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

Bibliographic information

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

Permanent URL

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

Copyright information

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
[Empty page]
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
[Empty page]
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
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
[Empty page]
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 Jupite