Galilei, Galileo, Discourse concerning the natation of bodies, 1663

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Author: Galilei, Galileo
Title: Discourse concerning the natation of bodies
Date: 1663

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Permanent URL: http://echo.mpiwg-berlin.mpg.de/MPIWG:E0RNKYA7

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Copyright: Max Planck Institute for the History of Science (unless stated otherwise)
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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
11[Figure 1]
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
2[Figure 2]
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
3[Figure 3]
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
4[Figure 4]
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
5[Figure 5]
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
6[Figure 6]
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
7[Figure 7]
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
8[Figure 8]
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
9[Figure 9]
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
10[Figure 10]
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
11[Figure 11]
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
12[Figure 12]
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
13[Figure 13]
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
14[Figure 14]
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
15[Figure 15]
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
16[Figure 16]
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
17[Figure 17]
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
18[Figure 18]
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,
19[Figure 19]
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.