Axis greater than ſeſquialter of the Se­
mi-parameter, but leſſe than to be unto the ſaid Semi­
parameter, in proportion as fifteen to fower, if it
have a leſſer proportion in Gravity to the Liquid, than
the Square made of the Exceſſe by which the Axis is
greater than Seſquialter of the Semi-parameter hath
to the Square made of the Axis, being demitted into
the Liquid, ſo as that its Baſe touch not the Liquid,
it ſhall neither return to Perpendicularity, nor conti­
nue inclined, ſave only when the Axis makes an
Angle with the Surface of the Liquid, equall to that
which we ſhall preſently ſpeak of.
Let there be a Portion as hath been ſaid; and let B D be equall
to the Axis: and let B K be double to K D; and R K equall

to the Semi-parameter: and let C B be Seſquialter of B R:
C D ſhall be alſo Sefquialter of K R. And as the Portion is to the
Liquid in Gravity, ſo let the Square F Q be to the Square D B;
and let F be double to Q: It is manifeſt, therefore, that F Q hath
to D B, leſs proportion than C B hath to B D; For C B is the
Exceſs by which the Axis is greater than Seſquialter of the Semi­

parameter: And, therefore, F Q is leſs than B C; and, for the

ſame reaſon, F is leſs than B R. Let R ψ be equall to F; and draw
ψ E perpendicular to B D; which let be in power or contence the
half of that which the Lines K R and ψ B containeth; and
draw a Line from B to E: It is to be demonſtrated, that the
1Portion demitted into the Liquid, like as hath been ſaid, ſhall ſtand
enclined ſo as that its Axis do make an Angle with the Surface of
the Liquid equall unto the Angle E B Ψ. For demit any Portion
into the Liquid ſo as that its Baſe
265[Figure 265]
touch not the Liquids Surface;
and, if it can be done, let the
Axis not make an Angle with the
Liquids Surface equall to the
Angle E B Ψ; but firſt, let it be
greater: and the Portion being
cut thorow the Axis by a Plane e­
rect unto [or upon] the Surface of
the Liquid, let the Section be A P
O L the Section of a Rightangled
Cone; the Section of the Surface of the Liquid X S; and let the
Axis of the Portion and Diameter of the Section be N O: and
draw P Y parallel to X S, and touching the Section A P O L in P;
and P M parallel to N O; and P I perpendicular to N O: and
moreover, let B R be equall to O ω, and R K to T ω; and let ω H
be perpendicular to the Axis. Now becauſe it hath been ſuppoſed

that the Axis of the Portion doth make an Angle with the Surface
of the Liquid greater than the Angle B, the Angle P Y I ſhall be
greater than the Angle B: Therefore the Square P I hath greater

proportion to the Square Y I, than the Square E Ψ hath to the
Square Ψ B: But as the Square P I is to the Square Y I, ſo is the

Line K R unto the Line I Y; and as the Square E Ψ is to the Square

Ψ B, ſo is half of the Line K R unto the Line Ψ B: Wherefore
(a) K R hath greater proportion to I Y, than the half of K R hath

to Ψ B: And, conſequently, I Y isleſſe than the double of Ψ B,
and is the double of O I: Therefore O I is leſſe than Ψ B; and I ω

greater than Ψ R: but Ψ R is equall to F: Therefore I ω is greater

than F. And becauſe that the Portion is ſuppoſed to be in Gra­
vity unto the Liquid, as the Square F Q is to the Square B D; and
ſince that as the Portion is to the Liquid in Gravity, ſo is the part
thereof ſubmerged unto the whole Portion; and in regard that as
the part thereof ſubmerged is to the whole, ſo is the Square P M to
the Square O N; It followeth, that the Square P M is to the Square
N O, as the Square F Q is to the Square B D: And therefore F

Q is equall to P M: But it hath been demonſtrated that P H is

greater than F: It is manifeſt, therefore, that P M is leſſe than
ſeſquialter of P H: And conſequently that P H is greater than
the double of H M. Let P Z be double to Z M: T ſhall be the Cen­
tre of Gravity of the whole Solid; the Centre of that part of it
which is within the Liquid, the Point Z; and of the remaining

part the Centre ſhall be in the Line Z T prolonged unto G. In
1the ſame manner we might demon­
266[Figure 266]
ſtrate the Line T H to be perpendi­
cular unto the Surface of the Liquid:
and that the Portion demerged with­
in the Liquid moveth or aſcend­
eth out of the Liquid according to
the Perpendicular that ſhall be
drawn thorow Z unto the Surface
of the Liquid; and that the part
that is above the Liquid deſcendeth
into the Liquid according to that
drawn thorow G: therefore the Portion will not continue ſo inclined
as was ſuppoſed: But neither ſhall it return to Rectitude or Per­
pendicularity; For that of the Perpendiculars drawn thorow Z and
G, that paſſing thorow Z doth fall on thoſe parts which are to­
wards L; and that that paſſeth thorow G on thoſe towards A:
Wherefore it followeth that the Centre Z do move upwards,
and G downwards: Therefore the parts of the whole Solid which
are towards A ſhall move downwards, and thoſe towards L up­
wards. Again let the Propoſition run in other termes; and let
the Axis of the Portion make an Angle with the Surface of the

Liquid leſſe than that which is at B. Therefore the Square P I
hath leſſer Proportion unto the Square
267[Figure 267]
I Y, than the Square E Ψ hath to the
Square Ψ B: Wherefore K R hath
leſſer proportion to I Y, than the half
of K R hath to Ψ B: And, for the
ſame reaſon, I Y is greater than dou­
ble of Ψ B: but it is double of O I:
Therefore O I ſhall be greater than
Ψ B: But the Totall O ω is equall
to R B, and the Remainder ω I leſſe
than ψ R: Wherefore P H ſhall alſo
be leſſe than F. And, in regard that
M P is equall to F Q, it is manifeſt that P M is greater than ſeſqui­
alter of P H; and that P H is leſſe than double of H M. Let P Z
be double to Z M. The Centre of Gravity of the whole Solid ſhall
again be T; that of the part which is within the Liquid Z; and
drawing a Line from Z to T, the Centre of Gravity of that which
is above the Liquid ſhall be found in that Line portracted, that is
in G: Therefore, Perpendiculars being drawn thorow Z and G

unto the Surface of the Liquid that are parallel to T H, it followeth
that the ſaid Portion ſhall not ſtay, but ſhall turn about till
that its Axis do make an Angle with the Waters Surface greater than
that which it now maketh. And becauſe that when before we
1did ſuppoſe that it made an Angle greater than the Angle B, the
Poriton did not reſt then neither; It is manifeſt that it ſhall ſtay

or reſt when it ſhall make an Angle eqnall to B. For ſo ſhall I O
be equall to Ψ B; and ω I equall to
268[Figure 268]
Ψ R; and P H equall to F: There­
fore M P ſhall be ſeſquialter of P H,
and P H double of H M: And there­
fore ſince H is the Centre of Gravity
of that part of it which is within the
Liquid, it ſhall move upwards along
the ſame Perpendicular according to
which the whole Portion moveth;
and along the ſame alſo ſhall the part
which is above move downwards:
The Portion therefore ſhall reſt; for­
aſmuch as the parts are not repulſed by each other.
A
B
C
D
E
F
G
(a) By 13. of the
fifth.
H
K
L
M
N
O
P
Q
COMMANDINE.
And let C B be ſeſquialter of B R: C D ſhall alſo be ſeſquialter

of K R.] In the Tranſlation it is read thus: Sit autem & CB quidem hemeolia
ipſius B R: C D autem ipſius K R. But we at the reading of this paſſage have thought
fit thus to correctit; for it is not ſuppoſed ſo to be, but from the things ſuppoſed is proved to
be ſo. For if B ψ be double of ψ D, D B ſhall be ſeſquialter of B ψ. And becauſe E B is
ſeſquialter of B R, it followeth that the (a) Remainder C D is ſeſquialter of ψ R; that is, of

the Semi-parameter: Wherefore B C ſhall be the Exceſſe by which the Axis is greater than
ſeſquialter of the Semi-parameter.
A
(a) By 19. of the
fifth.
And therefore F Q is leſſe than B C.] For in regard that the Portion hath

the ſame proportion in Gravity unto the Liquid, as the Square F Q hath to the Square D B;
and hath leſſer proportion than the Square made of the Exceſſe by which the Axis
is greater than Seſquialter of the Semi parameter, hath to the Square made of the Axis; that
is, leßer than the Square C B hath to the Square B D; for the Line B D was ſuppoſed to be
equall unto the Axis: Therefore the Square F Q ſhall have to the Square D B leſſer proporti­
on than the Sqnare C B to the ſame Square B D: And therefore the Square (b) F Q ſhall be

leße than the Square C B: And, for that reaſon, the Line F Q ſhall be leße than B C.
B
(b) By 8 of the
fifth.
And, for the ſame reaſon, F is leſſe than B R.] For C B being ſeſqui-

alter of B R, and F Q ſeſquialter of F: (c) F Q ſhall be likewiſe leſſe than B C; and F

leße than B R.
C
(c) By 14 of the
fifth.
Now becauſe it hath been ſuppoſed that the Axis of the Portion

doth make an Angle with the Surface of the Liquid greater than
the Angle B, the Angle P Y I ſhall be greater than the Angle B.]
For the Line P Y being parallel to the Surface of the Liquid, that is, to XS; (d) the Angle

P Y I ſhall be equall to the Angle contained betwixt the Diameter of the Portion N O, and the
Line X S: And therefore ſhall be greater than the Angle B.
D
(d) By 29 of the
firſt.
Therefore the Square P I hath greater proportion to the Square

Y I, than the Square E Ψ hath to the Square Ψ B] Let the Triangles P I Y
and E ψ B, be deſcribed apart: And ſeeing that the Angle P Y I is greater
than the Angle E B ψ, unto the Line I Y, and at the Point Y aſſigned in
269[Figure 269]
the ſame, make the Angle V Y I equall to the Angle E B ψ; But
the Right Angle at I, is equall unto the Right Angle at ψ; therefore the
1Remaining Angle Y V I is equall to the Remaining Angle B E ψ. And therefore the

(e) Line V I hath to the Line I Y the ſame proportion that the Line E ψ hath to ψ B: But
the (f) Line P I, which is greater than V I, hath unto I Y greater proportion than V I hath un-

to the ſame: Therefore (g) T I ſhall have greater proportion unto I Y, than E ψ hath to ψ B:
And, by the ſame reaſon, the Square T I ſhall have greater proportion to the Square I Y, than

the Square E ψ hath to the Square ψ B.
E
(e) By 4. of the
ſixth.
(f) By 8. of the
fifth.
(g) By 13 of the
fifth.
F
But as the Square P I is to the Square Y I, ſo is the Line K R unto
the Line I Y] For by 11. of the firſt of our Conicks, the Square P I is equall
to the Rectangle contained under the Line I O, and under the Parameter; which
we ſuppoſed to be eqnall to the Semi-parameter; that is, the double of K R:

But I Y is double of I O, by 33 of the ſame: And, therefore, the (h) Rectangle made of K R
and I Y, is equall to the Rectangle contained under the Line I O, and under the Parameter;

that is, to the Square P I: But as the (i) Rectangle compounded of K R and I Y is to the
Square I Y, ſo is the Line K R unto the Line I Y: Therefore the Line K R ſhall have unto I
Y, the ſame proportion that the Rectangle compounded of K R and I Y; that is, the Square P I
hath to the Square I Y.
(h) By 26. of the
ſixth.
(i) By Lem. 22 of
the tenth.
G
And as the Square E Ψ is to the Square Ψ B, ſo is half of the
Line K R unto the Line ψ B.] For the Square E ψ having been ſuppoſed equall
to half the Rectangle contained under the Line K R and ψ B; that is, to that contained under
the half of K R and the Line ψ B; and ſeeing that as the (k) Rectangle made of half K R

and of B ψ is to the Square ψ B, ſo is half K R unto the Line ψ B; the half of K R ſhall have
the ſame proportion to ψ B, as the Square E ψ hath to the Square ψ B.
(k) By Lem. 22 of
the tenth.
H
And, conſequently, I Y is leſſe than the double of ψ B.]
For, as half K R is to ψ B, ſo is K R to another Line: it ſhall be (1) greater than I Y; that

is, than that to which K R hath leſſer proportion; and it ſhall be double of ψ B: Therefore
I Y is leſſe than the double of ψ B.
(l) By 10 of the
fifth.
K
And I ω greater than ψ R.] For O having been ſuppoſed equall to B R,
if from B R, ψ B be taken, and from O ω, O I, which is leſſer than B, be taken; the
Remainder I ω ſhall be greater than the Remainder Ψ R.
L
And, therefore, F Q is equall to P M.] By the fourteenth of the fifth of
Euclids Elements: For the Line O N is equall to B D.
M
But it hath been demonſtrated that P H is greater than F.]
For it was demonſtrated that I ω is greater than F: And P H is equall to I ω.
N
In the ſame manner we might demonſtrate the Line T H
to be Perpendicular unto the Surface of the Liquid.] For T α is equall
to K R; that is, to the Semi-parameter: And, therefore, by the things above demonstrated,
the Line T H ſhall be drawn Perpendicular unto the Liquids Surface.
O
Therefore, the Square P I hath leſſer proportion unto the
Square I Y, than the Square E hath to the Square ψ B.]
Theſe, and other particulars of the like nature, that follow both in this and the following
Propoſitions, ſhall be demonſtrated by us no otherwiſe than we have done above.
P
Therefore Perpendiculars being drawn thorow Z and G, unto
the Surface of the Liquid, that are parallel to T H, it followeth
that the ſaid Portion ſhall not ſtay, but ſhall turn about till that its
Axis do make an Angle with the Waters Surface greater than that
which it now maketh.] For in that the Line drawn thorow G, doth fall perpendicu­
larly towards thoſe parts which are next to L; but that thorow Z, towards thoſe next to A;
It is neceſſary that the Centre G do move downwards, and Z upwards: and, therefore, the
parts of the Solid next to L ſhall move downwards, and thoſe towards A upwards, that the
Axis may makea greater Angle with the Surface of the Liquid.
Q
For ſo ſhall I O be equall to ψ B; and ω I equall to I R; and
P H equall to F.] This plainly appeareth in the third Figure, which is added by us.
1
PROP. IX. THE OR. IX.
The Right Portion of a Rightangled Conoid, when it
ſhall have its Axis greater than Seſquialter of the
Semi-parameter, but leſſer than to be unto the ſaid
Semi-parameter in proportion as fifteen to four, and
hath greater proportion in Gravity to the Liquid, than
the exceſs by which the Square made of the Axis is
greater than the Square made of the Exceſs, by which
the Axis is greater than Seſquialter of the Semi­
parameter, hath to the Square made of the Axis,
being demitted into the Liquid, ſo as that its Baſe
be wholly within the Liquid, and being ſet inclining
it ſhall neither turn about, ſo as that its Axis ſtand
according to the Perpendicular, nor remain inclined,
ſave only when the Axis makes an Angle with
the Surface of the Liquid, equall to that aßigned
as before.
Let there be a Portion as was ſaid; and ſuppoſe D B equall to
the Axis of the Portion: and let B K be double to K D; and
K R equall to the Semi-parameter: and C B Seſquialter of
B R. And as the Portion is to the Liquid in Gravity, ſo let the Ex­
ceſſe by which the Square B D exceeds the Square F Q be to the
Square B D: and let F be double to Q: It is manifeſt, therefore,
that the Exceſſe by which the
270[Figure 270]
Square B D is greater than the
Square B C hath leſser proportion
to the Square B D, than the Exceſs
by which the Square B D is greater
than the Square F Q hath to the
Square B D; for B C is the Exceſs
by which the Axis of the Portion is
greater than Seſquialter of the
Semi-parameter: And, therefore,

the Square B D doth more exceed
the Square F Q, than doth the
Square B C: And, conſequently, the Line F Q is leſs than B C;
1and F leſs than B R. Let R Ψ be equall to F; and draw Ψ E
perpendicular to B D; which let be in power the half of that
which the Lines K R and Ψ B containeth; and draw a Line from
B to E: I ſay that the Portion demitted into the Liquid, ſo as that
its Baſe be wholly within the Liquid, ſhall ſo ſtand, as that its Axis
do make an Angle with the Liquids Surface, equall to the Angle B.
For let the Portion be demitted into the Liquid, as hath been ſaid;
and let the Axis not make an Angle with the Liquids Surface, equall
to B, but firſt a greater: and the ſame being cut thorow the Axis
by a Plane erect unto the Surface of the Liquid, let the Section of
the Portion be A P O L, the Section of a Rightangled Cone; the
Section of the Surface of the Liquid Γ I; and the Axis of the
Portion and Diameter of the Section N O; which let be cut in
the Points ω and T, as before: and draw Y P, parallelto Γ I, and
touching the Section in P, and MP parallel to N O, and P S perpen­
dicular to the Axis. And becauſe now that the Axis of the Portion
maketh an Angle with the Liquids Surface greater than the Angle
B, the Angle S Y P ſhall alſo be greater than the Angle B: And,
therefore, the Square P S hath greater proportion to the Square

S Y, than the Square Ψ E hath to the Square Ψ B: And, for that
cauſe, K R hath greater proportion to S Y, than the half of K R
hath to Ψ B: Therefore, S Y is leſs than the double of Ψ B; and

S O leſs than ψ B: And, therefore, S ω is greater than R ψ; and

P H greater than F. And, becauſe that the Portion hath the
ſame proportion in Gravity unto the Liquid, that the Exceſs by
which the Square B D, is greater than the Square F Q, hath unto
the Square B D; and that as the Portion is in proportion to the
Liquid in Gravity, ſo is the part thereof ſubmerged unto the whole
Portion; It followeth that the part ſubmerged, hath the ſame
proportion to the whole Portion, that the Exceſs by which the
Square B D is greater than the Square F Q hath unto the Square
B D: And, therefore, the whole Portion ſhall have the ſame propor­

tion to that part which is above the
271[Figure 271]
Liquid, that the Square B D hath to
the Square F Q: But as the whole
Portion is to that part which is above
the Liquid, ſo is the Square N O unto
the Square P M: Therefore, P M
ſhall be equall to F Q: But it
hath been demonſtrated, that P H is
greater than F. And, therefore,
MH ſhall be leſs than que and P H
greater than double of H M. Let
therefore, P Z be double to Z M:
1and drawing a Line from Z to T pro­
272[Figure 272]
long it unto G. The Centre of
Gravity of the whole Portion ſhall
be T; of that part which is above
the Liquid Z; and of the Remain­
der which is within the Liquid, the
Centre ſhall be in the Line Z T pro­
longed; let it be in G: It ſhall be
demonſtrated, as before, that T H
is perpendicular to the Surface of
the Liquid, and that the Lines
drawn thorow Z and G parallel to the ſaid T H, are alſo perpen­
diculars unto the ſame: Therefore, the Part which is above the
Liquid ſhall move downwards, along that which paſseth thorow Z;
and that which is within it, ſhall move upwards, along that which
paſseth thorow G: And, therefore, the Portion ſhall not remain
ſo inclined, nor ſhall ſo turn about, as that its Axis be perpendicular

unto the Surface of the Liquid; for the parts towards L ſhall move
downwards, and thoſe towards A upwards; as may appear by
the things already demonſtrated. And, if the Axis ſhould make
an Angle with the Surface of the Liquid, leſs than the Angle B;
it ſhall in like manner be demonſtrated, that the Portion will not

reſt, but incline untill that its Axis do make an Angle with the
Surface of the Liquid, equall to the Angle B.
A
B
C
D
E
F
G
COMMANDINE.
And, therefore, the Square B D doth more exceed the Square

F Q, than doth the Square B C: And, conſequently, the Line
F Q, is leſs than B C; and F leſs than B R.] Becauſe the Exceſs by
which the Square B D exceedeth the Square B C; having leſs proportion unto the Square B D,
than the Exceſs by which the Square B D exceedeth the Square F Q, hath to the ſaid Square;
(a) the Exceſs by which the Square B D exceedeth the Square B C ſhall be leſs than the Exceſs

by which it exceedeth the Square F Q: Therefore, the Square F Q is leſs than the Square B C:
and, conſquently, the Line F Q leſs than the Line BC: But F Q hath the ſameproportion
to F, that B C hath to B R; for the Antecedents are each Seſquialter of their conſequents:
And (b) F Q being leſs than B C, F ſhall alſo be leſs than B R.
A
(a) By 8. of the
fifth.
(b) By 14. of the
fifth.
And, for that cauſe, K R hath greater proportion to S Y, than
the half of K R hath to ψ B.] For K R is to S Y, as the Square P S is to the Square

S Y: and the half of the Line K R is to the Line ψ B, as the Square E ψ is to the Square ψ B.
B
And S O leſs than ψ B.] For S Y is double of S O.
C
And P H greater than F.] For P H is equall to S ω, and R ψ equall to F.
D
And, therefore, the whole Portion ſhall have the ſame propor­

tion to that part which is above the Liquid, that the Square B D
hath to the Square F Q] Becauſe that the part ſubmerged, being to the whole Portion
as the Exceſs by which the Square B D is greater than the Square F Q, is to the Square B D;
the whole Portion, Converting, ſhall be to the part thereof ſubmerged, as the Square B D is to
1the Exceſs by which it exceedeth the Square F Q: And, therefore, by Converſion of Proportion,
the whole Portion is to the part thereof above the Liquid, as the Square B D is to the Square,
F que for the Square B D is ſo much greater than the Exceſs by which it exceedeth the Squar,
F Q as is the ſaid Square F que
E
F
For the parts towards L ſhall move downwards, and thoſe to­
wards A upwards.] We thus carrect theſe words, for in Tartaglia's Tranſlation it
is falſly, as I conceive, read Quoniam quæ ex parte L ad ſuperiora ferentur, becauſe
the Line thàt paſſeth thorow Z falls perpendicularly on the parts towards L, and that thorow
G falleth perpendicularly on the parts towards A: Whereupon the Centre Z, together with thoſe
parts which are towards L ſhall move downwards; and the Centre G, together with the parts
which are towards A upwards.
G
It ſhall in like manner be demonſtrated that the Portion ſhall not
reſt, but incline untill that its Axis do make an Angle with the
Surface of the Liquid, equall to the Angle B.] This may be eaſily demon­
ſtratred, as nell from what hath been ſaid in the precedent Propoſition, as alſo from the two
latter Figures, by us inſerted
PROP. X. THEOR. X.
The Right Portion of a Rightangled Conoid, lighter
than the Liquid, when it ſhall have its Axis greater
than to be unto the Semiparameter, in proportion as
fifteen to four, being demitted into the Liquid, ſo as

that its Baſe touch not the ſame, it ſhall ſometimes

ſtand perpendicular; ſometimes inclined; and ſome­
times ſo inclined, as that its Baſe touch the Surface
of the Liquid in one Point only, and that in two Po-

ſitions; ſometimes ſo that its Baſe be more ſubmer-

ged in the Liquid; and ſometimes ſo as that it doth
not in the leaſt touch the Surface of the Liquid;

according to the proportion that it hath to the Liquid
in Gravity. Every one of which Caſes ſhall be anon
demonſtrated.
A
B
C
D
E
Let there be a Portion, as hath been ſaid; and it being cut
thorow its Axis, by a Plane erect unto the Superficies of the
Liquid, let the Section be A P O L, the Section of a Right
angled Cone; and the Axis of the Portion and Diameter of the
Section B D: and let B D be cut in the Point K, ſo as that B K
be double of K D; and in C, ſo as that B D may have the ſame

proportion to K C, as fifteen to four: It is manifeſt, therefore,

that K C is greater than the Semi-parameter: Let the
1parameter be equall to K R: and
273[Figure 273]

let D S be Seſquialter of K R: but
S B is alſo Seſquialter of B R:
Therefore, draw a Line from A to
B; and thorow C draw C E Per­
pendicular to B D, cutting the Line
A B in the Point E; and thorow E
draw E Z parallel unto B D. Again,
A B being divided into two equall
parts in T, draw T H parallel to the
ſame B D: and let Sections of
Rightangled Cones be deſcribed, A E I about the Diameter E Z;
and A T D about the Diameter T H; and let them be like to the

Portion A B L: Now the Section of the Cone A E I, ſhall paſs

thorow K; and the Line drawn from R perpendicular unto B D,
ſhall cut the ſaid A E I; let it cut it in the Points Y G: and
thorow Y and G draw P Y Q and O G N parallels unto B D, and
cutting A T D in the Points F and X: laſtly, draw P Φ and O X
touching the Section A P O L in the Points P and O. In regard,

therefore, that the three Portions A P O L, A E I, and A T D are
contained betwixt Right Lines, and the Sections of Rightangled
Cones, and are right alike and unequall, touching one another, upon
one and the ſame Baſe; and N X G O being drawn from the
Point N upwards, and Q F Y P from Q: O G ſhall have to G X
a proportion compounded of the proportion, that I L hath to L A,
and of the proportion that A D hath to DI: But I L is to L A,
as two to five: And C B is to B D, as ſix to fifteen; that is, as two

to five: And as C B is to B D, ſo is E B to B A; and D Z to

D A: And of D Z and D A, L I and L A are double: and A D

is to D I, as five to one: But the proportion compounded of the
proportion of two to five, and of the proportion of five to one, is

the ſame with that of two to one: and two is to one, in double
proportion: Therefore, O G is double of GX: and, in the ſame
manner is P Y proved to be double of Y F: Therefore, ſince that
D S is Seſquialter of K R; B S ſhall be the Exceſs by which the
Axis is greater than Seſquialter of the Semi-parameter. If there­
fore, the Portion have the ſame proportion in Gravity unto the
Liquid, as the Square made of the Line B S, hath to the Square
made of B D, or greater, being demitted into the Liquid, ſo as hat
its Baſe touch not the Liquid, it ſhall ſtand erect, or perpendicular:
For it hath been demonſtrated above, that the Portion whoſe

Axis is greater than Seſquialter of the Semi-parameter, if it have
not leſser proportion in Gravity unto the Liquid, than the Square
1made of the Exceſs by which the Axis is greater than Seſquialter
of the Semi-parameter, hath to the Square made of the Axis, being
demitted into the Liquid, ſo as hath been ſaid, it ſhall ſtand erect,
or Perpendicular.
F
G
H
K
L
M
N
O
P
Q
R
COMMANDINE.
The particulars contained in this Tenth Propoſition, are divided by Archimedes
into five Parts and Concluſions, each of which he proveth by a diſtinct Demonſtration.
A
It ſhall ſometimes ſtand perpendicular.] This is the firſt Concluſion, the
Demonstration of which he hath ſubjoyned to the Propoſition.
B
And ſometimes ſo inclined, as that its Baſe touch the Surface
of the Liquid, in one Point only.] This is demonſtrated in the third Con­
cluſion.
Sometimes, ſo that its Baſe be moſt ſubmerged in the Liquid.]

This pertaineth unto the fourth Concluſion.
C
And, ſometimes, ſo as that it doth not in the leaſt touch the Sur­

face of the Liquid.] This it doth hold true two wayes, one of which is explained is
the ſecond, and the other in the fifth Concluſion.
D
According to the proportion, that it hath to the Liquid in Gra­

vity. Every one of which Caſes ſhall be anon demonſtrated.]
In Tartaglia's Verſion it is rendered, to the confuſion of the ſence, Quam autem pro­
portionem habeant ad humidum in Gravitate fingula horum demonſtrabuntur.
E
It is manifeſt, therefore, that K C is greater than the Semi­

parameter] For, ſince B D hath to K C the ſame proportion, as fifteen to four, and
hath unto the Semi-parameter greater proportion; (a) the Semi-parameter ſhall be leſs

than K C.
F
(a) By 10. of the
fifth.
Let the Semi-parameter be equall to KR.] We have added theſe words,

which are not to be found in Tartaglia.
G
But S B is alſo Seſquialter of BR.] For, D B is ſuppoſed Seſquialter of

B K; and D S alſo is Seſquialter of K R: Wherefore as (b) the whole D B, is to the whole
B K, ſo is the part D S to the part K R. Therefore, the Remainder S B, is alſo to the

Remainder B R, as D B is to B K.
H
(b) By 19 of the
fifth.
And let them be like to the Portion A B L.] Apollonius thus defineth

like Portions of the Sections of a Cone, in Lib. 6. Conicornm, as Eutocius writeth ^{*};

ὄν οἱ̄ς ἀχ δεισω̄ν ὄν ἑχάσῳ ωαραλλήλων τη̄ <35>ὰσει, ἵσων τὸ πλη̄ο<34>, αἱ παράλληλος, καὶ ἁι <35>άσεις ωρὸς τάς αποτρμ
νομένας ἀπὸ διαμέτσων τω̄ς κορυφαῑς ἐν τοῑς ἀντοῑς λόγοις εἰσι, καὶ αἱ ἀποτεμνόμεναι ωρὸς τὰς ἀ τεμνομίνασ
that is, In both of which an equall number of Lines being drawn parallel to the
Baſe; the parallel and the Baſes have to the parts of the Diameters, cut off from
the Vertex, the ſameproportion: as alſo, the parts cut off, to the parts cut off.
Now the Lines parallel to the Baſes are drawn, as I ſuppoſe, by making a Rectilineall Figure (cal-

led) Signally inſcribed [χη̄μα γιωρίμως ἐγν̀<36>ρόμενον] in both portions, having an equall num­
ber of Sides in both. Therefore, like Portions are cut off from like Sections of a Cone; and
their Diameters, whether they be perpendicular to their Baſes, or making equall Angles with their
Baſes, have the ſame proportion unto their Baſes.
K
* Upon prop. 3 lib. 2
Archim. Æqui­
pond.
Vide Archim, ante
prop. 2. lib. 2.
Æquipond.
L
Now the Section of the Cone A E I ſhall paſs thorow K.]
For, if it be poſſible, let it not paſs thorow K, but thorow ſome other Point of the Line D B, as
thorow V. Inregard, therefore, that in the Section of the Right-angled Cone A E I, whoſe
Diameter is E Z, A E is drawn and prolonged; and D B parallel unto the Diameter, cutteth
both A E and A I; A E in B, and A I in D; D B ſhall have to B V, the ſame proportion
1that A Z hath to Z D; by the fourth Propoſition of Archimedes, De quadratura Para­
bolæ: But A Z is Seſquialter of Z D; for it is as three to two, as we ſhallanon demon-

ſtrate: Therefore D B is Seſquialter of B V; but D B and B K are Seſquialter:
And, therefore, the Lines (c) B V and B K are equall: Which is imposſible:
Therefore the Section of the Right-angled Cone A E I, ſhall paſs thorow the Point K; which
we would demonstrate.
(c) By 9 of the
fifth,
In regard, therefore, that the three Portions A P O L, A E I

and A T D are contained betwixt Right Lines and the Sections
of Right-angled Cones, and are Right, alike and unequall,
touching one another, upon one and the ſame Baſe.] After theſe words,
upon one and the ſame Baſe, we may ſee that ſomething is obliterated, that is to be
deſired: and for the Demonſtration of theſe particulars, it is requiſite in this place to
premiſe ſome things: which will alſo be neceſſary unto the things that follow.
M
LEMMA. I.
Let there be a Right Line A B; and let it be cut by two Lines,
parallel to one another, A C and D E, ſo, that as A B is to
B D. ſo A C may be to D E. I ſay that the Line that con­
joyneth the Points C and B ſhall likewiſe paſs by E.
274[Figure 274]
For, if poſſible, let it not paſs by E, but either
above or below it. Let it first paſs below it,
as by F. The Triangles A B C and D B F ſhall
be alike: And, therefore, as (a) A B is to B D,

ſo is A C to D F: But as A B is to B D, ſo was
A C to D E: Therefore (b) D F ſhall be equall to

D E: that is, the part to the whole: Which is
abſurd. The ſame abſurditie will follow, if the
Line C B be ſuppoſed to paſs above the Point E:
And, therefore, C B muſt of necesſity paſs thorow
E: Which was required to be demonſtrated.
(a) By 4. of the
ſixth.
(b) By 9. of the
fifth.
LEMMA. II.
Let there be two like Portions, contained betwixt Right Lines,
and the Sections of Right-angled Cones; A B C the great­
er, whoſe Diameter let be B D; and E F C the leſser, whoſe
Diameter let be F G: and, let them be ſo applyed to one
another, that the greater include the leſser; and let their
Baſes A C and E C be in the ſame Right Line, that the ſame
Point C, may be the term or bound of them both: And,
then in the Section A B C, take any Point, as H; and draw
a Line from H to C. I ſay, that the Line H C, hath to that
part of it ſelf, that lyeth betwixt C and the Section E F C, the
ſame proportion that A C hath to C E.
Draw B C, which ſhall paſs thorow F, For, in regard, that the Portions are alike, the
Diameters with the Baſes contain equall Angles: And, therefore, B D and F G are parallel
to one another: and B D is to A C, as F G it to E C: and, Permutando, B D is to F G, as
A C is to C E; that is, (a) as their halfes D C to C G; therefore, it followeth, by the

preceding Lemma, that the Line B C ſhall paſs by the Point F. Moreover, from the Point
H unto the Diameter B D, draw the Line H K, parallel to the Baſe A C: and, draw a Line
1275[Figure 275]
from K to C, cutting the Diameter F G in L:
and, thorow L, unto the Section E F. G, on the
part E, draw the Line L M, parallel unto the
ſame Baſe A C. And, of the Section A B C,
let the Line B N be the Parameter; and, of the
Section E F C, let F O be the Parameter. And,
becauſe the Triangles C B D and C F G are alike;
(b) therefore, as B C is to C F, ſo ſhall D C be

to C G, and B D to F G. Again, becauſe the
Triangles C K B and C L F, are alſo alike to
one another; therefore, as B C is to C F, that is,
as B D is to F G, ſo ſhall K C be to C L, and B K to F L: Wherefore, K C to C L, and,

B K to F L, are as D C to C G; that is, (c) as their duplicates A C and C E: But as
B D is to F G, ſo is D C to C G; that is, A D to E G: And, Permutando, as B D is to
A D, ſo is F G to E G: But the Square A D, is equall to the Rectangle D B N, by the 11
of our firſt of Conicks: Therefore, the (d) three Lines B D, A D and B N are

Proportionalls. By the ſame reaſon, likewiſe, the Square E G being equall to the Rectangle
G F O, the three other Lines F G, E G and F O, ſhall be alſo Proportionals: And, as B D is
to A D, ſo is F G to E G: And, therefore, as A D is to B N, ſo is E G to F O: Ex equali,
therefore, as D B is to B N, ſo is G F to F O: And, Permutando, as D B is to G F, ſo is
B N to F O: But as D B is to G F, ſo is B K to F L: Therefore, B K is to F L, as
B N is to F O: And, Permutando, as B K is to B N, ſo is F L to F O. Again,
becauſe the (e) Square H K is equall to the Rectangle B N; and the Square M L, equall

to the Rectangle L F O, therefore, the three Lines B K, K H and B N ſhall be Proportionals:
and F L, L M, and F O ſhall alſo be Proportionals: And, therefore, (f) as the Line

B K is to the Line B N, ſo ſhall the Square B K, be to the Square H K: And, as the
Line F L is to the Line F O, ſo ſhall the Square F L be to the Square L M:
Therefore, becauſe that as B K is to B N, ſo is F L to F O; as the Square

B K is to the Square K H, ſo ſhall the Square F L be to the Square L M: Therefore,
(g) as the Line B K is to the Line K H, ſo is the Line F L to L M: And, Permutando,
as B K is to F L, ſo is K H to L M: But B K was to F L, as K C to C L: Therefore,
K H is to L M, as K C to C L: And, therefore, by the preceding Lemma, it is manifeſt that
the Line H C alſo ſhall paſs thorow the Point M: As K C, therefore, is to C L, that is,
as A C to C E, ſo is H C to C M; that is, to the ſame part of it ſelf, that lyeth betwixt C and
the Section E F C. And, in like manner might we demonſtrate, that the ſame happeneth
in other Lines, that are produced from the Point C, and the Sections E B C. And, that
B C hath the ſame proportion to C F, plainly appeareth; for B C is to C F, as D C to C G;
that is, as their Duplicates A C to C E.
(a) By 15. of the
fifth.
(b) By 4. of the
ſixth.
(c) By 15. of the
fifth.
(d) By 17. of the
ſixth.
(e) By 11 of our
firſt of Conicks.
(f) By Cor. of 20.
of the ſixth.
(g) By 23. of the
ſixth.
From whence it is manifeſt, that all Lines ſo drawn, ſhall be cut by the
ſaid Section in the ſame proportion. For, by Diviſion and Converſion,
C M is to M H, and C F to F B, as C E to E A.
LEMMA. III.
And, hence it may alſo be proved, that the Lines which are
drawn in like Portions, ſo, as that with the Baſes, they con­
tain equall Angles, ſhall alſo cut off like Portions; that is,
as in the foregoing Figure, the Portions H B C and M F C,
which the Lines C H and C M do cut off, are alſo alike to
each other.
For let C H and C M be divided in the midst in the Points P and que and thorow thoſe
Points draw the Lines R P S and T Q V parallel to the Diameters. Of the Portion
H S C the Diameter ſhall be P S, and of the Portion M V C the Diameter ſhall be
1Q V. And, ſuppoſe that as the Square C R is to the Square C P, ſo is the Line B N unto
another Line; which let be S X: And, as the Square C T is to the Square C Q ſo let F O
be to V Y. Now it is manifeſt, by the things which we have demonſtrated, in our Commentaries,
upon the fourth Propoſition of Archimedes, De Conoidibus & Spheæroidibus, that the
Square C P is equall to the Rectangle P S X; and alſo, that the Square C Q is equall to
the Rectangle Q V Y; that is, the Lines S X and V Y, are the Parameters of the Sections H S C
and M V C: But ſince the Triangles C P R and C Q T are alike; C R ſhall have to C P, the
ſame Proportion that C T hath to C Q: And, therefore, the (a) Square C R ſhall have

to the Square C P, the ſame proportion that the
276[Figure 276]
Square C T hath to the Square C Q: There­
fore, alſo, the Line B N ſhall be to the Line
S X, as the Line F O is to V Y: But H C was
to C M, as A C to C E: And, therefore, alſo,
their halves C P and C Q, are alſo to one
another, as A D and E G: And. Permu­
tando, C P is to A D, as C Q is to E G:
But it hath been proved, that A D is to B N,
as E G to F O; and B N to S X, as F O to
V Y: Therefore, exæquali, C P ſhall be
to S X, as C Q is to V Y. And, ſince the
Square C P is equall to the Rectangle P S X, and the Square C Q to the Rectangle Q V Y,
the three Lines S P, PC and S X ſhall be proportionalls, and V Q, Q C and V Y ſhal be
Proportionalls alſo: And therefore alſo S P ſhall be to P C as V Q to Q C And as P C
is to C H, ſo ſhall Q C. be to C M: Therefore, ex æquali, as S P the Diameter of the
Portion H S C is to its Baſe C H, ſo is V Q the Diameter of the portion M V S the
Baſe C M; and the Angles which the Diameter with the Baſes do contain, are equall; and the
Lines S P and V Q are parallel: Therefore the Portions, alſo, H S C and M V C ſhall be alike:
Which was propoſed to be demonſtrated
(a) By 22. of the
ſixth.
LEMMA. IV.
Let there be two Lines A B and C D; and let them be cut in the
Points E and F, ſo that as A E is to E B, C F may be to F D:
and let them be cut again in two other Points G and H; and
let C H be to H D, as A G is to G B. I ſay that C F ſhall be to
F H as A E is E G.
For in regard that as A E is to E B, ſo is C F to F D; it followeth that, by Compounding,
as A B is to E B, ſo ſhall C D be to F D. Again, ſince that as A G is to G B, ſo is C H, to
H D; it followeth that, by Compounding and Converting, as G B is to A B, ſo ſhall H D be
277[Figure 277]
C D: Therefore, ex æquali, and Converting as E B
is to G B, ſo ſhall F D be to H D; And, by Conver­
ſion of Propoſition, as E B is to E G, ſo ſhall F D
be to F H: But as A E is to E B, ſo is C F to F D:
Ex æquali, therefore, as A E is to E G, ſo
ſhall CF be to F H. Again, another way. Let
the Lines A B and C D be applyed to one another,
ſo as that they doe make an Angle at the parts A and C;
and let A and C be in one and the ſame Point: then
draw Lines from D to B, from H to G, and from F to E. And ſince that as A E is to E B,
ſo is C F, that is A F to F D; therefore F E ſhall be parallel to D B; (a) and likewiſe

H G ſhall be parallel to D B; for that A H is to H D, as A G to G B: (b) Therefore F E
and H G are parallel to each other: And conſequently, as A E is to E G, ſo is A H, that is,

C F to F H: Which was to be demonſtrated.
1
(a) By 2. of the
ſixth.
(b) By 30 of the
firſt.
LEMMA. V.
Again, let there be two like Portions, contained betwixt Right
Lines and the Sections of Right-angled Cones, as in the fore­
going figure, A B C, whoſe Diameter is B D; and E F C,
whoſe Diameter is F G; and from the Point E, draw the
Line E H parallel to the Diameters B D and F G; and let it
cut the Section A B C in K: and from the Point C draw C H
touching the Section A B C in C, and meeting with the Line
E H in H; which alſo toucheth the Section E F C in the ſame
Point C, as ſhall be demonſtrated: I ſay that the Line drawn
from C H unto the Section E F C ſo as that it be parallel to
the Line E H, ſhall be divided in the ſame proportion by the
Section A B C, in which the Line C A is divided by the Section
E F C; and the part of the Line C A which is betwixt the
two Sections, ſhall anſwer in proportion to the part of the Line
drawn, which alſo falleth betwixt the ſame Sections: that is,
as in the foregoing Figure, if D B be produced untill it meet
with C H in L, that it may interſect the Section E F C in the
Point M, the Line L B ſhall have to B M the ſame proportion
that C E hath to E A.
For let G F be prolonged untill it meet the ſame Line C H in N, cutting the Section A B C
in O; and drawing a Line from B to C, which ſhall paſſe by F, as hath been ſhewn, the
278[Figure 278]
Triangles C G F and C D B ſhall be alike; as
alſo the Triangles C F N and C B L: Wherefore
(a) as G F is to D B, ſo ſhall C F b to C B:

And as (b) C F is to C B, ſo ſhall F N be
to B L: Therefore G F ſhall be to D B, as F N

to B L: And, Permutando, G F ſhall be to
F N, as D B to B L: But D B is equall to
B L, by 35 of our Firſt Book of Conicks:
Therefore (c) G F alſo ſhall be equall to F N:

And by 33 of the ſame, the Line C H touch­
eth the Section E F C in the ſame Point. There­
fore, drawing a Line from C to M, prolong it
untill it meet with the Section A B C in P; and
from P unto A C draw P Q parallel to B D.
Becauſe, now, that the Line C H toucheth the
Section E F C in the Point C; L M ſhall have
the ſame proportion to M D that C D hath to D E,
by the Fifth Propoſition of Archimedes in his
Book De Quadratura Patabolæ: And by
reaſon of the Similitude of the Triangles C M D
and C P Q, as C M is to C D, ſo ſhall C P
be to C Q: And, Permutando, as C M is to
C P, ſo ſhall C D be to C Q: But as C M is to C P, ſo is C E to C A,; as we have but
even now demonſtrated: And therefore, as C E is to C A, ſo is C D to C que that is as the
whole is to the whole, ſo is the part to the part: The remainder, therefore, D E is to the
Remainder Q A, as C E is to C A; that is, as C D is to C Q: And, Permutando, C D
is to D E, as C Q is to Q A: And L M is alſo to M D, as C D to D E: Therefore L M is
1to M D, as C Q to Q A: But L B is to B D, by 5 of Archimedes, before recited, as C D
to D A: It is manifeſt therefore, by the precedent Lemma, that C D is to D Q, as L B is to
B M: But as C D is to D Q, ſo is C M to M P: Therefore L B is to B M, as C M to M P:

And it haveing been demonſtrated, that C M is to M P, as C E to E A; L B ſhall be to B M,
as C E to E A. And in like manner it ſhall be demonstrated that ſo is N O to O F; as alſo the
Remainders. And that alſo H K is to K E, as C E to E A, doth plainly appeare by the ſame
5. of Archimedes: Which is that that we propounded to be demonſtrated.
(a) By 4. of the
ſixth.
(b) By 11 of the
fifth,
(c) By 14 of the
fifth.
By 2. of the ſixth
LEMMA. VI.
And, therefore, let the things ſtand as above; and deſcribe
yet another like Portion, contained betwixt a Right Line, and
the Section of the Rightangled Cone D R C, whoſe Diameter
is R S, that it may cut the Line F G in T; and prolong S R
unto the Line C H in V, which meeteth the Section A B C in
X, and E F C in Y. I ſay, that B M hath to M D, a propor­
tion compounded of the proportion that E A hath to A C;
and of that which C D hath to D E.
For, we ſhall firſt demonſtrate, that the Line C H toucheth the Section D R C in the
Point C; and that L M is to M D, as alſo N F to F T, and V Y to Y R, as C D is to E D.
And, becauſe now that L B is to B M, as C E is to E A; therefore, Compounding and Conver­
ting, B M ſhall be to L M, as E A to A C: And, as L M is to M D, ſo ſhall C D be to
D E: The proportion, therefore, of B M to M D, is compounded of the proportion that
B M hath to L M, and of the proportion that L M hath to M D: Therefore, the proportion
of B M to M D, ſhall alſo be compounded of the proportion that E A hath to A C, and of
that which C D hath to D E. In the ſame manner it ſhal be demonſtrated, that O F hath to
F T, and alſo X Y to Y R, a proportion compounded of thoſe ſame proportions; and ſo in
the reſt: Which was to be demonstrated.
By which it appeareth that the Lines ſo drawn; which fall betwixt
the Sections A B C and D R C, ſhall be divided by the Section E F C
in the ſame Proportion.
And C B is to B D, as ſix to fifteen.] For we have ſuppoſed that B K is

double of K D: Wherefore, by Compoſition B D ſhall be to K D as three to one; that is, as
fifteen to five: But B D was to K C as fifteen to four; Therefore B D is to D C as fifteen to nine:
And, by Converſion of proportion and Convert­
ing, C B is to B D, as ſix to ſifteen.
N
279[Figure 279]
And as C B is to B D, ſo is

E B to B A; and D Z to D A.]
For the Triangles C B E and D B A being
alike; As C B is to B E, ſo ſhall D B be to B A:
And, Permutando, as C B is to B D, ſo ſhall
E B be to B A: Againe, as B C is to C E ſo
ſhall B D be to D A, And, Permutando, as
C B is to B D, ſo ſhall C E, that is, D Z
equall to it, be to D A.
O
And of D Z and D A, L I and

L A are double.] That the Line L A is
double of D A, is manifeſt, for that B D is the Diameter of the Portion. And that L I is
dovble to D Z ſhall be thus demonſtrated. For as much as ZD is to D A, as two to five:
therefore, Converting and Dividing, A Z, that is, I Z, ſhall be to Z D, as three to two:
1Again, by dividing, I D ſhall be to D Z, as one to two: But Z D was to D A, that is, to D L,
as two to five: Therefore, ex equali, and Converting, L D is to D I, as five to one: and, by
Converſion of Proportion, D L is to D I, as five to four: But D Z was to D L, as two to
five: Therefore, again, ex equali, D Z is to L I, as two to four: Therefort L I is double
of D Z: Which was to be demonſtrated.
P
Q
And, A D is to D I, as five to one.] This we have but juſt now demon­
ſtrated.
R
For it hath been demonſtrated, above, that the Portion whoſe
Axis is greater than Seſquialter of the Semi-parameter, if it have
not leſſer proportion in Gravity to the Liquid, &c.] He hath demonstra­
ted this in the fourth Propoſition of this Book.
CONCLVSION II.
If the Portion have leſſer proportion in Gravity to the

Liquid, than the Square S B hath to the Square
B D, but greater than the Square X O hath to the
Square B D, being demitted into the Liquid, ſo in­
clined, as that its Baſe touch not the Liquid, it ſhall
continue inclined, ſo, as that its Baſe ſhall not in the
leaſt touch the Surface of the Liquid, and its Axis
ſhall make an Angle with the Liquids Surface, greater
than the Angle X.
A
Therfore repeating the firſt figure, let the Portion have unto
the Liquid in Gravitie a proportion greater than the Square
X O hath to the ſquare B D, but leſſer than the Square made of
the Exceſſe by which the Axis is greater than Seſquialter of the Semi­
280[Figure 280]
Parameter, that is, of S B, hath to
the Square B D: and as the Portion
is to the Liquid in Gravity, ſo let
the Square made of the Line ψ be
to the Square B D: ψ ſhall be great­

er than X O, but leſſer than the
Exceſſe by which the Axis is grea­
ter than Seſquialter of the Semi­
parameter, that is, than S B. Let
a Right Line M N be applyed to
fall between the Conick-Sections
A M Q L and A X D, [parallel to
B D falling betwixt O X and B D,] and equall to the Line ψ: and let
it cut the remaining Conick Section A H I in the point H, and the

Right Line R G in V. It ſhall be demonſtrated that M H is double to
H N, like as it was demonſtrated that O G is double to G X.
1281[Figure 281]
And from the Point M draw M Y
touching the Section A M Q L in M;
and M C perpendicular to B D: and
laſtly, having drawn A N & prolong­
ed it to Q, the Lines A N & N Q ſhall
be equall to each other. For in
regard that in the Like Portions

A M Q L and A X D the Lines A Q
and A N are drawn from the Baſes
unto the Portions, which Lines
contain equall Angles with the ſaid
Baſes, Q A ſhall have the ſame proportion to A M that L A hath
to A D: Therefore A N is equall to N Q, and A Q parallel to M Y.

It is to be demonſtrated that the Portion being demitted into the
Liquid, and ſo inclined as that its Baſe touch not the Liquid, it
ſhall continue inclined ſo as that its Baſe ſhall not in the leaſt touch
the Surface of the Liquid, and its Axis ſhall make an Angle with
the Liquids Surface greater than the Angle X. Let it be demitted
into the Liquid, and let it ſtand, ſo, as that its Baſe do touch the
Surface of the Liquid in one Point only; and let the Portion be cut
thorow the Axis by a Plane erect unto the Surface of the Liquid,
282[Figure 282]
and Let the Section of the Super­
ficies of the Portion be A P O L,
the Section of a Rightangled Cone,
and let the Section of the Liquids
Surface be A O; And let the Axis
of the Portion and Diameter of the
Section be B D: and let B D be

cut in the Points K and R as hath
been ſaid; alſo draw P G Parallel to
A O and touching the Section
A P O L in P; and from that Point
draw P T Parallel to B D, and P S perpendicular to the ſame B D.
Now, foraſmuch as the Portion is unto the Liquid in Gravity, as
the Square made of the Line ψ is to the Square B D; and ſince that
as the portion is unto the Liquid in Gravitie, ſo is the part thereof
ſubmerged unto the whole Portion; and that as the part ſubmerged
is to the whole, ſo is the Square T P to the Square B D; It follow­
eth that the Line ψ ſhall be equall to T P: And therefore the Lines
M N and P T, as alſo the Portions A M Q and A P O ſhall like­
wiſe be equall to each other. And ſeeing that in the Equall and
Like Portions A P O L and A M Q L the Lines A O and A Q

are drawn from the extremites of their Baſes, ſo, as that the Portions
cut off do make Equall Angles with their Diameters; as alſo the
1Angles at Y and G being equall; therefore the Lines Y B and G B,
and B C and B S ſhall alſo be equall: And therefore C R and S R,
and M V and P Z, and V N and Z T, ſhall be equall likewiſe.

Since therefore M V is Leſſer than double of V N, it is manifeſt that
P Z is leſſer than double of Z T. Let P ω be double of ω T; and
drawing a Line from ω to K, prolong it to E. Now the Centre of
Gravity of the whole Portion ſhall be the point K; and the Centre
of that part which is in the Liquid ſhall be ω, and of that which is
above the Liquid ſhall be in the Line K E, which let be E: But the
Line K Z ſhall be perpendicular unto the Surface of the Liquid:
And therefore alſo the Lines drawn thorow the Points E and ω parall­

lell unto K Z, ſhall be perpendicular sunto the ſame: Therefore the
Portion ſhall not abide, but ſhall turn about ſo, as that its Baſe
do not in the leaſt touch the Surface of the Liquid; in regard that
now when it toucheth in but one Point only, it moveth upwards, on

the part towards A: It is therefore perſpicuous, that the Portion
ſhall conſiſt ſo, as that its Axis ſhall make an Angle with the Liquids
Surface greater than the Angle X.
B
C
D
E F
G
H
K
L
M
COMMANDINE.
A
If the Portion have leſſer proportion in Gravity to the Liquid,
than the Square S B hath to the Square B D, but greater than the
Square X O hath to the Square B D.] This is the ſecond part of the Tenth
propoſition; and the other pat is with their Demonſtrations, ſhall hereafter follow in the ſame Order.
Ψ ſhall be greater than X O, but leſſer than the Exceſs by

which the Axis is greater than Seſquialter of the Semi-parameter,
that is than S B.] This followeth from the 10 of the fifth Book of Euclids Elements.
B
C
It ſhall be demonſtrated, that M H is double to H N, like as it
was demonſtrated, that O G is double to G X.] As in the firſt Concluſion
of this Propoſition, and from what we have but even now written, thereupon appeareth:
D
For in regard that in the like Portions A M Q L and A X D, the
Lines A Q and A N are drawn from the Baſes unto the Portions,
which Lines contain equall Angles with the ſaid Baſes, Q A ſhall
have the ſame proportion to A N, that L A hath to A D.]
This we have demonstrated above.
E
Therefore A N is equall to N Q] For ſince that Q A is to A N, as L A to
A D; Dividing and Converting, A N ſhall be to N Q as A D to D L: But A D
is equall to D L; for that D B is ſuppoſed to be the Diameter of the Portion: Therefore

alſo (a) A N is equall to N que
(a) By 14 of the
fifth.
And A Q parallel to M Y.] By the fifth of the ſecond Book of Apollonius his Conicks.
F
And let B D be cut in the Points K and R as hath been ſaid.]

In the firſt Conciuſion of this Propoſition: And let it be cut in K, ſo, as that B K be double to
K D, and in R ſo, as that K R may be equall to the Semi-parameter.
G
And, ſeeing that in the Equall and Like Portions A P O L and

A M Q L, the Lines A O and A Q are drawn from the Extremities
of their Baſes, ſo, as that the Portions cut off, do make equall Angles
1with their Diameters; as alſo, the Angles at Y and G being equall;
Therefore, the Lines Y B and G B, & B C & B S, ſhall alſo be equall.]
Let the Line A Q cut the Diameter D B in γ, and let it cut A O in δ. Now becauſe that in
283[Figure 283]
the equall and like Portions A P O L & A M Q L,
from the Extremities of their Baſes, A O and
A Q are drawn, that contain equall Angles with
thoſe Baſes; and ſince the Angles at D, are both
Right; Therefore, the Remaining Angles A δ D
and A γ D ſhall be equall to one another: But
the Line P G is parallel unto the Line A O; alſo
M Y is parallel to A que and P S and M C to
A D: Therefore the Triangles P G S and M Y C,
as alſo the Triangles A δ D and A γ D, are all
alike to each other: (b) And as A D is to A δ,

ſo is A D to A γ: and, Permutando, the Lines
A D and A D are equall to each other: Therefore,
A δ and A γ are alſo equall: But A O and
A Q are equall to each other; as alſo their halves
A T and A N: Therefore the Remainders T δ and N γ; that is, TG and MY, are alſo

284[Figure 284]
equall. And, as (c) P G is to G S, ſo is M Y to
Y C: and Permutando, as P G is to M Y, ſo is
G S to Y C: And, therefore, G S and Y C are
equall; as alſo their halves B S and B C: From
whence it followeth, that the Remainders S R and C R
are alſo equall: And, conſequently, that P Z and
M V, and V N and Z T, are lkiewiſe equall to one
another.
H
(b) By 4. of the
ſixth.
(c) By 34 of the
firſt,
Since, therefore, that N V is leſſer

than double of V N.] For M H is double of
H N, and M V is leſſer than M H: Therefore, M V
is leſſer than double of H N, and much leſſer than
double of V N.
K
Therefore, the Portion ſhall not abide, but ſhall turn about,

ſo, as that its Baſe do not in the leaſt touch the Surface of
the Liquid; in regard that now when it toucheth in but one Point
only, it moveth upwards on the part towards A.] Tartaglia's his Tranſla­
tion hath it thus, Non ergo manet Portio ſed inclinabitur ut Baſis ipſius, nec ſecundum
unum tangat Superficiem Humidi, quon am nunc ſecundum unum tacta ipſa reclina­
tur: Which we have thought fit in this manner to correct, from other Places of
Archimedes, that the ſenſe might be the more perſpicuous. For in the ſixth Propoſition of this,
he thus writeth (as we alſo have it in the Tranſlation,) The Solid A P O L, therefore, ſhall
turn about, and its Baſe ſhall not in the leaſt touch the Surface of the Liquid. Again,
in the ſeventh Propoſition; From whence it is manifeſt, that its Baſe ſhall turn about in
ſuch manner, a that its Baſe doth in no wiſe touch the Surface of the Liquid; For
that now when it toucheth but in one Point only, it moveth downwards on the part
towards L. And that the Portion moveth upwards, on the part towards A, doth plainly ap­
pear: For ſince that the Perpendiculars unto the Surface of the Liquid, that paſs thorow ω, de
fall on the part towards A, and thoſe that paſs thorow E, on the part towards L; it is neceſſary
that the Centre ω do move upwards, and the Centre E downwards.
L
It is therefore perſpicuous, that the Portion ſhall conſiſt, ſo, as that
its Axis ſhall make an Angle with the Liquids Surface greater than
the Angle X.] For dræwing a Line from A to X, prolong it untill it do cut the Diamter
1285[Figure 285]
B D in λ; and from the Point O, and parallel to
A λ, draw O X; and let it touch the Section in O,
as in the first Figure: And the (d) Angle at X,

ſhall be equall alſo to the angle λ: But the angle at Y
is equall to the Angle at γ; and the (e) Angle

A Γ D greater than the Angle A λ D, which falleth
without it: Therefore the Angle at Y ſhall be great­
er than that at X. And becauſe now the Portion
turneth about, ſo, as that the Baſe doth not touch
the Liquid, the Axis ſhall make an Angle with its
Surface greater than the Angle G; that is, than the
Angle Y: And, for that reaſon, much greater than
the Angle X.
(d) By 29 of the
firſt.
(e) By 16. of the
firſt.
CONCLUSION III.
If the Portion have the ſame proportion in Gravity to the
Liquid, that the Square X O hath to the Square
BD, being demitted into the Liquid, ſo inclined, as that
its Baſe touch not the Liquid, it ſhall ſtand and
continue inclined, ſo, as that its Baſe touch the Sur­
face of the Liquid, in one Point only, and its Axis ſhall
make an Angle with the Liquids Surface equall to the
Angle X. And, if the Portion have the ſame proportion
in Gravity to the Liquid, that the Square P F hath
to the Square B D, being demitted into the Liquid,
& ſet ſo inclined, as that its Baſe touch not the Liquid,
it ſhall ſtand inclined, ſo, as that its Baſe touch the
Surface of the Liquid in one Point only, & its Axis ſhall
make an Angle with it, equall to the Angle Φ.
Let the Portion have the ſame proportion in Gravity to tho
Liquid that the Square XO hath to the Square B D; and let
it be demitted into the Liquid ſo inclined, as that its Baſe touch
286[Figure 286]
not the Liquid. And cutting it by
a Plane thorow the Axis, erect unto
the Surface of the Liquid, let the
Section of the Solid, be the Section
of a Right-angled Cone, A P M L;
let the Section of the Surface of the
Liquid be I M; and the Axis of the
Portion and Diameter of the Section
B D; and let B D be divided as be­
fore; and draw PN parallel to IM
1and touching the Section in P, and T P parallel to B D; and P S perpen­
dicular unto B D. It is to be demonſtrated that the Portion ſhall
287[Figure 287]
not ſtand ſo, but ſhall encline until
that the Baſe touch the Surface of
the Liquid, in one Point only, for let
the ſuperior figure ſtand as it was,
and draw O C, Perpendicular to B D;
and drawing a Line from A to X,
prolong it to Q: A X ſhalbe equall
to X que Then draw O X parallel
to A que And becauſe the Portion
is ſuppoſed to have the ſame pro­
portion in Gravity to the Liquid
that the ſquare X O hath to the
Square B D; the part thereof ſubmerged ſhall alſo have the ſame
proportion to the whole; that is, the Square T P to the Square

B D; and ſo T P ſhall be equal to X O: And ſince that of the Portions
I P M and A O Q the Diameters are equall, the portions ſhall alſo be

equall. Again, becauſe that in the Equall and Like Portions A O Q L

and AP ML the Lines A Q and I M, which cut off equall Por­
tions, are drawn, that, from the Extremity of the Baſe, and this
not from the Extremity; it appeareth that that which is drawn from
the end or Extremity of the Baſe, ſhall make the Acute Angle with
the Diameter of the whole Portion leſset. And the Angle at X

being leſſe than the Angle at N, B C ſhall be greater than B S; and
C R leſſer than S R: And, therfore O G ſhall be leſſer than P Z;
and G X greater than Z T: Therfore P Z is greater than double of
Z T; being that O G is double of G X. Let P H be double to H T;
and drawing a Line from H to K, prolong it to ω. The Center of
Gravity of the whole Portion ſhall be K; the Center of the part
which is within the Liquid H, and that of the part which is above
the Liquid in the Line K ω; which ſuppoſed to be ω. Therefore it
ſhall be demonſtrated, both, that K H is perpendicular to the Surface
of the Liquid, and thoſe Lines alſo that are drawn thorow the Points
Hand ω parallel to K H: And therfore the Portion ſhall not reſt, but
ſhall encline untill that its Baſe do touch the Surface of the Liquid
in one Point; and ſo it ſhall continue. For in the Equall Portions
A O Q L and A P M L, the
288[Figure 288]
Lines A Q and A M, that cut off
equall Portions, ſhall be dawn
from the Ends or Terms of the Baſes;
and A O Q and A P M ſhall be
demonſtrated, as in the former, to

be equall: Therfore A Q and A M,
do make equall Acute Angles with
the Diameters of the Portions; and
1the Angles at X and N are equall. And, therefore, if drawing HK,
it be prolonged to ω, the Centre of Gravity of the whole Portion ſhall
be K; of the part which is within the Liquid H; and of the part which
is above the Liquid in K ὠ as ſuppoſe in ω; and H K perpendicular to
289[Figure 289]
the Surface of the Liquid. Therfore
along the ſame Right Lines ſhall the
part which is within the Liquid move
upwards, and the part above it down­
wards: And therfore the Portion
ſhall reſt with one of its Points
touching the Surface of the Liquid,
and its Axis ſhall make with the

ſame an Angle equall to X. It is
to be demonſtrated in the ſame
manner that the Portion that hath
the ſame proportion in Gravity to the Liquid, that the Square P F hath
to the Square B D, being demitted into the Liquid, ſo, as that its
Baſe touch not the Liquid, it ſhall ſtand inclined, ſo, as that its Baſe
touch the Surface of the Liquid in one Point only; and its Axis ſhall
make therwith an Angle equall to the Angle φ.
A
B
C
D
E
F
COMMANDINE.
A
That is the Square T P to the Square B D.] By the twenty ſixth of the Book

of Archimedes, De Conoidibus & Sphæroidibus: Therefore, (a) the Square T P
ſhall be equall to the Square X O: And for that reaſon, the Line T P equall to the
Line X O.
(a) By 9 of the
fifth.
B
The Portions ſhall alſo be equall.] By the twenty fifth of the ſame Book.
C
Again, becauſe that in the Equall and Like Portions, A O Q L
and A P M L.] For, in the Portion A P M L, deſcribe the Portion A O Q equall
to the Portion I P M: The Point Q falleth beneath M; for otherwiſe, the Whole would be
equall to the Part. Then draw I V parallel to A Q, and cutting the Diameter is ψ; and
let I M cut the ſame ς; and A Q in ς. I ſay
that the Angle A υ D, is leſſer than the Angle
290[Figure 290]
I σ D. For the Angle I ψ D is equall to the
Angle A υ D: (b) But the interiour Angle

I ψ D is leſſer than the exteriour I σ D: There-

fore, (c) A υ D ſhall alſo be lefter than I σ D.
(b) By 29 of the
firſt.
(c) By 16 of the
firſt.
D
And the Angle at X, being leſſe
than the Angle at N.] Thorow O draw twe
Lines, O C perpendicular to the Diameter B D, and
O X touching the Section in the Point O, and cutting

the Diameter in X: (d) O X ſhall be parallel
to A que and the (e) Angle at X, ſhall be equall to

that at υ: Therefore, the (f) Angle at X,

ſhall be leſſer than the Angle at ς; that is, to
that at N: And, conſequently, X ſhall fall beneath N: Therefore, the Line X B is greater than
N B. And, ſince B C is equall to X B, and B S equall to N B; B C ſhall be greater than B S.
1
(d) By 5 of our ſe­
cond of Conicks.
(e) By 29 of the
firſt.
(f) By 39 of our
firſt of Conicks.
Therefore, A Q and A M do make equall Acute Angles with

the Diameters of the Portions.] We demonſtrate this as in the Commentaries
upon the ſecond Concluſion.
E
It is to be demonſtrated in the ſame manner, that the Portion

that hath the ſame proportion in Gravity to the Liquid, that the
Square P F hath to the Square B D,
being demitted into the Liquid, ſo,
291[Figure 291]
as that its Baſe touch not the Li­
quid, it ſhall ſtand inclined, ſo, as
that its Baſe touch the Surface of the
Liquid in one point only; and its Axis
ſhall make therewith an angle equall
to the Angle φ.] Let the Portion be to the
Liquid in Gravity, as the Square P F to the
Square B D: and being demitted into the
Liquid, ſo inclined, as that its Baſe touch not
the Liquid, let it be cut thorow the Axis by a
Plane erect to the Surface of the Liquid, that
that the Section may be A M O L, the Section
of a Rightangled Cone; and, let the Section of the Liquids Surface be I O; and the Axit
of the Portion and Diameter of the Section B D; which let be cut into the ſame parts as
we ſaid before, and draw M N parallel to I O, that it may touch the Section in the Point
M; and M T parallel to B D, and P M S perpe ndicular to the ſame. It is to be demon­
strated, that the Portion ſhall not reſt, but ſhall incline, ſo, as that it touch the Liquids
Surface, in one Point of its Baſe only. For,
292[Figure 292]
draw P C perpendicular to B D; and drawing
a Line from A to F, prolong it till it meet with
the Section in que and thorow P draw P φ pa­
rallel to A Q: Now, by the things allready de­
monſtrated by us, A F and F Q ſhall be equall
to one another. And being that the Portion hath
the ſame proportion in Gravity unto the Liquid,
that the Square P F hath to the Square B D; and
ſeeing that the part ſubmerged, hath the ſame pro-

partion to the whole Portion; that is, the Squàre
M T to the Square B D; (g) the Square M T
ſhall be equall to the Square P F; and, by the
ſame reaſon, the Line M T equall to the Line
P F. So that there being drawn in the equall & like
portions A P Q Land A M O L, the Lines A Q and I O which cut off equall Portions, the
firſt from the Extreme term of the Baſe, the laſt not from the Extremity; it followeth, that
A Q drawn from the Extremity, containeth a leſſer Acute Angle with the Diameter of the
Portion, than I O: But the Line P φ is parallel to the Line A Q, and M N to I O: There­
fore, the Angle at φ ſhall be leſſer than the Angle at N; but the Line B C greater than B S;
and S R, that is, M X, greater than C R, that is, than P Y: and, by the ſame reaſon, X T
leſſer than Y F. And, ſince P Y is double to Y F, M X ſhall be greater than double to
Y F, and much greater than double of X T. Let M H be double to H T, and draw a
Line from H to K, prolonging it. Now, the Centre of Gravity of the whole Portion
ſhall be the Point K; of the part within the Liquid H; and of the Remaining part above
the Liquid in the Line H K produced, as ſuppoſe in ω It ſhall be demonſtrated in the ſame
manner, as before, that both the Line K H and thoſe that are drawn thorow the Points H
and ω parallel to the ſaid K H, are perpendicular to the Surface of the Liquid: The
Portion therefore, ſhall not reſt; but when it ſhall be enclined ſo far as to touch the Sur­
face of the Liquid in one Point and no more, then it ſhall ſtay. For the Angle at N
1293[Figure 293]
ſhall be equall to the Angle at φ; and the Line B S
equall to the Line B C; and S R to C R: Where­
fore, M H ſhall be likewiſe equall to P Y. There­
fore, having drawn HK and prolonged it; the
Centre of Gravity of the whole Portion ſhall be
K; of that which is in the Liquid H; and of
that which is above it, the Centre ſhall be in
the Line prolonged: let it be in ω. There­
fore, along that ſame Line K H, which is per­
pendicular to the Surface of the Liquid, ſhall
the part which is within the Liquid move up­
wards, and that which is above the Liquld
downwards: And, for this cauſe, the Portion,
ſhall be no longer moved, but ſhall ſtay, and
reſt, ſo, as that its Baſe do touch the Liquids Surface in but one Point; and its Axis
maketh an Angle therewith equall to the Angle φ; And, this is that which we were to
demonſtrate.
F
(g) By 9 of t
fifth.
CONCLVSION IV.
If the Portion have greater proportion in Gravity
to the Liquid, than the Square F P to the Square
B D, but leſſer than that of the Square X O to the
Square B D, being demitted into the Liquid,
and inclined, ſo, as that its Baſe touch not the
Liquid, it ſhall ſtand and reſt, ſo, as that its Baſe
ſhall be more ſubmerged in the Liquid.
Again, let the Portion have greater proportion in
Gravity to the Liquid, than the Square F P to the
Square B D, but leſſer than that of the Square X O to
the Square B D; and as the Portion is in Gravity to the Liquid,
ſo let the Square made of the Line ψ be to the Square B D. Ψ
ſhall be greater than F P, and leſſer than X O. Apply, therefore,
the right Line I V to fall betwixt the Portions A V Q L and A X D;
and let it be equall to ψ, and parallel to B D; and let it meet
the Remaining Section in Y: V Y ſhall alſo be proved double
to Y I, like as it hath been demonſtrated, that O G is double off
G X. And, draw from V, the Line V ω, touching the Section
A V Q L in V; and drawing a Line from A to I, prolong it unto
que We prove in the ſame manner, that the Line A I is equall
to I que and that A Q is parallel to V ω. It is to be demonſtrated,
that the Portion being demitted into the Liquid, and ſo inclined,
as that its Baſe touch not the Liquid, ſhall ſtand, ſo, that its Baſe
ſhall be more ſubmerged in the Liquid, than to touch it Surface in
1but one Point only. For let it be de­
294[Figure 294]
mitted into the Liquid, as hath been
ſaid; and let it firſt be ſo inclined, as
that its Baſe do not in the leaſt
touch the Surface of the Liquid. And
then it being cut thorow the Axis,
by a Plane erect unto the Surface of
the Liquid, let the Section of the
Portion be A N Z G; that of the
Liquids Surface E Z; the Axis of
the Portion and Diameter of the
Section B D; and let B D be cut in
the Points K and R, as before; and
draw N L parallel to E Z, and touching the Section A N Z G
in N, and N S perpendicular to
295[Figure 295]
B D. Now, ſeeing that the Por­
tion is in Gravity unto the Liquid,
as the Square made of the Line
is to the Square B D; ψ ſhall
be equall to N T: Which is to
be demonſtrated as above: And,
therefore, N T is alſo equall to
V I: The Portions, therefore,
A V Q and E N Z are equall to
one another. And, ſince that in
the Equall and like Portions A V
Q L and A N Z G, there are drawn A Q and E Z, cutting off
equall Portions, that from the
296[Figure 296]
Extremity of the Baſe, this not
from the Extreme, that which is
drawn from the Extremity of the
Baſe, ſhall make the Acute Angle
with the Diameter of the Portion
leſſer: and in the Triangles N L S
and V ω C, the Angle at L is
greater than the Angle at ω:
Therefore, B S ſhall be leſſer
than B C; and S R leſſer than
C R: and, conſequently, N X
greater than V H; and X T leſſer than H I. Seeing, therefore,
that V Y is double to Y I; It is manifeſt, that N X is greater than
double to X T. Let N M be double to M T: It is manifeſt, from what
hath been ſaid, that the Portion ſhall not reſt, but will incline, untill
that its Bafe do touch the Surface of the Liquid: and it toucheth it in
one Point only, as appeareth in the Figure: And other things
1297[Figure 297]
ſtanding as before, we will again
demonſtrate, that N T is equall to
V I; and that the Portions A V Q
and A N Z are equall to each other.
Therefore, in regard, that in the
Equall and Like Portions A V Q L
and A N Z G, there are drawn
A Q and A Z cutting off equall Por­
tions, they ſhall with the Diameters
of the Portions, contain equall
Angles. Therefore, in the Triangles
N L S and V ω C, the Angles at
the Points L and ω are equall; and the Right Line B S equall to
B C; S R to C R; N X to V H; and X T to H I: And, ſince
V Y is double to Y I, N X ſhall be greater than double of X T.
Let therefore, N M be double to M T. It is hence again manifeſt,
that the Portion will not remain, but ſhall incline on the part
towards A: But it was ſuppoſed, that the ſaid Portion did
touch the Surface of the Liquid in one ſole Point: Therefore,
its Baſe muſt of neceſſity ſubmerge farther into the Liquid.
CONCLVSION V.
If the Portion have leſſer proportion in Gravity to
the Liquid, than the Square F P to the Square
B D, being demitted into the Liquid, and in­
clined, ſo, as that its Baſe touch not the Liquid,
it ſhall ſtand ſo inclined, as that its Axis ſhall
make an Angle with the Surface of the Liquid,
leſſe than the Angle ψ; And its Baſe ſhall
not in the leaſt touch the Liquids Surface.
Finally, let the Portion have leſſer proportion to the Liquid
in Gravity, than the Square F P hath to the Square B D; and
as the Portion is in Gravity to the Liquid, ſo let the
Square made of the Line ψ be to the Square B D. ψ ſhall be
leſſer than P F. Again, apply any Right Line as G I, falling
betwixt the Sections A G Q L and A X D, and parallel to B D;
and let it cut the Middle Conick Section in the Point H, and
1the Right Line R Y in Y. We
298[Figure 298]
ſhall demonſtrate G H to be double
to H I, as it hathbeen demonſtra­
ted, that O G is double to G X.
Then draw G ω touching the Section
A G Q L in G; and G C perpen di­
cular to B D; and drawing a Line
from A to I, prolong it to que Now
A I ſhall be equall to I que and
A Q parallel to G ω. It is to be
demonſtrated, that the Portion being
demitted into the Liquid, and inclined, ſo, as that its Baſe touch
the Liquid, it ſhall ſtand ſo incli­
299[Figure 299]
ned, as that its Axis ſhall make
an Angle with the Surface of the
Liquid leſſe than the Angle φ;
and its Baſe ſhall not in the leaſt
touch the Liquids Surface. For
let it be demitted into the Liquid,
and let it ſtand, ſo, as that its Baſe
do touch the Surface of the Liquid
in one Point only: and the Portion
being cut thorow the Axis by a
Plane erect unto the Surface of the Liquid, let the Section of
300[Figure 300]
the Portion be A N Z L, the Section
of a Rightangled Cone; that of
the Surface of the Liquid A Z; and
the Axis of the Portion and Dia­
meter of the Section B D; and let
B D be cut in the Points K and R
as hath been ſaid above; and draw
N F parallel to A Z, and touching
the Section of the Cone in the Point
N; and N T parallel to B D; and
N S perpendicular to the ſame. Be­
cauſe, now, that the Portion is in Gravity to the Liquid, as
the Square made of ψ is to the Square B D; and ſince that as the
Portion is to the Liquid in Gravity, ſo is the Square N T to the
Square B D, by the things that have been ſaid; it is plain, that
N T is equall to the Line ψ: And, therefore, alſo, the Portions
A N Z and A G Q are equall. And, ſeeing that in the Equall and
Like Portions A G Q L and A N Z L; there are drawn from the
Extremities of their Baſes, A Q and A Z which cut off equall Porti­
ons: It is obvious, that with the Diameters of the Portions they
1make equall Angles; and that in the Triangles N F S and G ω C
the Angles at F and ω are equall; as alſo, that S B and B C, and
S R and C R are equall to one another: And, therefore, N X and
G Y are alſo equall; and X T and Y I. And ſince G H is double
to H I, N X ſhall be leſſer than double of X T. Let N M therefore
be double to M T; and drawing a Line from M to K, prolong it
unto E. Now the Centre of Gravity of the whole ſhall be the
Point K; of the part which is in the Liquid the Point M; and
that of the part which is above the Liquid in the Line prolonged
as ſuppoſe in E. Therefore, by what was even now demonſtrated
it is manifeſt that the Portion ſhall not ſtay thus, but ſhall incline, ſo
as that its Baſe do in no wiſe touch the Surface of the Liquid
And that the Portion will ſtand, ſo, as to make an Angle with the
Surface of the Liquid leſſer than
301[Figure 301]
the Angle φ, ſhall thus be demon
ſtrated. Let it, if poſſible, ſtand,
ſo, as that it do not make an Angle
leſſer than the Angle φ; and diſpoſe
all things elſe in the ſame manner a
before; as is done in the preſet
Figure. We are to demonſtrat
in the ſame method, that N T is e­
quall to ψ; and by the ſame reaſor
equall alſo to G I. And ſince that in
the Triangles P φ C and N F S, the Angle F is not leſſer than the
Angle φ, B F ſhall not be greater than B C: And, therefore, neither
ſhall S R be leſſer than C R; nor N X than P Y: But ſince P F is
greater than N T, let P F be Seſquialter of P Y: N T ſhall be leſſer
than Seſquialter of N X: And, therefore, N X ſhall be greate
than double of X T. Let N M be double of M T; and drawing
Line from M to K prolong it. It is manifeſt, now, by what hath
been ſaid, that the Portion ſhall not continue in this poſition, but ſhall
turn about, ſo, as that its Axis do make an Angle with the Surface
of the Liquid, leſſer than the Angle φ.
FINIS.
1
A
DISCOURSE
PRESENTED
TO THE MOST SERENE
Don Coſimo II.
GREAT DUKE
OF
TUSCANY,
CONCERNING
The NATATION of BODIES Vpon,
And SUBMERSION In,
THE
WATER.
By GALILEUS GALILEI: Philoſopher and
Mathematician, unto His moſt Serene Highneſſe.
Engliſhed from the Second Edition of the ITALIAN,
compared with the Manuſcript Copies, and reduced
into PROPOSITIONS:
By THOMAS SALUSBURY, Eſque
LONDON:
Printed by WILLIAM LEYBOURN:
M D C LXIII.
1
A DISCOVRSE
Preſented to the Moſt Serene DON COSIMO II.
GREATDUKE of TUSC ANY:
CONCERNING
The Natation of BODIES Upon, or Submerſion
In, the WATER.
Conſidering (Moſt Serene Prince) that the
publiſhing this preſent Treatiſe, of ſo
different an Argument from that which

many expect, and which according to the
intentions I propoſed in my ^{*} Aſtronomi­
call Adviſo, I ſhould before this time
have put forth, might peradventure make
ſome thinke, either that I had wholly
relinquiſhed my farther imployment
about the new Celeſtiall Obſervations,
or that, at leaſt, I handled them very
remiſſely; I have judged fit to render an account, aſwell of my
deferring that, as of my writing, and publiſhing this treatiſe.
His Nuncio Sl­
derio.
As to the firſt, the laſt diſcoveries of Saturn to be tricorporeall, and
of the mutations of Figure in Venus, like to thoſe that are ſeen in the
Moon, together with the Conſequents depending thereupon, have
not ſo much occaſioned the demur, as the inveſtigation of the times
of the Converſions of each of the Four Medicean Planets about
piter, which I lighted upon in April the year paſt, 1611, at my being in
Rome; where, in the end, I aſſertained my ſelfe, that the firſt and neereſt
to Jupiter, moved about 8 gr. & 29 m. of its Sphere in an houre,
ing its whole revolution in one naturall day, and 18 hours, and almoſt
an halfe. The ſecond moves in its Orbe 14 gr. 13 min. or very neer,
in an hour, and its compleat converſion is conſummate in 3 dayes, 13
hours, and one third, or thereabouts. The third paſſeth in an hour,
2 gr. 6 min. little more or leſs of its Circle, and meaſures it all in 7
dayes, 4 hours, or very neer. The fourth, and more remote than the
reſt, goes in one houre, o gr 54 min. and almoſt an halfe of its Sphere,
and finiſheth it all in 16 dayes, and very neer 18 hours. But
cauſe the exceſſive velocity of their returns or reſtitutions, requires a
moſt ſcrupulous preciſeneſſe to calculate their places, in times paſt
1and future, eſpecially if the time be for many Moneths or Years; I
am therefore forced, with other Obſervations, and more exact than
the former, and in times more remote from one another, to correct
the Tables of ſuch Motions, and limit them even to the ſhorteſt
ment: for ſuch exactneſſe my firſt Obſervations ſuffice not; not only
in regard of the ſhort intervals of Time, but becauſe I had not as then
found out a way to meaſure the diſtances between the ſaid Planets
by any Inſtrument: I Obſerved ſuch Intervals with ſimple relation
to the Diameter of the Body of Jupiter; taken, as we have ſaid, by
the eye, the which, though they admit not errors of above a Minute,
yet they ſuffice not for the determination of the exact greatneſs of the
Spheres of thoſe Stars. But now that I have hit upon a way of
king ſuch meaſures without failing, ſcarce in a very few Seconds, I will
continue the obſervation to the very occultation of JVPITER,
which ſhall ſerve to bring us to the perfect knowledge of the
ons, and Magnitudes of the Orbes of the ſaid Planets, together

alſo with ſome other conſequences thence ariſing. I adde to theſe
things the obſervation of ſome obſcure Spots, which are
ed in the Solar Body, which changing, poſition in that, propounds
to our conſideration a great argument either that the Sun revolves in
it ſelfe, or that perhaps other Starts, in like manner as Venus and
Mercury, revolve about it, inviſible in other times, by reaſon of their
ſmall digreſſions, leſſe than that of Mercury, and only viſible when
they interpoſe between the Sun and our eye, or elſe hint the truth
of both this and that; the certainty of which things ought not to be
contemned, nor omitted.
The Authors
Obſervations of
the Solar Spots.
Continuall obſervation hath at laſt aſſured me that theſe Spots are
matters contiguous to the Body of the Sun, there continually produced
in great number, and afterwards diſſolved, ſome in a ſhorter, ſome in a
longer time, and to be by the Converſion or Revolution of the Sun in it
ſelfe, which in a Lunar Moneth, or thereabouts, finiſheth its Period,
caried about in a Circle, an accident great of it ſelfe, and greater for
its Conſequences.
The occaſion
ducing the
thor to write
this Treatiſe.
As to the other particular in the next place. ^{*} Many cauſes have
moved me to write the preſent Tract, the ſubject whereof, is the
Diſpute which I held ſome dayes ſince, with ſome learned men of
this City, about which, as your Highneſſe knows, have followed
many Diſcourſes: The principall of which Cauſes hath been the
Intimation of your Highneſſe, having commended to me Writing,
as a ſingular means to make true known from falſe, reall from
rent Reaſons, farr better than by Diſputing vocally, where the
one or the other, or very often both the Diſputants, through too
1greate heate, or exalting of the voyce, either are not underſtood,
or elſe being tranſported by oſtentation of not yeilding to one
ther, farr from the firſt Propoſition, with the novelty, of the
various Propoſals, confound both themſelves and their Auditors.
Moreover, it ſeemed to me convenient to informe your
neſſe of all the ſequell, concerning the Controverſie of which I
treat, as it hath been advertiſed often already by others: and becauſe
the Doctrine which I follow, in the diſcuſſion of the point in hand,
is different from that of Ariſtotle; and interferes with his Principles,
I have conſidered that againſt the Authority of that moſt famous
Man, which amongſt many makes all ſuſpected that comes not from
the Schooles of the Peripateticks, its farr better to give ones Reaſons
by the Pen than by word of mouth and therfore I reſolved to write the
preſent diſcourſe: in which yet I hope to demonſtrate that it was not
out of capritiouſneſſe, or for that I had not read or underſtood
Ariſtotle, that I ſometimes ſwerve from his opinion, but becauſe
ſeverall Reaſons perſwade me to it, and the ſame Ariſtotle hath

tought me to fix my judgment on that which is grounded upon
Reaſon, and not on the bare Authority of the Maſter; and it is
moſt certaine according to the ſentence of Alcinoos, that

ting ſhould be free. Nor is the reſolution of our Queſtion in my
judgment without ſome benefit to the Univerſall, foraſmuch as
treating whether the figure of Solids operates, or not, in their going,
or not going to the bottome in Water, in occurrences of building
Bridges or other Fabricks on the Water, which happen commonly
in affairs of grand import, it may be of great availe to know the
truth.
Ariſtotle prefers
Reaſon to the
Authority ofan
Author.
The benefit of
this Argument.
I ſay therfore, that being the laſt Summer in company with certain

Learned men, it was ſaid in the argumentation; That Condenſation
was the propriety of Cold, and there was alledged for inſtance, the
example of Ice: now I at that time ſaid, that, in my judgment,
the Ice ſhould be rather Water rarified than condenſed, and my

reaſon was, becauſe Condenſation begets diminution of Maſs, and
augmentation of gravity, and Rarifaction cauſeth greater Lightneſs,
and augmentarion of Maſſe: and Water in freezing, encreaſeth in
Maſſe, and the Ice made thereby is lighter than the Water on which
it ſwimmeth.
Condenſation
the Propriety of
Cold, according
to the
ticks.
Ice rather water
rarified, than
condenſed, and
why:
What I ſay, is manifeſt, becauſe, the medium ſubtracting from the
whole Gravity of Sollids the weight of ſuch another Maſſe of the ſaid

Medium; was Archimedes proves in his ^{*} Firſt Booke De Inſidentibus
Humido; when ever the Maſſe of the ſaid Solid encreaſeth by Diſtraction,
the more ſhall the Medium detract from its entire Gravity; and leſſe,
when by Compreſſion it ſhall be condenſed and reduced to a leſſe Maſſe.
1In lib: 1. of
tation of Bodies
Prop. 7.
Figure operates
not in the
tion of Sollids.
It was anſwered me, that that proceeded not from the greater Levity;

but from the Figure, large and flat, which not being able to
trate the Reſiſtance of the Water, is the cauſe that it ſubmergeth not.
I replied, that any piece of Ice, of whatſoever Figure, ſwims upon
the Water, a manifeſt ſigne, that its being never ſo flat and broad,
hath not any part in its floating: and added, that it was a manifeſt
proofe hereof to ſee a piece of Ice of very broad Figure being thruſt
to the botome of the Water, ſuddenly return to flote atoppe, which
had it been more grave, and had its ſwimming proceeded from its
Forme, unable to penetrate the Reſiſtance of the Medium, that
would be altogether impoſſible; I concluded therefore, that the Figure
was in ſort a Cauſe of the Natation or Submerſion of Bodies,
but the greater or leſſe Gravity in reſpect of the Water: and
fore all Bodyes heavier than it of what Figure ſoever they be,
rently go to the bottome, and the lighter, though of any figure, float
indifferently on the top: and I ſuppoſe that thoſe which hold
wiſe, were induced to that beliefe, by ſeeing how that diverſity
of Formes or Figures, greatly altereth the Veloſity, and Tardity
of Motion; ſo that Bodies of Figure broad and thin, deſcend
far more leaſurely into the Water, than thoſe of a more compacted
Figure, though both made of the ſame Matter: by which ſome
might be induced to believe that the Dilatation of the Figure might
reduce it to ſuch ampleneſſe that it ſhould not only retard but wholly
impede and take away the Motion, which I hold to be falſe. Upon
this Concluſion, in many dayes diſcourſe, was ſpoken much, and
many things, and divers Experiments produced, of which your
Highneſſe heard, and ſaw ſome, and in this diſcourſe ſhall have
all that which hath been produced againſt my Aſſertion, and what
hath been ſuggeſted to my thoughts on this matter, and for
firmation of my Concluſion: which if it ſhall ſuffice to remove that
(as I eſteem hitherto falſe) Opinion, I ſhall thinke I have not
unprofitably ſpent my paynes and time. and although that come
not to paſſe, yet ought I to promiſe another benefit to my ſelfe,
namely, of attaining the knowledge of the truth, by hearing my
Fallacyes confuted, and true demonſtrations produced by thoſe
of the contrary opinion.
And to proceed with the greateſt plainneſs and perſpicuity that
I can poſſible, it is, I conceive, neceſſary, firſt of all to declare
what is the true, intrinſecall, and totall Cauſe, of the aſcending of
ſome Sollid Bodyes in the Water, and therein floating; or on the
contrary, of their ſinking. and ſo much the rather in aſmuch as I
cannot ſatisfie my ſelfe in that which Ariſtotle hath left written on
this Subject.
The cauſe of the
Natation & ſub­
I ſay then the Cauſe why ſome Sollid Bodyes deſcend to
1Bottom of Water, is the exceſſe of their Gravity, above the

Gravity of the Water; and on the contrary, the exceſs of the
Waters Gravity above the Gravity of thoſe, is the Cauſe that others
do not deſcend, rather that they riſe from the Bottom, and aſcend
to the Surface. This was ſubtilly demonſtrated by Archimedes in
his Book Of the NATATION of BODIES: Conferred afterwards
by a very grave Author, but, if I erre not inviſibly, as below for
defence of him, I ſhall endeavour to prove.
merſion of
ids in the
ter.
I, with a different Method, and by other meanes, will endeavour
to demonſtrate the ſame, reducing the Cauſes of ſuch Effects to
more intrinſecall and immediate Principles, in which alſo are
vered the Cauſes of ſome admirable and almoſt incredible
dents, as that would be, that a very little quantity of Water, ſhould
be able, with its ſmall weight, to raiſe and ſuſtain a Solid Body, an
hundred or a thouſand times heavier than it.
And becauſe demonſtrative Order ſo requires, I ſhall define
tain Termes, and afterwards explain ſome Propoſitions, of which,
as of things true and obvious, I may make uſe of to my preſent
poſe.
DEFINITION I.
I then call equally Grave in ſpecie, thoſe Matters
of which equall Maſſes weigh equally.
As if for example, two Balls, one of Wax, and the other of ſome
Wood of equall Maſſe, were alſo equall in Weight, we ſay, that
ſuch Wood, and the Wax are in ſpecie equally grave.
DEFINITION II.
But equally grave in Abſolute Gravity, we call two
Sollids, weighing equally, though of Maſs they be
unequall.
As for example, a Maſs of Lead, and another of Wood, that
weigh each ten pounds, I call equall in Abſolute Gravity, though
the Maſs of the Wood be much greater then that of the Lead.
And, conſequently, leſs Grave in ſpecie.
DEFINITION III.
I call a Matter more Grave in ſpecie than another, of
which a Maſs, equall to a Maſs of the other, ſhall
weigh more.
1
And ſo I ſay, that Lead is more grave in ſpecie than Tinn, becauſe
if you take of them two equall Maſſes, that of the Lead weigheth
more.
DEFINITION IV.
But I call that Body more grave abſolutely than this, if
that weigh more than this, without any reſpect had to
the Maſſes.
And thus a great piece of Wood is ſaid to weigh more than a
little lump of Lead, though the Lead be in ſpecie more heavy than
the Wood. And the ſame is to be underſtood of the leſs grave in
ſpecie, and the leſs grave abſolutely.
Theſe Termes defined, I take from the Mechanicks two
ples: the firſt is, that
AXIOME. I.
Weights abſolutely equall, moved with equall Velocity,
are of equall Force and Moment in their operations.
DEFINITION V.
Moment, amongſt Mechanicians, ſigrifieth that
Vertue, that Force, or that Efficacy, with which
the Mover moves, and the Moveable reſiſts.
Which Vertue dependes not only on the ſimple Gravity, but on the
Velocity of the Motion, and on the diverſe Inclinations of the Spaces
along which the Motion is made: For a deſcending Weight makes a
greater Impetus in a Space much declining, than in one leſs declining;
and in ſumme, what ever is the occaſion of ſuch Vertue, it ever retaines
the name of Moment; nor in my Judgement, is this ſence new in our
Idiome, for, if I mistake not, I think we often ſay; This is a weighty
buſineſſe, but the other is of ſmall moment: and we conſider lighter
ters and let paſs thoſe of Moment; a Metaphor, I ſuppoſe, taken from
the Mechanicks.
As for example, two weights equall in abſolute Gravity, being
put into a Ballance of equall Arms, they ſtand in Equilibrium,
ther one going down, nor the other up: becauſe the equality of the
Diſtances of both, from the Centre on which the Ballance is
ted, and about which it moves, cauſeth that thoſe weights, the ſaid
Ballance moving, ſhall in the ſame Time move equall Spaces, that is,
ſhall move with equall Velocity, ſo that there is no reaſon for which
1this Weight ſhould deſcend more than that, or that more than this;
and therefore they make an Equilibrium, and their Moments continue
of ſemblable and equall Vertue.
The ſecond Principle is; That
AXIOME II.
The Moment and Force of the Gravity, is encreaſed by
the Velocity of the Motion.
So that Weights abſolutely equall, but conjoyned with Velocity
unequall, are of Force, Moment and Vertue unequall: and the
more potent, the more ſwift, according to the proportion of the
locity of the one, to the Velocity of the other. Of this we have a
very pertinent example in the Balance or Stiliard of unequall Arms,
at which Weights abſolutely equall being ſuſpended, they do not
weigh down, and gravitate equally, but that which is at a greater
diſtance from the Centre, about which the Beam moves, deſcends,
raiſing the other, and the Motion of this which aſcends is ſlow, and
the other ſwift: and ſuch is the Force and Vertue, which from the
Velocity of the Mover, is conferred on the Moveable, which receives
it, that it can exquiſitely compenſate, as much more Weight added to
the other ſlower Moveable: ſo that if of the Arms of the Balance,
one were ten times as long as the other, whereupon in the Beames
moving about the Centre, the end of that would go ten times as far
as the end of this, a Weight ſuſpended at the greater diſtance, may
ſuſtain and poyſe another ten times more grave abſolutely than it:
and that becauſe the Stiliard moving, the leſſer Weight ſhall move
ten times faſter than the bigger. It ought alwayes therefore to be
underſtood, that Motions are according to the ſame Inclinations,
namely, that if one of the Moveables move perpendicularly to the
Horizon, then the other makes its Motion by the like Perpendicular;
and if the Motion of one were to be made Horizontally; that then
the other is made along the ſame Horizontall plain: and in ſumme,
alwayes both in like Inclinations. This proportion between the
Gravity and Velocity is found in all Mechanicall Inſtruments: and
is conſidered by Ariſtotle, as a Principle in his Mechanicall Queſtions;
whereupon we alſo may take it for a true Aſſumption, That
AXIOME III.
Weights abſolutely unequall, do alternately counterpoyſe
and become of equall Moments, as oft as their
ties, with contrary proportion, anſwer to the Velocity of
their Motions.
1
That is to ſay, that by how much the one is leſs grave than the other,
by ſo much is it in a conſtitution of moving more ſwiftly than that.
Having prefatically explicated theſe things, we may begin to
quire, what Bodyes thoſe are which totally ſubmerge in Water, and
go to the Bottom, and which thoſe that by conſtraint float on the
top, ſo that being thruſt by violence under Water, they return to
ſwim, with one part of their Maſs viſible above the Surface of the
Water: and this we will do by conſidering the reſpective
on of the ſaid Solids, and of Water: Which operation followes
the Submerſion and ſinking; and this it is, That in the Submerſion

that the Solid maketh, being depreſſed downwards by its proper
Gravity, it comes to drive away the water from the place where it
ſucceſſively ſubenters, and the water repulſed riſeth and aſcends
above its firſt levell, to which Aſcent on the other ſide it, as being a
grave Body of its own nature, reſiſts: And becauſe the deſcending
Solid more and more immerging, greater and greater quantity of
Water aſcends, till the whole Sollid be ſubmerged; its neceſſary to
compare the Moments of the Reſiſtance of the water to Aſcenſion,
with the Moments of the preſſive Gravity of the Solid: And if the
Moments of the Reſiſtance of the water, ſhall equalize the Moments

of the Solid, before its totall Immerſion; in this caſe doubtleſs there
ſhall be made an Equilibrium, nor ſhall the Body ſink any farther.
But if the Moment of the Solid, ſhall alwayes exceed the Moments

wherewith the repulſed water ſucceſſively makes Reſiſtance, that
Solid ſhall not only wholly ſubmerge under water, but ſhall deſcend
to the Bottom. But if, laſtly, in the inſtant of totall Submerſion,

the equality ſhall be made between the Moments of the prement
Solid, and the reſiſting Water; then ſhall reſt enſue, and the ſaid
Solid ſhall be able to reſt indifferently, in whatſoever part of the
water. By this time is manifeſt the neceſſity of comparing the

Gravity of the water, and of the Solid; and this compariſon might
at firſt ſight ſeem ſufficient to conclude and determine which are the
Solids that float a-top, and which thoſe that ſink to the Bottom in the
water, aſſerting that thoſe ſhall float which are leſſe grave in ſpecie
than the water, and thoſe ſubmerge, which are in ſpecie more grave.
For it ſeems in appearance, that the Sollid in ſinking continually,
raiſeth ſo much Water in Maſs, as anſwers to the parts of its own
Bulk ſubmerged: whereupon it is impoſſible, that a Solid leſs grave
in ſpecie, than water, ſhould wholly ſink, as being unable to raiſe a
weight greater than its own, and ſuch would a Maſs of water equall
to its own Maſs be. And likewiſe it ſeems neceſſary, that the graver
Solids do go to the Bottom, as being of a Force more than ſufficient
for the raiſing a Maſſe of water, equall to its own, though inferiour
in weight. Nevertheleſs the buſineſs ſucceeds otherwiſe: and
1though the Concluſions are true, yet are the Cauſes thus aſſigned
deficient, nor is it true, that the Solid in ſubmerging, raiſeth and
repulſeth Maſſes of Water, equall to the parts of it ſelf ſubmerged;
but the Water repulſed, is alwayes leſs than the parts of the Solid

ſubmerged: and ſo much the more by how much the Veſſell in
which the Water is contained is narrower: in ſuch manner that it
hinders not, but that a Solid may ſubmerge all under Water,
out raiſing ſo much Water in Maſs, as would equall the tenth or
twentieth part of its own Bulk: like as on the contrary, a very

ſmall quantity of Water, may raiſe a very great Solid Maſs, though
ſuch Solid ſhould weigh abſolutely a hundred times as much, or
more, than the ſaid Water, if ſo be that the Matter of that ſame
Solid be in ſpecie leſs grave than the Water. And thus a great
Beam, as ſuppoſe of a 1000 weight, may be raiſed and born afloat
by Water, which weighs not 50: and this happens when the
ment of the Water is compenſated by the Velocity of its Motion.
How the
merſion of
lids in the
ter, is effected.
What Solids
ſhall float on the
Water.
What Solids
ſhall ſinke to the
botome.
What Solids
ſhall reſt in all
places of the
ter.
The Gravitie of
the Water and
Solid muſt be
compared in all
Problems, of
tation of Bodies.
The water
pulſed is ever leſs
than the parts of
the Sollid
merged.
A ſmall quantity
of water, may
float a very
great Solid Maſs.
But becauſe ſuch things, propounded thus in abſtract, are
what difficult to be comprehended, it would be good to demonſtrate
them by particular examples; and for facility of demonſtration, we
will ſuppoſe the Veſſels in which we are to put the Water, and place
the Solids, to be inviron'd and included with ſides erected
cular to the Plane of the Horizon, and the Solid that is to be put
into ſuch veſſell to be either a ſtreight Cylinder, or elſe an upright
Priſme
The which propoſed and declared, I proceed to demonstrate the truth
of what hath been hinted, forming the enſuing Theoreme.
THEOREME I.
The Maſs of the Water whichaſcends in the

merging of a Solid, Priſme or Cylinder, or that
abaſeth in taking it out, is leſs than the Maſs of
the ſaid Solid, ſo depreſſed or advanced: and
hath to it the ſame proportion, that the Surface
of the Water circumfuſing the Solid, hath to the
ſame circumfuſed Surface, together with the Baſe
of the Solid.
The Proportion
of the water
ſed to the Solid
ſubmerged.
Let the Veſſell be A B C D, and in it the Water raiſed up to the
Levell E F G, before the Solid Priſme H I K be therein immerged;
but after that it is depreſſed under Water, let the Water be raiſed as
high as the Levell L M, the Solid H I K ſhall then be all under Water,
and the Maſs of the elevated Water ſhall be L G, which is leſs than the
1302[Figure 302]
Maſſe of the Solid depreſſed, namely of
H I K, being equall to the only part E I K,
which is contained under the firſt Levell
E F G. Which is manifeſt, becauſe if
the Solid H I K be taken out, the Water
I G ſhall return into the place occupied by
the Maſs E I K, where it was continuate
fore the ſubmerſion of the Priſme. And
the Maſs L G being equall to the Maſs
E K: adde thereto the Maſs E N, and it
ſhall be the whole Maſs E M, compoſed of the parts of the Priſme E N,
and of the Water N F, equall to the whole Solid H I K: And,
fore, the Maſs L G ſhall have the ſame proportion to E M, as to the
Maſs H I K: But the Maſs L G hath the ſame proportion to the Maſs
E M, as the Surface L M hath to the Surface M H: Therefore it is
nifeſt, that the Maſs of Water repulſed L G, is in proportion to the Maſs
of the Solid ſubmerged H I K; as the Surface L M, namely, that of the
Water ambient about the Sollid, to the whole Surface H M, compounded
of the ſaid ambient water, and the Baſe of the Priſme H N. But if we
ſuppoſe the firſt Levell of the Water the according to the Surface H M,
and the Priſme allready ſubmerged H I K; and after to be taken out and
raiſed to E A O, and the Water to be faln from the firſt Levell H L M as
low as E F G; It is manifeſt, that the Priſme E A O being the ſame with
H I K, its ſuperiour part H O, ſhall be equall to the inferiour E I K:
and remove the common part E N, and, conſequently, the Maſs of the
Water L G is equall to the Maſs H O; and, therefore, leſs than the
Solid, which is without the Water, namely, the whole Priſme E A O, to
which likewiſe, the ſaid Maſs of Water abated L G, hath the ſame
tion, that the Surface of the Waters circumfuſed L M hath to the ſame
circumfuſed Surface, together with the Baſe of the Priſme A O: which
hath the ſame demonſtration with the former caſe above.
And from hence is inferred, that the Maſs of the Water, that riſeth in
the immerſion of the Solid, or that ebbeth in elevating it, is not equall to
all the Maſs of the Solid, which is ſubmerged or elevated, but to that
part only, which in the immerſion is under the firſt Levell of the Water,
and in the elevation remaines above the firſt Levell: Which is that
which was to be demonſtrated. We will now purſue the things that
remain.
And firſt we will demonſtrate that,
1
THEOREME II.
When in one of the above ſaid Veſſels, of what ever

breadth, whether wide or narrow, there is placed ſuch
a Priſme or Cylinder, inviron'd with Water, if we
vate that Solid perpendicularly, the Water
ſed ſhall abate, and the Abatement of the Water,
ſhall have the ſame proportion to the Elevation of the
Priſme, as one of the Baſes of the Priſme, hath to
the Surface of the Water Circumfuſed.
The proportion
of the water
ted, to the Solid
raiſed.
Imagine in the Veſſell, as is aforeſaid, the
303[Figure 303]
Priſme A C D B to be placed, and in the
reſt of the Space the Water to be
fuſed as far as the Levell E A: and
ſing the Solid, let it be transferred to
G M, and let the Water be abaſed from
E A to N O: I ſay, that the deſcent of
the Water, meaſured by the Line A O,
hath the ſame proportion to the riſe of the
Priſme, meaſured by the Line G A, as the Baſe of the Solid G H
hath to the Surface of the Water N O. The which is manifeſt:
becauſe the Maſs of the Solid G A B H, raiſed above the firſt Levell
E A B, is equall to the Maſs of Water that is abaſed E N O A.
Therefore, E N O A and G A B H are two equall Priſmes; for of
equall Priſmes, the Baſes anſwer contrarily to their heights:
fore, as the Altitude A O is to the Altitude A G, ſo is the
cies or Baſe G H to the Surface of the Water N O. If therefore,
for example, a Pillar were erected in a waſte Pond full of Water,
or elſe in a Well, capable of little more then the Maſs of the ſaid
Pillar, in elevating the ſaid Pillar, and taking it out of the Water,
according as it riſeth, the Water that invirons it will gradually abate,
and the abaſement of the Water at the inſtant of lifting out the
Pillar, ſhall have the ſame proportion, that the thickneſs of the Pillar
hath to the exceſs of the breadth of the ſaid Pond or Well, above
the thickneſs of the ſaid Pillar: ſo that if the breadth of the Well
were an eighth part larger than the thickneſs of the Pillar, and the

breadth of the Pond twenty five times as great as the ſaid thickneſs,
in the Pillars aſcending one foot, the water in the Well ſhall deſcend
ſeven foot, and that in the Pond only 1/25 of a foot.
Why a Solid
leſs grave in
cie than water,
ſtayeth not
der water, in
ry ſmall depthst.
This Demonſtrated, it will not be difficult to ſhew the true
cauſe, how it comes to paſs, that,
1
THEOREME III.
A Priſme or regular Cylinder, of a ſubſtance ſpecifically
leſs grave than Water, if it ſhould be totally ſubmerged
in Water, ſtayes not underneath, but riſeth, though the
Water circumfuſed be very little, and in abſolute
Gravity, never ſo much inferiour to the Gravity of the
ſaid Priſme.
Let then the Priſme A E F B, be put into the Veſſell C D F B, the
ſame being leſs grave in ſpecie than the Water: and let the
Water infuſed riſe to the height of the Priſme: I ſay, that the
Priſme left at liberty, it ſhall riſe, being born up
by the Water circumfuſed C D E A. For the
304[Figure 304]
Water C E being ſpecifically more grave than
the Solid A F, the abſolute weight of the water
C E, ſhall have greater proportion to the
lute weight of the Priſme A F, than the Maſs
C E hath to the Maſs A F (in regard the Maſs
hath the ſame proportion to the Maſs, that the
weight abſolute hath to the weight abſolute,
in caſe the Maſſes are of the ſame Gravity in ſpecie.) But
the Maſs C E is to the Maſs A F, as the Surface of the water A C, is
to the Superficies, or Baſe of the Priſme A B; which is the ſame
portion as the aſcent of the Priſme when it riſeth, hath to the deſcent
of the water circumfuſed C E.
Therefore, the abſolute Gravity of the water C E, hath greater
proportion to the abſolute Gravity of the Priſme A F; than the
Aſcent of the Priſme A F, hath to the deſcent of the ſaid
water C E. The Moment, therefore, compounded of the abſolute
Gravity of the water C E, and of the Velocity of its deſcent, whilſt
it forceably repulſeth and raiſeth the Solid A F, is greater than the
Moment compounded of the abſolute Gravity of the Priſme A F, and
of the Tardity of its aſcent, with which Moment it contraſts and
fiſts the repulſe and violence done it by the Moment of the water:
Therefore, the Priſme ſhall be
The Proportion
according to
which the
merſion & Na
tation of Solids
is made.
It followes, now, that we proceed forward to demonſtrate more
particularly, how much ſuch Solids ſhall be inferiour in Gravity to
the water elevated; namely, what part of them ſhall reſt ſubmerged,
and what ſhall be viſible above the Surface of the water: but firſt
it is neceſſary to demonſtrate the ſubſequent Lemma.
1
LEMMA I.
The abſolute Gravities of Solids, have a proportion com-

pounded of the proportions of their ſpecificall Gravities,
and of their Maſſes.
The abſolute
Gravity of
lids, are in a
portion
pounded of their
Specifick
ties, and of their
Maſſes.
Let A and B be two Solids. I ſay, that the Abſolute Gravity
of A, hath to the Abſolute Gravity of B, a proportion
pounded of the proportions of the ſpecificall Gravity of A, to
the Specificall Gravity of B, and of the Maſs
A to the Maſs B. Let the Line D have the
305[Figure 305]
ſame proportion to E, that the ſpecifick
Gravity of A, hath to the ſpecifick Gravity
of B; and let E be to F, as the Maſs A to the
Maſs B: It is manifeſt, that the proportion
of D to F, is compounded of the proportions
D and E; and E and F. It is requiſite,
therefore, to demonſtrate, that as D is to F, ſo the abſolute Gravity
of A, is to the abſolute Gravity of B. Take the Solid C, equall in
Maſs to the Solid A, and of the ſame Gravity in ſpecie with the Solid
B. Becauſe, therefore, A and C are equall in Maſs, the abſolute
Gravity of A, ſhall have to the abſolute Gravity of C, the ſame
portion, as the ſpecificall Gravity of A, hath to the ſpecificall Gravity
of C, or of B, which is the ſame in ſpecie; that is, as D is to E. And,
cauſe, C and B are of the ſame Gravity in ſpecie, it ſhall be, that as
the abſolute weight of C, is to the abſolute weight of B, ſo the Maſs
C, or the Maſs A, is to the Maſs B; that is, as the Line E to the Line
F. As therefore, the abſolute Gravity of A, is to the abſolute
Gravity of C, ſo is the Line D to the Line E: and, as the abſolute
Gravity of C, is to the abſolute Gravity of B, ſo is the Line E to the
Line F: Therefore, by Equality of proportion, the abſolute
vity of A, is to the abſolute Gravity of B, as the Line D to the
Line F: which was to be demonſtrated. I proceed now to
ſtrate, how that,
1
THEOREME
The proportion
of water
ſite to make a
Solid ſwim.
If a Solid, Cylinder, or Priſme, leſſe grave ſpecifically
than the Water, being put into a Veſſel, as above, of
whatſoever greatneſſe, and the Water, be afterwards
infuſed, the Solid ſhall reſt in the bottom, unraiſed, till
the Water arrive to that part of the Altitude, of the
ſaid Priſme, to which its whole Altitude hath the
ſame proportion, that the Specificall Gravity of the
Water, hath to the Specificall Gravity of the ſaid
Solid: but infuſing more Water, the Solid ſhall aſcend.
Let the Veſſell be M L G N of any bigneſs, and let there be
ced in it the Solid Priſme D F G E, leſs grave in ſpecie than the
water; and look what proportion the Specificall Gravity of
the water, hath to that of the Priſme, ſuch let the Altitude D F, have
to the Altitude F B. I ſay, that infuſing water to the Altitude F B,
the Solid D G ſhall not float, but ſhall ſtand in Equilibrium, ſo, that
that every little quantity of water, that is infuſed, ſhall raiſe it. Let
the water, therefore, be infuſed to the Levell A B C, and, becauſe
the Specifick Gravity of the Solid D G, is to the Specifick Gravity of
the water, as the altitude B F is to the altitude F D; that is, as the Maſs
B G to the Maſs G D; as the proportion of the Maſs B G is to the
Maſs G D, as the proportion of the Maſs G D is to the Maſs A F, they
compoſe the Proportion of the Maſs B G to the Maſs A F. Therefore,
the Maſs B G is to the Maſs A F, in a proportion compounded of the
proportions of the Specifick Gravity of the Solid G D, to the
fick Gravity of the water, and of the Maſs G D
to the Maſs A F: But the ſame proportions
306[Figure 306]
of the Specifick Gravity of G D, to the Specifick
Gravity of the water, and of the Maſs G D to
the Maſs A F, do alſo by the precedent Lemma,
compound the proportion of the abſolute
vity of the Solid D G, to the abſolute Gravity
of the Maſs of the water A F: Therefore,
as the Maſs B G is to the Maſs A F, ſo is the
Abſolute Gravity of the Solid D G, to the
ſolute Gravity of the Maſs of the water A F. But as the Maſs B G
is to the Maſs A F; ſo is the Baſe of the Priſme D E, to the Surface
of the water AB; and ſo is the deſcent of the water A B, to the
Elevation of the Priſme D G; Therefore, the deſcent of the
1water is to the elevation of the Priſme, as the abſolute Gravity of
the Priſme, is to the abſolute Gravity of the water: Therefore, the
Moment reſulting from the abſolute Gravity of the water A F, and
the Velocity of the Motion of declination, with which Moment it
forceth the Priſme D G, to riſe and aſcend, is equall to the Moment
that reſults from the abſolute Gravity of the Priſme D G, and from
the Velocity of the Motion, wherewith being raiſed, it would aſcend:
with which Moment it reſiſts its being raiſed: becauſe, therefore,
ſuch Moments are equall, there ſhall be an Equilibrium between the
water and the Solid. And, it is manifeſt, that putting a little more
water unto the other A F, it will increaſe the Gravity and Moment,
whereupon the Priſme D G, ſhall be overcome, and elevated till that
the only part B F remaines ſubmerged. Which is that that was to
be demonſtrated.
COROLLARY I.
By what hath been demonſtrated, it is manifeſt, that Solids leſs grave

in ſpecie than the water, ſubmerge only ſo far, that as much water in
Maſs, as is the part of the Solid ſubmerged, doth weigh abſolutely as
much as the whole Solid.
How far Solids
leſs grave in
cie than water,
do ſubmerge.
For, it being ſuppoſed, that the Specificall Gravity of the water,
is to the Specificall Gravity of the Priſme D G, as the Altitude
D F, is to the Altitude F B; that is, as the Solid D G is to the
Solid B G; we might eaſily demonſtrate, that as much water in Maſs
as is equall to the Solid B G, doth weigh abſolutely as much as the
whole Solid D G; For, by the Lemma foregoing, the Abſolute
Gravity of a Maſs of water, equall to the Maſs B G, hath to the
ſolute Gravity of the Priſme D G, a proportion compounded of the
proportions, of the Maſs B G to the Maſs G D, and of the Specifick
Gravit 7 of the water, to the Specifick Gravity of the Priſme: But
the Gravity in ſpecie of the water, to the Gravity in ſpecie of the
Priſme, is ſuppoſed to be as the Maſs G D to the Maſs G B.
fore, the Abſolute Gravity of a Maſs of water, equall to the Maſs
B G, is to the Abſolute Gravity of the Solid D G, in a proportion
compounded of the proportions, of the Maſs B G to the Maſs G D,
and of the Maſs D G to the Maſs G B; which is a proportion of
equalitie. The Abſolute Gravity, therefore, of a Maſs of Water
equall to the part of the Maſs of the Priſme B G, is equall to the
ſolute Gravity of the whole Solid D G.
1
COROLLARY
A Rule to
librate Solids in
the water.
It followes, moreover, that a Solid leſs grave than the water, being put
into a Veſſell of any imaginable greatneſs, and water being circumfuſed
about it to ſuch a height, that as much water in Maſs, as is the part of
the Solid ſubmerged, doth/> weigh abſolutely as much as the whole Solid;
it ſhall by that water be juſtly ſuſtained, be the circumfuſed Water in
quantity greater or leſſer.
For, if the Cylinder or Priſme M, leſs grave than the water, v.
gra. in Subſequiteriall proportion, ſhall be put into the
ous Veſſell A B C D, and the water raiſed about it, to three
quarters of its height, namely, to its Levell A D: it ſhall be ſuſtained
and exactly poyſed in
librium. The ſame will
pen, if the Veſſell E N S F
307[Figure 307]
were very ſmall, ſo, that
tween the Veſſell and the
lid M, there were but a very
narrow ſpace, and only capable of ſo much water, as the hundredth
part of the Maſs M, by which it ſhould be likewiſe raiſed and erected,
as before it had been elevated to three fourths of the height of the
Solid: which to many at the firſt ſight, may ſeem a notable Paradox,
and beget a conceit, that the Demonſtration of theſe effects, were
ſophiſticall and fallacious: but, for thoſe who ſo repute it, the
periment is a means that may fully ſatisfie them. But he that ſhall
but comprehend of what Importance Velocity of Motion is, and how
it exactly compenſates the defect and want of Gravity, will ceaſe to
wonder, in conſidering that at the elevation of the Solid M, the great
Maſs of water A B C D abateth very little, but the little Maſs of
water E N S F decreaſeth very much, and in an inſtant, as the Solid
M before did liſe, howbeit for a very ſhort ſpace: Whereupon the
Moment, compounded of the ſmall Abſolute Gravity of the water
E N S F, and of its great Velocity in ebbing, equalizeth the Force and
and Moment, that reſults from the compoſicion of the immenſe
vity of the water A B C D, with its great ſlowneſſe of ebbing;
ſince that in the Elevation of the Sollid M, the abaſement of the leſ­

ſer water E S, is performed juſt ſo much more ſwiftly than the great
Maſs of water A C, as this is more in Maſs than that which we thus
demonſtrate.
The proportion
according to
which water
ſeth and falls in
different Veſſels
at the
on and
on of solids.
In the riſing of the Solid M, its elevation hath the ſame proportion
to the circumfuſed water E N S F, that the Surface of the ſaid water,
hath to the Superficies or Baſe of the ſaid Solid M; which Baſe hath
the ſame proportion to the Surface of the water A D, that the
1ment or ebbing of the water A C, hath to the riſe or elevation of
the ſaid Solid M. Therefore, by Perturbation of proportion, in the
aſcent of the ſaid Solid M, the abaſement of the water A B C D, to
the abaſement of the water E N S F, hath the ſame proportion, that the
Surface of the water E F, hath to the Surface of the water A D;
that is, that the whole Maſs of the water E N S F, hath to the whole
Maſs A B C D, being equally high: It is manifeſt, therefore, that
in the expulſion and elevation of the Solid M, the water E N S F
ſhall exceed in Velocity of Motion the water A B C D, aſmuch as it
on the other ſide is exceeded by that in quantity: whereupon their
Moments in ſuch operations, are mutually equall.
And, for ampler confirmation, and clearer explication of this, let us
conſider the preſent Figure, (which if I be not deceived, may ſerve to
detect the errors of ſome Practick Mechanitians, who upon a falſe
tion ſome times attempt impoſſible enterprizes,) in which, unto the large
Veſſell E I D F, the narrow Funnell or Pipe I C A B is continued, and
poſe water infuſed into them, unto the Levell L G H, which water ſhall
reſt in this poſition, not without admiration in ſome, who cannot conceive
308[Figure 308]
how it can be, that the heavie charge of the great
Maſs of water G D, preſſing downwards, ſhould
not elevate and repulſe the little quantity of the
other, contained in the Funnell or Pipe C L, by
which the deſcent of it is reſisted and hindered:
But ſuch wonder ſhall ceaſe, if we begin to ſuppoſe
the water G D to be abaſed only to Q D, and
ſhall afterwards conſider, what the water C L
hath done, which to give place to the other, which
is deſcended from the Levell G H, to the Levell
Q O, ſhall of neceſſity have aſcended in the ſame
time, from the Levell Lunto A B. And the
aſcent L B, ſhall be ſo much greater than the
ſcent G Q, by how much the breadth of the Veſſell
G D, is greater than that of the Funnell I C;
which, in ſumme, is as much as the water G D,
is more than the water L C: but in regard that the Moment of the Velocity
of the Motion, in one Moveable, compenſates that of the Gravity of
ther, what wonder is it, if the ſwift aſcent of the leſſer Water C L, ſhall
reſiſt the ſlow deſcent of the greater G D?
The ſame, therefore, happens in this operation, as in the Stilliard,
in which a weight of two pounds counterpoyſeth an other of 200,
asoften as that ſhall move in the ſame time, a ſpace 100 times
er than this: which falleth out when one Arme of the Beam is an
1hundred times as long as the other. Let the erroneous opinion o

thoſe therefore ceaſe, who hold that a Ship is better, and eaſter born
up in a great abundance of water, then in a leſſer quantity, (this was
believed by Ariſtotle in his Problems, Sect. 23, Probl. 2.) it being or
the contrary true, that its poſſible, that a Ship may as well float in
ten Tun of water, as in an
A ſhip flotes as
well in ten Tun
of water as in an
Ocean.
A Solid
fiaclly graver
than the water,
cannot be born
up by any
tity of it.
But following our matter, I ſay, that by what hath been hitherto
demonſtrated, we may underſtand how, that
COROLLARY III.
One of the above named Solids, when more grave in ſpecie than the water,
can never be ſuſtained, by any whatever quantity of it.
For having ſeen how that the Moment wherewith ſuch a Solid
as grave in ſpecie as the water, contraſts with the Moment of any Maſs
of water whatſoever, is able to retain it, even to its totall Submerſion:
without its ever aſcending; it remaineth, manifeſt, that the water is
far leſs able to raiſe it up, when it exceeds the ſame in ſpecie:
that though you infuſe water till its totall Submerſion, it ſhall ſtill
ſtay at the Bottome, and with ſuch Gravity, and Reſiſtance to
tion, as is the exceſs of its Abſolute Gravity, above the Abſolute
vity of a Maſs equall to it, made of water, or of a Matter in ſpecie
equally grave with the water: and, though you ſhould moreover
adde never ſo much water above the Levell of that which equalizeth
the Altitude of the Solid, it ſhall not, for all that, encreaſe the Preſſion
or Gravitation, of the parts circumfuſed about the ſaid Solid, by
which greater preſſion, it might come to be repulſed, becauſe, the
Reſiſtance is not made, but only by thoſe parts of the water, which
at the Motion of the ſaid Solid do alſo move, and theſe are thoſe
only, which are comprehended by the two Superficies equidiſtant to
the Horizon, and their parallels, that comprehend the Altitude of the
Solid immerged in the water.
I conceive, I have by this time ſufficiently declared and opened
the way to the contemplation of the true, intrinſecall and proper
Cauſes of diverſe Motions, and of the Reſt of many Solid Bodies
diverſe Mediums, and particularly in the water, ſhewing how all
effect, depend on the mutuall exceſſes of the Gravity of the
bles and of the Mediums: and, that which did highly import,
moving the Objection, which peradventure would have begotter
much doubting, and ſcruple in ſome, about the verity of my
cluſion, namely, how that notwithſtanding, that the exceſs of the
Gravity of the water, above the Gravity of the Solid, demitted into
it, be the cauſe of its floating and riſing from the Bottom to the
face, yet a quantity of water, that weighs not ten pounds, can raiſe
1Solid that weighs above 100 pounds: in that we have
ted, That it ſufficeth, that ſuch difference be found between the
Specificall Gravities of the Mediums and Moveables, let the particular
and abſolute Gravities be what they will: inſomuch, that a Solid,
provided that it be Specifically leſs grave than the water, although
its abſolute weight were 1000 pounds, yet may it be born up and
elevated by ten pounds of water, and leſs: and on the contrary,
nother Solid, ſo that it be Specifically more grave than the water,
though in abſolute Gravity it were not above a pound, yet all the
water in the Sea, cannot raiſe it from the Bottom, or float it. This
ſufficeth me, for my preſent occaſion, to have, by the above declared
Examples, diſcovered and demonſtrated, without extending ſuch
matters farther, and, as I might have done, into a long Treatiſe:
yea, but that there was a neceſſity of reſolving the above propoſed
doubt, I ſhould have contented my ſelf with that only, which is
demonſtrated by Archimedes, in his firſt Book De Inſidentibus
mido: where in generall termes he infers and confirms the ſame


Concluſions, namely, that Solids (a) leſs grave than water, ſwim or

float upon it, the (b) more grave go to the Bottom, and the (c)

qually grave reſt indifferently in all places, yea, though they ſhould
be wholly under water.
Of Natation
(a) Lib. 1. Prop. 4.
(b) Id. Lib. 1.
Prop. 3.
(c) Id. Lib. 1.
Prop. 3.
But, becauſe that this Doctrine of Archimedes, peruſed,

bed and examined by Signor Franceſco Buonamico, in his fifth Book
of Motion, Chap. 29, and afterwards by him confuted, might by the
Authority of ſo renowned, and famous a Philoſopher, be rendered
dubious, and ſuſpected of falſity; I have judged it neceſſary to
fend it, if I am able ſo to do, and to clear Archimedes, from thoſe
cenſures, with which he appeareth to be charged. Buonamico

jecteth the Doctrine of Archimedes, firſt, as not conſentaneous with
the Opinion of Aristotle, adding, that it was a ſtrange thing to him,

that the Water ſhould exceed the Earth in Gravity, ſeeing on the
contrary, that the Gravity of water, increaſeth, by means of the

cipation of Earth. And he ſubjoyns preſently after, that he was
not ſatisfied with the Reaſons of Archimedes, as not being able with
that Doctrine, to aſſign the cauſe whence it comes, that a Boat and
a Veſſell, which otherwiſe, floats above the water, doth ſink to the
Bottom, if once it be filled with water; that by reaſon of the
quality of Gravity, between the water within it, and the other water
without, it ſhould ſtay a top; but yet, nevertheleſs, we ſee it to go to
the
The Authors
defence of
chimedes his
ctrine, againſt
the oppoſitions
of Buonamico.
His firſt
on againſt the
Doctrine of
chimedes.
His Second
jection.
His third
ction.
His ſourth
jection.
He farther addes, that Ariſtotle had clearly confuted the Ancients,
who ſaid, that light Bodies moved upwards, driven by the impulſe

of the more grave Ambient: which if it were ſo, it ſhould ſeem of
neceſſity to follow, that all naturall Bodies are by nature heavy,
1and none light: For that the ſame would befall the Fire and Air,
if put in the Bottom of the water. And, howbeit, Ariſtotle grants
a Pulſion in the Elements, by which the Earth is reduced into a
ricall Figure, yet nevertheleſs, in his judgement, it is not ſuch that it
can remove grave Bodies from their naturall places, but rather, that
it ſend them toward the Centre, to which (as he ſomewhat obſcurely
continues to ſay,) the water principally moves, if it in the interim
meet not with ſomething that reſiſts it, and, by its Gravity, thruſts
it out of its place: in which caſe, if it cannot directly, yet at leaſt
as well as it can, it tends to the Centre: but it happens, that light
Bodies by ſuch Impulſion, do all aſcend upward: but this properly
they have by nature, as alſo, that other of ſwimming. He concludes,

laſtly, that he concurs with Archimedes in his Concluſions; but not
in the Cauſes, which he would referre to the facile and difficult
ration of the Medium, and to the predominance of the Elements, ſo
that when the Moveable ſuperates the power of the Medium; as for
example, Lead doth the Continuity of water, it ſhall move thorow it,
elſe not.
The Ancients
denved Aoſolute
Levity.
The cauſes of
Natation &
merſion,
ing to the
pateticks.
This is all that I have been able to collect, as produced againſt
Archimedes by Signor Buonamico: who hath not well obſerved the
Principles and Suppoſitions of Archimedes; which yet muſt be
falſe, if the Doctrine be falſe, which depends upon them; but is
contented to alledge therein ſome Inconveniences, and ſome
nances to the Doctrine and Opinion of Ariſtotle. In anſwer to which
Objections, I ſay, firſt, That the being of Archimedes Doctrine,

ply different from the Doctrine of Ariſtotle, ought not to move any
to ſuſpect it, there being no cauſe, why the Authority of this ſhould
be preferred to the Authority of the other: but, becauſe, where the
decrees of Nature are indifferently expoſed to the intellectuall eyes of
each, the Authority of the one and the other, loſeth all
neſs of Perſwaſion, the abſolute power reſiding in Reaſon; therefore
I paſs to that which he alledgeth in the ſecond place, as an abſurd

ſequent of the Doctrine of Archimedes, namely, That water ſhould
be more grave than Earth. But I really find not, that ever
medes ſaid ſuch a thing, or that it can be rationally deduced from his
Concluſions: and if that were manifeſt unto me, I verily believe, I
ſhould renounce his Doctrine, as moſt erroneous. Perhapsthis
ction of Buonamico, is founded upon that which he citeth of the
ſſel, which ſwims as long as its voyd of water, but once full it ſinks to
the Bottom, and underſtanding it of a Veſſel of Earth, he infers againſt
Archimedes thus: Thou ſayſt that the Solids which ſwim, are leſs grave
than water: this Veſſell ſwimmeth: therefore, this Veſſell is leſſe grave
than water. If this be the Illation. I eaſily anſwer, granting that this
Veſſell is leſſe grave than water, and denying the other conſequence,
1namely, that Earth is leſs Grave than Water. The Veſſel that ſwims
occupieth in the water, not only a place equall to the Maſs of the
Earth, of which it is formed; but equall to the Earth and to the Air
together, contained in its concavity. And, if ſuch a Maſs
ded of Earth and Air, ſhall be leſs grave than ſuch another quantity
of water, it ſhall ſwim, and ſhall accord with the Doctrine of
medes; but if, again, removing the Air, the Veſſell ſhall be filled
with water, ſo that the Solid put in the water, be nothing but
Earth, nor occupieth other place, than that which is only poſſeſt by
Earth, it ſhall then go to the Bottom, by reaſon that the Earth is
heavier than the water: and this correſponds well with the meaning
of Archimedes. See the ſame effect illuſtrated, with ſuch another
Experiment, In preſſing a Viall Glaſs to the Bottom of the water,
when it is full of Air, it will meet with great reſiſtance, becauſe it is
not the Glaſs alone, that is preſſed under water, but together with
the Glaſs a great Maſs of Air, and ſuch, that if you ſhould take as
much water, as the Maſs of the Glaſs, and of the Air contained in it,
you would have a weight much greater than that of the Viall, and of
its Air: and, therefore, it will not ſubmerge without great violence:
but if we demit only the Glaſs into the water, which ſhall be when
you ſhall fill the Glaſs with water, then ſhall the Glaſs deſcend to
the Bottom; as ſuperiour in Gravity to the water.
The Authors
ſwer to the firſt
Objection.
The Authors
ſwer to the
cond Objection.
Returning, therefore, to our firſt purpoſe; I ſay, that Earth is
more grave than water, and that therefore, a Solid of Earth goeth to
the bottom of it; but one may poſſibly make a compoſition of Earth
and Air, which ſhall be leſs grave than a like Maſs of Water; and
this ſhall ſwim: and yet both this and the other experiment ſhall
very well accord with the Doctrine of Archimedes. But becauſe that
in my judgment it hath nothing of difficulty in it, I will not
ly affirme that Signor Buonamico, would by ſuch a diſcourſe object
unto Archimedes the abſurdity of inferring by his doctrine, that Earth
was leſs grave than Water, though I know not how to conceive what
other accident he could have induced thence.
Perhaps ſuch a Probleme (in my judgement falſe) was read by
Signor Buonamico in ſome other Author, by whom peradventure it
was attributed as a ſingular propertie, of ſome particular Water, and
ſo comes now to be uſed with a double errour in confutation of
chimedes, ſince he ſaith no ſuch thing, nor by him that did ſay it was it
meant of the common Element of Water.
The third difficulty in the doctrine of Archimedes was, that he

could not render a reaſon whence it aroſe, that a piece of Wood,
and a Veſſell of Wood, which otherwiſe floats, goeth to the bottom,
if filled with Water. Signor Buonamico hath ſuppoſed that a Verſſell
of Wood, and of Wood that by nature ſwims, as before is ſaid,
1goes to the bottom, if it be filled with water; of which he in the
lowing Chapter, which is the 30 of the fifth Book copiouſly
eth: but I (ſpeaking alwayes without diminution of his ſingular
Learning) dare in defence of Archimedes deny this experiment, being
certain that a piece of Wood which by its nature ſinks not in Water,
ſhall not ſinke though it be turned and converted into the forme of
ny Veſſell whatſoever, and then filled with Water: and he that would
readily ſee the Experiment in ſome other tractable Matter, and that is
eaſily reduced into ſeveral Figures, may take pure Wax, and
king it firſt into a Ball or other ſolid Figure, let him adde to it ſo
much Lead as ſhall juſt carry it to the bottome, ſo that being a graine
leſs it could not be able to ſinke it, and making it afterwards into
the forme of a Diſh, and filling it with Water, he ſhall finde that
out the ſaid Lead it ſhall not ſinke, and that with the Lead it ſhall
ſcend with much ſlowneſs: & in ſhort he ſhall ſatisfie himſelf, that the
Water included makes no alteration. I ſay not all this while, but that
its poſſible of Wood to make Barkes, which being filled with water,
ſinke; but that proceeds not through its Gravity, encreaſed by the
Water, but rather from the Nailes and other Iron Workes, ſo that
it no longer hath a Body leſs grave than Water, but one mixt of Iron
and Wood, more grave than a like Maſſe of Water. Therefore let
Signor Buonamico deſiſt from deſiring a reaſon of an effect, that is
not in nature: yea if the ſinking of the Woodden Veſſell when its full
of Water, may call in queſtion the Doctrine of Archimedes, which
he would not have you to follow, is on the contrary conſonant and
greeable to the Doctrine of the Peripateticks, ſince it aptly aſſignes a
reaſon why ſuch a Veſſell muſt, when its full of Water, deſcend to the
bottom; converting the Argument the other way, we may with
ſafety ſay that the Doctrine of Archimedes is true, ſince it aptly
eth with true experiments, and queſtion the other, whoſe
ons are faſtened upon etroneouſs Concluſions. As for the other point
hinted in this ſame Inſtance, where it ſeemes that Benonamico
ſtands the ſame not only of a piece of wood, ſhaped in the forme of a
Veſſell, but alſo of maſſie Wood, which filled, ſcilicet, as I believe, he
would ſay, ſoaked and ſteeped in Water, goes finally to the bottom
that happens in ſome poroſe Woods, which, while their Poroſity is
pleniſhed with Air, or other Matter leſs grave than Water, are
ſes ſpecificially leſs grave than the ſaid Water, like as is that Viall of
Glaſs whileſt it is full of Air: but when, ſuch light Matter
ing, there ſucceedeth Water into the ſame Poroſities and Cavities,
there reſults a compound of Water and Glaſs more grave than a like
Maſs of Water: but the exceſs of its Gravity conſiſts in the Matter
of the Glaſs, and not in the Water, which cannot be graver than it
ſelf: ſo that which remaines of the Wood, the Air of its
1ties departing, if it ſhall be more grave in ſpecie than Water, fil but its
Poroſities with Water, and you ſhal have a Compoſt of Water and
of Wood more grave than Water, but not by vertue of the Water
ceived into and imbibed by the Poroſities, but of that Matter of the
Wood which remains when the Air is departed: and being ſuch it
ſhall, according to the Doctrine of Archimedes, goe to the bottom,
like as before, according to the ſame Doctrine it did ſwim.
The Authors
ſwer to the third
Objection.
As to that finally which preſents it ſelf in the fourth place, namely,

that the Ancients have been heretofore confuted by Ariſtotle, who
denying Poſitive and Abſolute Levity, and truely eſteeming all
dies to be grave, ſaid, that that which moved upward was driven by
the circumambient Air, and therefore that alſo the Doctrine of
Archimedes, as an adherent to ſuch an Opinion was
victed and confuted: I anſwer firſt, that Signor Buonamico in my
judgement hath impoſed upon Archimedes, and deduced from his
words more than ever he intended by them, or may from his
ſitions be collected, in regard that Archimedes neither denies, nor
mitteth Poſitive Levity, nor doth he ſo much as mention it: ſo that
much leſs ought Buonamico to inferre, that he hath denyed that it
might be the Cauſe and Principle of the Aſcenſion of Fire, and other
Light Bodies: having but only demonſtrated, that Solid Bodies

more grave than Water deſcend in it, according to the exceſs of their
Gravity above the Gravity of that, he demonſtrates likewiſe, how the

leſs grave aſcend in the ſame Water, accordng to its exceſs of
ty, above the Gravity of them. So that the moſt that can be
ed from the Dem onſtration of Archimedes is, that like as the exceſs
of the Gravity of the Moveable above the Gravity of the Water, is
the Cauſe that it deſcends therein, ſo the exceſs of the Gravity of
the water above that of the Moveable, is a ſufficient Cauſe why it
cends not, but rather betakes it ſelf to ſwim: not enquiring
ther of moving upwards there is, or is not any other Cauſe contrary
to Gravity: nor doth Archimedes diſcourſe leſs properly than if one
ſhould ſay: If the South Winde ſhall aſſault the Barke with greater
Impetus than is the violence with which the Streame of the River
ries it towards the South, the motion of it ſhall be towards the North:
but if the Impetus of the Water ſhall overcome that of the Winde, its
motion ſhall be towards the South. The diſcourſe is excellent and
would be unworthily contradicted by ſuch as ſhould oppoſe it, ſaying:
Thou miſ-alledgeſt as Cauſe of the motion of the Bark towards the
South, the Impetus of the Stream of the Water above that of the
South Winde; miſ-alledgeſt I ſay, for it is the Force of the North
Winde oppoſite to the South, that is able to drive the Bark towards
the South. Such an Objection would be ſuperfluous, becauſe he which
alledgeth for Cauſe of the Motion the ſtream of the Water, denies not
1but that the Winde oppoſite to the South may do the ſame, but only
affirmeth that the force of the Water prevailing over the
Wind, the Bark ſhall move towards the South: and ſaith no more
than is true. And juſt thus when Archimedes ſaith, that the Gravity
of the Water prevailing over that by which the moveable deſcends to
the Bottom, ſuch moveable ſhall be raiſed from the Bottom to the
face alledgeth a very true Cauſe of ſuch an Accident, nor doth he
firm or deny that there is, or is not, a vertue contrary to Gravity, called
by ſome Levity, that hath alſo a power of moving ſome Matters up
wards. Let therefore the Weapons of Signor Buonamico be directed

gainſt Plato, and other Ancients, who totally denying Levity, and taking
all Bodies to be grave, ſay that the Motion upwards is made, not
from an intrinſecal Principle of the Moveable, but only by the
pulſe of the Medium; and let Archimedes and his Doctrine eſcape
him, ſince he hath given him no Cauſe of quarelling with him
But if this Apologie, produced in defence of Archimedes, ſhould ſeen
to ſome inſufficient to free him from the Objections and Arguments
produced by Ariſtotle againſt Plato, and the other Ancients, as if they
did alſo fight againſt Archimedes, alledging the Impulſe of the Water

as the Cauſe of the ſwimming of ſome Bodies leſs grave than it, I would
not queſtion, but that I ſhould be able to maintaine the Doctrine of
Plato and thoſe others to be moſt true, who abſolutely deny Levity,
and affirm no other Intrinſecal Principle of Motion to be in
tary Bodies ſave only that towards the Centre of the Earth, nor no

other Cauſe of moving upwards, ſpeaking of that which hath the
ſemblance of natural Motion, but only the repulſe of the Medium, ſluid,
and exceeding the Gravity of the Moveable: and as to the Reaſons
of Ariſtotle on the contrary, I believe that I could be able fully to

anſwer them, and I would aſſay to do it, if it were abſolutely
ry to the preſent Matter, or were it not too long a Digreſſion for this
ſhort Treatiſe. I will only ſay, that if there were in ſome of our
mentary Bodies an Intrinſecall Principle and Naturall Inclination
to ſhun the Centre of the Earth, and to move towards the Concave
of the Moon, ſuch Bodies, without doubt, would more ſwiftly aſcend
through thoſe Mediums that leaſt oppoſe the Velocity of the Moveable,
and theſe are the more tenuous and ſubtle; as is, for example, the
Air in compariſon of the Water, we daily proving that we can with

farre more expeditious Velocity move a Hand or a Board to and
gain in one than in the other: nevertheleſs, we never could finde any
Body, that did not aſcend much more ſwiftly in the water than in the

Air. Yea of Bodies which we ſee continually to aſcend in the Water,
there is none that having arrived to the confines of the Air, do not
ly loſe their Motion; even the Air it ſelf, which riſing with great
lerity through the Water, being once come to its Region it loſeth all
1
The Authors
anſwer to the
fourth
ion.
Of Natation,
Lib. 1. Prop. 7.
Of Natation,
Lib. 1. Prop. 4.
Plato denyeth
Poſitive
ty.
The Authors
defence of the
doctrine of Plato
and the Ancients,
who abſolutely
deny Levity:
According to
Plato there is no
Principle of the
Motion of
ſcent in Naturall
Bodies, ſave that
to the Centre.
No cauſe of
the motion of
A cent, ſave the
Impulſe of the
Medium,
ing the
able in
tie.
Bodies aſcend
much ſwifter in
the Water, than
in the Air.
All Bodies
cending through
Water, loſe
their Motion,
comming to the
confines of the
Air.
And, howbeit, Experience ſhewes, that the Bodies, ſucceſſively

leſs grave, do moſt expeditiouſly aſcend in water, it cannot be
ed, but that the Ignean Exhalations do aſcend more ſwiftly

through the water, than doth the Air: which Air is ſeen by
ence to aſcend more ſwiftly through the Water, than the Fiery
lations through the Air: Therefore, we muſt of neceſſity conclude,
that the ſaid Exhalations do much more expeditiouſly aſcend through
the Water, than through the Air; and that, conſequently, they are
moved by the Impulſe of the Ambient Medium, and not by an
ſick Principle that is in them, of avoiding the Centre of the Earth;
to which other grave Bodies tend.
The lighter
Bodies alſend
more ſwiftly
through Water.
Fiery
ons ascend
row the Water
more ſwiftly
than doth the
Air; & the Air
aſcends more
ſwiftly thorow
the Water, than
Fire thorow the
Air.
To that which for a finall concluſion, Signor Buonamico produceth

of going about to reduce the deſcending or not deſcending, to the
eaſie and uneaſie Diviſion of the Medium, and to the predominancy
of the Elements: I anſwer, as to the firſt part, that that cannot in any
manner be admitted as a Cauſe, being that in none of the Fluid
Mediums, as the Air, the Water, and other Liquids, there is any

Reſiſtance againſt Diviſion, but all by every the leaſt Force, are
vided and penetrated, as I will anon demonſtrate: ſo, that of ſuch
Reſiſtance of Diviſion there can be no Act, ſince it ſelf is not in
ing. As to the other part, I ſay, that the predominancy of the

ments in Moveables, is to be conſidered, as far as to the exceſſe or
defect of Gravity, in relation to the Medium: for in that Action,
the Elements operate not, but only, ſo far as they are grave or light:
therefore, to ſay that the Wood of the Firre ſinks not, becauſe Air
predominateth in it, is no more than to ſay, becauſe it is leſs grave
than the Water. Yea, even the immediate Cauſe, is its being leſs
grave than the Water: and it being under the predominancy of the

Air, is the Cauſe of its leſs Gravity: Therefore, he that alledgeth the
predominancy of the Element for a Cauſe, brings the Cauſe of the
Cauſe, and not the neereſt and immediate Cauſe. Now, who knows
not that the true Cauſe is the immediate, and not the mediate?

Moreover, he that alledgeth Gravity, brings a Cauſe moſt perſpicuous
to Sence: The cauſe we may very eaſily aſſertain our ſelves;
whether Ebony, for example, and Firre, be more or leſs grave than
water: but whether Earth or Air predominates in them, who ſhall

make that manifeſt? Certainly, no Experiment can better do it
than to obſerve whether they ſwim or ſink. So, that he who knows,
not whether ſuch a Solid ſwims, unleſs when he knows that Air
dominates in it, knows not whether it ſwim, unleſs he ſees it ſwim,
for then he knows that it ſwims, when he knows that it is Air that
predominates, but knows not that Air hath the predominance, unleſs
he ſees it ſwim: therefore, he knows not if it ſwims, till ſuch time
as he hath ſeen it ſwim.
1
The Authors
confutation of
the Peripateticks
Cauſes of
tion &
on.
Water & other
fluids void of
Reſiſtance
gainſt Diviſion.
The
nancy of
ments in
ables to be
ſidered only in
relation to their
excefs or defect
of Gravity in
reference to the
Medium.
The
ate Cauſe of
tation is that the
Moveable is leſs
grave than the
Water.
The P
ticks alledge for
the reaſon of
Natation the
Cauſe of the
Cauſe.
Gravity a
Cauſe moſt
ſpicuous to
ſence:
Let us not then deſpiſe thoſe Hints, though very dark, which
Reaſon, after ſome contemplation, offereth to our Intelligence,
lets be content to be taught by Archimedes, that then any Body

ſubmerge in water, when it ſhall be ſpecifically more grave than it
and that if it ſhall be leſs grave, it ſhall of neceſſity ſwim, and

that it will reſt indifferently in any place under water, if its
be perfectly like to that of the
Lib 1. of
tation Prop. 7.
Id. Lib. 1.
Prop. 4.
Id. Lib. 1:
Prop. 3.
Theſe things explained and proved, I come to conſider that which
offers it ſelf, touching what the Diverſity of figure given unto the
ſaid Moveable hath to do with theſe Motions and Reſts; and
ceed to affirme, that,
THEOREME V.
The diverſity of Figures given to this or that Solid

cannot any way be a Cauſe of its abſolute Sinking
Swimming.
Diverſity of
Figure no Cauſe
of its abſolute
Natation or
merſion.
So that if a Solid being formed, for example, into a Spherical
Figure, doth ſink or ſwim in the water, I ſay, that being formed
into any other Figure, the ſame figure in the ſame water,
ſink or ſwim: nor can ſuch its Motion by the Expanſion or by
ther mutation of Figure, be impeded or taken
The
on of Figure,
tards the
ty of the aſcent
or deſcent of the
Moveable in the
water; but doth
not deprive it of
all Motion.
The Expanſion of the Figure may indeed retard its Velocity,
well of aſcent as deſcent, and more and more according as the ſaid
gure is reduced to a greater breadth and thinneſs: but that it may bere
duced to ſuch a form as that that ſame matter be wholly hindred from
moving in the ſame water, that I hold to be impoſſible. In this I have
met with great contradictors, who producing ſome Experiments, and
in perticular a thin Board of Ebony, and a Ball of the ſame Wood
and ſhewing how the Ball in Water deſcended to the bottom, and
the Board being put lightly upon the Water ſubmerged not, but
ed; have held, and with the Authority of Ariſtotle, confirmed them
ſelves in their Opinions, that the Cauſe of that Reſt was the
of the Figure, u able by its ſmall weight to pierce and penetrate the
Reſiſtance of the Waters Craſſitude, which Reſiſtance is readily
vercome by the other Sphericall Figure.
This is the Principal point in the preſent Queſtion, in which I
ſwade my ſelf to be on the right ſide.
Therefore, beginning to inveſtigate with the examination of
quiſite Experiments that really the Figure doth not a jot alter the
cent or Aſcent of the ſame Solids, and having already
ted that the greater or leſs Gravity of the Solid in relation to the
vity of the Medium is the cauſe of Deſcent or Aſcent: when ever we
1would make proof of that, which about this Effect the diverſity of
gure worketh, its neceſſary to make the Experiment with Matter
wherein variety of Gravities hath no place. For making uſe of
ters which may be different in their Specifical Gravities, and meeting
with varieties of effects of Aſcending and Deſcending, we ſhall
wayes be left unſatisfied whether that diverſity derive it ſelf really
from the ſole Figure, or elſe from the divers Gravity alſo. We may
remedy this by takeing one only Matter, that is tractable and eaſily
reduceable into every ſort of Figure. Moreover, it wil be an excellent
expedient to take a kinde of Matter, exactly alike in Gravity unto the
Water: for that Matter, as far as pertaines to the Gravity, is
different either to Aſcend or Deſcend; ſo that we may preſently
ſerve any the leaſt difference that derives it ſelf from the diverſity of
Figure.
Now to do this, Wax is moſt apt, which, beſides its incapacity of

receiveing any ſenſible alteration from its imbibing of Water, is
ile or pliant, and the ſame piece is eaſily reduceable into all Figures:
and being in ſpecie a very inconſiderable matter inferiour in Gravity
to the Water, by mixing therewith a little of the fileings of Lead it is
reduced to a Gravity exactly equall to that of the Water.
An
ment in Wax,
that proveth
gute to have no
Operation in
Natation &
merſion.
This Matter prepared, and, for example, a Ball being made
of as bigge as an Orange or biger, and that made ſo grave as to
ſink to the bottom, but ſo lightly, that takeing thence one only Grain
of Lead, it returnes to the top, and being added, it ſubmergeth to
the bottom, let the ſame Wax afterwards be made into a very broad
and thin Flake or Cake; and then, returning to make the ſame
periment, you ſhall ſee that it being put to the bottom, it ſhall, with the
Grain of Lead reſt below, and that Grain deducted, it ſhall aſcend to
the very Surface, and added again it ſhall dive to the bottom. And
this ſame effect ſhall happen alwaies in all ſort of Figures, as wel
gular as irregular: nor ſhall you ever finde any that will ſwim
out the removall of the Grain of Lead, or ſinke to the bottom unleſs
it be added: and, in ſhort, about the going or not going to the
tom, you ſhall diſcover no diverſity, although, indeed, you ſhall about
the quick and ſlow deſcent: for the more expatiated and diſtended
Figures move more ſlowly aſwel in the diveing to the bottom as in
the riſing to the top; and the other more contracted and compact
gures, more ſpeedily. Now I know not what may be expected from
the diverſity of Figures, if the moſt contrary to one another operate
not ſo much as doth a very ſmall Grain of Lead, added or removed.
Me thinkes I hear ſome of the Adverſaries to raiſe a doubt upon

my produced Experiment. And firſt, that they offer to my
tion, that the Figure, as a Figure ſimply, and disjunct from the Matter
workes not any effect, but requires to be conjoyned with the
1and, furthermore, not with every Matter, but with thoſe
wherewith it may be able ro execute the deſired operation.
as we ſee it verified by Experience, that the Acute and ſharp Angle
more apt to cut, than the Obtuſe; yet alwaies provided, that
the one and the other, be joyned with a Matter apt to cut, as
example, with Steel. Therefore, a Knife with a fine and
edge, cuts Bread or Wood with much eaſe, which it will not do,
the edge be blunt and thick: but he that will inſtead of Steel,
Wax, and mould it into a Knife, undoubtedly ſhall never know
effects of ſharp and blunt edges: becauſe neither of them will
the Wax being unable by reaſon of its flexibility, to overcome
hardneſs of the Wood and Bread. And, therefore, applying
like diſcourſe to our purpoſe, they ſay, that the difference of Figure
will ſhew different effects, touching Natation and Submerſion,
not conjoyned with any kind of Matter, but only with thoſe
which, by their Gravity, are apt to reſiſt the Velocity of the
whence he that would elect for the Matter, Cork or other light
unable, through its Levity, to ſuperate the Craſſitude of the
and of that Matter ſhould forme Solids of divers Figures, woulld
vain ſeek to find out what operation Figure hath in Natation or
merſion; becauſe all would ſwim, and that not through any property
of this or that Figure, but through the debility of the Matter,
ing ſo much Gravity, as is requiſite to ſuperate and overcome the
Denſity and Craſſitude of the water.
An objection
gainſt the
riment in Wax.
Its needfull, therefore, if wee would ſee the effect wrought by
Diverſity of Figure, firſt to make choice of a Matter of its
apt to penetrate the Craſſitude of the water. And, for this

they have made choice of ſuch a Matter, as fit, that being readily
duced into Sphericall Figure, goes to the Bottom; and it is Ebony
of which they afterwards making a ſmall Board or Splinter, as thin
a Lath, have illuſtrated how that this, put upon the Surface of the
water, reſts there without deſcending to the Bottom: and making, on
the otherſide, of the ſame wood a Ball, no leſs than a hazell Nut,
they ſhew, that this ſwims not, but deſcendes. From which
ment, they think they may frankly conclude, that the Breadth ofthe
Figure in the flat Lath or Board, is the cauſe of its not deſcendingto
the Bottom, foraſmuch as a Ball of the ſame Matter, not
from the Board in any thing but in Figure, ſubmergeth in the
water to the Bottom. The diſcourſe and the Experiment hath
ſo much of probability and likely hood of truth in it, that it would be
no wonder, if many perſwaded by a certain curſory
ſhould yield credit to it; nevertheleſs, I think I am able to diſcover,
how that it is not free from falacy.
An
ment in Ebany,
brought to
prove the
timent in Wax.
Beginning, therefore, to examine one by one, all the particulars
1have been produced, I ſay, that Figures, as ſimple Figures, not only

operate not in naturall things, but neither are they ever ſeperated
from the Corporeall ſubſtance: nor have I ever alledged them ſtript
of ſenſible Matter, like as alſo I freely admit, that in our
ing to examine the Diverſity of Accidents, dependant upon the
riety of Figures, it is neceſſary to apply them to Matters, which
ſtruct not the various operations of thoſe various Figures: and I
mit and grant, that I ſhould do very ill, if I would experiment the
fluence of Acuteneſſe of edge with a Knife of Wax, applying it to cut
an Oak, becauſe there is no Acuteneſs in Wax able to cut that
very hard wood. But yet ſuch an Experiment of this Knife, would
not be beſides the purpoſe, to cut curded Milk, or other very yielding
Matter: yea, in ſuch like Matters, the Wax is more commodious
than Steel; for finding the diverſity depending upon Angles, more or
leſs Acute, for that Milk is indifferently cut with a Raiſor, and with
a Knife, that hath a blunt edge. It needs, therefore, that regard be
had, not only to the hardneſs, ſolidity or Gravity of Bodies, which
under divers figures, are to divide and penetrate ſome Matters, but it
forceth alſo, that regard be had, on the other ſide, to the Reſiſtance
of the Matters, to be divided and penetrated. But ſince I have in
making the Experiment concerning our Conteſt, choſen a Matter
which penetrates the Reſiſtance of the water; and in all figures
cendes to the Bottome, the Adverſaries can charge me with no defect;
yea, I have propounded ſo much a more excellent Method than they,
in as much as I have removed all other Cauſes, of deſcending or
not deſcending to the Bottom, and retained the only ſole and pure
variety of Figures, demonſtrating that the ſame Figures all deſcende
with the only alteration of a Grain in weight: which Grain being
removed, they return to float and ſwim; it is not true, therefore,
(reſuming the Example by them introduced) that I have gon about
to experiment the efficacy of Acuteneſs, in cutting with Matters
able to cut, but with Matters proportioned to our occaſion; ſince
they are ſubjected to no other variety, then that alone which depends
on the Figure more or leſs a
Figure is
ſeperable from
Corporeall
ſtance.
The anſwer to
the Objection
gainſt the
riment of the
Wax.
But let us proceed a little farther, and obſerve, how that indeed
the Conſideration, which, they ſay, ought to be had about the Election
of the Matter, to the end, that it may be proportionate for the
king of our experiment, is needleſly introduced, declaring by the
ample of Cutting, that like as Acuteneſs is inſufficient to cut, unleſs
when it is in a Matter hard and apt to ſuperate the Reſiſtance of the
wood or other Matter, which we intend to cut; ſo the aptitude of
deſcending or notdeſcending in water, ought and can only be known
in thoſe Matters, that are able to overcome the Renitence, and
rate the Craſſitude of the water. Unto which, I ſay, that to make
diſtinction and election, more of this than of that Matter, on which to
1impreſs the Figures for cutting or penetrating this or that Body,
as the ſolidity or obdurateneſs of the ſaid Bodies ſhall be greater
or leſs, is very neceſſary: but withall I ſubjoyn, that ſuch
ion, election and caution would be ſuperfluous and unprofitable, if
the Body to be cut or penetrated, ſhould have no Reſiſtance, or
ſhould not at all withſtand the Cutting or Penitration: and if the
Knife were to be uſed in cutting a Miſt or Smoak, one of Paper
would be equally ſerviceable with one of Damaſcus Steel: and ſo
by reaſon the water hath not any Reſiſtance againſt the Penitration
of any Solid Body, all choice of Matter is ſuperfluous and needleſs,
and the Election which I ſaid above to have been well made of a
Matter reciprocall in Gravity to water, was not becauſe it was
ceſſary, for the overcoming of the craſſiitude of the water, but its
Gravity, with which only it reſiſts the ſinking of Solid Bodies: and
for what concerneth the Reſiſtance of the craſſitude, if we narrowly
conſider it, we ſhall find that all Solid Bodies, as well thoſe that
ſink, as thoſe that ſwim, are indifferently accomodated and apt to
bring us to the knowledge of the truth in queſtion. Nor will I
be frighted out of the belief of theſe Concluſions, by the
ments which may be produced againſt me, of many ſeverall Woods,
Corks, Galls, and, moreover, of ſubtle ſlates and plates of all ſorts
of Stone and Mettall, apt by means of their Naturall Gravity, to
move towards the Centre of the Earth, the which, nevertheleſs,
ing impotent, either through the Figure (as the Adverſaries thinke)
or through Levity, to break and penetrate the Continuity of the
parts of the water, and to diſtract its union, do continue to ſwimm
without ſubmerging in the leaſt: nor on the other ſide, ſhall the
Authority of Ariſtotle move me, who in more than one place,
meth the contrary to this, which Experience ſhews me.
No Solid of
ſuch Levity, nor
of ſuch Figure,
but that it doth
penetrate the
Craſſitude of
the Water.
I return, therefore, to aſſert, that there is not any Solid of ſuch
Levity, nor of ſuch Figure, that being put upon the water, doth not
divide and penetrate its Craſſitude: yea if any with a more
ſpicatious eye, ſhall return to obſerve more exactly the thin Boards
of Wood, he ſhall ſee them to be with part of their thickneſs under

water, and not only with their inferiour Superficies, to kiſſe the
Superiour of the water, as they of neceſſity muſt have believed, who
have ſaid, that ſuch Boards ſubmerge not, as not being able to
vide the Tenacity of the parts of the water: and, moreover, he
ſhall ſee, that ſubtle ſhivers of Ebony, Stone or Metall, when they
float, have not only broak the Continuity of the water, but are with
all their thickneſs, under the Surface of it; and more and more,
according as the Matters are more grave: ſo that a thin Plate of
Lead, ſhall be lower than the Surface of the circumfuſed water, by
at leaſt twelve times the thickneſs of the Plate, and Gold ſhall dive
1below the Levell of the water, almoſt twenty times the thickneſs
of the Plate, as I ſhall anon declare.
Bodies of all
Figures, laid
on the water, do
penetrate its
Craſſitude, and
in what
tion.
But let us proceed to evince, that the water yields and ſufters it
ſelf to be penetrated by every the lighteſt Body; and therewithall
demonſtrate, how, even by Matters that ſubmerge not, we may
come to know that Figure operates nothing about the going or
not going to the Bottom, ſeeing that the water ſuffers it ſelf to be
penetrated equally by every Figure.
Make a Cone, or a Piramis of Cypreſs, of Firre, or of other

Wood of like Gravity, or of pure Wax, and let its height be
what great, namely a handfull, or more, and put it into the water
with the Baſe downwards: firſt, you ſhall ſee that it will penetrate
the water, nor ſhall it be at all impeded by the largeneſs of the Baſe,
nor yet ſhall it ſink all under water, but the part towards the point
ſhall lye above it: by which ſhall be manifeſt, firſt, that that Solid
forbeares not to ſink out of an inabillity to divide the Continuity
of the water, having already divided it with its broad part, that in
the opinion of the Adverſaries is the leſs apt to make the diviſion.
The Piramid being thus fixed, note what part of it ſhall be
merged, and revert it afterwards with the point downwards, and
you ſhall ſee that it ſhall not dive into the water more than before,
but if you obſerve how far it ſhall ſink, every perſon expert in
Geometry, may meaſure, that thoſe parts that remain out of the
water, both in the one and in the other Experiment are equall to
an hair: whence he may manifeſtly conclude, that the acute Figure
which ſeemed moſt apt to part and penetrate the water, doth not
part or penetrate it more than the large and ſpacious.
The
ment of a Cone,
demitted with
its Baſe, and
ter with its
Point
wards.
And he that would have a more eaſie Experiment, let him take
two Cylinders of the ſame Matter, one long and ſmall, and the
ther ſhert, but very broad, and let him put them in the water, not
diſtended, but erect and endways: he ſhall ſee, if he diligently
meaſure the parts of the one and of the other, that in each of them
the part ſubmerged, retains exactly the ſame proportion to that
out of the water, and that no greater part is ſubmerged of that
long and ſmall one, than of the other more ſpacious and broad:
howbeit, this reſts upon a very large, and that upon a very little
Superficies of water: therefore the diverſity of Figure, occaſioneth
neither facility, nor difficulty, in parting and penetrating the
tinuity of the water; and, conſequently, cannot be the Cauſe of the
Natation or Submerſion. He may likewiſe diſcover the
operating of variety of Figures, in ariſing from the Bottom of the
water, towards the Surface, by taking Wax, and tempering it with
a competent quantity of the filings of Lead, ſo that it may become
a conſiderable matter graver than the water: then let him make
1it into a Ball, and thruſt it unto the Bottom of the water; and
faſten to it as much Cork, or other light matter, as juſt ſerveth to
raiſe it, and draw it towards the Surface: for afterwards changing
the ſame Wax into a thin Cake, or into any other Figure, that
ſame Cork ſhall raiſe it in the ſame manner to a hair.
This ſilenceth not my Antagoniſts, but they ſay, that all the
diſcourſe hitherto made by me little importeth to them, and that it
ſerves their turn, that they have demonſtrated in one only
cular, and in what matter, and under what Figure pleaſeth them,
namely, in a Board and in a Ball of Ebony, that this put in the
water, deſcends to the Bottom, and that ſtays atop to ſwim:
and the Matter being the ſame, and the two Bodies differing in
thing but in Figure, they affirm, that they have with all perſpicuity
demonſtrated and ſenſibly manifeſted what they undertook; and
laſtly, that they have obtained their intent. Nevertheleſs, I believe,
and thinke, I can demonſtrate, that that ſame Experiment proveth
nothing againſt my Concluſion.
And firſt, it is falſe, that the Ball deſcends, and the Board not:

for the Board ſhall alſo deſcend, if you do to both the Figures, as
the words of our Queſtion requireth; that is, if you put them both
into the
In
ments of
tion, the Solid
is to be put into,
not upon the
water.
The Queſtion
of Natation
ted.
The words were theſe. That the Antagoniſts having an opinion, that
the Figure would alter the Solid Bodies, in relation to the deſcending
or not deſcending, aſcending or not aſcending in the ſame Medium, as
v. gr. in the ſame water, in ſuch ſort, that, for Example, a Solid that
being of a Sphericall Figure, ſhall deſcend to the Bottom, being reduced
into ſome other Figure, ſhall not deſcend: I holding the contrary, do
affirm, that a Corporeall Solid Body, which reduced into a Sphericall
gure, or any other, ſhall go to the Bottom, ſhall do the like under whatſoever
other Figure, &c.
But to be in the water, implies to be placed in the water, and by

Ariſtotles own Definition of place, to be placed, importeth to be
vironed by the Superficies of the Ambient Body, therefore, then
ſhall the two Figures be in the water, when the Superficies of the
water, ſhall imbrace and inviron them: but when the Adverſaries
ſhew the Board of Ebony not deſcending to the Bottom, they put it
not into the water, but upon the water, where being by a certain
pediment (as by and by we will ſhew) retained, it is invironed, part
by water, and part by air, which thing is contrary to our agreement,
that was, that the Bodies ſhould be in the water, and not part in
water, and part in air.
1
Place defined
according to
Ariſtotle.
The which is again made manifest, by the queſtions being put as well
about the things which go to the Bottom, as thoſe which ariſe from the
Bottom to ſwimme, and who ſees not that things placed in the Bottom,
muſt have water about them.
It is now to be noted, that the Board of Ebany and the Ball, put

into the water, both ſink, but the Ball more ſwiftly, and the Board
more ſlowly; and ſlower and ſlower, according as it ſhall be more
broad and thin, and of this Tardity the breadth of the Figure is the
true Cauſe: But theſe broad Boards that ſlowly deſcend, are the
ſame, that being put lightly upon the water, do ſwimm: Therefore,
if that were true which the Adverſaries affirm, the ſame numerical
Figure, would in the ſame numericall water, cauſe one while Reſt, and
another while Tardity of Motion, which is impoſſible: for every

ticular Figure which deſcends to the Bottom, hath of neceſſity its own
determinate Tardity and ſlowneſs, proper and naturall unto it,
ding to which it moveth, ſo that every other Tardity, greater or leſſer
is improper to its nature: if, therefore, a Board, as ſuppoſe of a foot
ſquare, deſcendeth naturally with ſix degrees of Tardity, it is
ble, that it ſhould deſcend with ten or twenty, unleſs ſome new
diment do arreſt it. Much leſs can it, by reaſon of the ſame Figure
reſt, and wholly ceaſe to move; but it is neceſſary, that when ever it
reſteth, there do ſome greater impediment intervene than the breadth
of the Figure. Therefore, it muſt be ſomewhat elſe, and not the
gure, that ſtayeth the Board of Ebany above water, of which Eigure
the only Effect is the retardment of the Motion, according to which
it deſcendeth more ſlowly than the Ball. Let it be confeſſed,
fore, rationally diſcourſing, that the true and ſole Cauſe of the Ebanys
going to the Bottom, is the exceſs of its Gravity above the Gravity of
the water: and the Cauſe of the greater or leſs Tardity, the breadth
of this Figure, or the contractedneſs of that: but of its Reſt, it can
by no means be allowed, that the quallity of the Figure, is the Cauſe
thereof: aſwell, becauſe, making the Tardity greater, according as
the Figure more dilateth, there cannot be ſo immenſe a Dilatation, to
which there may not be found a correſpondent immence Tardity.
without reduſing it to Nullity of Motion; as, becauſe the Figures
produced by the Antagoniſts for effecters of Reſt, are the ſelf ſame
that do alſo go to the
The
on of the
riment in the
Ebany.
Every perticular
Figure hath its
own peculiat
Tardity.
* The Figure &
Reſiſtance of
the Medium
gainſt Diviſion,
have nothing to
do with the
fect of Natation
or Submerſion,
by an
ment in
nut tree,
I will not omit another reaſon, founded alſo upon Experience, and
if I deceive not my ſelf, manifeſtly concluding, how that the
ducton of the breadth or amplitude of Figure, and the Reſiſtance of
the water againſt penetration, have nothing to do in the Effect of
ſcending, or aſcending, or reſting in the water. ^{*}Take a piece of wood
or other Matter, of which a Ball aſcends from the Bottom of the water
1to the Surface, more ſlowly than a Ball of Ebony of the ſame bigneſſe,
ſo that it is manifeſt, that the Ball of Ebony more readily divideth the
water in deſcending, than the other in aſcending; as for Example, let
the Wood be Walnut-tree. Then take a Board of Walnut-tree, like
and equall to that of Ebony of the Antagoniſts, which ſwims; and if
it be true, that this floats above water, by reaſon of the Figure, unable
through its breadth, to pierce the Craſſitude of the ſame, the other of
Wallnut-tree, without all queſtion, being thruſt unto the Bottom, will
ſtay there, as leſs apt, through the ſame impediment of Figure, to
vide the ſaid Reſiſtance of the water. But if we ſhall find, and by
experience ſee, that not only the thin Board, but every other Figure
of the ſame Wallnut-tree will return to float, as undoubtedly we ſhall,
then I muſt deſier my oppoſers to forbear to attribute the floating of
the Ebony, unto the Figure of the Board, in regard that the Reſiſtance
of the water is the ſame, as well to the aſcent, as to the deſcent, and the
force of the Wallnut-trees aſcenſion, is leſſe than the Ebonys force in
going to the Bottom.
Nay, I will ſay more, that if we ſhall conſider Gold in compariſon

of water, we ſhall find, that it exceeds it in Gravity almoſt twenty times,
ſo that the Force and Impetus, wherewith a Ball of Gold goes to the
Bottom, is very great. On the contrary, there want not matters, as
Virgins Wax, and ſome Woods, which are not above a fiftieth part leſs
grave than water, whereupon their Aſcenſion therein is very ſlow, and
a thouſand times weaker than the Impetus of the Golds deſcent: yet
notwithſtanding, a plate of Gold ſwims without deſcending to the
Bottom, and, on the contrary, we cannot make a Cake of Wax, or thin
Board of Wood, which put in the Bottom of the Water, ſhall reſt there
without aſcending. Now if the Figure can obſtruct the Penetration,
and impede the deſcent of Gold, that hath ſo great an Impetus, how
can it chooſe but ſuffice to reſiſt the ſame Penetration of the other
ter in aſcending, when as it hath ſcarce a thouſandth part of the Impetus
that the Gold hath in deſcending? Its therefore, neceſſary, that that
which ſuſpends the thin Plate of Gold, or Board of Ebony, upon the
water, be ſome thing that is wanting to the other Cakes and Boards of
Matters leſs grave than the water; ſince that being put to the Bottom,
and left at liberty, they riſe up to the Surface, without any obſtruction:
But they want not for flatneſs and breadth of Figure: Therefore, the
ſpaciouſneſſe of the Figure, is not that which makes the Gold and Ebony
to ſwim.
An
ment in Gold, to
prove the
operating of
gure in Natation
and Submerſion.
And, becauſe, that the exceſs of their Gravity above the Gravity of
the water, is queſtionleſs the Cauſe of the ſinking of the flat piece of
Ebony, and the thin Plate of Gold, when they go to the Bottom,
fore, of neceſſity, when they float, the Cauſe of their ſtaying above
water, proceeds from Levity, which in that caſe, by ſome Accident,
1peradventure not hitherto obſerved, cometh to meet with the ſaid
Board, rendering it no longer as it was before, whilſt it did fink more
ponderous than the water, but leſs.
Now, let us return to take the thin Plate of Gold, or of Silver, or the
thin Board of Ebony, and let us lay it lightly upon the water, ſo that it
ſtay there without ſinking, and diligently obſerve its effect. And
firſt, ſee how falſe the aſſertion of Aristotle, and our oponents is, to wit,
that it ſtayeth above water, through its unability to pierce and
trate the Reſiſtance of the waters Craſſitude: for it will manifeſtly
appear, not only that the ſaid Plates have penetrated the water, but
alſo that they are a conſiderable matter lower than the Surface of the
ſame, the which continueth eminent, and maketh as it were a Rampert
on all ſides, round about the ſaid Plates, the profundity of which they
ſtay ſwimming: and, according as the ſaid Plates ſhall be more grave
than the water, two, four, ten or twenty times, it is neceſſary, that
their Superficies do ſtay below the univerſall Surface of the water, ſo
much more, than the thickneſs of thoſe Plates, as we ſhal more diſtinctly
ſhew anon. In the mean ſpace, for the more eaſie underſtanding of what
I ſay, obſerve with me a little the preſent
309[Figure 309]
Scheme: in which let us ſuppoſe the Surface
of the water to be diſtended, according to the
Lines F L D B, upon which if one ſhall put a
board of matter ſpecifically more grave than
water, but ſo lightly that it ſubmetge not, it
ſhall not reſt any thing above, but ſhall enter with its whole thickneſs
into the water: and, moreover, ſhall ſink alſo, as we ſee by the Board
A I, O I, whoſe breadth is wholly ſunk into the water, the little
perts of water L A and D O incompaſſing it, whoſe Superficies is
tably higher than the Superficies of the Board. See now whether it be
true, that the ſaid Board goes not to the Bottom, as being of Figure
unapt to penetrate the Craſſitude of the water.
But, if it hath already penetrated, and overcome the Continuity of

the water, & is of its own nature more grave than the ſaid water, why
doth it not proceed in its ſinking, but ſtop and ſuſpend its ſelf within
that little dimple or cavitie, which with its ponderoſity it hath made in
the water? I anſwer; becauſe that in ſubmerging it ſelf, ſo far as till its
Superficies come to the Levell with that of the water, it loſeth a part
of its Gravity, and loſeth the reſt of it as it ſubmergeth & deſcends
neath the Surface of the water, which maketh Ramperts and Banks
round about it, and it ſuſtaines this loſs by means of its drawing after it,
and carrying along with it, the Air that is above it, and by Contact
herent to it, which Air ſucceeds to fill the Cavity that is invironed by
the Ramperts of water: ſo that that which in this caſe deſcends and is
placed in the water, is not only the Board of Ebony or Plate of Iron,
1but a compoſition of Ebony and Air, from which reſulteth a Solid
no longer ſuperiour in Gravity to the water, as was the ſimple Ebony,
or the ſimple Gold. And, if we exactly conſider, what, and how
great the Solid is, that in this Experiment enters into the water, and
contraſts with the Gravity of the ſame, it will be found to be all that
which we find to be beneath the Surface of the water, the which is
an aggregate and Compound of a Board of Ebony, and of almoſt
the like quantity of Air, or a Maſs compounded of a Plate of Lead,
and ten or twelve times as much Air. But, Genrlemen, you that
are my Antagoniſts in our Queſtion, we require the Identity of
Matter, and the alteration only of the Figure; therefore, you muſt
remove that Air, which being conjoyned with the Board, makes it
become another Body leſs grave than the Water, and put only the
Ebony into the Water, and you ſhall certainly ſee the Board deſcend
to the Bottom; and, if that do not happen, you have got the day.

And to ſeperate the Air from the Ebony, there needs no more but
only to bath the Superficies of the ſaid Board with the ſame Water:
for the Water being thus interpoſed between the Board and the Air,
the other circumfuſed Water ſhall run together without any
ment, and ſhall receive into it the ſole and bare Ebony, as it was to do.
Why ſolids
having
ted the Water,
do not proceed
to a totail
merſion.
How to
rate the Air from
Solids in
ting them into
the water.
But, me thinks I hear ſome of the Adverſaries cunningly oppoſing
this, and telling me, that they will not yield, by any means, that
their Board be wetted, becauſe the weight added thereto by the
Water, by making it heavier than it was before, draws it to the
Bottom, and that the addition of new weight is contrary to our
greement, which was, that the Matter be the ſame.
To this, I anſwer, firſt; that treating of the operation of Figure
in Bodies put into the Water, none can ſuppoſe them to be put into
the Water without being wet; nor do I deſire more to be done to
the Board, then I will give you leave to do to the Ball. Moreover,
it is untrue, that the Board ſinks by vertue of the new Weight added
to it by the Water, in the ſingle and ſlight bathing of it: for I will
put ten or twenty drops of Water upon the ſame Board, whilſt it is
ſuſtained upon the water, which drops, becauſe not conjoyned with
the other Water circumfuſed, ſhall not ſo encreaſe the weight of it, as
to make it ſink: but if the Board being taken out, and all the water
wiped off that was added thereto, I ſhould bath all its Superficies
with one only very ſmall drop, and put it again upon the water,
out doubt it ſhall ſink, the other Water running to cover it, not
ing retained by the ſuperiour Air; which Air by the interpoſition of
the thin vail of water, that takes away its Contiguity unto the Ebony,
ſhall without Renitence be ſeperated, nor doth it in the leaſt oppoſe
the ſucceſſion of the other Water: but rather, to ſpeak better, it
ſhall deſcend freely; becauſe it ſhall be all invironed and covered
1with water, as ſoon as its ſuperiour Superficies, before vailed with
water, doth arrive to the Levell of the univerſall Surface of the ſaid
water. To ſay, in the next place, that water can encreaſe the weight

of things that are demitted into it, is moſt falſe, for water hath no
Gravity in water, ſince it deſcends not: yea, if we would well
der what any immenſe Maſs of water doth put upon a grave Body;

that is placed in it, we ſhall find experimentally, that it, on the
trary, will rather in a great part deminiſh the weight of it, and that
we may be able to lift an huge Stone from the Bottom of the water,
which the water being removed, we are not able to ſtir. Nor let
them tell me by way of reply, that although the ſuperpoſed water
augment not the Gravity of things that are in it, yet it increaſeth the
ponderoſity of thoſe that ſwim, and are part in the water and part

in the Air, as is ſeen, for Example, in a Braſs Ketle, which whilſt it
is empty of water, and repleniſhed only with Air ſhall ſwim, but
pouring of Water therein, it ſhall become ſo grave, that it ſhall ſink
to the Bottom, and that by reaſon of the new weight added thereto.
To this I will return anſwer, as above, that the Gravity of the
Water, contained in the Veſſel is not that which ſinks it to the
tom, but the proper Gravity of the Braſs, ſuperiour to the Specificall

Gravity of the Water: for if the Veſſel were leſs grave than
water, the Ocean would not ſuffice to ſubmerge it. And, give me
leave to repeat it again, as the fundamentall and principall point in
this Caſe, that the Air contained in this Veſſel before the infuſion of
the Water, was that which kept it a-float, ſince that there was made

of it, and of the Braſs, a Compoſition leſs grave than an equall
ty of Water: and the place that the Veſſel occupyeth in the
Water whilſt it floats, is not equall to the Braſs alone, but to the
Braſs and to the Air together, which filleth that part of the Veſſel
that is below the Levell of the water: Moreover, when the Water
is infuſed, the Air is removed, and there is a compoſition made of
Braſs and of water, more grave in ſpecie than the ſimple water, but
not by vertue of the water infuſed, as having greater Specifick
Gravity than the other water, but through the proper Gravity of
the Braſs, and through the alienation of the Air. Now, as he that
ſhould ſay that Braſs, that by its nature goes to the Bottom, being

formed into the Figure of a Ketle, acquireth from that Figure a
vertue of lying in the Water without ſinking, would ſay that which
is falſe; becauſe that Braſs faſhioned into any whatever Figure,
goeth always to the Bottom, provided, that that which is put into the
water be ſimple Braſs; and it is not the Figure of the Veſſel that
makes the Braſs to float, but it is becauſe that that is not purely
Braſs which is put into the water, but an aggregate of Braſs and of
Air: ſo is it neither more nor leſs falſe, that a thin Plate of Braſs
1or of Ebony, ſwims by vertue of its dilated & broad Figure: for the
truth is, that it bares up without ſubmerging, becauſe that that which
is put in the water, is not pure Braſs or ſimple Ebony, but an
gregate of Braſs and Air, or of Ebony and Air. And, this is not
contrary unto my Concluſion, the which, (having many a time ſeen
Veſſels of Mettall, and thin pieces of diverſe grave Matters float, by
vertue of the Air conjoyned with them) did affirm, That Figure
was not the Cauſe of the Natation or Submerſion of ſuch Solids as
were placed in the water. Nay more, I cannot omit, but muſt
my Antagoniſts, that this new conceit of denying that the
cies of the Board ſhould be bathed, may beget in a third perſon an
opinion of a poverty of Arguments of defence on their part, ſince
that ſuch bathing was never inſiſted upon by them in the beginning
of our Diſpute, and was not queſtioned in the leaſt, being that the
Originall of the diſcourſe aroſe upon the ſwiming of Flakes of Ice,
wherein it would be ſimplicity to require that their Superficies might
bedry: beſides, that whether theſe pieces of Ice be wet or dry they
alwayes ſwim, and as the Adverſaries ſay, by reaſon of the Figure.
Water hath
no Gravity in
Water.
Water
miniſheth the
Gravity of
lids immerged
therein.
The
ment of a Braſs
Ketle ſwiming
when empty, &
ſinking when
full, alledged to
prove that water
gravitates in
water, anſwered.
An Ocean
ficeth not to
ſink a Veſſel
cifically leſs
grave than
ter.
Air, the Cauſe
of the Natation
of empty Veſſels
of Matters
ver in ſpecie than
the water.
Neither Figure,
nor the breadth
of Figure, is the
Cauſe of
tion.
Some peradventure, by way of defence, may ſay, that wetting the
Board of Ebony, and that in the ſuperiour Superficies, it would,
though of it ſelf unable to pierce and penetrate the water, be born
downwards, if not by the weight of the additionall water, at
by that deſire and propenſion that the ſuperiour parts of the water
have to re-unite and rejoyn themſelves: by the Motion of which
parts, the ſaid Board cometh in a certain manner, to be depreſſed

The Bathed
Solid deſcends
not out of any
affectation of
nion in the upper
parts of the
ter.
This weak Refuge will be removed, if we do but conſider, that
the repugnancy of the inferiour parts of the water, is as great against
Diſ-union, as the Inclination of its ſuperiour parts is to union: nor can
the uper unite themſelves without depreſſing the board, nor can it
deſcend without diſuniting the parts of the nether Water: ſo that
it doth follow, by neceſſary conſequence, that for thoſe reſpects, it ſhall
not deſcend. Moreover, the ſame that may be ſaid of the upper
parts of the water, may with equall reaſon be ſaid of the nethe,
namely, that deſiring to unite, they ſhall force the ſaid Board
upwards.
Happily, ſome of theſe Gentlemen that diſſent from me, will
der, that I affirm, that the contiguous ſuperiour Air is able to
that Plate of Braſs or of Silver, that ſtayeth above water; as if I

would in a certain ſence allow the Air, a kind of Magnetick vertue
of ſuſtaining the grave Bodies, with which it is contiguous. To
tisſie all I may, to all doubts, I have been conſidering how by ſome
other ſenſible Experiment I might demonſtrate, how truly that little
contiguous and ſuperiour Air ſuſtaines thoſe Solids, which being by
1nature apt to deſcend to the Bottom, being placed lightly on the water
ſubmerge not, unleſs they be firſt thorowly bathed; and have found,
that one of theſe Bodies having deſcended to the Bottom, by
ing to it (without touching it in the leaſt) a little Air, which conjoyneth
with the top of the ſame; it becometh ſufficient, not only, as before to
ſuſtain it, but alſo to raiſe it, and to carry it back to the top, where it
ſtays and abideth in the ſame manner, till ſuch time, as the aſſiſtance
of the conjoyned Air is taken away. And to this effect, I have taken a
Ball of Wax, and made it with a little Lead, ſo grave, that it leaſurely
deſcends to the Bottom, making with all its Superficies very ſmooth and
pollite: and this being put gently into the water, almoſt wholly

mergeth, there remaining viſſible only a little of the very top, the which
solong as it is conjoyned with the Air, ſhall retain the Ball a-top, but
the Contiguity of the Air taken away by wetting it, it ſhall deſcend to
the Bottom and there remain. Now to make it by vertue of the Air, that
before ſuſtained it to return again to the top, and ſtay there, thruſt into
the water a Glaſs reverſed with the mouth downwards, the which ſhall
carry with it the Air it contains, and move this towards the Ball, abaſing
it till ſuch time that you ſee, by the tranſparency of the Glaſs, that the

contained Air do arrive to the ſummity of the Ball: then gently
draw the Glaſs upwards, and you ſhall ſee the Ball to riſe, and afterwards

stay on the top of the water, if you carefully part the Glaſs and the water
without overmuch commoving and diſturbing it. There is, therefore, a
certain affinity between the Air and other Bodies, which holds them
ed, ſo, that they ſeperate not without a kind of violence. The ſame

likewiſe is ſeen in the water; for if we ſhall wholly ſubmerge ſome Body
in it, ſo that it be thorowly bathed, in the drawing of it afterwards
ly out again, we ſhall ſee the water follow it, and riſe notably above its
Surface, before it ſeperates from it. Solid Bodies, alſo, if they be equall

and alike in Superficies, ſo, that they make an exact Contact without
the interpoſition of the leaſt Air, that may part them in the ſeperation
and yield untill that the ambient Medium ſucceeds to repleniſh the place,
do hold very firmly conjoyned, and are not to be ſeperated without great
force but, becauſe, the Air, Water, and other Liquids, very
tiouſly ſhape themſelves to contact with any Solid Bodies, ſo that their
Superficies do exquiſitely adopt themſelves to that of the Solids, without
any thing remaining between them, therefore, the effect of this
junction and Adherence is more manifeſtly and frequently obſerved in
them, than in hard and inflexible Bodies, whoſe Superficies do very
ly conjoyn with exactneſs of Contact. This is therefore that

tick vertue, which with firm Connection conjoyneth all Bodies, that do
touch without the interpoſition of flexible fluids; and, who knows, but
that that a Contact, when it is very exact, may be a ſufficient Cauſe of
the Union and Continuity of the parts of a naturall Body?
1
A Magnetiſme in
the Air, by which
it bears up thoſe
Solids in the
ter, that are
tiguous with it.
The Effect of
the Airs
guity in the
tation of Solids.
The force of
Contact.
An
on of
ion betwixt
lids and the Air
contiguous to
them.
The like
ation of
junction
twixt Solids &
the water.
Alſo the like
affectation and
Conjunction
twixt Solids
themſeives.
Contact may
be the Cauſe of
the Continuity
of Naturall
dies.
Now, purſuing my purpoſe, I ſay; that it needs not, that we have
recourſe to the Tenacity, that the parts of the water have amongſt
ſelves, by which they reſiſt and oppoſe Diviſion, Diſtraction, and Seper­
ration, becauſe there is no ſuch Coherence and Reſiſtance of
for if there were, it would be no leſs in the internall parts than in
nearer the ſuperiour or externall Surface, ſo that the ſame Board,
ing alwayes the ſame Reſiſtance and Renitence, would no leſs ſtop
the middle of the water than about the Surface, which is falſe.
over, what Reſiſtance can we place in the Continuity of the water
if we ſee that it is impoſſible to ſind any Body of whatſoever Matter
Figure or Magnitude, which being put into the water, ſhall be
and impeded by the Tenacity of the parts of the water to one another
ſo, but that it is moved upwards or downwards, according as the Cauſe
of their Motion tranſports it? And, what greater proof of it can we
ſier, than that which we daily ſee in Muddy waters, which being put into
Veſſels to be drunk, and being, after ſome hours ſetling, ſtill, as we

thick in the end, after four or ſix dayes they are wholly ſetled, and be­
come pure and clear? Nor can their Reſiſtance of Penetration ſtay thoſe
impalpable and inſenſible Atomes of Sand, which by reaſon of
exceeding ſmall force, ſpend ſix dayes in deſcending the ſpace of
a yard.
The ſettlement
of Muddy
ter, proveth that
that Element
hath no
on to Diviſion.
Nor let them ſay, that the ſeeing of ſuch ſmall Bodies, conſume ſix dayes
deſcending ſo little a way, is a ſufficient Argument of the Waters
of Diviſion; becauſe that is no reſiſting of Diviſion, but a retarding of

Motion; and it would be ſimplicity to ſay, that a thing oppoſeth Diviſion
and that in the ſame inſtant, it permits it ſelf to be divided: nor doth the
Retardation of Motion at all favour the Adverſaries cauſe, for that they
to inſtance in a thing that wholly prohibiteth Motion, and procureth
it is neceſſary, therefore, to find out Bodies that ſtay in the water, if one would
ſhew its repugnancy to Diviſion, and not ſuch as move in it, howbeit
ſlowly.
Water cannot
oppoſe diviſion,
and at the ſame
time permit it
ſelf to be
ded.
What then is this Craſſitude of the water, with which it reſiſteth Di­
viſion? What, I beſeech you, ſhould it be, if we (as we have ſaid
with all diligence attempting the reduction of a Matter into ſo like a
Gravity with the water, that forming it into a dilated Plate it reſts ſuſ­
pended as we have ſaid, between the two waters, it be impoſſible
effect it, though we bring them to ſuch an Equiponderance, that
much Lead as the fourth part of a Grain of Muſterd-ſeed, added to
ſame expanded Plate, that in Air [i. e. out of the water] ſhall weigh four
or fix pounds, ſinketh it to the Bottom, and being ſubſtracted, it
to the Surface of the water? I cannot ſee, (if what I ſay be true, as it
moſt certain) what minute vertue and force we can poſſibly find or
gine, to which the Reſiſtance of the water againſt Diviſion and
1tion is not inferiour; whereupon, we muſt of neceſſity conclude
that it is nothing: becanſe, if it were of any ſenſible power, ſome
large Plate might be found or compounded of a Matter alike in
vity to the water, which not only would ſtay between the two
ters; but, moreover, ſhould not be able to deſcend or aſcend
out notable force. We may likewiſe collect the ſame from an

ther Experiment, ſhewing that the Water gives way alſo in the ſame
manner to tranſverſall Diviſion; for if in a ſetled and ſtanding water
we ſhould place any great Maſs that goeth not to the bottom,
ing it with a ſingle (Womans) Hair, we might carry it from place to
place without any oppoſition, and this whatever Figure it hath,
though that it poſſeſs a great ſpace of water, as for inſtance, a great
Beam would do moved ſide-ways. Perhaps ſome might oppoſe me
and ſay, that if the Reſiſtance of water againſt Diviſion, as I affirm,
were nothing; Ships ſhould not need ſuch a force of Oars and Sayles
for the moving of them from place to place in a tranquile Sea, or
ſtanding Lake. To him that ſhould make ſuch an objection, I would

reply, that the water contraſteth not againſt, nor ſimply reſiſteth
Diviſion, but a ſudden Diviſion, and with ſo much greater
tence, by how much greater the Velocity is: and the Cauſe of this
Reſiſtance depends not on Craſſitude, or any other thing that
lutely oppoſeth Diviſion, but becauſe that the parts of the water
divided, in giving way to that Solid that is moved in it, are
ſelves alſo neceſſitated locally to move, ſome to the one ſide, and ſome
to the other, and ſome downwards: and this muſt no leſs be done
by the waves before the Ship, or other Body ſwimming through the
water, than by the poſteriour and ſubſequent; becauſe, the Ship
proceeding forwards, to make it ſelf a way to receive its Bulk, it is
requiſite, that with the Prow it repulſe the adjacent parts of the
water, as well on one hand as on the other, and that it move them
as much tranſverſly, as is the half of the breadth of the Hull: and
the like removall muſt thoſe waves make, that ſucceeding the Poump
do run from the remoter parts of the Ship towards thoſe of the
middle, ſucceſſively to repleniſh the places, which the Ship in
vancing forwards, goeth, leaving vacant. Now, becauſe, all

tions are made in Time, and the longer in greater time: and it being
moreover true, that thoſe Bodies that in a certain time are moved
by a certain power ſuch a certain ſpace, ſhall not be moved the ſame
ſpace, and in a ſhorter Time, unleſs by a greater Power: therefore,
the broader Ships move ſlower than the narrower, being put on by
an equall Force: and the ſame Veſſel requires ſo much greater
force of Wind, or Oars, the faſter it is to move.
1
An hair will
draw a great
Maſs thorow the
Water; which
proveth, that it
hath no
ance againſt
tranſverſall
viſion.
How ſhips are
moved in the
water.
Bodies moved
a certain ſpace in
a certain Time,
by a certain
power, cannot be
moved the
ſame ſpace, and
in a ſhorter time,
but by a greater
power.
But yet for all this, any great Maſs ſwimming in a ſtanding Lake, may
be moved by any petit force; only it is true, that a leſſer force
ſlowly moves it: but if the waters Reſiſtance of Diviſion, were in any
manner ſenſible, it would follow, that the ſaid Maſs, ſhould,
ſtanding the percuſſion of ſome ſenſible force, continue immoveable, which is

not ſo. Yea, I will ſay farther, that ſhould we retire our ſelves into the
more internall contemplation of the Nature of water and other Fluids,
perhaps we ſhould diſcover the Conſtitution of their parts to be ſuch, that
they not only do not oppoſe Diviſion, but that they have not any thing in
them to be divided: ſo that the Reſiſtance that is obſerved in moving

through the water, is like to that which we meet with in paſſing through
a great Throng of People, wherein we find impediment, and not by
difficulty in the Diviſion, for that none of thoſe perſons are divided
whereof the Croud is compoſed, but only in moving of thoſe perſons
ways which were before divided and disjoyned: and thus we find
Reſiſtance in thruſting a Stick into an heap of Sand, not becauſe any part
of the Sand is to be cut in pieces, but only to be moved and raiſed. two

manners of Penetration, therefore, offer themſelves to us, one in
whoſe parts were continuall, and here Diviſion ſeemeth neceſſary; the

other in the aggregates of parts not continuall, but contiguous only, and
here there is no neceſſity of dividing but of moving only. Now, I
not well reſolved, whether water and other Fluids may be eſteemed to
be of parts continuall or contiguous only; yet I find my ſelf indeed incli­

ned to think that they are rather contiguous (if there be in Naturno
other manner of aggregating, than by the union, or by the touching of the
extreams:) and I am induced thereto by the great difference that I ſee >
between the Conjunction of the parts of an hard or Solid Body, and the

Conjunction of the ſame parts when the ſame Body ſhall be made Liquid
and Fluid: for if, for example, I take a Maſs of Silver or other Solid
and hard Mettall, I ſhall in dividing it into two parts, find not only the

reſiſtance that is found in the moving of it only, but an other
greater, dependent on that vertue, whatever it be, which holds the parts
united: and ſo if we would divide again thoſe two parts into other two
and ſucceſſively into others and others, we ſhould ſtill find a like
ance, but ever leſs by how much ſmaller the parts to be divided ſhall be;
but if, laſtly, employing moſt ſubtile and acute Inſtruments, ſuch as are
the moſt tenuous parts of the Fire, we ſhall reſolve it (perhaps) into
laſt and leaſt Particles, there ſhall not be left in them any longer either
Reſiſtance of Diviſion, or ſo much as a capacity of being farther
ded, eſpecially by Inſtruments more groſſe than the acuities of Fire:
what Knife or Raſor put into well melted Silver can we finde, that will
divide a thing which ſurpaſſeth the ſeparating power of Fire?
none: becauſe either the whole ſhall be reduced to the moſt minute
ultimate Diviſions, or if there remain parts capable ſtill of other Suddi­
1diviſions, they cannot receive them, but only from acuter Diviſors than
Fire; but a Stick or Rod of Iron, moved in the melted Met all, is not
ſuch a one. Of a like Conſtitution and Conſiſtence, I account the parts

of Water, and other Liquids to be, namely, incapable of Diviſion by
reaſon of their Temtity; or if not abſolutely indiviſible, yet at leaſt
not to be divided by a Board, or other Solid Body, palpable unto the
band, the Sector being alwayes required to be more ſharp than the Solid
to be cut. Solid Bodies, therefore, do only move, and not divide the

Water, when put into it; whoſe parts being before divided to the
treameſt minuity, and therefore capable of being moved, either many of
them at once, or few, or very few, they ſoon give place to every ſmall
puſcle, that deſcends in the ſame: for that, it being little and light,
ſcending in the Air, and arriving to the Surface of the Water, it meets
with Particles of Water more ſmall, and of leſs Reſiſtance againſt
Motion and Extruſion, than is its own prement and extruſive force,
whereupon it ſubmergeth, and moveth ſuch a portion of them, as is
portionate to its Power. There is not, therefore, any Reſiſtance in
Water againſt Diviſion, nay, there is not in it any diviſible parts. I
adde, moreover, that in caſe yet there ſbould be any ſmall Reſiſtance

found (which is abſolutely falſe) haply in attempting with an Hair to
move a very great natant Machine, or in eſſaying by the addition of one
ſmall Grain of Lead to ſink, or by removall of it to raiſe a very broad
Plate of Matter, equall in Gravity with Water, (which likewiſe will
not happen, in caſe we proceed with dexterity) we may obſerve that that
Reſiſtance is a very different thing from that which the Adverſaries
duce for the Cauſe of the Natation of the Plate of Lead or Board of
ny, for that one may make a Board of Ebony, which being put upon the
Water ſwimmeth, and cannot be ſubmerged, no not by the addition of an
bundred Grains of Lead put upon the ſame, and afterwards being
thed, not only ſinks, though the ſaid Lead be taken away, but though
moreover a quantity of Cork, or of ſome other light Body faſtened to it,
ſufficeth not to hinder it from ſinking unto the bottome: ſo that you
ſee, that although it were granted that there is a certain ſmall
ance of Diviſion found in the ſubstance of the Water, yet this hath
thing to do with that Cauſe which ſupports the Board above the Water,
with a Reſiſtance an hundred times greater than that which men can
find in the parts of the Water: nor let them tell me, that only the Sur-

face of the Water hath ſuch Reſiſtance, and not the internall parts, or
that ſuch Reſiſtance is found greateſt in the beginning of the Submerſion,
as it alſo ſeems that in the beginning, Motion meets with greater
on, than in the continuance of it; becauſe, firſt, I will permit, that the

Water be ſtirred, and that the ſuperiour parts be mingled with the
dle, and inferiour parts, or that thoſe above be wholly removed, and
thoſe in the middle only made uſe off, and yet you ſhall ſee the effect for
1all that, to be still the ſame: Moreover, that Hair which draws
Beam through the Water, is likewiſe to divide the upperparts, and
alſo to begin the Motion, and yet it begins it, and yet it divides it: and
finally, let the Board of Ebony be put in the midway, betwixt the bottome
and the top of the Water, and let it there for a while be ſuſpended and
ſetled, and afterwards let it be left at liberty, and it will instantly begin
its Motion, and will continue it unto the bottome. Nay, more, the Board
ſo ſoon as it is dimitted upon the Water, hath not only begun to
and divide it, but is for a good ſpace dimerged into it.
The parts of
Liquids, ſo farte
from reſiſting
Diviſion, that
they contain not
any thing that
may be divided.
The
ance a Solid
findeth in
ving through
the water, like
to that we meet
with in paſſing
through a
throng of
ple;
Or in
ing a Stick into
an heap of Sand.
Two kinds of
Penetration, one
in Bodies
nuall, the other
in Bodies only
contiguous.
Water conſiſts
not of
all, but only
of contiguous
parts.
Set what
faction he hath
given, as to this
point, in Lib. de
Motu. Dial. 2.
Great
ence betwixt the
Conjunction of
the parts of a
dy when Solid,
and when fluid.
Water conſiſts
of parts that
mit of no
ther diviſion.
Solids
ted into the
ter, do onely
move, and not
divide it.
If there were
any Reſiſtance
of Diviſion in
water, it muſt
needs be ſmall,
in that it is
come by an
Hair, a Grain of
Lead, or a ſlight
bathing of the
Solid.
The uper parts
of the Water, do
no more reſiſt
Diviſion, than
the middle or
loweſt parts.
Waters
ſiſtance of
ſion, not greater
in the
ning of the
merſion.
Let us receive it, therefore, for a true and undoubted
on, That the Water hath not any Renitence againſt ſimple
on, and that it is not poſſible to find any Solid Body, be it of what
Figure it will, which being put into the Water, its Motion upwards
or downwards, according as it exceedeth, or ſhall be exceeded by
the Water in Gravity (although ſuch exceſſe and difference be
ſenſible) ſhall be prohibited, and taken away, by the Craſſitude of
the ſaid Water. When, therefore, we ſee the Board of Ebony, or
of other Matter, more grave than the Water, to ſtay in the
fines of the Water and Air, without ſubmerging, we muſt have
courſe to ſome other Originall, for the inveſting the Cauſe of
Effect, than to the breadth of the Figure, unable to overcome
Renitence with which the Water oppoſeth Diviſion, ſince there is
no Reſiſtance; and from that which is not in being, we can
no Action. It remains moſt true, therefore, as we have ſaid before,
this ſo ſucceds, for that that which in ſuch manner put upon the
ter, not the ſame Body with that which is put into the Water:
this which is put into the Water, is the pure Board of Ebony, which
for that it is more grave than the Water, ſinketh, and that which is
put upon the Water, is a Compoſition of Ebony, and of ſo much
Air, that both together are ſpecifically leſs grave than the
and therefore they do not deſcend.
I will farther confirm this which I ſay. Gentlemen, my
niſts, we are agreed, that the exceſs or defect of the Gravity of the
Solid, unto the Gravity of the Water, is the true and proper
of Natation or
Great Caution
to be had in
perimenting the
operation of
gure in
on.
Now, if you will ſhew that beſides the former Cauſe, there is
ther which is ſo powerfull, that it can hinder and remove the
merſion of thoſe very Solids, that by their Gravity ſink, and if
will ſay, that this is the breadth or ampleneſs of Figure, you are
lieged, when ever you would ſhew ſuch an Experiment, firſt to make
the circumſtances certain, that that Solid which you put into the
Water, be not leſs grave in ſpecie than it, for if you ſhould not do ſo
any one might with reaſon ſay, that not the Figure, but the
was the cauſe of that Natation. But I ſay, that when you ſhall
1mit a Board of Ebony into the Water, you do not put therein a Solid
more grave in ſpecie than the Water, but one lighter, for be ſides the
Ebony, there is in the Water a Maſs of Air, united with the Ebony,
and ſuch, and ſo light, that of both there reſults a Compoſition leſs
grave than the Water: See, therefore, that you remove the Air, and
put the Ebony alone into the Water, for ſo you ſhall immerge a
lid more grave then the Water, and if this ſhall not go to the Bottom,
you have well Philoſophized, and I ill.
Now, ſince we have found the true Cauſe of the Natation of thoſe
Bodies, which otherwiſe as being graver than the Water, would
ſcend to the bottom, I think, that for the perfect and diſtinct
ledge of this buſineſs, it would be good to proceed in a way of
covering demonſtratively thoſe particular Accidents that do attend
theſe effects, and,
PROBL. I.
To finde what proportion ſeverall Figures of different

Matters ought to have, unto the Gravity of the
Water, that ſo they may be able by vertue of the
Contigucus Air to ſtay afloat.
To finde the
proportion
gures ought to
have to the
ters Gravity,
that by help of
the contiguous
Air, they may
ſwim.
Let, therefore, for better illuſtration, D F N E be a Veſſell,
wherein the water is contained, and ſuppoſe a Plate or Board,
whoſe thickneſs is comprehended between the Lines I C and
O S, and let it be of Matter exceeding the water in Gravity, ſo that
being put upon the water, it dimergeth and abaſeth below the Levell
of the ſaid water, leaving the little Banks A I and B C, which are at
the greateſt height they can be, ſo that if the Plate I S ſhould but
deſcend any little ſpace farther, the little Banks or Ramparts would
no longer conſiſt, but expulſing the Air A I C B, they would
fuſe themſelves over the Superficies I C, and
would ſubmerge the Plate. The height AIBC
is therefore the greateſt profundity that the
310[Figure 310]
little Banks of water admit of. Now I ſay,
that from this, and from the proportion in
vity, that the Matter of the Plate hath to the
water, we may eaſily ſinde of what thickneſs, at moſt, we may make
the ſaid Plates, to the end, they may be able to bear up above water:
for if the Matter of the Plate or Board I S were, for Example, as
heavy again as the water, a Board of that Matter ſhall be, at the moſt
of a thickneſs equall to the greateſt height of the Banks, that is, as
thick as A I is high: which we will thus demonſtrate. Lot the
lid I S be donble in Gravity to the water, and let it be a regular
1Priſme, or Cylinder, to wit, that hath its two flat Superficies,
our and inferiour, alike and equall, and at Right Angles with the
ther laterall Superficies, and let its thickneſs I O be equall to the
greateſt Altitude of the Banks of water: I ſay, that if it be put upon
the water, it will not ſubmerge: for the Altitude
A I being equall to the Altitude I O, the
of the Air A B C I ſhall be equall to the Maſs
311[Figure 311]
the Solid C I O S: and the whole Maſs A O S
double to the Maſs I S; And ſince the
of the Air A C, neither encreaſeth nor
niſheth the Gravity of the Maſs I S, and the Solid I S was
double in Gravity to the water; Therefore as much water as
Maſs ſubmerged A O S B, compounded of the Air A I C B, and of
the Solid I O S C, weighs juſt as much as the ſame ſubmerged Maſs
A O S B: but when ſuch a Maſs of water, as is the ſubmerged part
the Solid, weighs as much as the ſaid Solid, it deſcends not farther,

but reſteth, as by (a) Archimedes, and above by us, hath been de­>
monſtrated: Therefore, I S ſhall deſcend no farther, but ſhall reſt.
And if the Solid I S ſhall be Seſquialter in Gravity to the water, it
ſhall float, as long as its thickneſs be not above twice as much as the
greateſt Altitude of the Ramparts of water, that is, of A I. For I S
being Seſquialter in Gravity to the water, and the Altitude O I
being double to I A, the Solid ſubmerged A O S B, ſhall be alſo
Seſquialter in Maſs to the Solid I S. And becauſe the Air A C,
neither increaſeth nor diminiſheth the ponderoſity of the Solid I S:
Therefore, as much water in quantity as the ſubmerged Maſs AOSB,
weighs as much as the ſaid Maſs ſubmerged: And, therefore, that
Maſs ſhall reſt. And briefly in generall.
Of Natation
Lib. 1. Prop. 3.
THEOREME. VI.
When ever the exceſs of the Gravity of the Solid above

the Gravity of the Water, ſhall have the ſame
portion to the Gravity of the Water, that the
tude of the Rampart, hath to the thickneſs of the
Solid, that Solid ſhall not ſink, but being never ſo
tle thicker it ſhall.
The
on of the
eſt thickneſs of
Solids, beyond
which
ſed they ſink.
Let the Solid I S be ſuperior in Gravity to the water, and of ſuch
thickneſs, that the Altitude of the Rampart A I, be in
on to the thickneſs of the Solid I O, as the exceſs of the
ty of the ſaid Solid I S, above the Gravity of a Maſs of water equall
to the Maſs I S, is to the Gravity of the Maſs of water equall to the
1Maſs I S. I ſay, that the Solid I S ſhall not
ſinke, but being never ſo little thicker it ſhall
go to the bottom: For being that as A I is
312[Figure 312]
to I O, ſo is the Exceſs of the Gravity of the
Solid I S, above the Gravity of a Maſs of water
equall to the Maſs I S, to the Gravity of the
ſaid Maſs of water: Therefore, compounding, as A O is to O I, ſo
ſhall the Gravity of the Solid I S, be to the Gravity of a Maſs of water
equall to the Maſs I S: And, converting, as I O is to O A, ſo ſhall the
Gravity of a Maſs of water equall to the Maſs I S, be to the Gravity
of the Solid I S: But as I O is to O A, ſo is a Maſs of water I S, to a
Maſs of water equall to the Maſs A B S O: and ſo is the Gravity of
a Maſs of water I S, to the Gravity of a Maſs of water A S: Therefore
as the Gravity of a Maſs of water, equall to the Maſs I S, is to the
Gravity of the Solid I S, ſo is the ſame Gravity of a Maſs of water
I S, to the Gravity of a Maſs of Water A S: Therefore the
vity of the Solid I S, is equall to the Gravity of a Maſs of water
quall to the Maſs A S: But the Gravity of the Solid I S, is the ſame
with the Gravity of the Solid A S, compounded of the Solid I S,
and of the Air A B C I. Therefore the whole compounded Solid
A O S B, weighs as much as the water that would be compriſed in the
place of the ſaid Compound A O S B: And, therefore, it ſhall make
an Equilibrium and reſt, and that ſame Solid I O S C ſhall ſinke no
farther. But if its thickneſs I O ſhould be increaſed, it would be
ceſſary alſo to encreaſe the Altitude of the Rampart A I, to
tain the due proportion: But by what hath been ſuppoſed, the
tude of the Rampart A I, is the greateſt that the Nature of the
Water and Air do admit, without the waters repulſing the Air
herent to the Superficies of the Solid I C, and poſſeſſing the ſpace
A I C B: Therefore, a Solid of greater thickneſs than I O, and of the
ſame Matter with the Solid I S, ſhall not reſt without ſubmerging,
but ſhall deſcend to the bottome: which was to be demonſtrated.
In conſequence of this that hath been demonſtrated, ſundry and
rious Concluſions may be gathered, by which the truth of my
cipall Propoſition comes to be more and more confirmed, and the
imperfection of all former Argumentations touching the preſent
Queſtion cometh to be diſcovered.
And firſt we gather from the things demonstrated, that,
1
THEOREME
The heavieſt
Bodies may
ſwimme.
All Matters, how heavy ſoever, even to Gold it ſelf,
heavieſt of all Bodies, known by us, may float upon
the Water.
Becauſe its Gravity being conſidered to be almoſt twenty times
greater than that of the water, and, moreover, the greateſt Alti­
tude that the Rampart of water can be extended to, without break
ing the Contiguity of the Air, adherent to the Surface of the Solid,
that is put upon the water being predetermined, if we ſhould make
a Plate of Gold ſo thin, that it exceeds not the nineteenth part ofthe
Altitude of the ſaid Rampart, this put lightly upon the water ſhall
reſt, without going to the bottom: and if Ebony ſhall chance to be
in ſeſquiſeptimall proportion more grave than the water, the greateſt
thickneſs that can be allowed to a Board of Ebony, ſo that it may be
able to ſtay above water without ſinking, would be ſeaven times
more than the height of the Rampart Tinn, v. gr. eight times
grave than water, ſhall ſwimm as oft as the thickneſs of its Plate,

exceeds not the 7th part of the Altitude of the Rampart.
He elſewhere
cites this as a
Propoſition,
fore I make it of
that number.
And here I will not omit to note, as a ſecond Corrollary dependent
upon the things demonſtrated, that,
THEOREME
Natation and
Submerſion,
lected from the
thickneſs,
ding the length
and breadth of
Plates.
The Expanſion of Figure not only is not the Cauſe of
Natation of thoſe grave Bodies, which
do ſubmerge, but alſo the determining what be
Boards of Ebony, or Plates of Iron or Gold that
ſwimme, depends not on it, rather that ſame
tion is to be collected from the only thickneſs of
Figures of Ebony or Gold, wholly excluding the
ſideration of length and breadth, as having no way
any ſhare in this Effect.
It hath already been manifeſted, that the only cauſe of the
tion of the ſaid Plates, is the reduction of them to be leſs grave
than the water, by means of the connexion of that Air, which
ſcendeth together with them, and poſſeſſeth place in the water;
which place ſo occupyed, if before the circumfuſed water diffuſeth
it ſelf to fill it, it be capable of as much water, as ſhall weigh equall
with the Plate, the Plate ſhall remain ſuſpended, and ſinke
farther.
1
Now let us ſee on which of theſe three dimenſions of the Solid
depends the terminating, what and how much the Maſs of that ought
to be, that ſo the aſſiſtance of the Air contiguous unto it, may ſuffice
to render it ſpecifically leſs grave than the water, whereupon it may
reſt without Submerſion. It ſhall undoubtedly be found, that the
length and breadth have not any thing to do in the ſaid
tion, but only the height, or if you will the thickneſs: for, if we take
a Plate or Board, as for Example, of Ebony, whoſe Altitude hath
unto the greateſt poſſible Altitude of the Rampart, the proportion
above declared, for which cauſe it ſwims indeed, but yet not if we
never ſo little increaſe its thickneſs; I ſay, that retaining its
neſs, and encreaſing its Superficies to twice, four times, or ten times
its bigneſs, or dminiſning it by dividing it into four, or ſix, or
twenty, or a hundred parts, it ſhall ſtill in the ſame manner continue
to float: but encreaſing its thickneſs only a Hairs breadth, it will
alwaies ſubmerge, although we ſhould multiply the Superficies a
hundred and a hundred times. Now foraſmuch as that this is a
Cauſe, which being added, we adde alſo the Effect, and being
ved, it is removed; and by augmenting or leſſening the length or
breadth in any manner, the effect of going, or not going to the
tom, is not added or removed: I conclude, that the greatneſs and
ſmalneſs of the Superficies hath no influence upon the Natation or
Submerſion. And that the proportion of the Altitude of the
parts of Water, to the Altitude of the Solid, being conſtituted in
the manner aforeſaid, the greatneſs or ſmalneſs of the Superficies,
makes not any variation, is manifeſt from that which hath been above
demonſtrated, and from this, that, The Priſms and Cylinders which

have the ſame Baſe, are in proportion to one another as their heights:
Whence Cylinders or Prifmes, namely, the Board, be they great or
little, ſo that they be all of equall thickneſs, have the ſame proportion
to their Conterminall Air, which hath for Baſe the ſaid Superficies of
the Board, and for height the Ramparts of water; ſo that alwayes
of that Air, and of the Board, Solids are compounded, that in Gravity
equall a Maſs of water equall to the Maſs of the Solids, compounded
of Air, and of the Board: whereupon all the ſaid Solids do in the
ſame manner continue afloat. We will conclude in the third place,
that,
1
Priſmes and
Cylinders
ving the ſame
Baſe, are to one
another as their
heights.
THEOREME.
All Figures
of all Matters,
float by hep of
the Rampart
pleniſhed with
Air, and ſome
but only touch
the water.
All ſorts of Figures of whatſoever Matter, albeit more
grave than the Water, do by Benefit of the ſaid
part, not only float, but ſome Figures, though of the
graveſt Matter, do ſtay wholly above Water, wetting
only the inferiour Surface that toucheth the Water.
And theſe ſhall be all Figures, which from the inferiour Baſe up­
wards, grow leſſer and leſſer; the which we ſhall exemplifie for
this time in Piramides or Cones, of which Figures the paſſions sre
common. We will demonſtrate therefore, that,
It is poſſible to form a Piramide, of any whatſoever Matter propoſed,
which being put with its Baſe upon the Water, reſts not only
ſubmerging, but without wetting it more then its Baſe.
For the explication of which it is requiſite, that we firſt
the ſubſequent Lemma, namely, that,
LEMMA II.
Solids whoſe Maſſes anſwer in proportion contrarily to

their Specificall Gravities, are equall in Abſolute
Gravities.
Solids whoſe
Maſſes are in
contrary
portion to their
Specifick
vities, are equall
in abſolute Gra
vity.
Let A C and B be two Solids, and let the Maſs A C be to the
Maſs B, as the Specificall Gravity of the Solid B, is to the Speci­
ficall Gravity of the Solid A C: I ſay, the Solids A C and B are
equall in abſolute weight, that is, equally grave. For
313[Figure 313]
if the Maſs A C be equall to the Maſs B, then, by the
Aſſumption, the Specificall Gravity of B, ſhall be
quall to the Specificall Gravity of A C, and being
quall in Maſs, and of the ſame Specificall Gravity
ſhall abſolutely weigh one as much as another. But
if their Maſſes ſhall be unequall, let the Maſs A C be greater, and in it
take the part C, equall to the Maſs B. And, becauſe the Maſſes B
and C are equall; the Abſolute weight of B, ſhall have the ſame
portion to the Abſolute weight of C, that the Specificall Gravity of
B, hath to the Specificall Gravity of C; or of C A, which is the
ſame in ſpecie: But look what proportion the Specificall Gravity of
B, hath to the Specificall Gravity of C A, the like proportion, by the
Aſſumption, hath the Maſs C A, to the Maſs B; that is, to the Maſs C:
1Therefore, the abſolute weight of B, to the abſolute weight of C, is
as the Maſs A C to the Maſs C: But as the Maſs AC, is to the Maſs C,
ſo is the abſolute weight of A C, to the abſolute weight of C:
fore the abſolute weight of B, hath the ſame proportion to the
lute weight of C, that the abſolute weight of A C, hath to the
ſolute weight of C: Therefore, the two Solids A C and B are equall
in abſolute Gravity: which was to be demonſtrated. Having
monſtrated this, I ſay,
THEOREME X.
That it is poſſible of any aſſigned Matter, to form a Pi-

ramide or Cone upon any Baſe, which being put upon
the Water ſhall not ſubmerge, nor wet any more than
its Baſe.
There may be
Cones and
mides of any
Matter, which
demittedinto the
water, reſt only
their Baſes.
Let the greateſt poſſible Altitude of the Rampart be the Line D B,
and the Diameter of the Baſe of the Cone to be made of any
ter aſſigned B C, at right angles to D B: And as the Specificall Gravity
of the Matter of the Piramide or Cone to be made, is to the Specificall
Gravity of the water, ſo let the Altitude of the
314[Figure 314]
Rampart D B, be to the third part of the Piramide
or Cone A B C, deſcribed upon the Baſe, whoſe
Diameter is B C: I ſay, that the ſaid Cone A B C,
and any other Cone, lower then the ſame, ſhall reſt
upon the Surface of the water B C without ſinking.
Draw D F parallel to B C, and ſuppoſe the Priſme
or Cylinder E C, which ſhall be tripple to the Cone
A B C. And, becauſe the Cylinder D C hath the ſame proportion
to the Cylinder C E, that the Altitude D B, hath to the Altitude B E:
But the Cylinder C E, is to the Cone A B C, as the Altitude E B is to
the third part of the Altitude of the Cone: Therefore, by Equality of
proportion, the Cylinder D C is to the Cone A B C, as D B is to the
third part of the Altitude B E: But as D B is to the third part of B E,
ſo is the Specificall Gravity of the Cone A B C, to the Specificall
vity of the water: Therefore, as the Maſs of the Solid D C, is to the
Maſs of the Cone A B C, ſo is the Specificall Gravity of the ſaid Cone,
to the Specificall Gravity of the water: Therefore, by the precedent
Lemma, the Cone A B C weighs in abſolute Gravity as much as a
Maſs of Water equall to the Maſs D C: But the water which by the
impoſition of the Cone A B C, is driven out of its place, is as much
as would preciſely lie in the place D C, and is equall in weight to the
Cone that diſplaceth it: Therefore, there ſhall be an Equilibrium,
and the Cone ſhall reſt without farther ſubmerging. And its
nifeſt,
1
COROLARY
Amongſt Cones
of the ſame Baſe,
thoſe of leaſt
titude ſhall ſink
the leaſt.
That making upon the ſame Baſis, a Cone of a leſs Altitude, it ſhall be
alſo leſs grave, and ſhall ſo much the more reſt without Submerſion.
COROLARY II.
It is manifeſt, alſo, that one may make Cones and Piramids of any Matter

whatſoever, more grave than the water, which being put into the
water, with the Apix or Point downwards, reſt without Submerſion.
There may be
Cones and
mides of any
Matter, which
demitted with
the Point
wards do float
top.
Becauſe if we reaſſume what hath been above demonſtrated,
Priſms and Cylinders, and that on Baſes equall to thoſe of the
ſaid Cylinders, we make Cones of the ſame Matter, and
times as high as the Cylinders, they ſhall reſt afloat, for that in Maſs
and Gravity they ſhall be equall to thoſe Cylinders, and by having
their Baſes equall to thoſe of the Cylinders, they ſhall leave equall
Maſſes of Air included within the Ramparts. This, which for
ple ſake hath been demonſtrated, in Priſms, Cylinders, Cones and
Piramids, might be proved in all other Solid Figures, but it would
require a whole Volume (ſuch is the multitude and variety of their
Symptoms and Accidents) to comprehend the particuler demonſtration
of them all, and of their ſeverall Segments: but I will to avoid prolixity
in the preſent Diſcourſe, content my ſelf, that by what I have declared
every one of ordinary Capacity may comprehend, that there is not
any Matter ſo grave, no not Gold it ſelf, of which one may not form
all ſorts of Figures, which by vertue of the ſuperiour Air adherent to
them, and not by the Waters Reſiſtance of Penetration, do remain
afloat, ſo that they ſink not. Nay, farther, I will ſhew, for removing
that Error, that,
THEOREME
A Piramide or
Cone, demitted
with the Point
downwards ſhal
ſwim, with its
Baſe downward
ſhall ſink.
A Piramide or Cone put into the Water, with the Point
downward ſhall ſwimme, and the ſame put with the
Baſe downwards ſhall ſinke, and it ſhall be impoſſible
to make it float.
Now the quite contrary would happen, if the difficulty of Pene­
trating the water, were that which had hindred the deſcent, for
that the ſaid Cone is far apter to pierce and penetrate with its ſharp
Point, than with its broad and ſpacious Baſe.
And, to demonſtrate this, let the Cone be A B C, twice as grave
as the water, and let its height be tripple to the height of the Rampart
D A E C: I ſay, firſt, that being put lightly into the water with the
1Point downwards, it ſhall not deſcend to the
tom: for the Aeriall Cylinder contained betwixt
315[Figure 315]
the Ramparts D A C E, is equall in Maſs to the
Cone A B C; ſo that the whole Maſs of the Solid
compounded of the Air D A C E, and of the Cone
A B C, ſhall be double to the Cone A C B: And,
becauſe the Cone A B C is ſuppoſed to be of Matter double in
vity to the water, therefore as much water as the whole Maſſe
D A B C E, placed beneath the Levell of the water, weighs as much
as the Cone A B C: and, therefore, there ſhall be an Equilibrium,
and the Cone A B C ſhall deſcend no lower. Now, I ſay farther,
that the ſame Cone placed with the Baſe downwards, ſhall ſink to
the bottom, without any poſſibility of returning again, by any means
to ſwimme.
Let, therefore, the Cone be A B D, double in Gravity to the
water, and let its height be tripple the height
316[Figure 316]
of the Rampart of water L B: It is already
manifeſt, that it ſhall not ſtay wholly out of
the water, becauſe the Cylinder being
prehended betwixt the Ramparts L B D P,
equall to the Cone A B D, and the Matter of
the Cone, beig double in Gravity to the
water, it is evident that the weight of the ſaid
Cone ſhall be double to the weight of the Maſs of water equall to the
Cylinder L B D P: Therefore it ſhall not reſt in this ſtate, but
ſhall deſcend.
COROLARY I.
I ſay farther; that much leſſe ſhall the ſaid Cone stay afloat, if one

immerge a part thereof.
Much leſs ſhall
the ſaid Cone
ſwim, if one
merge a part
thereof.
Which you may ſee, comparing with the water as well the part
that ſhall immerge as the other above water. Let us therefore
of the Cone A B D, ſubmergeth part N T O S, and advance the
Point N S F above water. The Altitude of the Cone F N S, ſhall
either be more than half the whole Altitude of the Cone F T O, or
it ſhall not be more: if it ſhall be more than half, the Cone F N S
ſhall be more than half of the Cylinder E N S C: for the Altitude
of the Cone F N S, ſhall be more than Seſquialter of the Altitude
of the Cylinder E N S C: And, becauſe the Matter of the Cone is
ſuppoſed to be double in Specificall Gravity to the water, the water
which would be contained within the Rampart E N S C, would be
leſs grave abſolutely than the Cone F N S; ſo that the whole Cone
F N S cannot be ſuſtained by the Rampart: But the part immerged
N T O S, by being double in Specificall Gravity to the water, ſhall
1tend to the bottom: Therefore, the whole Cone F T O, as well in
reſpect of the part ſubmerged, as the part above water ſhall
ſcend to the bottom. But if the Altitude of the Point F N S, ſhall
be half the Altitude of the whole Cone F T O, the ſame Altitude of
the ſaid Cone F N S ſhall be Seſquialter to the Altitude E N: and,
therefore, E N S C ſhall be double to the Cone F N S; and as much
water in Maſs as the Cylinder E N S C, would weigh as much as the
part of the Cone F N S. But, becauſe the other immerged part
N T O S, is double in Gravity to the water, a Maſs of water equall
to that compounded of the Cylinder E N S C, and of the Solid N T O S,
ſhall weigh leſs than the Cone F T O, by as much as the weight of
a Maſs of water equall to the Solid N T O S: Therefore, the Cone
ſha l alſo deſcend. Again, becauſe the Solid N T O S, is ſeptuple
to the Cone F N S, to which the Cylinder E S is double, the
tion of the Solid N T O S, ſhall be to the Cylinder E N S C, as ſeaven
to two: Therefore, the whole Solid compounded of the Cylinder
E N S C, and of the Solid N T O S, is much leſs than double the
Solid N T O S: Therefore, the ſingle Solid N T O S, is much graver
than a Maſs of water equall to the Maſs, compounded of the C
linder E N S C, and of N T O S.
COROLARY
Part of the
Cones towards
the Cuſpis
ved, it ſhall ſtill
ſink.
From whence it followeth, that though one ſhould remove and take
way the part of the Cone F N S, the ſole remainder N T O S would
go to the bottom.
COROLARY III.
And if we ſhould more depreſs the Cone F T O, it would be ſo much the

more impoſſible that it ſhould ſuſtain it ſelf afloat, the part ſubmerged
N T O S ſtill encreaſing, and the Maſs of Air contained in the Rampart
diminiſhing, which ever grows leſs, the more the Cone ſubmergeth.
The more the
Cone is
ged, the more
impoſſible is its
floating.
That Cone, therefore, that with its Baſe upwards, and its
Cuſpis downwards doth ſwimme, being dimitted with its Baſe
downward muſt of neceſſity ſinke. They have argued farre
from the truth, therefore, who have aſcribed the cauſe of Natation
to waters reſiſtance of Diviſion, as to a paſſive principle, and to the
breadth of the Figure, with which the diviſion is to be made, as the
Efficient.
I come in the fourth place, to collect and conclude the reaſon of
that which I have propoſed to the Adverſaries, namely,
1
THE OREME XII.
That it is poſſible to fo m Solid Bodies, of what Figure

and greatneſs ſoever, that of their own Nature goe
to the Bottome; But by the help of the Air
tained in the Rampart, reſt without ſubmerging.
Solids of any
Figure &
neſſe, that
rally ſink, may
by help of the
Air in the
part ſwimme.
The truth of this Propoſition is ſufficiently manifeſt in all thoſe
Solid Figures, that determine in their uppermoſt part in a plane
Superficies: for making ſuch Figures of ſome Matter
cally as grave as the water, putting them into the water, ſo that the
whole Maſs be covered, it is manifeſt, that they ſhall reſt in all
places, provided, that ſuch a Matter equall in weight to the water,
may be exactly adjuſted: and they ſhall by conſequence, reſt or
lie even with the Levell of the water, without making any Rampart.
If, therefore, in reſpect of the Matter, ſuch Figures are apt to reſt
without ſubmerging, though deprived of the help of the Rampart,
it is manifeſt, that they may admit ſo much encreaſe of Gravity,
(without encreaſing their Maſſes) as is the weight of as much water
as would be contained within the Rampart, that is made about their
upper plane Surface: by the help of which being ſuſtained, they
ſhall reſt afloat, but being bathed, they ſhall deſcend, having been
made graver than the water. In Figures, therefore, that determine
above in a plane, we may cleerly comprehend, that the Rampart
added or removed, may prohibit or permit the deſcent: but in thoſe
Figures that go leſſening upwards towards the top, ſome Perſons
may, and that not without much ſeeming Reaſon, doubt whether
the ſame may be done, and eſpecially by thoſe which terminate in a
very acute Point, ſuch as are your Cones and ſmall Piramids.
ing theſe, therefore, as more dubious than the reſt, I will endeavour
to demonſtrate, that they alſo lie under the ſame Accident of going,
or not going to the Bottom, be they of any whatever bigneſs. Let
therefore the Cone be A B D, made of a matter
ſpecifically as grave as the water; it is manifeſt
317[Figure 317]
that being put all under water, it ſhall reſt in
all places (alwayes provided, that it ſhall weigh
exactly as much as the water, which is almoſt
impoſſible to effect) and that any ſmall weight
being added to it, it ſhall ſink to the bottom:
but if it ſhall deſcend downwards gently, I ſay,
that it ſhall make the Rampart E S T O, and
that there ſhall ſtay out of the water the point A S T, tripple in
height to the Rampart E S: which is manifeſt, for the Matter of the
1Cone weighing equally with the water, the part ſubmerged S B D T,
becomes indifferent to move downwards or upwards; and the Cone
A S T, being equall in Maſs to the water that would be contained in
the concave of the Rampart E S T O, ſhall be alſo equall unto it in
Gravity: and, therefore, there ſhall be a perfect Equilibrium, and,
conſequently, a Reſt. Now here ariſeth a doubt, whether the
Cone A B D may be made heavier, in ſuch ſort, that when it is put
wholly under water, it goes to the bottom, but yet not in ſuch ſort,
as to take from the Rampart the vertue of ſuſtaining it that it ſink not,
and, the reaſon of the doubt is this: that although at ſuch time as
the Cone A B D is ſpecifically as grave as the water, the Rampart
E S T O ſuſtaines it, not only when the point A S T is tripple in
height to the Altitude of the Rampart E S, but alſo when a leſſer
part is above water; [for although in the Deſcent of the Cone the
Point A S T by little and little diminiſheth, and ſo likewiſe the
Rampart E S T O, yet the Point diminiſheth in
318[Figure 318]
greater proportion than the Rampart, in that
it diminiſheth according to all the three
menſions, but the Rampart according to two
only, the Altitude ſtill remaining the ſame;
or, if you will, becauſe the Cone S T goes
miniſhing, according to the proportion of the
cubes of the Lines that do ſucceſſively become
the Diameters of the Baſes of emergent Cones,
and the Ramparts diminiſh according to the proportion of the
Squares of the ſame Lines; whereupon the proportions of the Points
are alwayes Seſquialter of the proportions of the Cylinders,
tained within the Rampart; ſo that if, for Example, the height of
the emergent Point were double, or equall to the height of the
Rampart, in theſe caſes, the Cylinder contained within the
part, would be much greater than the ſaid Point, becauſe it would be
either ſeſquialter or tripple, by reaſon of which it would perhaps
ſerve over and above to fuſtain the whole Cone, ſince the part
merged would no longer weigh any thing;] yet, nevertheleſs, when
any Gravity is added to the whole Maſs of the Cone, ſo that alſo the
part ſubmerged is not without ſome exceſſe of Gravity above the
Gravity of the water, it is not manifeſt, whether the Cylinder
tained within the Rampart, in the deſcent that the Cone ſhall make,
can be reduced to ſuch a proportion unto the emergent Point, and to
ſuch an exceſſe of Maſs above the Maſs of it, as to compenſate the
exceſſe of the Cones Specificall Gravity above the Gravity of the
ter: and the Scruple ariſeth, becauſe that howbeit in the deſcent
made by the Cone, the emergent Point A S T diminiſheth, whereby
there is alſo a diminution of the exceſs of the Cones Gravity above
1the Gravity of the water, yet the caſe ſtands ſo, that the Rampart
doth alſo contract it ſelf, and the Cylinder contained in it doth
miniſh. Nevertheleſs it ſhall be demonſtrated, how that the Cone
A B D being of any ſuppoſed bigneſſe, and made at the firſt of a
Matter exactly equall in Gravity to the Water, if there may
be affixed to it ſome Weight, by means of which it may deſcend to
the bottom, when ſubmerged under water, it may alſo by vertue of
the Rampart ſtay above without ſinking.
Let, therefore, the Cone A B D be of any ſuppoſed greatneſſe,
and alike in ſpecificall Gravity to the water. It is manifeſt, that
being put lightly into the water, it ſhall reſt without deſcending;
and it ſhall advance above water, the Point
319[Figure 319]
AS T, tripple in height to the height of the
Rampart E S: Now, ſuppoſe the Cone A B D
more depreſſed, ſo that it advance above
ter, only the Point A I R, higher by half than
the Point A S T, with the Rampart about it
C I R N. And, becauſe, the Cone A B D is
to the Cone A I R, as the cube of the Line S T
is to the cube of the Line I R, but the
der E S T O, is to the Cylinder C I R N, as the Square of S T to
the Square of I R, the Cone A S T ſhall be Octuple to the Cone
A I R, and the Cylinder E S T O, quadruple to the Cylinder C I R N:
But the Cone A S T, is equall to the Cylinder E S T O: Therefore,
the Cylinder C I R N, ſhall be double to the Cone A I R: and the
water which might be contained in the Rampart C I R N, would be
double in Maſs and in Weight to the Cone A I R, and, therefore,
would be able to ſuſtain the double of the Weight of the Cone AIR:
Therefore, if to the whole Cone A B D, there be added as much
Weight as the Gravity of the Cone A I R, that is to ſay, the eighth
part of the weight of the Cone A S T, it alſo ſhall be ſuſtained by
the Rampart C I R N, but without that it ſhall go to the bottome:
the Cone A B D, being, by the addition of the eighth part of the
weight of the Cone A S T, made ſpecifically more grave than the
water. But if the Altitude of the Cone A I R, were two thirds
of the Altitude of the Cone A S T, the Cone A S T would be to the
Cone A I R, as twenty ſeven to eight; and the Cylinder E S T O, to
the Cylinder C I R N, as nine to four, that is, as twenty ſeven to
twelve; and, therefore, the Cylinder C I R N, to the Cone A I R,
as twelve to eight; and the exceſs of the Cylinder C I R N, above
the Cone A I R, to the Cone A S T, as four to twenty ſeven:
fore if to the Cone A B D be added ſo much weight as is the four
twenty ſevenths of the weight of the Cone A S T, which is a little
more then its ſeventh part, it alſo ſhall continue to ſwimme, and
1the height of the emergent Point ſhall be double to the height of the
Rampart. This that hath been demonſtrated in Cones, exactly holds
in Piramides, although the one or the other ſhould be very ſharp in

their Point or Cuſpis: From whence we conclude, that the ſame
Accident ſhall ſo much the more eaſily happen in all other Figures,
by how much the leſs ſharp the Tops ſhall be, in which they
mine, being aſſiſted by more ſpacious Ramparts.
Natatiou
eſt effected in
Figures broad
toward the top.
THEOREME
All Figures ſink
or ſwim, upon
bathing or not
bathing of their
tops.
All Figures, therefore, of whatever greatneſſe, may
go, and not go, to the Bottom, according as their
ties or Tops ſhall be bathed or not bathed.
And this Accident being common to all ſorts of Figures, without
exception of ſo much as one. Figure hath, therefore, no part
in the production of this Effect, of ſometimes ſinking, and
times again not ſinking, but only the being ſometimes conjoyned
to, and ſometimes ſeperated from, the ſupereminent Air: which
cauſe, in fine, who ſo ſhall rightly, and, as we ſay, with both his
Eyes, conſider this buſineſs, will find that it is reduced to, yea, that
it really is the ſame with, the true, Naturall and primary cauſe of
Natation or Submerſion; to wit, the exceſs or deficiency of the
Gravity of the water, in relation to the Gravity of that Solid
nitude, that is demitted into the water. For like as a Plate of Lead,
as thick as the back of a Knife, which being put into the water by it
ſelf alone goes to the bottom, if upon it you faſten a piece of Cork
four fingers thick, doth continue afloat, for that now the Solid that
is demitted in the water, is not, as before, more grave than the water,
but leſs, ſo the Board of Ebony, of its own nature more grave than
water; and, therefore, deſcending to the bottom, when it is
ted by it ſelf alone into the water, if it ſhall be put upon the water,
conjoyned with an Expanded vail of Air, that together with the
Ebony doth deſcend, and that it be ſuch, as that it doth make with
it a compound leſs grave than ſo much water in Maſs, as equalleth
the Maſs already ſubmerged and depreſſed beneath the Levell of the
waters Surface, it ſhall not deſcend any farther, but ſhall reſt, for
no other than the univerſall and moſt common cauſe, which is that
Solid Magnitudes, leſs grave inſpecie than the water, go not to the
bottom.
So that if one ſhould take a Plate of Lead, as for Example, a finger
thick, and an handfull broad every way, and ſhould attempt to make
it ſwimme, with putting it lightly on the water, he would loſe his
Labour, becauſe that if it ſhould be depreſſed an Hairs breadth
1yond the poſſible Altitude of the Ramparts of water, it would dive
and ſink; but if whilſt it is going downwards, one ſhould make
certain Banks or Ramparts about it, that ſhould hinder the do fuſion
of the water upon the ſaid Plate, the which Banks ſhould riſe ſo
high, as that they might be able to contain as much water, as ſhould
weigh equally with the ſaid Plate, it would, without all Queſtion,
deſcend no lower, but would reſt, as being ſuſtained by vertue of
the Air contained within the aforeſaid Ramparts: and, in ſhort,
there would be a Veſſell by this means formed with the bottom of
Lead. But if the thinneſs of the Lead ſhall be ſuch, that a very
ſmall height of Rampart would ſuffice to contain ſo much Air, as might
keep it afloat, it ſhall alſo reſt without the Artificiall Banks or
parts, but yet not without the Air, becauſe the Air by it ſelf makes
Banks ſufficient for a ſmall height, to reſiſt the Superfuſion of the
water: ſo that that which in this caſe ſwimmes, is as it were a
Veſſell filled with Air, by vertue of which it continueth afloat.
I will, in the laſt place, with an other Experimeut, attempt to
remove all difficulties, if ſo be there ſhould yet be any doubt leſt in
any one, touching the opperation of this ^{*}Continuity of the Air, with

the thin Plate which ſwims, and afterwards put an end to this part of
my diſcourſe.
*Or rather
tiguity,
I ſuppoſe my ſelf to be queſtioning with ſome of my Oponents.
Whether Figure have any influence upon the encreaſe or

tion of the Reſiſtance in any Weight againſt its being raiſed in the
Air, and I ſuppoſe, that I am to maintain the Affirmative,
ing that a Maſs of Lead, reduced to the Figure of a Ball, ſhall be
raiſed with leſs force, then if the ſame had been made into a thinne
and broad Plate, becauſe that it in this ſpacious Figure, hath a great
quantity of Air to penetrate, and in that other, more compacted and
contracted very little: and to demonſtrate the truth of ſuch my
pinion, I will hang in a ſmall thred firſt the Ball or Bullet, and put
that into the water, tying the thred that upholds it to one end of
the Ballance that I hold in the Air, and to the other end I by degrees
adde ſo much Weight, till that at laſt it brings up the Ball of Lead
out of the water: to do which, ſuppoſe a Gravity of thirty Ounces
ſufficeth; I afcerwards reduce the ſaid Lead into a flat and thinne
Plate, the which I likewiſe put into the water, ſuſpended by three
threds, which hold it parallel to the Surface of the water, and
ting in the ſame manner, Weights to the other end, till ſuch time as
the Place comes to be raiſed and drawn out of the water: I finde
that thirty ſix ounces will not ſuffice to ſeperate it from the water,
and raiſe it thorow the Air: and arguing from this Experiment, I
firm, that I have fully demonſtrated the truth of my Propoſition.
He re my Oponents deſires me to look down, ſhewing me a thing
1which I had not before obſerved, to wit, that in the Aſcent of the
Plate out of the water, it draws after it another Plate (if I may ſo
call it) of water, which before it divides and parts from the inferiour
Surface of the Plate of Lead, is raiſed above the Levell of the other
water, more than the thickneſs of the back of a Knife: Then he
goeth to repeat the Experiment with the Ball, and makes me ſee,
that it is but a very ſmall quantity of water, which cleaves to its
compacted and contracted Figure: and then he ſubjoynes, that its
no wonder, if in ſeperating the thinne and broad Plate from the
water, we meet with much greater Reſiſtance, than in ſeperating the
Ball, ſince together with the Plate, we are to raiſe a great quantity of
water, which occurreth not in the Ball: He telleth me moreover,
how that our Queſtion is, whether the Reſiſtance of Elevation be
greater in a dilated Plate of Lead, than in a Ball, and not whether
more reſiſteth a Plate of Lead with a great quantity of water, or a
Ball with a very little water: He ſheweth me in the cloſe, that the
putting the Plate and the Ball firſt into the water, to make proofe
thereby of their Reſiſtance in the Air, is beſides our caſe, which
treats of Elivating in the Air, and of things placed in the Air, and
not of the Reſiſtance that is made in the Confines of the Air and
water, and by things which are part in Air and part in water: and
laſtly, they make me feel with my hand, that when the thinne Plate
is in the Air, and free from the weight of the water, it is raiſed with
the very ſame Force that raiſeth the Ball. Seeing, and
ing theſe things, I know not what to do, unleſs to grant my ſelf
vinced, and to thank ſuch a Friend, for having made me to ſee that
which I never till then obſerved: and, being advertiſed by this ſame
Accident, to tell my Adverſaries, that our Queſtion is, whether a
Board and a Ball of Ebony, equally go to the bottom in water, and
not a Ball of Ebony and a Board of Ebony, joyned with another
flat Body of Air: and, farthermore, that we ſpeak of ſinking, and
not ſinking to the bottom, in water, and not of that which happeneth
in the Confines of the water and Air to Bodies that be part in the
Air, and part in the water; nor much leſs do we treat of the greater
or leſſer Force requiſite in ſeperating this or that Body from the Air;
not omitting to tell them, in the laſt place, that the Air doth reſiſt,
and gravitate downwards in the water, juſt ſo much as the water (if
I may ſo ſpeak) gravitates and reſiſts upwards in the Air, and that the
ſame force is required to ſinke a Bladder under water, that is full of
Air, as to raiſe it in the Air, being full of water, removing the
ſideration of the weight of that Filme or Skinne, and confidering the
water and the Air only. And it is likewiſe true, that the ſame Force
is required to ſink a Cup or ſuch like Veſſell under water, whilſt it is
full of Air, as to raiſe it above the Superficies of the water, keeping
1it with the mouth downwards; whilſt it is full of water, which is
conſtrained in the ſame manner to follow the Cup which contains it,
and to riſe above the other water into the Region of the Air, as the
Air is forced to follow the ſame Veſſell under the Surface of the
ter, till that in this caſe the water, ſurmounting the brimme of the
Cup, breaks in, driving thence the Air, and in that caſe, the ſaid
brimme coming out of the water, and arriving to the Confines of the
Air, the water falls down, and the Air ſub-enters to fill the cavity of
the Cup: upon which enſues, that he no leſs tranſgreſſes the
cles of the Convention, who produceth a Plate conjoyned with much
Air, to ſee if it de ſeend to the bottom in water, then he that makes
proof of the Reſiſtance againſt Elevation in Air with a Plate of Lead,
joyned with a like quantity of water.
An
ment of the
peration of
gures, in
creaſing or
ſening of the
Airs Reſiſtance
of Diviſion.
I have ſaid all that I could at preſent think of, to maintain the

Aſſertion I have undertook. It remains, that I examine that which
Ariſtotle hath writ of this matter towards the end of his Book De Cælo;
wherein I ſhall note two things: the one that it being true as hath

been demonſtrated, that Figure hath nothing to do about the moving
or not moving it ſelf upwards or downwards, it ſeemes that Aristotle
at his firſt falling upon this Sp. culation, was of the ſame opinion, as
in my opinion may be collected from the examination of his words.
Tis true, indeed, that in eſſaying afterwards to render a reaſon of
ſuch effect, as not having in my conceit hit upon the right, (which
in the ſecond place I will examine) it ſeems that he is brought to
admit the largeneſſe of Figure, to be intereſſed in this operation.
As to the firſt particuler, hear the preciſe words of Aristotle.
Ariſtotles
nion touching
the Operation
of Figure
amined.
Ariſtot de Cælo,
Lib. 4. Cap. 66.
Figures are not the Cauſes of moving ſimply upwards or downwards,

but of moving more ſlowly or ſwiftly, and by what means this comes to
paſs, it is not difficult to ſee.
Ariſtotle makes
not Figure the
cauſe of Motion
abſolutely, but
of ſwiſt or ſlow
motion,
Here firſt I note, that the terms being four, which fall under the
preſent conſideration, namely, Motion, Reſt, Slowly and Swiftly:

And Ariſtotle naming Figures as Cauſes of Tardity and Velocity,
cluding them from being the Cauſe of abſolute and ſimple Motion,
it ſeems neceſſary, that he exclude them on the other ſide, from being
the Cauſe of Reſt, ſo that his meaning is this. Figures are not the
Cauſes of moving or not moving abſolutely, but of moving quickly
or ſlowly: and, here, if any ſhould ſay the mind of Ariſtotle is to
exclude Figures from being Cauſes of Motion, but yet not from
being Cauſes of Reſt, ſo that the ſence would be to remove from
Figures, there being the Cauſes of moving ſimply, but yet not there
being Cauſes of Reſt, I would demand, whether we ought with
Aristotle to underſtand, that all Figures univerſally, are, in ſome
manner, the cauſes of Reſt in thoſe Bodies, which otherwiſe would
move, or elſe ſome particular Figures only, as for Example, broad
1and thinne Figures: If all indifferently, then every Body ſhall reſt:
becauſe every Body hath ſome Figure, which is falſe: but if ſome
particular Figures only may be in ſome manner a Cauſe of Reſt, as,
for Example, the broad, then the others would be in ſome manner
the Cauſes of Motion: for if from ſeeing ſome Bodies of a contracted
Figure move, which after dilated into Plates reſt, may be inferred,
that the Amplitude of Figure hath a part in the Cauſe of that Reſt;
ſo from ſeeing ſuch like Figures reſt, which afterwards contracted
move, it may with the ſame reaſon be affirmed, that the united and
contracted Figure, hath a part in cauſing Motion, as the remover of
that which impeded it: The which again is directly oppoſite to what
Ariſtotle ſaith, namely, that Figures are not the Cauſes of Motion.
Beſides, if Ariſtotle had admitted and not excluded Figures from
ing Cauſes of not moving in ſome Bodies, which moulded into
ther Figure would move, he would have impertinently propounded
in a dubitative manner, in the words immediately following, whence
it is, that the large and thinne Plates of Lead or Iron, reſt upon the
water, ſince the Cauſe was apparent, namely, the Amplitude of
Figure. Let us conclude, therefore, that the meaning of Ariſtotle
in this place is to affirm, that Figures are not the Cauſes of abſolutely
moving or not moving, but only of moving ſwiftly or ſlowly: which
we ought the rather to believe, in regard it is indeed a meſt true
ceipt and opinion. Now the mird of Ariſtotle being ſuch, and
pearing by conſequence, rather contrary at the firſt ſight, then
vourable to the aſſertion of the Oponents, it is neceſſary, that their
Interpretation be not exactly the ſame with that, but ſuch, as being
in part underſtood by ſome of them, and in part by others, was ſet
down: and it may eaſily be indeed ſo, being an Interpretation
conſonent to the ſence of the more famous Interpretors, which is,
that the Adverbe Simply or Abſolutely, put in the Text, orght not to
be joyned to the Verbe to Move, but with the Noun Cauſes: ſo that
the purport of Ariſtotles words, is to affirm, That Figures are not the
Cauſes abſolutely of moving or not moving, but yet are Cauſes
cundum quid, viz in ſome ſort; by which means, they are called
Auxiliary and Concomitant Cauſes: and this Propoſition is received
and aſſerted as true by Signor Buonamico Lib. 5. Cap. 28. where he
thus writes. There are other Cauſes concomitant, by which ſome
things float, and others ſink, among which the Figures of Bodies hath
the firſt place, &c.
Lib. 4. Cap. 61
Text. 42.
Concerning this Propoſition, I meet with many doubts and
culties, for which me thinks the words of Ariſtotle are not capable of
ſuch a conſtruction and ſence, and the difficulties are theſe.
Firſt in the order and diſpoſure of the words of Ariſtotle, the
ticle Simpliciter, or if you will abſoluté, is conjoyned with the Verb
1to move, and ſeperated from the Noun Cauſes, the which is a great
preſumption in my favour, ſeeing that the writing and the Text
ſaith, Figures are not the Cauſe of moving ſimply upwards or
downwards, but of quicker or ſlower Motion: and, ſaith not,
Figures are not ſimply the Cauſes of moving upwards or
wards, and when the words of a Text receive, tranſpoſed, a ſence
different from that which they found, taken in the order wherein
the Author diſpoſeth them, it is not convenient to inverte them.
And who will affirm that Ariſtotle deſiring to write a Propoſition,
would diſpoſe the words in ſuch ſort, that they ſhould import a
different, nay, a contrary ſence? contrary, I ſay, becauſe
ſtood as they are written; they ſay, that Figures are not the
Cauſes of Motion, but inverted, they ſay, that Figures are the
Cauſes of Motion, &c.
Moreover, if the intent of Aristotle had been to ſay, that Figures
are not ſimply the Cauſes of moving upwards or downwards, but
only Cauſes Secundum quid, he would not have adjoyned thoſe
words, but they are Cauſes of the more ſwift or ſlow Motion; yea, the
ſubjoining this would have been not only ſuperfluous but falſe, for
that the whole tenour of the Propoſition would import thus much.
Figures are not the abſolute Cauſes of moving upwards or
wards, but are the abſolute Cauſe of the ſwift or ſlow Motion;
which is not true: becauſe the primary Cauſes of greater or leſſer
Velocity, are by Ariſtotle in the 4th of his Phyſicks, Text. 71.
buted to the greater or leſſer Gravity of Moveables, compared
mong themſelves, and to the greater or leſſer Reſiſtance of the
Medium's, depending on their greater or leſs Craſſitude: and theſe
are inſerted by Ariſtotle as the primary Cauſes; and theſe two only
are in that place nominated: and Figure comes afterwards to be
conſidered, Text. 74. rather as an Inſtrumentall Cauſe of the force
of the Gravity, the which divides either with the Figure, or with
the Impetus; and, indeed, Figure by it ſelf without the force of
Gravity or Levity, would opperate nothing.
Iadde, that if Ariſtotle had an opinion that Figure had been in
ſome ſort the Cauſe of moving or not moving, the inquiſition
which he makes immediately in a doubtfull manner, whence it
comes, that a Plate of Lead flotes, would have been impertinent;
for if but juſt before he had ſaid, that Figure was in a certain ſort
the Cauſe of moving or not moving, he needed not to call in
Queſtion, by what Cauſe the Plate of Lead ſwims, and then
bing the Cauſe to its Figure; and framing a diſcourſe in this manner.
Figure is a Cauſe Secundum quid of not ſinking: but, now, if it be
doubted, for what Cauſe a thin Plate of Lead goes not to the bottom;
it ſhall be anſwered, that that proceeds from its Figure: a diſcourſe
1which would be indecent in a Child, much more in Ariſtotle; For
where is the occaſion of doubting? And who ſees not, that if Ariſtotle
had held, that Figure was in ſome ſort a Cauſe of Natation, he
would without the leaſt Heſitation have writ; That Figure is in a
certain ſort the Cauſe of Natation, and therefore the Plate of Lead
in reſpect of its large and expatiated Figure ſwims; but if we take
the propoſition of Ariſtotle as I ſay, and as it is writte n, and as
deed it is true, the enſuing words come in very oppoſitely, as well in
the introduction of ſwift and ſlow, as in the queſtion, which very
pertinently offers it ſelf, and would ſay thus much.
Figures are not the Cauſe of moving or not moving ſimply
wards or downwards, but of moving more quickly or ſlowly: But if
it be ſo, the Cauſe is doubtfull, whence it proceeds, that a Plate of
Lead or of Iron broad and thin doth ſwim, &c. And the occaſion of
the doubt is obvious, becauſe it ſeems at the firſt glance, that the
Figure is the Cauſe of this Natation, ſince the ſame Lead, or a leſs
quantity, but in another Figure, goes to the bottom, and we have
already affirmed, that the Figure hath no ſhare in this effect.
Laſtly, if the intent of Ariſtotle in this place had been to ſay,
that Figures, although not abſolutely, are at leaſt in ſome meaſure
the Cauſe of moving or not moving: I would have it conſidered,
that he names no leſs the Motion upwards, than the other
wards: and becauſe in exemplifying it afterwards, he produceth
no other Experiments than of a Plate of Lead, and Board of Ebony,
Matters that of their own Nature go to the bottom, but by vertue
(as our Adverſaries ſay) of their Figure, reſt afloat; it is ſit that
they ſhould produce ſome other Experiment of thoſe Matters, which
by their Nature ſwims, but retained by their Figure reſt at the
bottom. But ſince this is impoſſible to be done, we conclude, that
Ariſtotle in this place, hath not attributed any action to the Figure
of ſimply moving or not moving.
But though he hath exquiſitely Philoſophiz'd, in inveſtigating
the ſolution of the doubts he propoſeth, yet will I not undertake
to maintain, rather various difficulties, that preſent themſelves
unto me, give me occaſion of ſuſpecting that he hath not entirely
diſplaid unto us, the true Cauſe of the preſent Concluſion: which
difficulties I will propound one by one, ready to change opinion,
when ever I am ſhewed, that the Truth is different from what I ſay;
to the confeſſion whereof I am much more inclinable than to

Ariſtotle erred
in affirming a
Needle dimitted
long wayes to
ſink.
Ariſtotle having propounded the Queſtion, whence it proceeds,
that broad Plates of Iron or Lead, float or ſwim; he addeth (as
it were ſtrengthening the occaſion of doubting) foraſmuch as other
things, leſs, and leſs grave, be they round or long, as for inſtance a
1Needle go to the bottom. Now I here doubt, or rather am certain,
that a Needle put lightly upon the water, reſts afloat, no leſs than the
thin Plates of Iron or Lead. I cannot believe, albeit it hath been
told me, that ſome to defend Ariſtotle ſhould ſay, that he intends a
Needle demitted not longwayes but endwayes, and with the Point
downwards; nevertheleſs, not to leave them ſo much as this, though
very weak refuge, and which in my judgement Ariſtotle himſelf
would refuſe, I ſay it ought to be underſtood, that the Needle muſt
be demitted, according to the Dimenſion named by Ariſtotle, which
is the length: becauſe, if any other Dimenſion than that which is
named, might or ought to be taken, I would ſay, that even the Plates
of Iron and Lead, ſink to the bottom, if they be put into the water
edgewayes and not flatwayes. But becauſe Ariſtotle ſaith, broad
Figures go not to the bottom, it is to be underſtood, being demitted
broadwayes: and, therefore, when he ſaith, long Figures as a
Needle, albeit light, reſt not afloat, it ought to be underſtood of
them when demitted longwayes.
Morcover, to ſay that Ariſtotle is to be underſtood of the Needle
mitted with the Point downwards, is to father upon him a great
tinency; for in this place he ſaith, that little Particles of Lead or Iron,
if they be round or long as a Needle, do ſink to the bottome; ſo that by
his Opinion, a Particle or ſmall Grain of Iron cannot ſwim: and if he
thus believed, what a great folly would it be to ſubjoyn, that neither
would a Needle demitted endwayes ſwim? And what other is ſuch a
Needle, but many ſuch like Graines accumulated one upon another? It
was too unworthy of ſuch a man to ſay, that one ſingle Grain of Iron could
not ſwim, and that neither can it ſwim, though you put a hundred more
upon it.
Laſtly, either Ariſtotle believed, that a Needle demitted
wayes upon the water, would ſwim, or he believed that it would
not ſwim: If he believed it would not ſwim, he might well ſpeak
as indeed he did; but if he believed and knew that it would ſloat,
why, together with the dubious Problem of the Natation of broad
Figure, though of ponderous Matter, hath he not alſo introduced
the Queſtion; whence it proceeds, that even long and ſlender
gures, howbeit of Iron or Lead do ſwim? And the rather, for that
the occaſion of doubting ſeems greater in long and narrow Figures,
than in broad and thin, as from Aristotles not having doubted of it,
is manifeſted.
No leſſer an inconvenience would they faſten upon Ariſtotle, who
in his defence ſhould ſay, that he means a Needle pretty thick, and
not a ſmall one; for take it for granted to be intended of a ſmall
1and it ſhall ſuffice to reply, that he believed that it would ſwim;
and I will again charge him with having avoided a more wonderfull
and intricate Probleme, and introduced the more facile and leſs
wonderfull.
We ſay freely therefore; that Ariſtotle did hold, that only the
broad Figure did ſwim, but the long and ſlender, ſuch as a Needle,
not. The which nevertheleſs is falſe, as it is alſo falſe in round
Bodies: becauſe, as from what hath been predemonſtrated, may be
thered, little Balls of Lead and Iron, do in like manner ſwim.
He propoſeth likewiſe another Concluſion, which likewiſe ſeems

different from the truth, and it is, That ſome things, by reaſon of
their littleneſs fly in the Air, as the ſmall duſt of the Earth, and the
thin leaves of beaten Gold: but in my Opinion, Experience ſhews
us, that that happens not only in the Air, but alſo in the water, in
which do deſcend, even thoſe Particles or Atomes of Earth, that
diſtur be it, whoſe minuity is ſuch, that they are not deſervable, ſave
only when they are many hundreds together. Therefore, the duſt
of the Earth, and beaten Gold, do not any way ſuſtain themſelves
in the Air, but deſcend downwards, and only fly to and again in
the ſame, when ſtrong Windes raiſe them, or other agitations of the
Air commove them: and this alſo happens in the commotion of the
water, which raiſeth its Sand from the bottom, and makes it muddy.
But Ariſtotle cannot mean this impediment of the commotion, of
which he makes no mention, nor names other than the lightneſs of
ſuch Minutiæ or Atomes, and the Reſiſtance of the Craſſitudes of the
Water and Air, by which we ſee, that he ſpeakes of a calme, and
not diſturbed and agitated Air: but in that caſe, neither Gold nor
Earth, be they never ſo ſmall, are ſuſtained, but ſpeedily
Ariſtotle
fir meth ſome
Bodies volatile
for their
ity, Text. 42.
Democritus
ced the Cauſe of
Natation in
certain ſiery
tomes.
He paſſeth next to confute Democritus, which, by his Teſtimony
would have it, that ſome Fiery Atomes, which continually aſcend
through the water, do ſpring upwards, and ſuſtain thoſe grave Bodies,
which are very broad, and that the narrow deſcend to the bottom,

for that but a ſmall quantity of thoſe Atomes, encounter and reſiſt
them.
Ariſtot. De Cœlo
lib. 4. cap. 6.
text. 43.
I ſay, Ariſtotle confutes this poſition, ſaying, that that ſhould

much more occurre in the Air, as the ſame Democritus inſtances
gainſt himſelf, but after he had moved the objection, he ſlightly
ſolves it, with ſaying, that thoſe Corpuſcles which aſcend in the Air,
make not their Impetus conjunctly. Here I will not ſay, that the

reaſon alledged by Democritus is true, but I will only ſay, it ſeems
in my judgement, that it is not wholly confuted by Ariſtotle, whilſt he
ſaith, that were it true, that the calid aſcending Atomes, ſhould
ſuſtain Bodies grave, but very broad, it would much more be done
in the Air, than in Water, for that haply in the Opinion of Ariſtotle,
1the ſaid calid Atomes aſcend with much greater Force and Velocity
through the Air, than through the water. And if this be ſo, as I
ly believe it is, the Objection of Ariſtotle in my judgement ſeems to
give occaſion of ſuſpecting, that he may poſſibly be deceived in more
than one particular: Firſt, becauſe thoſe calid Atomes, (whether
they be Fiery Corpuſcles, or whether they be Exhalations, or in
ſhort, whatever other matter they be, that aſcends upwards through
the Air) cannot be believed to mount faſter through Air, than
through water: but rather on the contrary, they peradventure move
more impetuouſly through the water, than through the Air, as hath
been in part demonſtrated above. And here I cannot finde the
ſon, why Ariſtotle ſeeing, that the deſeending Motion of the ſame
Moveable, is more ſwift in Air, than in water, hath not advertiſed
us, that from the contrary Motion, the contrary ſhould neceſſarily
follow; to wit, that it is more ſwift in the water, than in the Air: for
ſince that the Moveable which deſcendeth, moves ſwifter through
the Air, than through the water, if we ſhould ſuppoſe its Gravity
gradually to diminiſh, it would firſt become ſuch, that deſcending
ſwiftly through the Air, it would deſcend but ſlowly through the
water: and then again, it might be ſuch, that deſcending in the
Air, it ſhould aſcend in the water: and being made yet leſs grave,
it ſhall aſcend ſwiftly through the water, and yet deſcend likewiſe
through the Air: and in ſhort, before it can begin to aſcend, though
but ſlowly through the Air, it ſhall aſcend ſwiftly through the water:
how then is it true, that aſcending Moveables move ſwifter through
the Air, than through the water?
Democritus
futed by
ſtotle, text 43.
Ariſtotles
futation of
mocritus refuted
by the Author.
That which hath made Ariſtotle believe, the Motion of Aſcent to be
ſwifter in Air, than in water, was firſt, the having referred the
Cauſes of ſlow and quick, as well in the Motion of Aſcent, as of
Deſcent, only to the diverſity of the Figures of the Moveable, and to
the more or leſs Reſiſtance of the greater or leſſer Craſſitude, or
rity of the Medium; not regarding the compariſon of the Exceſſes
of the Gravities of the Moveables, and of the Mediums: the which
notwithſtanding, is the moſt principal point in this affair: for if the
augmentation and diminution of the Tardity or Velocity, ſhould
have only reſpect to the Denſity or Rarity of the Medium, every Body
that deſcends in Air, would deſcend in water: becauſe whatever
difference is found between the Craſſitude of the water, and that of
the Air, may well be found between the Velocity of the ſame
able in the Air, and ſome other Velocity: and this ſhould be its
proper Velocity in the water, which is abſolutely falſe. The other
occaſion is, that he did believe, that like as there is a poſitive and
trinſecall Quality, whereby Elementary Bodies have a propenſion
of moving towards the Centre of the Earth, ſo there is another
1wiſe intrinſecall, whereby ſome of thoſe Bodies have an Impetus of

flying the Centre, and moving upwards: by Vertue of which
trinſe call Principle, called by him Levity, the Moveables which have
that ſame Motion more eaſily penetrate the more ſubtle Medium,
than the more denſe: but ſuch a Propoſition appears likewiſe
certain, as I have above hinted in part, and as with Reaſons and
Experiments, I could demonſtrate, did not the preſent Argument
portune me, or could I diſpatch it in few words.
Lib. 4. Cap. 5.
The Objection therefore of Ariſtotle againſt Democritus, whilſt
he ſaith, that if the Fiery aſcending Atomes ſhould ſuſtain Bodies
grave, but of a diſtended Figure, it would be more obſervable in
the Air than in the water, becauſe ſuch Corpuſcles move ſwifter in
that, than in this, is not good; yea the contrary would evene, for
that they aſcend more ſlowly through the Air: and, beſides their
moving ſlowly, they aſcend, not united together, as in the water,
but diſcontinue, and, as we ſay, ſcatter: And, therefore, as
Democritus well replyes, reſolving the inſtance they make not their
puſh or Impetus conjunctly.
Ariſtotle, in the ſecond place, deceives himſelf, whilſt he will
have the ſaid grave Bodies to be more eaſily ſuſtained by the ſaid
Fiery aſcending Atomes in the Air than in the Water: not
ing, that the ſaid Bodies are much more grave in that, than in this,
and that ſuch a Body weighs ten pounds in the Air, which will not
in the water weigh 1/2 an ounce; how can it then be more eaſily
ſuſtained in the Air, than in the Water?
Let us conclude, therefore, that Democritus hath in this particular
better Philoſophated than Ariſtotle. But yet will not I affirm, that De-

mocritus hath reaſon'd rightly, but I rather ſay, that there is a
nifeſt Experiment that overthrows his Reaſon, and this it is, That
if it were true, that calid aſcending Atomes ſhould uphold a Body,
that if they did not hinder, would go to the bottom, it would follow,
that we may find a Matter very little ſuperiour in Gravity to the
water, the which being reduced into a Ball, or other contracted
Figure, ſhould go to the bottom, as encountring but few Fiery
tomes; and which being diſtended afterwards into a dilated and
thin Plate, ſhould come to be thruſt upwards by the impulſion of a
great Multitude of thoſe Corpuſcles, and at laſt carried to the very
Surface of the water: which wee ſee not to happen; Experience
ſhewing us, that a Body v. gra. of a Sphericall Figure, which very
hardly, and with very great leaſure goeth to the bottom, will reſt
there, and will alſo deſcend thither, being reduced into whatſoever
other diſtended Figure. We muſt needs ſay then, either that in the
water, there are no ſuch aſcending Fiery Atoms, or if that ſuch there
be, that they are not able to raiſe and lift up any Plate of a Matter,
1that without them would go to the bottom: Of which two Pofitions,
I eſteem the ſecond to be true, underſtanding it of water, conſtituted
in its naturall Coldneſs. But if we take a Veſſel of Glaſs, or Braſs,
or any other hard matter, full of cold water, within which is put a
Solid of a flat or concave Figure, but that in Gravity exceeds the
water ſo little, that it goes ſlowly to the bottom; I ſay, that putting
ſome burning Coals under the ſaid Veſſel, as ſoon as the new Fiery
Atomes ſhall have penetrated the ſubſtance of the Veſſel, they ſhall
without doubt, aſcend through that of the water, and thruſting
gainſt the foreſaid Solid, they ſhall drive it to the Superficies, and
there detain it, as long as the incurſions of the ſaid Corpuſcles ſhall
laſt, which ceaſing after the removall of the Fire, the Solid being
bandoned by its ſupporters, ſhall return to the bottom.
Democritus
futed by the
Authour.
But Democritus notes, that this Caufe only takes place when we
treat of raiſing and ſuſtaining of Plates of Matters, but very little
heavier than the water, or extreamly thin: but in Matters very
grave, and of ſome thickneſs, as Plates of Lead or other Mettal, that
ſame Effect wholly ceaſeth: In Teſtimony of which, let's obſerve
that ſuch Plates, being raiſed by the Fiery Atomes, aſcend through
all the depth of the water, and ſtop at the Confines of the Air, ſtill
ſtaying under water: but the Plates of the Opponents ſtay not, but
only when they have their upper Superficies dry, nor is there any
means to be uſed, that when they are within the water, they may
not ſink to the bottom. The cauſe, therefore, of the Supernatation
of the things of which Democritus ſpeaks is one, and that of the
natation of the things of which we ſpeak is another. But, returning

to Ariſtotle, methinks that he hath more weakly confuted Democritus,
than Democritus himſelf hath done: For Ariſtotle having propounded
the Objection which he maketh againſt him, and oppoſed him with
ſaying, that if the calid aſcendent Corpuſcles were thoſe that raiſed
the thin Plate, much more then would ſuch a Solid be raiſed and
born upwards through the Air, it ſheweth that the deſire in Ariſtotle
to detect Democritus, was predominate over the exquiſiteneſs of Solid
Philoſophizing: which deſire of his he hath diſcovered in other
caſions, and that we may not digreſs too far from this place, in the
Text precedent to this Chapter which we have in hand; where he

attempts to confute the ſame Democritus, for that he, not
ing himſelf with names only, had eſſayed more particularly to
clare what things Gravity and Levity were; that is, the Cauſes of
deſcending and aſcending, (and had introduced Repletion and
cuity) aſcribing this to Fire, by which it moves upwards, and that to
the Earth, by which it deſcends; afterwards attributing to the
Air more of Fire, and to the water more of Earth. But Ariſtotle
deſiring a poſitive Cauſe, even of aſcending Motion, and not as Plato,
1or theſe others, a ſimple negation, or privation, ſuch as Vacuity

would be in reference to Repletion, argueth againſt Democritus and
ſaith: If it be true, as you ſuppoſe, then there ſhall be a great Maſs
of water, which ſhall have more of Fire, than a ſmall Maſs of Air,
and a great Maſs of Air, which ſhall have more of Earth than a
tle Maſs of water, whereby it would enſue, that a great Maſs of Air,
ſhould come more ſwiftly downwards, than a little quantity of
water: But that is never in any caſe ſoever: Therefore Democritus
diſcourſeth erroneouſly.
Ariſtotle ſhews
his deſire of
finding
critus in an
ror, to exceed
that of
veting Truth.
Cap. 5. Text 41.
Id. ibid.
But in my opinion, the Doctrine of Democritus, is not by this
gation overthrown, but if I erre not, the manner of Ariſtotle deduction
either concludes not, or if it do conclude any thing, it may with
quall force be reſtored againſt himſelf. Democritus will grant to
Ariſtotle, that there may be a great Maſs of Air taken, which
tains more Earth, than a ſmall quantity of water, but yet will deny,
that ſuch a Maſs of Air, ſhall go faſter downwards than a little water,
and that for many reaſons. Firſt, becauſe if the greater quantity
of Earth, contained in the great Maſs of Air, ought to cauſe a greater
Velocity than a leſs quantity of Earth, contained in a little quantity
of water, it would be neceſſary, firſt, that it were true, that a
greater Maſs of pure Earth, ſhould move more ſwiftly than a leſs:
But this is falſe, though Ariſtotle in many places affirms it to be true:
becauſe not the greater abſolute, but the greater ſpecificall Gravity,

is the cauſe of greater Velocity: nor doth a Ball of Wood,
ing ten pounds, deſcend more ſwiftly than one weighing ten Ounces,
and that is of the ſame Matter: but indeed a Bullet of Lead of four
Ounces, deſcendeth more ſwiftly than a Ball of Wood of twenty
Pounds: becauſe the Lead is more grave in ſpecie than the Wood.
Therefore, its not neceſſary, that a great Maſs of Air, by reaſon of
the much Earth contained in it, do deſcend more ſwiftly than a little

Maſs of water, but on the contrary, any whatſoever Maſs of water,
ſhall move more ſwiftly than any other of Air, by reaſon the
pation of the terrene parts in ſpecie is greater in the water, than in the
Air. Let us note, in the ſecond place, how that in multiplying the
Maſs of the Air, we not only multiply that which is therein of terrene,
but its Fire alſo: whence the Cauſe of aſcending, no leſs encreaſeth,
by vertue of the Fire, than that of deſcending on the account of its
multiplied Earth. It was requiſite in increaſing the greatneſs of the
Air, to multiply that which it hath of terrene only, leaving its Fire
in its firſt ſtate, for then the terrene parts of the augmented Air,
overcoming the terrene parts of the ſmall quantity of water, it might
with more probability have been pretended, that the great
ty of Air, ought to deſcend with a greater Impetus, than the little
quantity of water.
1
The greater
Specificall, not
the greater
ſolute Gravity,
is the Cauſe of
Velocity.
Any Maſs of
water ſhal move
more ſwiftly,
than any of Air,
and why.
Therefore, the Fallacy lyes more in the Diſcourſe of Ariſtotle, than
in that of Democritus, who with ſeverall other Reaſons might oppoſe
Ariſtotle, and alledge; If it be true, that the extreame Elements be
one ſimply grave, and the other ſimply light, and that the mean
Elements participate of the one, and of the other Nature; but the
Air more of Levity, and the water more of Gravity, then there ſhall
be a great Maſs of Air, whoſe Gravity ſhall exceed the Gravity of a
little quantity of water; and therefore ſuch a Maſs of Air ſhall
ſcend more ſwiftly than that little water: But that is never ſeen to
occurr: Therefore its not true, that the mean Elements do
pate of the one, and the other quality. This argument is fallacious,
no leſs than the other againſt Democritus.
Laſtly, Aristotle having ſaid, that if the Poſition of Democritus
were true, it would follow, that a great Maſs of Air ſhould move
more ſwiftly than a ſmall Maſs of water, and afterwards ſubjoyned,
that that is never ſeen in any Caſe: methinks others may become
ſirous to know of him in what place this ſhould evene, which he
duceth againſt Democritus, and what Experiment teacheth us, that
it never falls out ſo. To ſuppoſe to ſee it in the Element of water,
or in that of the Air is vain, becauſe neither doth water through
water, nor Air through Air move, nor would they ever by any
whatever participation others aſſign them, of Earth or of Fire: the
Earth, in that it is not a Body fluid, and yielding to the mobility of
other Bodies, is a moſt improper place and Medium for ſuch an
periment: Vacuum, according to the ſame Ariſtotle himſelf, there
is none, and were there, nothing would move in it: there remaine
the Region of Fire, but being ſo far diſtant from us, what
ment can aſſure us, or hath aſſertained Ariſtotle in ſuch ſort, that he
ſhould as of a thing moſt obvious to ſence, affirm what he
ceth in confutation of Democritus, to wit, that a great Maſs of Air,
is moved no ſwifter than a little one of water? But I will dwell no
longer upon this matter, whereon I have ſpoke ſufficiently: but
leaving Democritus, I return to the Text of Ariſtotle, wherein he
goes about to render the true reaſon, how it comes to paſs, that the
thin Plates of Iron or Lead do ſwim on the water; and, moreover,
that Gold it ſelf being beaten into thin Leaves, not only ſwims in
water, but flyeth too and again in the Air. He ſuppoſeth that of

Continualls, ſome are eaſily diviſible, others not: and that of the
eaſily diviſible, ſome are more ſo, and ſome leſs: and theſe he
affirms we ſhould eſteem the Cauſes. He addes that that is eaſily
diviſible, which is well terminated, and the more the more diviſible,
and that the Air is more ſo, than the water, and the water than the
Earth. And, laſtly, he ſuppoſeth that in each kind, the leſſe
tity is eaſlyer divided and broken than the greater.
1
De Cœlo l. 4. c.
6. t. 44.
Here I note, that the Concluſions of Ariſtotle in generall are all
true, but methinks, that he applyeth them to particulars, in which
they have no place, as indeed they have in others, as for Example,
Wax is more eaſily diviſible than Lead, and Lead than Silver,
aſmuch as Wax receives all the terms more eaſiler than Lead, and
Lead than Silver. Its true, moreover, that a little quantity of
ver is eaſlier divided than a great Maſs: and all theſe Propoſitions
are true, becauſe true it is, that in Silver, Lead and Wax, there
is ſimply a Reſiſtance againſt Diviſion, and where there is the
lute, there is alſo the reſpective. But if as well in water as in Air,
there be no Renitence againſt ſimple Diviſion, how can we ſay, that
the water is eaſlier divided than the Air? We know not how to
tricate our ſelves from the Equivocation: whereupon I return to
anſwer, that Reſiſtance of abſolute Diviſion is one thing, and
ſiſtance of Diviſion made with ſuch and ſuch Velocity is another.
But to produce Reſt, and to abate the Motion, the Reſiſtance of
abſolute Diviſion is neceſſary; and the Reſiſtance of ſpeedy
viſion, cauſeth not Reſt, but ſlowneſs of Motion. But that as well
in the Air, as in water, there is no Reſiſtance of ſimple Diviſion, is
manifeſt, for that there is not found any Solid Body which divides
not the Air, and alſo the water: and that beaten Gold, or ſmall
duſt, are not able to ſuperate the Reſiſtance of the Air, is contrary
to that which Experience ſhews us, for we ſee Gold and Duſt to go
waving to and again in the Air, and at laſt to deſcend
wards, and to do the ſame in the water, if it be put therein, and
parated from the Air. And, becauſe, as I ſay, neither the water,
nor the Air do reſiſt ſimple Diviſion, it cannot be ſaid, that the water
reſiſts more than the Air. Nor let any object unto me, the
ple of moſt light Bodies, as a Feather, or a little of the pith of
der, or water-reed that divides the Air and not the water, and from
this infer, that the Ait is eaſlier diviſible than the water; for I ſay
unto them, that if they do well obſerve, they ſhall ſee the ſame

Body likewiſe divide the Continuity of the water, and ſubmerge in
part, and in ſuch a part, as that ſo much water in Maſs would weigh
as much as the whole Solid. And if they ſhal yet perſiſt in their doubt,
that ſuch a Solid ſinks not through inability to divide the water, I will
return them this reply, that if they put it under water, and then let it
go, they ſhall ſee it divide the water, and preſently aſcend with no leſs
celerity, than that with which it divided the Air in deſcending: ſo that
to ſay that this Solid aſcends in the Air, but that coming to the water,
it ceaſeth its Motion, and therefore the water is more difficult to be
divided, concludes nothing: for I, on the contrary, will propoſe them
a piece of Wood, or of Wax, which riſeth from the bottom of the
water, and eaſily divides its Reſiſtance, which afterwards being
1ved at the Air, ſtayeth there, and hardly toucheth it; whence I may
aswell ſay, that the water is more eaſier divided than the Air
Archimed. De
Inſident, humi lib.
2. prop. 1.
I will not on this occaſion forbear to give warning of another
lacy of theſe perſons, who attribute the reaſon of ſinking or ſwimming
to the greater or leſſe Reſiſtance of the Craſſitude of the water againſt
Diviſion, making uſe of the example of an Egg, which in ſweet water
goeth to the bottom, but in ſalt water ſwims; and alledging for the
cauſe thereof, the faint Reſiſtance of freſh water againſt Diviſion, and
the ſtrong Reſiſtance of ſalt water But if I miſtake not, from the ſame
Experiment, we may aswell deduce the quite contrary; namely, that
the freſh water is more denſe, and the ſalt more tenuous and ſubtle,
ſince an Egg from the bottom of ſalt water ſpeedily aſcends to the
top, and divides its Reſiſtance, which it cannot do in the freſh, in whoſe
bottom it ſtays, being unable to riſe upwards. Into ſuch like
ities, do falſe Principles Lead men: but he that rightly Philoſophating,
ſhall acknowledge the exceſſes of the Gravities of the Moveables and
of the Mediums, to be the Cauſes of thoſe effects, will ſay, that the
Egg ſinks to the bottom in freſh water, for that it is more grave than
it, and ſwimeth in the ſalt, for that its leſs grave than it: and ſhall
without any abſurdity, very ſolidly eſtabliſh his Concluſions.
Therefore the reaſon totally ceaſeth, that Ariſtotle ſubjoyns in the

Text ſaying; The things, therefore, which have great breadth remain
above, becauſe they comprehend much, and that which is greater,
is not eaſily divided. Such diſcourſing ceaſeth, I ſay, becauſe its not
true, that there is in water or in Air any Reſiſtance of Diviſion;
ſides that the Plate of Lead when it ſtays, hath already divided and
penetrated the Craſſitude of the water, and profounded it ſelf ten or
twelve times more than its own thickneſs: beſides that ſuch Reſiſtance
of Diviſion, were it ſuppoſed to be in the water, could not rationally
be affirmed to be more in its ſuperiour parts than in the middle, and
lower: but if there were any difference, the inferiour ſhould be the
more denſe, ſo that the Plate would be no leſs unable to penetrate
the lower, than the ſuperiour parts of the water; nevertheleſs we ſee
that no ſooner do we wet the ſuperious Superficies of the Board or
thin Piece of Wood, but it precipitatly, and without any retenſion,
deſcends to the bottom.
Text 45.
I believe not after all this, that any (thinking perhaps thereby to
defend Aristotle) will ſay, that it being true, that the much water
ſiſts more than the little, the ſaid Board being put lower deſcendeth,
becauſe there remaineth a leſs Maſs of water to be divided by it:
cauſe if after the having ſeen the ſame Board ſwim in four Inches of
water, and alſo after that in the ſame to ſink, he ſhall try the ſame
Experiment upon a profundity of ten or twenty fathom water, he
ſhall ſee the very ſelf ſame effect. And here I will take occaſion to
1remember, for the removall of an Error that is too common; That
that Ship or other whatſoever Body, that on the depth of an hundred
or a thouſand fathom, ſwims with ſubmerging only ſix fathom of its
own height, [or in the Sea dialect, that draws ſix fathom water] ſhall
ſwim in the ſame manner in water, that hath but ſix fathom and half

an Inch of depth. Nor do I on the other ſide, think that it can be
ſaid, that the ſuperiour parts of the water are the more denſe,
though a moſt grave Authour hath eſteemed the ſuperiour water in
the Sea to be ſo, grounding his opinion upon its being more ſalt, than
that at the bottom: but I doubt the Experiment, whether hitherto
in taking the water from the bottom, the Obſervatour did not light
upon ſome ſpring of freſh water there ſpouting up: but we plainly
ſee on the contrary, the freſh Waters of Rivers to dilate themſelves
for ſome miles beyond their place of meeting with the ſalt water of
the Sea, without deſcending in it, or mixing with it, unleſs by the
intervention of ſome commotion or turbulency of the Windes.
A Ship that
in 100 Fathome
water draweth
6 Fathome, ſhall
float in 6
thome and 1/2 an
Inch of depth.
But returning to Aristotle, I ſay, that the breadth of Figure hath
nothing to do in this buſineſs more or leſs, becauſe the ſaid Plate of

Lead, or other Matter, cut into long Slices, ſwim neither more nor
leſs; and the ſame ſhall the Slices do, being cut anew into little
pieces, becauſe its not the breadth but the thickneſs that operates in
this buſineſs. I ſay farther, that in caſe it were really true, that the

Renitence to Diviſion were the proper Cauſe of ſwimming, the
gures more narrow and ſhort, would much better ſwim than the more
ſpacious and broad, ſo that augmenting the breadth of the Figure,
the facility of ſupernatation will be deminiſhed, and decreaſing, that
this will encreaſe.
Thickneſs not
breadth of
gure to be
ſpected in
tation.
Were
tence the cauſe
of Natation,
breadth of
gure would
hinder the
ſwiming of
dies.
And for declaration of what I ſay, conſider that when a thin Plate
of Lead deſcends, dividing the water, the Diviſion and
ation is made between the parts of the water, invironing the
ter or Circumference of the ſaid Plate, and according to the
neſs greater or leſſer of that circuit, it hath to divide a greater or
leſſer quantity of water, ſo that if the circuit, ſuppoſe of a Board,
be ten Feet in ſinking it flatways, it is to make the ſeperation and
diviſion, and to ſo ſpeak, an inciſſion upon ten Feet of water; and
likewiſe a leſſer Board that is four Feet in Perimeter, muſt make an
inceſſion of four Feet. This granted, he that hath any knowledge
in Geometry, will comprehend, not only that a Board ſawed in many
long thin pieces, will much better float than when it was entire, but
that all Figures, the more ſhort and narrow they be, ſhall ſo much the
better ſwim. Let the Board ABCD be, for Example, eight
Palmes long, and five broad, its circuit ſhall be twenty ſix Palmes;
and ſo many muſt the inceſſion be, which it ſhall make in the water to
deſcend therein: but if we do ſaw ir, as ſuppoſe into eight little
1pieces, according to the Lines E F, G H, &c. making ſeven Segments,
we muſt adde to the twenty ſix Palmes of the circuit of the whole
Board, ſeventy others; whereupon the eight little pieces ſo cut and
ſeperated, have to cut ninty ſix Palmes of water. And, if moreover,
we cur each of the ſaid pieces into five parts,
320[Figure 320]
ducing them into Squares, to the circuit of ninty
ſix Palmes, with four cuts of eight Palmes apiece;
we ſhall adde alſo ſixty four Palmes, whereupon
the ſaid Squares to deſcend in the water, muſt
divide one hundred and ſixty Palmes of water,
but the Reſiſtance is much greater than that of
twenty ſix; therefore to the leſſer Superficies,
we ſhall reduce them, ſo much the more eaſily
will they float: and the ſame will happen in all
other Figures, whoſe Superficies are ſimular amongſt themſelves, but
different in bigneſs: becauſe the ſaid Superficies, being either
ſhed or encreaſed, always diminiſh or encreaſe their Perimeters in
ſubduple proportion; to wit, the Reſiſtance that they find in
trating the water; therefore the little pieces gradually ſwim, with more
and more facility as their breadth is leſſened.
This is manifeſt; for keeping ſtill the ſame height of the Solid, with
the ſame proportion as the Baſe encreaſeth or deminiſheth, doth the ſaid
Solid alſo encreaſe or diminiſh; whereupon the Solid more diminiſhing
than the Circuit, the Cauſe of Submerſion more diminiſheth than the Cauſe
of Natation: And on the contrary, the Solid more encreaſing than the
Circuit, the Cauſe of Submerſion encreaſeth more, that of Natation
leſs.
And this may all be dedueed out of the Doctrine of Ariſtotle
gainſt his own Doctrine.
Laſtly, to that which we read in the latter part of the Text, that

is to ſay, that we muſt compare the Gravity of the Moveable with
the Reſiſtance of the Medium againſt Diviſion, becauſe if the force of
the Gravity exceed the Reſiſtance of the Medium, the Moveable will
deſcend, if not it will float. I need not make any other anſwer,
but that which hath been already delivered; namely, that its not
the Reſiſtance of abſolute Diviſion, (which neither is in Water nor
Air) but the Gravity of the Medium that muſt be compared with the
Gravity of the Moveables; and if that of the Medium be greater, the
Moveable ſhall not deſcend, nor ſo much as make a totall Submerſion,
but a partiall only: becauſe in the place which it would occupy in
the water, there muſt not remain a Body that weighs leſs than a like
quantity of water: but if the Moveable be more grave, it ſhall
cend to the bottom, and poſſeſs a place where it is more conformable
1 for it to remain, than another Body that is leſs grave. And this
is the only true proper and abſolute Cauſe of Natation and
merſion, ſo that nothing elſe hath part therein: and the Board of the
Adverſaries ſwimmeth, when it is conjoyned with as much Air,
as, together with it, doth form a Body leſs grave than ſo much water
as would fill the place that the ſaid Compound occupyes in the
water; but when they ſhall demit the ſimple Ebony into
the water, according to the Tenour of our
ſtion, it ſhall alwayes go to the bottom,
though it were as thin as a
Paper.
Lib. 4. c. 6.
Text 45.
FINIS.
1
THE
TROUBLESOME
INVENTION
OF
Nicolas Tartalea:
BEING
A Generall way to recover from the bottome of the Water,
any SHIP that's Sunke, Or any other Ponderous Maſſe, though
it were a Solid TOWER of Metal.
TOGETHER WITH
An Artificiall way of DIVING, and ſtaying a long
time under Water, to ſeeke any thing Sunke in the
greateſt DEPTHS.
AS ALSO,
A SVPPLEMENT, Shewing a
Generall and Secure Way to Grapple, &c. any
Submerged SHIP.
Engliſhed, By THO. SALUSBURY, Eſque
321[Figure 321]
LONDON,
Printed by WILLIAM LEYBOURN, Anno Dom.
MDC LXIV.
1
To the moſt Serene, and moſt Illustrious
Prince, FRANCESCO DONATO
Duke of VENICE.
It having been told me here at
Breſcia, Moſt Serene and Moſt
Illuſtrious Prince, that about ten
years ſince, that a Ship full-laden
did ſinke near to Malamoccho, in
about 5 Fathome of Water, and
that to endeavour the recovering and getting it from
thence, there had been uſed all thoſe Means, and
tifull Offers and Tenders that could be imagined, aſwel
by the Illuſtrious Signory, for the Preſervation of the
Port, as by the chief Owners of the Ship and its Cargo:
and that although there were many that had tried, and
attempted the ſame, by ſundry and divers wayes, of no
ſmall expence, and that it had been ſever all times well
grappled and begirt, yet nevertheleſs as far as I could
hear, none of them were able to raiſe her from that ſmall
depth: And it being alſo told me, that of late there was
another ſunk again in leſs than four Fathome of Water,
ſo that all its Poope and Prow, and a greate part of its
Hull, was above Water, and that yet not with ſtanding this
alſo was judged by the fruitleſs Experiments and
penſes made about the former, to be irrecoverable, ſo
1that for the clearing of the Port, it is preſently reſolved,
that the ſaid Ship ſhould be broken up, & taken to pieces
at low Water: and ſo, for ought that I hear, it hath been.
Now I having conſidered of how great prejudice the
breaking up of ſuch a Veſſel was, beſides the loſs of the
Cargo, I deliberated about the finding of a way or Rule,
that might remedy ſuch detriment all Occurrences: And
having found out one thats generall and unquestionable, I
thought fit, for the common benefit of this renowned City,
to declare, and by Figures to dilucidate the ſame in the
preſent Tractate, and to offer and dedicate the ſame to
your Highneſs; not as a preſent worthy of yon (for indeed
theſe Mechanicall Matters are exceeding
onate to your Highneſs Merits) but only with an
tion to Enoble and Dignifie my Book with your Glorious
Name; In confidence that like as the Sun doth not
dain that all ſorts of Perſons ſhould make uſe of its light
and heat, ſoneither will Your accuſtomed Humanity be
offended with this my Preſumption; and therefore I
humbly lay my ſelf at your Highneſs Feet,
Nicolas Tartalea.
1
THE
Induſtrious or Troubleſome
INVENTION
OF
Nicolas Tartalea:
BOOKEI.
The Figure of a Ship ſunke according to the Relation made of that
which was cauſed to be broken up neere Malamoccho, as being
judged irrecoverable.
322[Figure 322]
EXPLANATION I.
Before I come to declare the promiſed way
to recover any laden or empty Ship when
it is ſunke; I thinke it convenient (Moſt
Serene and Illuſtrious Prince,) firſt to
clare the reall cauſe of its ſinking.
1
Archimed. of
Natation, Lib. 2.
Prop. 1.
I ſay then; That its impoſſible that the water ſhould wholly
ſwallow or receive into it any materiall Body lighter than it ſelf (as
to ſpecies;) but it will leave or cauſe one part thereof to lie above
the Superficies of the ſaid water, that is uncovered by it. And as
the whole Body demitted into the water, is to the part thereof,
which ſhall be received or admitted by the water, ſo ſhall the
cificall Gravity of the water, be unto the Specificall Gravity of the
ſaid Solid Body.
Archimed. of
Natation, Lib. 1.
Prop. 7.
But thoſe Solid Bodies which are more grave than the water;
ing demitted into the ſaid water, ſuddenly make the water to give
place; and not only enter wholly into the ſame, but they do go
continually deſcending, till they arrive at the bottom: And they
deſcend with ſo much greater Velocity, by how much they exceed
the water in ſpecificall Gravity.
A chimed. of
Natation, Lib. 1.
Prop. 111.
And thoſe again which happen to be of the ſame Gravity with the
water, of neceſſary conſequence being put into it, are admitted
and received totally into the ſame, but yet they ſtay in the Surface
of the ſaid water; that is, they ſuffer not any part to lie above the
Superficies of the ſaid water, nor much leſs doth the water conſent
to their deſcent to the bottom.
And all this is demonſtrated by Archimedes of Syracuſa, in that
his Tract De inſidentibus aquæ, by us tranſlated. And becauſe the
greateſt part of woods are lighter, or leſs grave than the water; he
therefore that ſhall build a Ship or other Veſſel meerly of wood,
lighter than water, its manifeſt that he cannot (though he ſhould
fill the ſame with water, as full as it would hold) make the ſame
totally to ſink, but that neceſſarily ſome one part or other of the
ſaid Ship or Veſſel ſhall ſtand above the Surface of the water: For
its a thing very clear, that all that ſame Body, compounded of wood
and of water, would be much lighter than if it were all only of water
without wood: Such a compound Body therefore being leſs grave
than the water, its neceſſary (for the reaſons above produced) that
a part of the ſame remain above the Surface of the water.
And if the ſaid Ship or Bark ſhall be built (as it is uſual) with
Bolts, Nailes, and other Materials of Iron, and that ſuch
works be not of ſuch quantity, as to make that Body compounded
of wood and Iron, graver than the water, but that it continue ſtill
leſs grave than the water (as I judge all Ships and Barks to be;) The
ſame will follow as did before, namely, that filling the ſaid Ship
with water, as full as is poſible, it cannot by any means go to the
bottom If then a Ship or other Veſſel being wholly fill'd with
water, cannot be thereby ſunk to the bottom; It is a thing evident,
that if ſuch a Ship or Veſſel ſhall be totally fill'd with a Matter
lighter than the water; not only its totall ſinking under that weight
1will be impoſſible, but alſo its floating in ſome part above the
face of the water will be neceſſary: And ſo much the greater part
ſhall be viſible above the water, by how much the Matter of the
Lading, is lighter than the water.
Therefore, if all the Cargo of a Ship (for inſtance) Buts of Oyl,
and that no other Matters of a graver Nature than water were
duced, and that the ſaid Ship ſhould by ſome Accident be filled
up with water, it is not only manifeſt that the Ship cannot be
by ſunk to the bottom, but that a part thereof muſt neceſſarily float
above the Surface of the water: Becauſe all that Compoſition of
Wood, Water and Oyl, would be lighter than if it had been all
ſimply of water. The very ſame would follow, if the Cargo had
been ſoley of Wine, Wax, Camphor, Spices, or the like Matters,
lighter than the water. But becauſe the Merchandizes that fraight
Ships, or other Veſſels, are ſome (ſpecifically) graver, and ſome
(ſpecifically) lighter than the water: (The graver are all forts of
Mettals, as Iron, Tinn, Lead, Braſs, Copper, Silver, Gold, and
nite other Species of Commodities; likewiſe the perſons of Men,
Stones, Ballaſts, and the like:) And that alſo there are ſome ſorts of
Commodities that chance to differ very little in Gravity from the
water: Therefore I conclude, that as oft as any Ship accidentally
is fill'd with water, and ſo ſinks by degrees to the bottom, it is
ceſſary to grant that all the Compoſition, namely, of the Fraight,
of the Veſſel, and of the water that entered into it, is more grave,
than if the compoſition had been all ſimply of water, by the reaſons
before alledg'd.
And therefore in ſuch a caſe things graver than the water, muſt
of neceſſity exceed in force thoſe that be lighter: and by how much
things graver than the water, exceed the lighter, ſo much the more
Force will be required to recover ſuch a Ship or other Veſſel being
ſunk, and on the contrary, ſo much leſs Force will be required,
when the Maſs of the Materials more grave than the water, ſhall
not differ much from the Maſs of the leſs grave: provided the
covery be undertaken in ſome ſhort time after the Ship ſhall be ſunk,
For if the Ship lie many dayes under water, the delay will intro.
duce many difficulties: One will be, that it will conſolidate with
and dock or work it ſelf farther into the Mudd or Sand, which will
not a little hinder its Recovery; and again, the water will
ally carry into the ſaid Ship, Ouze, Mudd, and Sand, which
ter is much graver than the water, whereby the Ship is continually
made graver as to the water, than it was at the beginning when it
was firſt ſubmerg'd. And moreover the corruptible Matters, which
are by nature lighter than the water, will corrupt, and corrupting
will change into other earthy ſubſtances much graver than the
1water: inſomuch that at the length, it ought to be preſuppoſed in
order to the recovery of the ſaid Ship, as if it were ſolely laden
with Mire, Dirt, and Sand: which doing, you will not be deceived
in the operation, that is to ſay, preparing and working with a Force
equivalent to that its Gravity. The way to know how to prepare
Forces equivalent to the Gravity ſhall be ſhewn in the eight
nation of this.
EXPLANATION II.
Now to give beginning to the buſineſs propoſed, I ſay, that
in the Recovery of a Foundred Ship laden, or any other
den Veſſel that is foundered or ſunk, there interveneth more
eſpecially theſe three great Obſtructions. The firſt difficulty is, how
to imbreech and grapple it with ſuch, and ſo many Ropes, as may
ſuffice to bear it up; for if this either by ill chance cannot be done
(whether through its being in a place two deep, or too far dockt in
the Mudd or Sand) all our other labour will be fruſtrate and vain.
The ſecond difficulty, when once it is grappled, is how with
terity to ſeperate it from the bottom of the Sea; and this difficulty
will be much greater, the Ship being in a Miry or Sandy bottom,
than if it ſhall be in a Stony place; and it ſhall be alſo a greater
difficulty to ſeperate it from a very deep bottom, than from a
low; (alwayes ſuppoſing that the two bottoms be both alike,
ly, either both Stony or both Sandy;) and alſo far greater ſhall the
ſaid difficulty be in a Ship long ſunk, than in one newly four dered;
(as we have already ſaid in the precedent Explanation:) But when
ſhe is once water-born, or ſeperated from the bottom, its an caſie
matter to raiſe her up to the Surface of the water; for then ſhe ſhall
not be a little aleviated in her Gravity: But the truth is, the
ing of it after wards above the Superficies of the water, is no very
ſie matter, but is extream hard to be done; and this is the third
difficulty; the principal cauſe of which two laſt difficulties ſhall be
aſſigned by and by.
But becauſe the means to obviate and ſuperate the firſt difficulties

as more ^{*} common, we ſhall forbear to ſpeak of them untill the
next Book. To provide, and that briefly, to the ſecond and third
impediments (which are the leaſt known) that is, not only to
perate the Ship from the bottom, but to raiſe it alſo ſomewhat above
the Surface of the water.
1
* The Author
lieved (as he
clareth in the
piſtle to the
ing Suppliment of
this his
on) that the
riners converſant in theſe affairs, had many wayes to imbreech a Veſſel uuder water; and for that reaſon he
over paſſeth it here, and is very curſive upon the ſame Point, in the ſecond Book, but giveth a generall Rule
for it in the ſaid Suppliment: to which the Reader is referred for fuller Satisfaction.
And this is the Rule that you muſt obſerve; If the Ship be newly
ſunk, you muſt immediately, if it be poſſible, find two other Ships,
that be each of them rather of greater bulk than the foundered Ship
than leſs: and when you have found theſe two Ships, you muſt
free them of all the inward and outward lading, and rigging,
cially of thoſe things which are by nature more grave than the water,
as are the Guns, the Shot, and any kind of Ballaſt, which is
poſed to be in the Hold, and of other things of impediment; and
when theſe Ships are thus cleared, you muſt ſtop all the Loop-holes,
Cat-holes, Skuppers and Hauſes, which you ſhall finde between or
above Decks, graving and calking them ſo with Okum, and paying
them with Pitch, that the water can neither get in nor out thereat.
And next you muſt join or grapple theſe two Ships together with five
or more Tires or Orders of thick and ſtrong Beames tripplicated;
that is, that each of the ſaid Orders conſiſt of three Beams, joyned
lengthways; and that each of the three Beams be ſomewhat longer
than the bredth of the Deck or Hull of each Ship; and that theybe
thick and ſtrong, as being to ſupport the Foundered Ship, as you
ſhall ſee it made to appear preſently: and couple the ſaid Ships
gether, at ſuch a diſtance from each other, that you give berth, or
leave room enough betwixt for the foundered Ship to play; and
you muſt make this couppling in ſuch ſort, that the length or ſide
of the one Ship, look towards the length or ſide of the other; and
albeit this conjunction or grappling may be made with many Orders
or Tires of thoſe Bcams tripplicated lengthways, as was ſaid above,
The Figurall repreſentation of the two empty Ships, conjoyned with
five Orders of Beams, and towed juſt over the place where the
Foundered Ship is.
323[Figure 323]
yet that we may not cauſe confuſion in the Figure, we would have
this colligation to be made only of five Rows, as appeareth in the
1Scheme: and although the ſaid Rows of Beames cannot be all
placed equidiſtant from the Surface of the water, for that the
Wailes or Rifings of the two Ships are not fluſh, but cuved, it is
not of any importance, ſo that they be well faſtened and
ened in thoſe places where they reſt upon the ſaid Rifings: upon
which Riſings, you ſhall conjoyn the ſaid Beams, namely, the two
ends of them, which two ends ſhall be the ſtrongeſt place, able to
ſupport any great weight. Yet the truth is, that to fit theſe Tires
of Beams, you need not have regard to make them paſs through from
ſide to ſide, in that weak part of the Ships Poop and Prow, to reſt
them on the Rifings or Gun-wales of the Deck of thoſe Ships, and
to go croſs the Hull in thoſe places. And next you are to make upon
theſe Beams, that is upon the mouths of both the Ships, a Plat-form
of Planks for to ſtand upon whilſt you are about the work; leaving
diverſe Scuttles or Spaces open, whereby to deſcend, aud for other
uſes: And all this being done, you are to tow or hall theſe Veſſels
to the place where the Ship is that did ſink, and to lay them Board
and Board in ſuch faſhion, that the one may lie on one ſide of it, and
the other upon the other, as in the Scheme is apparent.
This being done, fill thoſe two Ships as full of water as they can
hold or ſwim, (the way to free them with great facility and
dition, ſhall be ſhewn in the twelfth Explanation;) and being full,
wait the time of low water; that is, when the Tide returning, the
Sea doth low as much as it can do; and at that inſtant of time,
make the Ship very faſt with thoſe ends of Cords or Cables (with
which it was Swite or bound) to thoſe five, or more Tires of Beams,
wherewith the foreſaid two Ships were imbreecht or grappled: And
having well belayd or faſtned thoſe Cables, you muſt bale or take
out a ſmall part of the water out of one of the two Ships, and then
let it reſt ſo, till ſuch time as you have baled or taken a little more
than that quantity out of the other Ship; and then again take a
little more out of the firſt Ship, and leave it ſo till you have taken
another ſuch a quantity from the other Ship, and thus proceed
dually, till you find the Foundered Ship, water-born or looſned
from the bottom: but being water-born (if it be in a Showle
tom, as was that at Malamoccho) you are to take out the ſaid water,
equally from both the Ships, at one and the ſaid time, to the end
the Ship may riſe evenly without ſwagging or ſhaking; and thus you
are to proceed till you have taken all the water from the one & the
other of the two Ships: In ſo doing, you ſhall ſee the two Shpis
ſurely and gently raiſe the Ship that was ſunk, ſo high above the
Surface of the water, that you may commodiouſly free it, and
diſcharge it of its lading, as appeareth in the following Figures.
And if you would not keep the two Ships ſo long imploy'd, you may
1warpe or towe the Foundered Ship at high-water to ſome place
where it may lie a-ground: and by that means upon the Ebbe or
Receſſion of the Tide, it will lie much more above water; and then
you may ſafely unfaſten it from thoſe five or more Tires of Beames,
to which it was at firſt tyed, to hall it to a place of ſafety, as it was
our purpoſe to do; and this ſhall ſucceed as well in an ouzie
tom, as in a Stony, This though you may take notice of, that if
the Cargo of this new Foundred Ship was ſuch, that the things more
grave than the water, did not much exceed the leſs grave, it would
be eaſie to effect the recovery with two Ships, very much leſs than
thoſe which we have ſpoken of above; yet nevertheleſs it will be
good prudence to take them rather bigger than leſſer, that ſo they
may exceed 200000 pounds in Power, rather than want one only
ounce in Act; eſpecially in caſe you would in a deep place at the
firſt motion hoiſt it by meer Force ſomewhat above the Surface of
the water, for in that point alone it will require incomparably much
more force, than in all the other operations.
How you are to preceed, in caſe the Ship ſhould be ſunk in a
place very deep, ſhall be declared in the ſeaventh Explanation. The
Figures of this Explanation are theſe two that folllow.
The Figure of the two Ships filled with water, to raiſe the Ship that
is ſunk
324[Figure 324]
1
The Figure of the two Ships emptied as they lie, with the other Ship
raiſed up above water.
325[Figure 325]
EXPLANATION III.
But if it ſo fall out, that you cannot on ſnch an inſtant, finde
two Ships of the ſame Bulk with the Ship ſunk, you may take
four ſmaller; provided, that all the four together hold twice
as much burden as the Ship ſunk, and rather more than leſs. Which
four ſmall Ships being all firſt cleer'd of their lading, and well ſtopt
in all their Skuppers and Portholes (as was ſaid in the two) you muſt
couple them with Beams and good Planks, by two and two, as you
uſe to do with two Lighters, when you would make a Bridge of
them: and theſe two pair of Hoys or Barkes thus coupled together,
you muſt afterwards faſten one pair to another, with ſeven of thoſe
Tires or Rows of thick and ſtrong Beams tripplicated, as was ſaid in
the precedent Explanation; and place them at ſuch a diſtance one
pair from another, as that you may leave berth or ſpace enough for
the ſunk or foundered Ship to riſe between them, and ſome what
more, (as was ſaid of the two.) And though this conjunction of the
two pair of Ships, may be made three ſeverall wayes, yet I will have
you make the two Poops or Hin decks of the one couple, to lie
poſite to the two Poops of the other couple. And to make this
conjunction, you are to place two Tires of thoſe great Beams along
the upper parts of the ſaid Poops, ſo, that they may reſt in the
ſide on thoſe leſſer Beams and Planks, where with each of thoſe two
pair of Ships were coupled: and each of theſe Orders or Tires of
1Beames ought to be compoſed of three Beams conjoyned
wayes, as was ſaid in the precedent Explanation; and make two of
the Tires lie upon the Ships; and to thoſe Tires, let that ſunk Ship
be grappled: and another Tire of the ſaid Beams is to be placed in
the midſt between the one and the other couple; and two other
Tires of the ſaid Beams ought to be faſtened upon the one and other
ſide, that is, upon the Rifings or Bends of thoſe two couples of
Ships; and that being done, there will be in all ſeven Tires or
ders of Beams; which ſeaven Orders of Beams ought conjunctly to
be prolonged, on the one and on the other ſide. almoſt to the
length of the Hull of each Ship, as in the Figure is represented: and
The Figurall example how to recover a Foundered Ship with four
ſmall Ships
326[Figure 326]
this being done, you are to proceed, as hath been ſhewn in the two,
that is, fill them top full of water, and at low water, imbreech the
Ship ſunk very well, withall thoſe ends of Ropes or Cables, that
you did belay to thoſe ſeven Tires of Beams: and when thoſe
Grapplings ſhall be well made faſt; you ſhall at high water bale or
free the water by little and little out of the Ships, one pair after
nother, till you feel the foundered Ship is diſengaged from the
tom, and water-born, as was ſaid in the two. And having
ted it from the bottom (if it be in a ſhallow place, as was that where
the Ship was foundered neer Malamoccho) you are to proceed to let
out the reſt of the ſaid water, but take it equally and gradually from
the one and the other pair, that they may deſcend evenly, and
out heeling, as was ſaid of the two; and in ſo doing, the ſaid Ship
ſhall not only be hoiſted up to the Surface of the water, but much
1above the ſame; ſo that you may in that poſture free or drain it
and diſcharge it of the Cargo. But if you cannot ſo long ſpare
thoſe four Ships from other uſes, then you may at high water tow
it to ſome place, where running it on ground, you may at the ebbe
of the Tide (for that then there will lie much more of it above
ter) ſafely looſe it from thoſe Beames, as was alſo ſaid in the
dent Explanation of the two Ships.
But in caſe the Foundered Ship ſhould chance to be in a very deep
Sea, in the ſeventh Explanation (to be the briefer in this place)
ſhall be ſhewn how you are to proceed.
EXPLANATION IV.
And if it happen that it ſhould be in a place where there are
no Ships to be got, either great cr little; you may take of
other kind of Pinaces, Barks or Barges, but endeavour to
get ſuch as are floaty, and higheſt built in there Rifings, that ſo they
may, at ſuch time as they are full of water, deſcend very far under
water, (or according to the Mariners phraſe, may draw much
ter) and of theſe you muſt ſtop all the Skuppers, Hawſes, Cat-holes
and Port holes, that you finde, as in the Ships, that they may hold
the more water, and conſequently draw the more water, or be
preſſed deeper into the ſame; and take ſo many couple of theſe
Botes, that they may all together contain double the burden of
the Ship to be recovered, and rather much more, than any thing
leſs. And of all theſe Boats or Barks, make two Squadrons, conjoyning
each Squadron with good ſmall Timbers & Planks, as you uſe to do,
when you would make a Bridge of Boats: And theſe ſame Veſſels of
the one and other diviſion, ſhould be placed board and board, that ſo
the great Beams, which are to conjoyn one Squadron to the other,
may bear upon the Rifings, Bends or Wales, of the ſaid Veſſels. And
this being done, you are to couple theſe two Squadrons, to each other
with thoſe thick and ſtrong Tires of Beams, mentioned in the former
Explanations, which Orders of Beams ſhould be fixed between two &
two of thoſe Botes, as is ſaid above, to the end, that they may bear or
reſt upon the Bends of thoſe Boats; and place another Tire upon the
outſides of both the Diviſions, upon the ends of the croſs ſmall Beams
which hold the ſeverall Veſſels together: So that if the Squadrons
ſiſted each of four Barks, the Tires of the ſaid Beams would come to
be five,; and if there ſhould be five in a Squadron, the Tires of
Beams would be ſix, and ſo forwards; that is, the Orders of Beams, by
this means, ſhall be alwayes one more than the number of Botes in
each Squadron. But in the Ships you muſt obſerve another method,
becauſe of thoſe two Orders, which are placed in each Poop; by
1
The way to recover a Foundered Ship with many Barks or Wherryes.
327[Figure 327]
which means in every two Ships to a Diviſion (which in all make
four Ships) there muſt be ſeven Orders of Beams, and in three Ships
to a Squadron, there muſt be ten Orders of Beams, and in four
Ships to a Squadron thirteen; and thus proceeding forwards to a
greater number of Ships in a Squadron. And having underſtood the
way of coupling many Barks or Wherryes in Squadrons; as alſo the
manner how to joyn or faſten them to each other, and with how
many Orders of Beams; you are to proceed in the reſt, as in the
precedent Explanations hath been demonſtrated in ſhowle bottoms,
but the directions how to manage this affair in deep places, ſhall be
declared in the ſeventh Explanation.
EXPLANATION V.
To remove this inconvenience of taking Ships or other Veſſels;
and of ſtanding to lighten them of their Guns & lading, and of
ſtopping their Loop-holes; you may inſuch a misfortune cauſe
to be made two great Veſſels, almoſt in form of ^{*} Cheſts without

vers, the length of each to be equal to the Hull of a middle rate Ship,
and the breadth equall to that of the ſame Ship at the Main-maſt,
and the height alſo the ſame with that of the Ship in the Bow, ſo
that each of theſe Plat forms or Cheſts, ſhall hold much more than
a common Ship, and thus both will contain more than the double
burden of ſuch a Ship. And for the making of theſe Veſſels, you
muſt firſt make the Models in Carvel-manner of thick and ſtrong
Timber, with their Eutertaces, Tranſomes and Knees, to hold their
ſides and ends together: and this done, ſpike down to them certain
1thick and ſtrong Planks; and then cauſe them to be well graved and
calked in the Seames or Strakes by a Calker, with Okum, and paid
with Pitch, as you uſe to do Ships or Gallyes, and then apply them
to your purpoſe. And when you would uſe them, you need only
faſten them together with thoſe five or more Orders of thick and
luſty Beams, trippled lengthwayes, that is, prolonged both wayes,
ſo as that they may lie athwart the Decks of the ſaid two Veſſels,
and place the ſaid Ships ſo far diſtant from each other, as you gueſſe
the bredth of the Foundered Ship to be, and ſomething more: And
then make upon the Deck of each of them, that is, upon thoſe
Beams, a Plat-form of Planks, as was ſaid in the two Ships of the
ſecond Explanation, and afterwards proceed as in thoſe two Ships.
* Of theſe
ſels Cardinall
Richleiu made
uſe at the Siege
of Rochell to
up the Haven.
EXPLANATION VI.
And incaſe you think the making of a couple of ſuch great
Modles or Veſſels, as we mentioned in the foregoing
planation, would be too great a trouble or expence; you
may make two pair of ſuch Cheſts, each of them but of halſ the
bulk of one of the former: but if you judge theſe two pair too
troubleſome, you may make three, four, or more pairs; alwayes
provided, that amongſt them all they hold about twiſe the burden
of the Ship ſunk; and theſe Frames when you would uſe them, muſt
be joyned together in two Ranks, with leſſer Beams and Planks,
as was ſaid of the four Boats or Wherryes; and then faſten theſe
two Ranks to each other at the requiſite diſtance, with great and
ſtrong tripplicated Beams, as was ſaid of the Ships, Barks and Boats;
and then operate as you was to do with thoſe: alwayes remembring
in the freeing or emptying the ſaid Veſſels, to bale out the water by
little and little firſt from one Rank, and then from the other; and
ſo proceed interchangeably till you percieve that the Ship is clear of
the bottom: and being diſengaged, if it be in a ſhallow place,
continue taking the water equally out of the one and other
on of Veſſels, till all the water be drained out of them, as was
red upon the former Explanations: but if it be ſunk in a deep Sea,
the next Explanation ſhall ſhew how you are to proceed; and that
briefly.
EXPLANATION VII.
And in caſe the ſaid Ship newly ſunk, chance to be in a very
deep bottom; It will be neceſſary firſt to fix upon thoſe
two or four Ships, or upon thoſe two Squadrons of Barks,
Fly-boats or Wherryes, at leaſt ſix or eight Capſtains, Ship-Cranes
1or Windlaſſes, with their neceſſary Garnets or Pullies, requiſite to
ſnch a weight: and you may eaſily accomodate theſe Pullies, to thoſe
Orders of great Beams, wherewith the ſaid Veſſels were conjoyned.
And having prepared theſe Capſtains, you are to proceed in all
things, as hath been directed you in the precedent Explanations,
excepting only in this, that whilſt you are freeing the water
nately by degrees out of the two or more Ships, or from the two
Squadrons of Barks, Fly-boats or Wherryes, as ſoon as you finde
the Foundered Ship to be water-born or got clear of the bottom of
the Sea, I would have you ceaſe to take any more water forth of
the ſaid Ships, or leſſer Veſſels before filled; and I would have you
with thoſe Capſtains, attempt to draw the ſaid Ship that was funk
unto the Levell or Surtace of the water, or to lie Horizontal unto it,
which may be eaſily done, for that its ponderoſity will be much
miniſhed. And when you have drawn it to the Surface of the water,
then I would have you diſcharge all the other water out of the two
Ships, or the two Squadrons of ſmall Veſſels. And this ſecond
ter, I would have raken equally, and at the ſame time, from the one
and the other Ship, or from each Rank of Barks or Boats, as hath
been ſaid of the other. And thus thoſe Ships or Squadrons of Boats
ſhall hoiſt the ſaid Foundered Ship, ſo high above the Superficies of
the water, that you may free it of the water which was got into it,
and unlade its Cargo, which was our purpoſe.
You muſt note, that all that hath been hitherto ſaid of a Ship
newly ſunk, ought to be underſtood of all other kind of Foundered
Ships, proceeding alwayes proportionately as was directed in that
Ship. And again, I give you no Figure how you are to fit and fix
the Capſtains and Pullies, as being a thing common and manifeſt.
EXPLANATION VIII.
But if it ſo fall out, that the ſaid Ship or other Veſſel hath been
ſunk many Months; albeit that there might have been many
matters in the Cargo of a lighter nature than water, yet you
muſt ſuppoſe the caſe as if the Ship were as heavy as if it had been
fil'd with Sand or Gravel; yea and much heavier, for many Reaſons,
as hath been alledg'd in the firſt Explanation. Therefore that you
may not deceive your ſelves in the deſigned recovering of it, you
would do well to double the Forces required to the recovery of a
new ſunk Ship; that is, you muſt take four Ships, each as big as
the Foundered Ship, and combine theſe four Ships, as you were
quired to joyn the four ſmall Ships in the third Explanation. And
if you cannot procure them of that burthen, take eight leſſer,
vided that altogether they be quadruple in contence to the Ship to
1to be recovered: and divide theſe eight leſſer Ships or Barks into
two Squadrons, of four in a Squadron, according as you was
rected in the four Ships in the third direction. And if you cannot
cure Ships great or ſmal, take ſo many pair of other Veſſels, Fly boats
or Wherryes, that in all they may at leaſt contain four times the
then of the Foundered Ship: And reduce theſe Barks, Boats or
Wherryes into two Diviſions, as you are taught in the fourth
planation: and in all other particulars, proceed according to the
method preſcribed in the recovery of the Ship newly ſunk; and
that as well in deep, as ſhallow places; that is, placing in a deep
Sea upon the ſaid Ships, or Squadrons of Boats, at leaſt twelve or
ſixteen Capſtains, which it will be eaſie to do, for that you will have
a large ſpace upon thoſe Ships or ranks of Boats, as alſo there will
not want room to faſten their Pullies to thoſe Tires of Beams, which
combine the ſaid Ships or ranks of Boats. In all things elſe proceed
preciſely according as you have been directed in the ſecond, third,
fourth, fifth, ſixth and ſeventh Explanations.
This indeed muſt be granted, that incaſe the ſaid Ship long ſunk,
ſhould be in a Stony bottom, or where ſhe hath a great current, the
which current ſuffereth not any great bed or ſhelves of Mudd to
gather about the ſaid Ship, it may then eaſily be got clear of the
tom, with the ſame Forces as were imploy'd in that newly ſunk, to
recover it; and alſo may as eaſily be drawn to the Surface of the
water: But whether you can raiſe it with part of its Hull above
the Superficies of the water, is a thing much to be doubted;
yet if it ſhould prove ſo upon the Experiment, namely, that you
cannot elevate its Hull above the Surface of the water, you may in
ſuch a caſe hall it at high water to ſhore, or to ſome place where it
may lie a ground, whereby at the retreat of the Tide, it will lye with
part of its Hull above water, ſo that you may commodiouſly clear
it of the imbibed water and Cargo.
EXPLANATION IX.
And to the end that this invention may be of generall uſe
for the re covery or raiſing any kind of Colloſſus, that may
happen to be ſunk, to wit, of all Species of Solid Bodies,
whether of Stone, Iron, Pewter, Braſs, Lead, Silver or Gold (as you
may have many occaſions voluntarily to ſink them in time of war, to
preſerve them) and then that you may know how to get them up
again, you muſt obſerve this Rule: If the Solid long time
ged were of Brick; ſo ſoon as it is imbreecht, you muſt take ſo
ny couple of Ships, Barks, Hoyes or Wherryes, that the ſum of their
contents put together, may exceed the Square of the Solid Area
of the ſubmerged Solid: and if the Solid ſo long ſunk were of
1ble, the Solid Content of all the Vacua of thoſe Ships or Veſſels
ded together, muſt not be leſs than Septuple to the Solid Content
of the ſubmerged Body; namely, ſeven times as much. And if
that long ſunk Solid chance to be of Iron; you muſt make the Solid
Content of all the Vacuum's of thoſe Veſſels to be no leſſe in the
Aggregate than 12 3/2 times as much as the Solid Content of that
merged Solid: and the like muſt be done, if the ſubmerged Solid
be of Pewter, for that Iron and Pewter differ not much in Gravity.
But and if the drowned Solid be of Copper, it is requiſite that the
Solid Content of all the Veſſels Cavities in ſum, be no leſs than
thirteen times as much as the Solid Content of the ſaid Solid ſunk.
And if the ſubmerged Solid were of Lead, the Solid Content of all
the Vacua of thoſe Ships, wherewith you would recover it, ſhould
be no leſs than twenty times as much as the Solid content of the
drowned Solid, and rather more than leſs; and almoſt the ſame
proportion ought to be obſerved, if the ſubmerged Solid were of fine
Silver, for that Lead and pure Silver differ not much in Gravity:
truth is, that Lead is ſomewhat more weighty than Silver, but not
much.
But if the Solid which was ſunk, ſhould chance to be of pure
Gold, you muſt for its recovery take ſo many couple of Barks or
Boats, that the Solid Content of their Vacua, taken in aggregate,
may be no leſs than 34 times as much as the Solid content of the
ſaid Golden Solid ſubmerged. And that you may the better
ſtand me, I will put an Example, that you were to recover or raiſe
out of the water, a Solid Body reſembling a great Tower, which I
imagine to be in length an 100 Paces, and in breadth 10, and in
thickneſs alſo ten: and I ſuppoſe that it is all one Solid, that is to
ſay, not hollow within. And firſt we put the caſe that this Tower
were made of Brick. Now becauſe the Solid Content of this
poſed Solid would be 10000 cubical Paces: therefore in this caſe,
if you would recover this ſame Body, that is, not only looſen it from
the bottom of the Sea, but alſo raiſe it a good height above water,
it will be requiſite, as is ſaid above, to take ſo many pair of Ships,
Barks, Boats, or other Veſſels, (as hath been ſhewn in the 5 and 6
Explanation) that the Solid Content of all the Vacua of them put
together, be not leſs than four times the ſaid ſum of 10000 cubick
Paces; that is, it muſt not be under 40000 cubicall Paces, as was
above determined. And ſo ìf it happen that the ſaid ſubmerged
lid ſhould be all of Marble, the Solid Content of all the Vacuities
of the ſaid Ships, ought not to be leſs than 70000 cubicall Paces,
namely Septuple, as was before concluded. And thus if the ſunk.
Solid were all of Iron or Pewter, the aggregate of all the Solid
tent of all thoſe Vacuums put together, muſt be rather more than
1leſs then 126666 2/3 cubical Paces. And in caſe the Solid were all of
Copper, the Solid Content of the ſaid Vacua ought to be about
130000 cubick Paces. And likewiſe if the Solid were all of Lead
or Silver, the Solid Content of all the ſaid Vacua is to be no leſs than
200000 Paces cubical. Laſtly, if ſuch ſubmerged Solid be
pounded all of fine Gold, the ſum of thoſe Cavities ought to be no
leſs than 340000 cubick Paces.
The manner how to proceed in the recovery of thoſe ſeverall
kinds of Solids, is to be underſtood to be like to that which was
preſcribed in the recovery of the Ship: and that as well in deep, as
ſhallow waters. And the greater number of Ships or Boats are
quired to opperate in the recovery of the ſaid ſubmerged Solid in a
deep Channell, ſo much the more room muſt yon take upon the
one and the other Squadron, for to be able to pitch ſuch a number
of Capſtens as ſhall be needfull, and more if occaſion be. Yet you
muſt obſerve, that in the taking the water alternately from the one
and other Squadron, when you perceive the ſaid Solid to be
engaged from the bottom, you are to forbear taking out any more
from either of them; as was appointed touching the Ship, in the
ſeventh Explanation. And make uſe of as many Pullies as you ſhall
ſee cauſe for, not only to lift it to, but alſo to draw it above the
waters Surface: and that if notwholly, yet for the greater part:
and when it is lifted as high as is poſible, then take the remaining
water by equall meaſures, out of the one and other Squadron, or
Rank of Ships; which being done, it ſhall be hoiſted ſo high out of
the water, that you may put under it as many Lighters or Flat-boats,
as ſhall be ſufficient to bear it up, and to carry it to any place, as
occaſion ſhall require.
EXPLANATION X.
Albeit Vitruvius, Vegetius and Valturius do teach diverſe and
dry wayes to carry water up on high, many whereof may
ſtand us in much ſtead in this our Invention, for the
dious filling and emptying all the ſeverall kinds of Veſſels ſpoken of
above; of which alſo, many are very well known and familiar to
every one; to wit, with Bur-pumps, Chain pumps, common-pumps,
and many others: yet nevertheleſs to fill the ſaid Ships or other
Veſſels with water, with great facility and dexterity; I judge this
more expedient than any of them; namely, to make a Hole in the
bottom of each of thoſe Ships or other Veſſels, of two or three inches
Diameter at leaſt, and for every Ship to appoint a Boome or long
tapered Pole like a Plugg or Tapp, ſo that being thruſt into the ſaid
Hole, it will ſtop it ſo cloſe, that unleſs you conſent thereto, no
1water can enter in thereat, and this Pole is to be ſomewhat longer
than to reach from the Keel to the upper deck of the ſaid Ship; and
near the other end, put another piece of a Pole croſs wayes; that
you may be able by means of that to rule it; namely, to pull it up,
when you would unſtop the Hole, to let in the water that ſhould
fill the Ship, and to thruſt it down when you would ſtop the Hole
that no more water may enter; and this ſame Pole ſhould paſs
through two Rings, fixed in the Hold of the Ship, which are to
keep the ſaid Pole directly over the Hole, that if you would ſtop it,
the Plugg or Spiggot may not go beſides the Hole, when you thruſt
the Pole downwards. And that I may be the better underſtood, I
have here below drawn the ſame Pole, with its Tapp or Plugg at the
end. And when you go about to recover any Ship, you muſt ſtop
the ſaid Holes, till ſuch time as the ſaid Ships are carried
328[Figure 328]
and fitted upon the place, as is ſhewn above. And
when you would fill them with water, it is but
drawing the ſaid Poles, and opening the Holes; and
faſten them at that ſtay, till you have a mind to ſtop
the Holes; and then look downwards, and obſerve
when the Ships are as full as they can ſwim, or when
they are full enough, which will be in a very ſhort
time: and then let down thoſe Poles, and ſtop the
Holes very cloſe. And when they are as full as they
need, in the ebb of the Tide, combine the Ship with the Pullies, to
thoſe five or more Orders of Beams often mentioned: and then draw
out the water with Pumps by little and little, and one while out of
one, and another while out of the other Ship, as was appointed in
the ſecond Explication: and in all other particulars proceed, as was
alſo there directed But if the Gravity of thoſe Veſſels, cauſeth
them not to fill faſt enough, you muſt fill them at the top, that is
by baling in water by the Deck (I mean the ſaid Poles being firſt
thruſt down) to make the ſaid Veſſels to deſcend faſter, and to raiſe
the Matter ſubmerged with more Force; many other new wayes
might be ſhewn, as well to empty, as to fill theſe Veſſels; but for
the preſent this ſhall ſuffice.
EXPLANATION XI.
If you would attempt to recover a Ship or other Veſſel by the
wayes here preſcribed: you muſt go about the ſame, when the

Moon is in the Auge of the Excentrick, for at that time the Sea
ebbeth and floweth more than at any other time in the Moneth;
and this happens in her Coujunction and Oppoſition, which is a
matter of great avail in theſe operations: and herewith we conclude
this our firſt Book.
1
i.e. At a ſpring,
tide, which is
greateſt the third
day after the fuil
and change.
THE
Induſtrious or Troubleſome
INVENTION
OF
Nicholaus Tartalea:
BOOKE II.
In which are taught, ſome artificial wayes of Diving
and ſtaying long under Water: whereby one may
eaſily deſcend to the Bottom, to finde out, not
ly a Ship ſunke, but alſo, any other ſmall thing of
Value: And the place being darke, many wayes
are ſhewn how to enlighten it: And the thing
ſunk being found, ſeverall wayes and means are
preſcribed how to imbreach them, as well in a
Deepe, as Shallow Channel.
EXPLANATION I.
Having underſtood, Moſt Serene Prince, from
dry Sea men, that there are many now adayes,
who without any particular Artifice or help, do
upon occaſion dive and continue a long time
under Water, and in places very deep; I had
thought to have added nothing touching the
way of Artificiall Diving, and ſtaying under
water, to ſeeke and finde out a Ship, Boare,
or other thing of Value ſubmerged, and that for two Reaſons. Firſt,
Fearing that I ſhould be derided by thoſe kinde of men, it being to
them a ſuperfluous thing to go about to do thoſe things by Art,
which they know how to execute without any arrificiall help.
1Secondly, doubting, by reaſon of my ſmall experience in Maratine
Affairs, to incurre ſome Soleciſme: but there coming into my mind
an excellent expreſſion of a famous Philoſopher of this Renowned
City; who upon a time perſwading me to write ſomething that
was new, and I having anſwered (it being incident for humanly to
erre) that I was afraid leaſt my ſo great deſire to publiſh my fund y
new Conjectures, might run me into ſome fantaſtical conceits, that
might make me become the ſubject of vulgar diſcourſe, this
lent perſon replied: That if Nature ſhould forbear her operations for
fear of producing ſometimes ſome monſtrous things, the worlds
ſtruction would enſue, for that they onely are free from erring who
do nothing, whoſe ſpeech hath emboldened me to ſpeak of a point,
which I never thought to have medled with; namely, To declare
ſome of my conjectural wayes of artificial diving, and continuing
under water, to ſeek out any thing that was ſunk in the ſame, though
in places very deep. And I judge theſe the moſt expedient that can
be deviſed: and becauſe theſe and the like wayes may be varied
into ſeveral forms, and ſorts, one more ingenious, and artificial than
another; the prettieſt, and moſt ingenious is this, I would have you

get, made at Murano, a hollow Globe of Tranſparent Glaſſe, the
ameter of which I would have to be at leaſt two foot, with a round
mouth, that the Diameter of the ſaid mouth may be at leaſt one
foot, or wrather more; that is, ſo much as one may eaſily put his
head therein, and at pleaſure draw it forth; and next you muſt
make two round Boards of a Diameter ſomething bigger then that
of the ſaid Globe, and with theſe two round Boards, and four
der pieces of Wood, as long as a man is high, and a little more, you
muſt make a little Modell for a man to ſtand betwixt theſe four

ces of Wood; and with one of the round Boards above, and the
ther beneath; and theſe round Boards are to be very faſt nailed or
otherwiſe faſtened to the four pieces of the Frame, and in the top of
this Machine, you muſt fit and fix the ſaid Sphere of Glaſſe with the
mouth downwards, ſo, that if a man ſtand upright in the ſaid Frame,
he may hold his head in the ſaid glaſſe without ſtooping. And this
being done, take neer upon as much Lead as all this Machine weighs,
and make it into a round figure, of the compaſſe of the round
Boards, and then faſten and nail it to the bottome of the ſaid
dell, namely, underneath the lowermoſt Board on which your feet
ſtand when you put it into the Water: And then, (or before)
make an hole as big as a Shilling in the Centre of this Lead and
Board, paſſing through them both; and this ſame Lead will be able
to draw almoſt all the Machine together with him that ſhall be
therein under Water. Truth is, that the Experiment requireth that
the ſaid Lead be ſo limitted that it may be able to draw the
1chine and perſon in it under Water, but ſo, that the ſupreme or up
per part of the ſame, that is the uppermoſt round Board, may ſtay at
the Superficies of the Water; that is, if the Lead chance to be ſo
ponderous, that it cauſe the Engine to ſink leiſurely to the bottome,
you muſt take away ſome of the ſaid Lead; and on the contrary,
if it chance that the Lead be not able to draw it all in that manner
under Water, ſo as to make the ſaid upper round Board to lye and
ſtay exactly level with the Surface of the Water, but that a part of it
reſts viſible above the Water, you muſt encreaſe the ſaid Lead ſo,
that the upper Board may lye and abide preciſely, as was ſaid
fore, in the Surface of the Water: and when you have thus
ſted the ſaid Lead, I would have you take a Ball or Bullet of Lead
weighing two or three pounds, (that is to ſay of ſuch a weight, that
it may be ſufficient to make the Machine and perſon diving to
ſcend to the bottome as oft as it is interpoſed, or added,) with an
Iron Ring in the ſaid Ball, to which bend or faſten a Rope as long as
the ſaid Water is deep, in which the Diver is to deſcend, and
what more; and reeve or paſſe the other end of the ſaid
Cord through the hole
made in the Board and
Lead through the
329[Figure 329]
tom of the Model; and
faſten that ſame end
of the Cord in a place
of the Machine, ſo, that
the Diver may take it,
and draw it, or ſlack
it as he pleaſeth: and
this being done, the
ſaid Machine will be
finiſhed. And that you
may better
ſtand it, I have here
ſerted it graphically:
yet I ſhould have told
you, that for many
ons you ſhould in the beginning have faſtened a Ring in the
tre of the upper Board, on the outſide, to tye a Cord to the ſame as
occaſion ſerveth.
1
A Place near to
Venice, where the
famous Glahes
are made.
Like the Frame
of an
glaſſe.
EXPLANATION II.
Having underſtood the manner how to make this ſame
gine, it remains to ſhew how it is to be uſed; And for your
direction therein, I ſay, That he that would dive or go under
Water to ſeek any thing that was ſunk, ſhould carry the ſaid
chine to the place where he reſolves to deſcend, and firſt to let that
Ball of Lead with the Line go to the bottome, and then to put in
the Machine it ſelf, which by means of its heavy bottome of Lead
will reſt upright in the Water, with almoſt all the Globe of Glaſſe
above Water, in ſuch ſort, that he that would may eaſily enter into
the ſame: yet you muſt be dexterous in going into it, that you do
not much ſway the Machine ſidewayes, for that, if it lye too oblique
the Water will enter into the Globe of Glaſſe, and drive the Aire
thence that was in the ſame, or at leaſt in part, but holding it
right when you enter the ſame, the Water ſhall keep in the Aire on
all ſides, whereby the water will be kept from entring. And therefore
if he that ſhall enter into the ſaid Machine, do nimbly thruſt his head
into the ſaid Globe by the hole thereof, he ſhall finde it quite
led with Ayre; in which place he may breath for verry many
ſpirations, without the leaſt obſtruction from the Water: And
cauſe this Machine will ſtay with its upper end level with the
ters ſurface (the affixed Lead having been ſo limited) therefore
deſiring to deſcend to the bottom, the Diver ſhould hale the Ball
and Line upwards, which was ſent before to the Bottom, in haling
of which the ſaid Machine will deſcend as much under Water as he
hales the Corde; and if he continue haling it, till there be none of
it left, he ſhall deſcend to the Bottome; and in the deſcent, and after
that he ſhall be got to the bottom, he muſt look round about him
through that tranſparent Globe for to finde out the thing he ſeeks,
and ſeeing it, he may many wayes with caſe transferre himſelf
thither without riſing again to the top; And when he would
turn upwards to the toppe of the Water, he needs do no more but
ſlacken that corde faſtned to the Ball of Lead, for thereupon the
Machine ſhall begin to riſe upwards, and letting the ſaid Corde goe,
it ſhall not ſtay till the Machines upper parte arrive at the ſurface of
the Water; and being aſcended thither, the Diver may come out
thereof, and ſwim to the top, and provide himſelf afterwards of
ſuch things as are neceſſary for embreching the ſaid Ship or other
matter ſunke: And in caſe the Diver cannot ſwim, it will be
ry to faſten a Corde to the Ring placed in the Centre of the upper
Board, and thereby to draw the Modell above the Surface of the
1Water; but knowing how to ſwim, he may enter, aſcend, and
deſcend of himſelf, without any help.
EXPLANATION III.
But if you chance to be in a place where you cannot procure
the ſaid Globe to be made of Glaſſe, it may be made of Wood;
but then you muſt make therein great Sights, or Eyeholes of
clear Glaſſe of each ſide to look four ſeverall wayes; and pay it
without, and alſo within if you ſee cauſe with Pitch. And if you
cannot get ſuch a Ball of Wood, you may make ſhift with a little
Cubicall Cheſt or Boxe, like one of thoſe Cheſts wherein they plant
Ceaders, which muſt be well joyned graved and pitch't, with four
ſuch Sights of Glaſſe as before, namely one upon every lateral flat
or plain, ſo placed, that the Diver may ſee through them every way,
and be able to look downwards, it would be good to make the
Box ſomewhat narrower towards the mouth, that ſo the four
rall Planes may look ſomewhat ſloping: and in the entrance,
ſcent, aſcent, and coming forth, you are to uſe the ſame Rules as
fore; aud if you have a deſire to deſcend faſter, you muſt make the
Ball of Lead ſomewhat heavier, that was tyed to the end of the
Corde, and this done the Machine ſhall deſcend faſter to the bottom
upon halling the ſaid Corde and Ball; and when you vere or let
looſe the Cord, the Engine will re-aſcend but according to its former
ſpeed: But if you would alſo make it ſwifter in its aſcent you are
to proceed quite contrary, that is, you muſt ſomewhat diminiſh the
Lead, which is under the Baſe of the fiame; and the more you
miniſh the ſaid Lead, the ſwifter ſhall it be in aſcending. But you
muſt remember withall to encreaſe the Ball of Lead, ſo that it may
be able to draw the ſaid Machine to the bottome ſpeedily or
ly according as occaſion requires.
EXPLANATION IV.
But if there be any likelihood of any obnoxious Fiſh in the place
where the Diver is to deſcend, that may hurt him, being quite
ked; though that in the former kind of Machine with four pillars you
may ſe u e him with a wire Grate, made in the manner of doors to the
ſame, yet to the end that you may know that this Invention may be
varied ſundry ways; you may in this caſe have a Globe of tranſparent
glaſs made at Murano, of ſuch a bigneſs, that a man ſtanding on his feet,
or elſe ſitting, may be contain'd therein, having amouth or round hole
of capacity ſufficient for a man, commodiouſly to enter and goe out
thereby, and ſomewhat larger: & then coffin or encloſe the ſaid Globe
1between two round Boards of ſomewhat a greater Diameter than
the Globe, with four pillars, as in the enſuing figure doth graphically
appear. But in the round Board which is put over the hole or mouth
of the ſaid Globe, you muſt alſo make a round hole ſomewhat
rower than that of the Globe, but yet big enough for a man to paſſe
in and out thereat. Afterwards under this round Board ſo bored,
you muſt place and fix another round bored piece of Lead of ſuch
thickneſſe, as that it may be able to draw the ſaid Ball or Globe of
Glaſſe, together with the Diver in ſuch manner under Water, that
the upper round Board do reſt in the Surface of the Water, namely,
that it may not be ſo heavy as to ſink the Globe and Diver to the
bottome, but only to retain it beneath the Surface of the Water,
which by tryal may be eaſily proportioned, namely, by adding or
taking away Lead from the Baſe, according as occaſion ſhall require.
Next you are to frame a ſeat for the Diver to ſit commodiouſly in
the ſaid Ball or Globe, and next faſten a Ball of Lead to the end of
a Rope, as many fathom long as the water is deep into which you
would deſcend, and ſomewhat more, as was ſaid in the preceding
Explanation. And that Ball of Lead ſhould be of ſuch bigneſſe, that
applied to the ſaid Model, it may be ſufficient to make it deſcend to
the bottome leiſurely, or ſwiftly, as he ſeeth cauſe who is to dive.
And make an handle or peg in the ſaid Globe whereat to faſten or
belay the other end of
the ſaid Rope, and to
draw it eaſily upwards,
330[Figure 330]
or let it looſe at the
pleaſure of him that is
within, and this may be
eaſily done by joyning
and faſtening four
pieces of wood upright
in the mouth or hole of
that bored Board and
Lead, which ſhall be
about the mouth of the
ſaid Globe; and that
I may be the better
underſtood, I will give
it you in figure with the
Diver ſitting therein.
If you would deſcend to the bottome of ſome deep water by help
of this Machine, you are to proceed according to the directions
ven in the precedent Explanation.
1
EXPLANATION V.
In caſe you ſhould be in a place where you could not have ſuch
a Globe made of Glaſſe, you may procure one of Copper or

Lead, round in faſhion of a greater ^{*} Churne, wide in the
tome and narrow in the mouth, and at leaſt five foot high, and four
foot broad. It may indeed be made quadrangular, that is, ſo that
the mouth be at leaſt three foot ſquare every way, and the bottome
at leaſt four foot every ſide, and not under five foot high, and this
ſame veſſel, making it of Lead, muſt be ſo contrived, or
ned, that the corporeal or ſolid Area, or Content of its interiour
cuity, or ſpace, be about oruple to the ſolid Area of the Lead,
which is imployed in making the ſaid Veſſel; that is, make the Lead
of ſuch a thickneſſe, that the Veſſels vacuity may be nine tenths of
the ſolid Area of all the whole Frame, which may be eaſily done by
any one that is not ignorant of practical Geometry: and this Veſſel
being made, you ſhould place or ſet therein four great Fye holes or
Sights of tranſparent or criſtaline Glaſſe, ſo placed as to ſee any way
as you ſhall need or deſire: and furthermore, in the framing of this
ſame Veſſel, you muſt make ſome proviſion for the ſetling or
ing your feet, and to ſit down, and likewiſe you muſt make a
Pulley to hall the Ball of Lead up, or let it down, which is faſtened
to the end of the long cord, as was ſaid in the two precedent caſes.
And moreover, in the making of this Veſſel, you are to faſten four
Rings of Iron to the bottome without, namely, to the four Angles,
it being Quadrangular; (and being round, let them divide the
cumference into four equal parts) and betwixt theſe four Rings,
you muſt place a ſquare or round Deal Board. And this Veſſel thus
modellized ſhall be ſo contrived, that putting it into the water with
the mouth downwards, with him in it who is to Dive, it ſhall but juſt
ſtay in the Surface of the water with that bottome of wood; but if
it chance that it ſhall not ſtay at the Surface of the water by helpof
that bottome of Board, but that it will deſcend, you muſt upon that
bottome faſten another, or two, or more ſquare or round Boards to
the four Rings, in ſuch wiſe, that by means of the ſaid Boaids it may
be reduced to ſuch a quality, that it may reſt with the ſaid round
Boards in the Surface of the water, and deſcend no farther. Having
with judgement and experience provided all theſe things, and the
Diver being deſirous to deſcend of himſelf, and likewiſe to return
to the top when he pleaſeth, this may be performed with that Ball
of Lead tied to the end of that long Rope, as hath been ſaid in the
precedent Explanations, that is, to ſend the Ball firſt to the bottom in
he place where the Diver would deſcend, and then to enter into the
1Machine, and to ſettle himſelf therein; and then to pull the Ball
upwards, which ſhould be of that Gravity, that it may be apt to
make ſuch a Veſſel or Machine deſcend together with the Diver; and
if the Machine chance to be juſtly contrived, as hath been ſaid
bove, I hold that a Ball of ſive or ſix pounds may be ſufficient to
make it deſcend nimbly upon the pulling of the Cord, and lifting
the Ball from the bottome, and continuing to draw the ſaid Cord,
as long as there is any remaining, he ſhall arrive at the bottome; and
whenever he would return upwards, he need but only vere or
en that Cord, and letting it all go he will not ceaſe aſcending till the
Machine attains with its top (covered with thoſe ſquare or round
Boards) unto the Surface of the Water, as hath been ſaid of the
thers. I will not ſtand to ſhew you the many particularities which
might be inſerted for the tranſporting your ſelves from one place to
another, keeping at the bottome, that is, without returning to the
top, for that they are almoſt infinite, but it ſhall ſuffice to let you
know, that he may eaſily do it, carrying with him a long Hitcher, or
a Boom, or a Spike with a Hook at the end.
* Brenta, a Veſſel
in which they
in Italy carry
Grapes to the
Preſs.
Many other particulars there might be inſiſted on, and eſpecially
how many may ſimply (that is, without any of the forsaid
chines) go to the bottome, and ſtay for many hours under Water,
which, beſides the many profitable concluſions that might from
thence be inferred for Diving in indifferent depths, being
nied with the helps preſcribed in the foregoing Explanations, they
would be much to the purpoſe, for that the Liver being once
cted with the Machine near unto the thing ſunk, he might come out
of the ſaid Machine, and go and ſtay for a long time about the ſame,
to faſten, or prepare thoſe things that are neceſſary for the raiſing
it: And farthermore, there is ſomething to be ſaid, when the thing
ſunk is in a muddy or dark Water, how the Diver may in ſundry
wayes, kindle there a great and flaming light, which flaming fire,
beſides that it would make him diſcern the thing ſunk, it would alſo
ſecure him in his going forth of the Machine from any devouring
Fiſhes, for that all ſuch as ſhould chance to be near that place would
be affrighted at ſuch an unuſual ſpectacle, and would make far
from it. I might alſo ſhew many wayes to embreech and grapple a
Ship when it is found, as well in deep as ſhallow Channels, which
particulars I ſhall reſerve for another time.
I will not ſtand to ſhew how this kind of Diving Machine might
be made of Boards, and that in ſundry faſhions, well calked and
pitcht, with four Lights or Sights, faſtening about the mouth of the
ſame as much Lead as ſhould be neceſſary, oraſinuch as by what
hath been ſpoken in the third Explanation, it is ſufficiently manifeſt.
1
A
SUPPLEMENT
OF THE
Induſtrious or Troubleſome
INVENTION
OF
Nicholaus Tartalea:
In which is ſhewn a general and ſafe way to
breech Cables, and hitch Grappling irons to any
Ship that's ſunk, aſwell in a deep as ſhallow
tome, provided you know the exact place where
the ſaid Ship is. Together with another new way
of raiſing or recovering the ſame.
Whereunto is, laſt of all, added ſome new ways to conduct a Light, or
Flaming Matter, unto the Bottome of the Water, to enlighten, upon
caſion, any dark Bottome, for the diſcovery, not onely, of a Ship or Bark,
but alſo any ſmall thing of value that is ſunk, and that in the night
well as in the day.
To the Moſt
Illuſtrious and moſt Serene
PRINCE
Franceſco Donato,
Duke of
VENICE.
Having not long ſince, Most Serene, and Moſt
Illuſtrious Prince, publiſhed under the Glorious
Name of your Highneſſe, ſundry and diverſe
way storaiſe a Ship ſunk, with its Cargo in it (when once
1it is Grappled) I muſt confeſſe I was not then ſollicitous to
find a way to imbreach or grapple the ſaid Ship (though
it is neceſſary to be known) and the cauſe thereof was, for
that I concluded that amongſt Mariners there were a
thouſand means to effect it, and I was loath to enquire
ter ſuch things as are commonly known to many, although
I be ignorant of them; but delight to ſearch into thoſe
things which none elſe can do. Now, having been ſince
told and aſſured by many, that Mariners, and all other
perſons of ingenuity find far greater difficulty in
ching and Grappling ſuch a Ship, than they do, (when
once they have hold of it) to raiſe the ſame: I
ding the ſame, preſently deliberated upon ſome way that
ſhould be general and ſecure, and to adde it in the end of
my Treatiſe, that ſo it might not, for want thereof, be vain
and uſeleſs. And thus; of many that I have found, that
which to me hath ſeemed moſt univerſal and eaſy to be
explained by writing; I have here ſubjoined, together
with another new way to recover the ſaid Ship: and the
manner how to illuminate the bottome of a dark Water,
but still under the Illustrious Name of your Serene
Highneſſe, at whoſe feet I once more humbly throw my
ſelf
NICOLO TARTAGLIA.
1
A Supplement.
EXPLANATION I.
To hitch therefore, and ſling, or grapple faſt a laden Ship
that is ſunk, being in a ſhowle bottome, as was that broken
up near to Malamoccho, you are to take a very ſtrong
Sheat-anchor Cable, of ſuch a length as is ſufficient for
the Uſes hereafter to be underſtood, and at one end of
ſuch a Cable you are to ſeiz or faſten very well a thick and ſtrong Iron
Ring, big enough for the other end of the Cable to paſſe through with
eaſe, and make thereof a running Parbunckle: and then, near to this
Ring (that is under this Cable at the place where it ſhall be bent to
the Ring) you muſt ſeiz or faſten one of the Flooks of a thick and
ſtrong Anchor, and about three fathoms ſpace from that firſt
chor hitch the Flook of another ſecond Anchor into the ſaid Cable,
ſeizing or faſtening it that it ſtir not: and about two fathoms
ſtance from this ſecond Anchor, ſeiz, as before the Flook of a third
Anchor, and ſo two fathom from that a fourth Anchor; and ſo
ceed, placing in that manner as many Anchors as ſuffice to go round
the Hull of the ſaid Ship under its Wails, and rather leſſe than more,
to the end the laſt Anchor may be no hinderance to the running of
the Parbunckle at the Ring at ſuch time as it is to be rouſed or vered,
that is, to be drawn or let ſlip. The truth is, that in the part of the
Cable marked E, in the Figure following, and in the oppoſite
part marked G (which parts you are to place ſo that they may fall
one at the Stem, the other at the Stern) no Anchor is to be placed,
but you muſt leave at leaſt three fathom interval betwixt thoſe
chors at G, as was required to be done betwixt the firſt and ſecond
at E. And then form the ſaid Running Parbunckle, that is, reeve the
other end of the Cable through the Ring of Iron; and, that being
made, you are to place many perſons upon Flat-bottome Boats
ſtened in an Oval Figure round the place where the Ship lyeth: and
then vere or ſlacken the Parbunckle, but in an Oval Form, to that
wideneſſe, that it may at four or five foot diſtance, inviron the
dered Ship: and this done, you muſt let all the Anchors, together
with this Girdle or Parbunckle, (being kept at that wideneſſe)
ly and equally fall to the bottome of the Sea, keeping the Ship in
the midſt of the Ovall: and when you perceive all the Anchors
ſcended to the bottome, you muſt vere there ſeveral Cables, that
they may ſink deep into the ſand or Ouze; and then after this you
1muſt draw, and bring them by degrees cloſe underneath the Hull of
the Veſſel, and then hall or ſtrain hard the end of the Sheat Anchor
Cable which was reeved through the Ring; and begirt the Hull
of the Ship therewith, as with a Girdle (and to ſtrain it very taught, it
would not be amiſſe to make uſe of a Capſtan) and when this
Girdle is drawn to its due exactneſſe, to the end it may not ſlip (in
the elevation of the Ship) faſten to that part which you hold above
Water another Ring of Iron, and paſſe through this Ring one of
the Anchor-Cables that is on the ſame ſide as the firſt Ring is on,
and almoſt as far from the ſaid Ring, as the ſecond Ring is diſtant
from the firſt; whereupon making this ſecond Ring to ſlip along
the ſaid Anchor Cable, and then in the Elevation halling the ſame,
it ſhall make the ſaid Girdle taught under the ſaid Ship: and that I
may be the better underſtood, I have here underneath repreſented
the ſaid Girdle pul'd together in an Oval Figure as it is to lye under
the Rake of the Ships Hull with fourteen Flooks of fourteen
chors under the ſame (except in the part inked E, and in its
ſite part G,) well
ed; of which Girdle, or
Parbunckle, the firſt
331[Figure 331]
Ring ſhall be A,
through which the
Sheat-Anchor Cable
paſſeth, namely, the
Cable A B, to which
Cable was faſtened a
ſecond Ring in the
point B, through which
ſecond Ring, (to the
end the Girdle might
not ſlio) we will reeve
the Cable of the
chor C; which Anchor
C we ſuppoſe to be
ſomewhat farther from
the Ring A, than the ſecond Ring B is from the firſt Ring A, and
then make the ſaid Ring B to ſlip along the Cable of the ſaid Anchot
C, till it come to the point C. And thus the Ship ſhall be ſecurely
and ſtrongly grappled and begirt. Which done, proceeding as we
directed in the firſt Book of our Indnſtrious Invention, you will
cute your purpoſe; That is, when the two or more coupled Ships
ſhall be full of water, at the ebbing of the Tide you are to faſten
and belay to thoſe Tires of Beams that couple the ſaid Ships, all
thoſe fourteen Cables, taking a little more care in tying, and
1ing that of the Anchor C, which will keep the Girdle from ſlipping
in the Elevation.
But if you doubt that that ſingle Cable, to which the Anchors
are faſtened, is not ſufficient for ſo great a weight, you may above
that, place another with a Ring alſo, through which (as before) the
end of it may paſſe, by that means begirting the Ship with two of
thoſe Girdles, and obſerving the ſame Rules you may take three or
four of thoſe ſlipping ſheat-anchor Cables, each with its Ring
wherein to run in the manner of a Nooſe. And when the ſaid new
Girdle is pulled ſtrait and cloſe to the Ship, faſten to the ſaid Cable,
(or to each of them if you uſe more) another ſecond Ring, to gird
and hold the ſaid Nooſe faſt, that it ſlip not with the Cable of the
Anchor C, or with more of thoſe Anchor-Cables if there be
ſion.
And in caſe that thoſe fourteen Cables be thought inſufficient
to bear ſo great a burden, you may take twenty or thirty of them, or
as many as you pleaſe, tying them cloſer to one the other, under
the running Cable, and make half of them to be placed on one ſide,
and the other half on the other ſide of the ſaid Ship.
And if again it be doubted that the ſingle Cable of the Anchor
C s not able to hold the Nooſe faſt, you may take two or three of
them, for you may judge what the ſtreſs of that anchor is by means of
the height of the water. Truth is, this office might be diſtributed
amongſt more Anchors, by adding a third Ring to the main Cable,
as far from the ſecond, as the Anchor D is diſtant from the Anchor
C, ſo that the Cable of the Anchor D, paſſing through that third
Ring, and ſlipping the ſaid Ring along till it come to D, it will
low that thoſe two Cables of thoſe two Anchors C and D, will keep
the Parbunckle ſtraight; aud in this manner you may proceed by
ding new Rings, and imploying more Anchor-Cables, for the
er ſecurity.
EXPLANATION II.
The ſame method may alſo be obſerved when the Ship is in a
deep place, provided that the depth exceed not the length of the
Hull of the Ship, becauſe then there may be alwaies found ſome one
or more Cables ſufficient to reeve through the ſecond and
ing Rings of the Main Cable to ſecure the Nooſe from ſlipping, or
growing ſlack, as in the preceding declaration hath been ſaid. But if
it chance that the depth of the place be far greater than the length
of the Ship, you can no longer ſecure the Nooſe with that ſecond
Ring, but muſt find out ſome other way, and though there might be
many found out, I ſhall inſtance but in this one.
1
After you have ſtrained, drawn the ſaid Girdle as taught as you
can, you may take the Cable thereof, and the Cable of the anchor
next adjoyning on the ſame ſide that the firſt Ring is on (namely,
the Cable marked F,) and twiſt and wind them together, and then
reeve the ſingle Cable of the Girdle A B, through the Ring of a
Sheat-anchor, (without its Cable) and let the anchor ſlide
wards along the ſaid Main Cable, which by reaſon of its weight will
run almoſt cloſe to the Ring A, of the Main Cable, preſſing the twiſt
of the two Cables cloſe at A; and this done, once more twine or
twiſt a little the two former Cables, namely the Sheat anchor-cable
B, and the leſſer Cable F, and then ſeaſe thoſe two Cables ſeverally
to the Orders of Beams, that is, one to one Order, and the other to
another at ſome diſtance from the former, to the end they drive
down the twiſting near to the Ring of the anchor: which twiſting
will keep the Nooſe from ſlipping or opening in elevating the Ship.
And if there be any occaſion to uſe a Capſtain (as was ſaid in the
ſeventh Explanation of the firſt Book) you muſt always take care
to ſtrain theſe two Cables equally, and much aſunder, which doing,
the Girdle ſhall be kept ſtrait. Many other ways might be ſhewen
for to keep the ſaid Grand Cable from ſlipping, but eſteeming them
ſuperfluous, I omit them.
EXPLANATION III.
He that is deſirous to recover a foundered Ship laden with
Fraight, by other ways than thoſe preſcribed in the firſt Book,
namely, without ſtanding to fill thoſe two or more Ships, or other
Veſſels with water, and then to empty them, may only by force of
Capſtains or Cranes eaſily effect the ſame in the manner following,
(ſtill making uſe of the Parbunckle and flooks of anchors explained
in the firſt Explanation of this) namely: By taking from their
chors Rings all their Cables, except that which is to make faſt the
Main-Cable Nooſe that begirts the Ship, and in their places make
faſt to each Ring a ſtrong Pulley or Block, in ſuch ſort, that all the
ſaid Pulleys or Blocks have equal number of Shivers, or wheels, and
thoſe as many as you can make them: and through theſe Shivers or
wheels reeve their proper and convenient Cables or Ropes,
ting each Pulley with its ſuperiour; and this done, make two
drons of Barks, or Lighters, or Flat-boats, according to the method
laid down in the fourth Explanation of the firſt Book, collated and
bound together with thoſe Tires of thick and ſtrong Beams tripled,
and with a great and ſpacious platform of thick Planks upon each
ſquadron, and upon thoſe two ſpacious platforms place as many
Capſters or Ship-cranes as you ſhall judge neceſſary for ſuch a
1weight, and rather much more, then ever ſo little leſs, and then let
fall the ſaid Anchors leiſurely, with the Girdle opened in an Oval
Figure, untill they come to the bottome of the Sea, ſo that the Girdle
do encircle or ſurround the foundered Ship. And having once
girt it carefully, approximate all the Anchors with the Girdle to the
Hull of the Ship, and then ſharpen or make taught the Girdle-cable
by halling it hard and ſtreight to the Ships hull, and when it is
drawn cloſe, belay it that it may not ſlacken, with that ſingle
chor-cable, or more, according to that ſecure way ſpoken of but
now, or by ſome other than ſhall ſeem more expedient, (for many
more, if one think thereon may be found:) and this being done,
ſeek to looſen the Ship by degrees from its bed of Ouze, a little on
one ſide, and a little on the other with the aforeſaid Capſters, and,
being once water born, then draw it upwards equally on both ſides,
and proceed in this manner till ſuch time as you have hoiſted it
ficiently above the Waters ſurface, and then pump out the Water,
and unlade its Cargo.
EXPLANATION IV.
Having in the ſecond Book ſhewn ſeveral ways of Diving under
Water in ſearch of things ſunk, in this place I have thought
fit to add, in caſe that ſome little thing of value ſhould fall
into a Water in ſome ſhady place, and where its bottome is obſcure
and dark, a way how to conveigh a Light thither that may give light
enough for the diſcerning of that little thing, provided that it be not
buried in, or covered with the old Ouze. Now to perform this, and
that with expedition, we may in ſmall depths take one of thoſe braſs
Buckets or Pails, which are uſed in carrying and keeping of Water
for houſehold uſes: and thoſe of them that are ſhaped long and
deep, with feet ſhall be better then thoſe that are made round and
ſhallow, without feet; and the bigger and higher it is, ſo much the
better it ſhall be. And having made choice of ſuch a Bucket, you
are to faſten to the Ears of it two ſmall Ropes of about two yardes
apiece, in ſuch a faſhion, as that they may one croſs the other at the
mouth of the Bucket, making upon it a perfect croſs, and that the
Knot of the Ropes may be in the midſt of the Buckets bottom
out, making of the ropes a Hoop over the bottome whereat to faſten
another Rope of greater length; ſo that the Bucket being held by
that laſt Rope may come to hang with its mouth perpendicularly
downwards. And this done, faſten as much Lead to the two Eares of
the Bucket as may juſt make it ſink to the Bottome, and then ſet
and faſten a little Wax candle lighted in the interſection that thoſe
two Ropes make over the mouth of the Bucket, that is, in the centre
1of that perfect croſs; ſo that the candle with its light may be
in, and near the bottome of the ſaid Bucket. This being done, let
down the Bucket, with the candle in it gently unto the bottome,
which doing, you ſhall ſee the burning candle clearly enlighten the
bottome of the Water. And this Bucket you may remove from
place to place, without drawing it upwards. The truth is, that this
candle will not long continue burning, but will ſerve for a little
while, and when it ſhall go out of it ſelf, it may be drawn up,
lighted, and let down, as occaſion requires: but the greater that the
Bucket, and the leſſer that the candle ſhall be, ſo much the longer
time ſhall it keep its light under Water: and therefore if the ſaid
bottome were very deep, it would be requiſite to perform that eſſect
with ſo much a greater Veſſel, as a great Caldron, but yet of Brals,
or by that means the candle ſhall continue longer lighted.
EXPLANATION V.
But in caſe that a Ship or Bark were foundered in ſome ſpacious
and profound Gulph, and that the exact place where it ſunk
were unknown, and that the bottome of the ſaid ſpacious Gulph
were very obſcure, it is manifeſt that ſo little a light as that ſpoke
of in the precedent Explanation would hardly ſerve. And therefore
if you would convey thither one much bigger, you may do it
rall wayes, of which one is this. Take nine ounces of refined
peter, ſix ounces (Greek weight) of Brimſtone that is clear and
tranſparent, three ounces of Camphire refined, and one ounce of
Maſtick; and beat all theſe things ſeverally, not very ſmall; and
when you have beaten them, mix them all together in an Earthen
Pan; and when they are well mingled, put thereto three pounds of
common Gunpowder, and then remingle them very well together;
and afterwards put therein four ounces of oyl of Stone, and mix all
very well; and this done, take a Cartredge thereof, and give fire to
it; and if it burn too ſlowly, put a little more Gunpowder to it,
but if it burn too vehemently and ſuddenly, add thereto more oyl.
Put this Compoſition, after this, into a little Bag of double Canvis,
of ſuch a wideneſſe, that when all the mixture is out, therein it may
be as broad, as high, and cram the Compoſition hard down into the
Bag; and then with very good Pack thread ſew up the mouth of the
Sack, cutting away the ſuperfluous Canvas. Then winde a good
hempen cord round about it very hard every way, reducing it to the
form of a round Ball, and after it is very well bound and ſwathed
bout many ſeverall times, you muſt melt Brimſtone into a great
ſel, and when it is melted, roll the ſaid Ball therein ſo, as that it may
be covered all over with a cruſt of Brimſtone. And this being done
1affix a piece of Lead unto the Ball by an iron Wire, and make it
ry faſt, and frame in the top of the Ball a Bow or Nooſe with the
ſaid Wire, and to that faſten a long Rope, and then in the oppoſite
place where the Lead is fixed, make an hole with an iron rod into
the middle of the Ball, and ſtop that hole with a little fine
der, holding it ſuſpended by the Rope: and when you would have
that Light deſcend into the bottome of the Sea or Gulph, goe to the
place, and give fire to the little hole, and when it is inkindled, let
down the Ball and Lead, lengthwayes, almoſt to the bottome, where
he ſhall be that would find the thing ſunk, and you ſhall find that
the ſaid fire will illuminate very much round about the ſaid bottom,
and ſhall laſt a long time, and more or leſs, according to the hole
made in the Ball. 'Tis to be noted, that the Ball is to be held over
the head of him that diveth, for that the ſmoke proceeding from it
will much obſcure the Waters above it, ſo as that it will give Light
only downwards; and this fire will be a dreadful ſight unto the Fiſh,
ſo that they will fly from ſo new a ſpectacle.
The END of the firſt part
of the Second TOME.