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<?xml version="1.0"?>

<!DOCTYPE archimedes SYSTEM "../dtd/archimedes.dtd" ><archimedes> <info>

<author>Galilei, Galileo</author>

<title>Natation</title>

<title>Mechanics</title>

<place>London</place>

<translator>Thomas Salusbury</translator>

<cvs_file>galil_natat_074_en_1663.xml</cvs_file>

<cvs_file>galil_mecha_070_en_1665.xml</cvs_file>

<cvs_version></cvs_version>

</info> <text> <front> <section>

<pb/>

<s>GALILEUS, <lb/>HIS <lb/>MECHANICKS: <lb/>OF THE BENEFIT DERIVED <lb/>FROM THE SCIENCE OF MECHANICKS, <lb/>AND FROM ITS INSTRUMENTS.</s> </section> </front> <body> <chap>

<s>A <lb/>DISCOURSE <lb/><emph type="italics"/>PRESENTED<emph.end type="italics"/><lb/>TO THE MOST SERENE <lb/>Don Co&longs;imo II. <lb/>GREAT DUKE <lb/><emph type="italics"/>OF<emph.end type="italics"/><lb/>TUSCANY, <lb/>CONCERNING <lb/>The <emph type="italics"/>NATATION<emph.end type="italics"/> of BODIES Vpon, <lb/>And <emph type="italics"/>SUBMERSION<emph.end type="italics"/> In, <lb/>THE <lb/>WATER.</s>

<s>I judged it extreamly nece&longs;&longs;ary, before our <lb/>de&longs;cending to the Speculation of Mecha<lb/>nick In&longs;truments, to con&longs;ider how I might, <lb/>as it were, &longs;et before your eyes in a gene<lb/>ral Di&longs;cour&longs;e, the many benefits that are <lb/>derived from the &longs;aid In&longs;truments: and <lb/>this I have thought my &longs;elf the more ob<lb/>liged to do, for that (if I am not mi&longs;taken) <lb/>I have &longs;een the generality of <emph type="italics"/>M<emph.end type="italics"/>echaniti<lb/>ans deceive them&longs;elves in going about to apply Machines to many <lb/>operations of their own nature impo&longs;&longs;ible; by the &longs;ucce&longs;&longs;e where<lb/>of they have been di&longs;appointed, and others likewi&longs;e fru&longs;trate of <lb/>the hope which they had conceived upon the promi&longs;e of tho&longs;e pre<lb/>&longs;umptuous undertakers: of which mi&longs;takes I think I have found <lb/>the principall cau&longs;e to be the belief and con&longs;tant opinion the&longs;e <pb xlink:href="070/01/002.jpg" pagenum="272"/>Artificers had, and &longs;till have, that they are able with a &longs;mall force <lb/>to move and rai&longs;e great weights; (in a certain manner with their <lb/>Machines cozening nature, who&longs;e In&longs;tinct, yea mo&longs;t po&longs;itive con<lb/>&longs;titution it is, that no Re&longs;i&longs;tance can be overcome, but by a Force <lb/>more potent then it:) which conjecture how fal&longs;e it is, I hope by <lb/>the en&longs;uing true and nece&longs;&longs;ary Demon&longs;trations to evince.</s>

<s>By GALILEUS GALILEI: Philo&longs;opher and <lb/>Mathematician, unto His mo&longs;t Serene Highne&longs;&longs;e.</s>

<s>In the mean time, &longs;ince I have hinted, that the benefit and help <lb/>derived from Machines is not, to be able with le&longs;&longs;e Force, by help <lb/>of the Machine to move tho&longs;e weights, which, without it, could <lb/>not be moved by the &longs;ame Force: it would not be be&longs;ides the <lb/>purpo&longs;e to declare what the Commodities be which are derived to <lb/>us from &longs;uch like faculties, for if no profit were to be hoped for, <lb/>all endeavours employed in the acqui&longs;t thereof will be but lo&longs;t <lb/>labour.</s>

<s>Engli&longs;hed from the Second Edition of the ITALIAN, <lb/>compared with the Manu&longs;cript Copies, and reduced <lb/>into PROPOSITIONS: <lb/>By <emph type="italics"/>THOMAS SALUSBURY,<emph.end type="italics"/> <expan abbr="E&longs;q;">E&longs;que</expan></s>

<s>Proceeding therefore according to the nature of the&longs;e Studies, <lb/>let us fir&longs;t propo&longs;e four things to be con&longs;idered. </s>

<s><emph type="italics"/>LONDON<emph.end type="italics"/>: <lb/>Printed by WILLIAM LEYBOURN: <lb/><emph type="italics"/>M D C LXIII.<emph.end type="italics"/></s></section><section>

<s>A DISCOVRSE <lb/>Pre&longs;ented to the Mo&longs;t Serene DON COSIMO II. <lb/>GREATDUKE of <emph type="italics"/>TUSC ANY:<emph.end type="italics"/><lb/>CONCERNING<lb/><emph type="italics"/>The Natation of BODIES Upon, or Submer&longs;ion <lb/>In, the WATER.<emph.end type="italics"/></s> </section> </front> <body> <chap>

<s>Con&longs;idering (Mo&longs;t Serene Prince) that the <lb/>publi&longs;hing this pre&longs;ent Treati&longs;e, of &longs;o <lb/>different an Argument from that which <lb/><arrow.to.target n="marg1393"></arrow.to.target><lb/>many expect, and which according to the <lb/>intentions I propo&longs;ed in my ^{*} A&longs;tronomi<lb/>call <emph type="italics"/>Advi&longs;o,<emph.end type="italics"/> I &longs;hould before this time <lb/>have put forth, might peradventure make <lb/>&longs;ome thinke, either that I had wholly <lb/>relinqui&longs;hed my farther imployment <lb/>about the new Cele&longs;tiall Ob&longs;ervations, <lb/>or that, at lea&longs;t, I handled them very <lb/>remi&longs;&longs;ely; I have judged fit to render an account, a&longs;well of my <lb/>deferring that, as of my writing, and publi&longs;hing this treati&longs;e.</s>

<s><margin.target id="marg1393"></margin.target>His Nuncio Sl<lb/>derio.</s>

<s>As to the fir&longs;t, the la&longs;t di&longs;coveries of <emph type="italics"/>Saturn<emph.end type="italics"/> to be tricorporeall, and <lb/>of the mutations of Figure in <emph type="italics"/>Venus,<emph.end type="italics"/> like to tho&longs;e that are &longs;een in the

<lb/>Moon, together with the Con&longs;equents depending thereupon, have

<lb/>not &longs;o much occa&longs;ioned the demur, as the inve&longs;tigation of the times

<lb/>of the Conver&longs;ions of each of the Four Medicean Planets about <emph type="italics"/>Ju

<lb/>piter,<emph.end type="italics"/> which I lighted upon in <emph type="italics"/>April<emph.end type="italics"/> the year pa&longs;t, 1611, at my being in

<lb/><emph type="italics"/>Rome<emph.end type="italics"/>; where, in the end, I a&longs;&longs;ertained my &longs;elfe, that the fir&longs;t and neere&longs;t

<lb/>to <emph type="italics"/>Jupiter,<emph.end type="italics"/> moved about 8 <emph type="italics"/>gr.<emph.end type="italics"/> & 29 <emph type="italics"/>m.<emph.end type="italics"/> of its Sphere in an houre, make

<lb/>ing its whole revolution in one naturall day, and 18 hours, and almo&longs;t

<lb/>an halfe. </s><s>The &longs;econd moves in its Orbe 14 <emph type="italics"/>gr. </s><s>13 min.<emph.end type="italics"/> or very neer,

<lb/>in an hour, and its compleat conver&longs;ion is con&longs;ummate in 3 dayes, 13

<lb/>hours, and one third, or thereabouts. </s><s>The third pa&longs;&longs;eth in an hour,

<lb/>2 <emph type="italics"/>gr. </s><s>6 min.<emph.end type="italics"/> little more or le&longs;s of its Circle, and mea&longs;ures it all in 7

<lb/>dayes, 4 hours, or very neer. </s><s>The fourth, and more remote than the

<lb/>re&longs;t, goes in one houre, o <emph type="italics"/>gr 54 min.<emph.end type="italics"/> and almo&longs;t an halfe of its Sphere,

<lb/>and fini&longs;heth it all in 16 dayes, and very neer 18 hours. </s><s>But be

<lb/>cau&longs;e the exce&longs;&longs;ive velocity of their returns or re&longs;titutions, requires a

<lb/>mo&longs;t &longs;crupulous preci&longs;ene&longs;&longs;e to calculate their places, in times pa&longs;t

<pb pagenum="402"/>and future, e&longs;pecially if the time be for many Moneths or Years; I

<lb/>am therefore forced, with other Ob&longs;ervations, and more exact than

<lb/>the former, and in times more remote from one another, to correct

<lb/>the Tables of &longs;uch Motions, and limit them even to the &longs;horte&longs;t mo

<lb/>ment: for &longs;uch exactne&longs;&longs;e my fir&longs;t Ob&longs;ervations &longs;uffice not; not only

<lb/>in regard of the &longs;hort intervals of Time, but becau&longs;e I had not as then

<lb/>found out a way to mea&longs;ure the di&longs;tances between the &longs;aid Planets

<lb/>by any In&longs;trument: I Ob&longs;erved &longs;uch Intervals with &longs;imple relation

<lb/>to the Diameter of the Body of <emph type="italics"/>Jupiter<emph.end type="italics"/>; taken, as we have &longs;aid, by

<lb/>the eye, the which, though they admit not errors of above a Minute,

<lb/>yet they &longs;uffice not for the determination of the exact greatne&longs;s of the

<lb/>Spheres of tho&longs;e Stars. </s><s>But now that I have hit upon a way of ta

<lb/>king &longs;uch mea&longs;ures without failing, &longs;carce in a very few Seconds, I will

<lb/>continue the ob&longs;ervation to the very occultation of <emph type="italics"/>JVPITER,<emph.end type="italics"/>

<lb/>which &longs;hall &longs;erve to bring us to the perfect knowledge of the Moti

<lb/>ons, and Magnitudes of the Orbes of the &longs;aid Planets, together

<lb/>al&longs;o with &longs;ome other con&longs;equences thence ari&longs;ing. </s><s>I adde to the&longs;e

<lb/>things the ob&longs;ervation of &longs;ome ob&longs;cure Spots, which are di&longs;cover

<lb/>ed in the Solar Body, which changing, po&longs;ition in that, propounds

<lb/>to our con&longs;ideration a great argument either that the Sun revolves in

<lb/>it &longs;elfe, or that perhaps other Starts, in like manner as <emph type="italics"/>Venus<emph.end type="italics"/> and

<lb/><emph type="italics"/>Mercury,<emph.end type="italics"/> revolve about it, invi&longs;ible in other times, by rea&longs;on of their

<lb/>&longs;mall digre&longs;&longs;ions, le&longs;&longs;e than that of <emph type="italics"/>Mercury,<emph.end type="italics"/> and only vi&longs;ible when

<lb/>they interpo&longs;e between the Sun and our eye, or el&longs;e hint the truth

<lb/>of both this and that; the certainty of which things ought not to be

<lb/>contemned, nor omitted.</s>

<s><margin.target id="marg1394"></margin.target>The Authors

<lb/>Ob&longs;ervations of

<lb/>the Solar Spots.</s>

<s><emph type="italics"/>Continuall ob&longs;ervation hath at la&longs;t a&longs;&longs;ured me that the&longs;e Spots are

<lb/>matters contiguous to the Body of the Sun, there continually produced

<lb/>in great number, and afterwards di&longs;&longs;olved, &longs;ome in a &longs;horter, &longs;ome in a

<lb/>longer time, and to be by the Conver&longs;ion or Revolution of the Sun in it

<lb/>&longs;elfe, which in a Lunar Moneth, or thereabouts, fini&longs;heth its Period,

<lb/>caried about in a Circle, an accident great of it &longs;elfe, and greater for

<lb/>its Con&longs;equences.<emph.end type="italics"/>

<s><margin.target id="marg1395"></margin.target>The occa&longs;ion in

<lb/>ducing the Au

<lb/>thor to write

<lb/>this Treati&longs;e.</s>

<s>As to the other particular in the next place. ^{*} Many cau&longs;es have

<lb/>moved me to write the pre&longs;ent Tract, the &longs;ubject whereof, is the

<lb/>Di&longs;pute which I held &longs;ome dayes &longs;ince, with &longs;ome learned men of

<lb/>this City, about which, as your Highne&longs;&longs;e knows, have followed

<lb/>many Di&longs;cour&longs;es: The principall of which Cau&longs;es hath been the

<lb/>Intimation of your Highne&longs;&longs;e, having commended to me Writing,

<lb/>as a &longs;ingular means to make true known from fal&longs;e, reall from appa

<lb/>rent Rea&longs;ons, farr better than by Di&longs;puting vocally, where the

<lb/>one or the other, or very often both the Di&longs;putants, through too

<pb pagenum="403"/>greate heate, or exalting of the voyce, either are not under&longs;tood,

<lb/>or el&longs;e being tran&longs;ported by o&longs;tentation of not yeilding to one ano

<lb/>ther, farr from the fir&longs;t Propo&longs;ition, with the novelty, of the

<lb/>various Propo&longs;als, confound both them&longs;elves and their Auditors.</s>

<s>Moreover, it &longs;eemed to me convenient to informe your High

<lb/>ne&longs;&longs;e of all the &longs;equell, concerning the Controver&longs;ie of which I

<lb/>treat, as it hath been adverti&longs;ed often already by others: and becau&longs;e

<lb/>the Doctrine which I follow, in the di&longs;cu&longs;&longs;ion of the point in hand,

<lb/>is different from that of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>; and interferes with his Principles,

<lb/>I have con&longs;idered that again&longs;t the Authority of that mo&longs;t famous

<lb/>Man, which among&longs;t many makes all &longs;u&longs;pected that comes not from

<lb/>the Schooles of the Peripateticks, its farr better to give ones Rea&longs;ons

<lb/>by the Pen than by word of mouth and therfore I re&longs;olved to write the

<lb/>pre&longs;ent di&longs;cour&longs;e: in which yet I hope to demon&longs;trate that it was not

<lb/>out of capritiou&longs;ne&longs;&longs;e, or for that I had not read or under&longs;tood

<lb/><emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> that I &longs;ometimes &longs;werve from his opinion, but becau&longs;e

<lb/>&longs;everall Rea&longs;ons per&longs;wade me to it, and the &longs;ame <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hath </s>

<lb/>tought me to fix my judgment on that which is grounded upon

<lb/>Rea&longs;on, and not on the bare Authority of the Ma&longs;ter; and it is

<lb/>mo&longs;t certaine according to the &longs;entence of <emph type="italics"/>Alcinoos,<emph.end type="italics"/> that philo&longs;opha

<lb/>ting &longs;hould be free. </s><s>Nor is the re&longs;olution of our Que&longs;tion in my

<lb/>judgment without &longs;ome benefit to the Univer&longs;all, fora&longs;much as

<lb/>treating whether the figure of Solids operates, or not, in their going,

<lb/>or not going to the bottome in Water, in occurrences of building

<lb/>Bridges or other Fabricks on the Water, which happen commonly

<lb/>in affairs of grand import, it may be of great availe to know the

<lb/>truth.</s>

<s><margin.target id="marg1396"></margin.target><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> prefers

<lb/>Rea&longs;on to the

<lb/>Authority ofan

<lb/>Author.</s>

<s><margin.target id="marg1397"></margin.target>The benefit of

<lb/>this Argument.</s>

<s>I &longs;ay therfore, that being the la&longs;t Summer in company with certain

<lb/>Learned men, it was &longs;aid in the argumentation; That Conden&longs;ation

<lb/>was the propriety of Cold, and there was alledged for in&longs;tance, the

<lb/>example of Ice: now I at that time &longs;aid, that, in my judgment,

<lb/>the Ice &longs;hould be rather Water rarified than conden&longs;ed, and my

<lb/>rea&longs;on was, becau&longs;e Conden&longs;ation begets diminution of Ma&longs;s, and

<lb/>augmentation of gravity, and Rarifaction cau&longs;eth greater Lightne&longs;s,

<lb/>and augmentarion of Ma&longs;&longs;e: and Water in freezing, encrea&longs;eth in

<lb/>Ma&longs;&longs;e, and the Ice made thereby is lighter than the Water on which

<lb/>it &longs;wimmeth.</s>

<s><margin.target id="marg1398"></margin.target>Conden&longs;ation

<lb/>the Propriety of

<lb/>Cold, according

<lb/>to the Peripate

<lb/>ticks.</s>

<s><margin.target id="marg1399"></margin.target>Ice rather water

<lb/>rarified, than

<lb/>conden&longs;ed, and

<s><emph type="italics"/>What I &longs;ay, is manife&longs;t, becau&longs;e, the medium &longs;ubtracting from the

<lb/>whole Gravity of Sollids the weight of &longs;uch another Ma&longs;&longs;e of the &longs;aid<emph.end type="italics"/>

<lb/><emph type="italics"/>Medium; was<emph.end type="italics"/> Archimedes <emph type="italics"/>proves in his ^{*} Fir&longs;t Booke<emph.end type="italics"/> De In&longs;identibus

<lb/>Humido; <emph type="italics"/>when ever the Ma&longs;&longs;e of the &longs;aid Solid encrea&longs;eth by Di&longs;traction,

<lb/>the more &longs;hall the<emph.end type="italics"/> Medium <emph type="italics"/>detract from its entire Gravity; and le&longs;&longs;e,

<lb/>when by Compre&longs;&longs;ion it &longs;hall be conden&longs;ed and reduced to a le&longs;&longs;e Ma&longs;&longs;e.<emph.end type="italics"/></s>

<s><margin.target id="marg1400"></margin.target>In lib: 1. of Na

<lb/>tation of Bodies

<s><margin.target id="marg1401"></margin.target>Figure operates

<lb/>not in the Nata

<lb/>tion of Sollids.</s>

<s>It was an&longs;wered me, that that proceeded not from the greater Levity;

<lb/>but from the Figure, large and flat, which not being able to pene

<lb/>trate the Re&longs;i&longs;tance of the Water, is the cau&longs;e that it &longs;ubmergeth not.

<lb/></s><s>I replied, that any piece of Ice, of what&longs;oever Figure, &longs;wims upon

<lb/>the Water, a manife&longs;t &longs;igne, that its being never &longs;o flat and broad,

<lb/>hath not any part in its floating: and added, that it was a manife&longs;t

<lb/>proofe hereof to &longs;ee a piece of Ice of very broad Figure being thru&longs;t

<lb/>to the botome of the Water, &longs;uddenly return to flote atoppe, which

<lb/>had it been more grave, and had its &longs;wimming proceeded from its

<lb/>Forme, unable to penetrate the Re&longs;i&longs;tance of the <emph type="italics"/>Medium,<emph.end type="italics"/> that

<lb/>would be altogether impo&longs;&longs;ible; I concluded therefore, that the Figure

<lb/>was in &longs;ort a Cau&longs;e of the Natation or Submer&longs;ion of Bodies,

<lb/>but the greater or le&longs;&longs;e Gravity in re&longs;pect of the Water: and there

<lb/>fore all Bodyes heavier than it of what Figure &longs;oever they be, indiffe

<lb/>rently go to the bottome, and the lighter, though of any figure, float

<lb/>indifferently on the top: and I &longs;uppo&longs;e that tho&longs;e which hold other

<lb/>wi&longs;e, were induced to that beliefe, by &longs;eeing how that diver&longs;ity

<lb/>of Formes or Figures, greatly altereth the Velo&longs;ity, and Tardity

<lb/>of Motion; &longs;o that Bodies of Figure broad and thin, de&longs;cend

<lb/>far more lea&longs;urely into the Water, than tho&longs;e of a more compacted

<lb/>Figure, though both made of the &longs;ame Matter: by which &longs;ome

<lb/>might be induced to believe that the Dilatation of the Figure might

<lb/>reduce it to &longs;uch amplene&longs;&longs;e that it &longs;hould not only retard but wholly

<lb/>impede and take away the Motion, which I hold to be fal&longs;e. </s><s>Upon

<lb/>this Conclu&longs;ion, in many dayes di&longs;cour&longs;e, was &longs;poken much, and

<lb/>many things, and divers Experiments produced, of which your

<lb/>Highne&longs;&longs;e heard, and &longs;aw &longs;ome, and in this di&longs;cour&longs;e &longs;hall have

<lb/>all that which hath been produced again&longs;t my A&longs;&longs;ertion, and what

<lb/>hath been &longs;ugge&longs;ted to my thoughts on this matter, and for con

<lb/>firmation of my Conclu&longs;ion: which if it &longs;hall &longs;uffice to remove that

<lb/>(as I e&longs;teem hitherto fal&longs;e) Opinion, I &longs;hall thinke I have not

<lb/>unprofitably &longs;pent my paynes and time. </s><s>and although that come

<lb/>not to pa&longs;&longs;e, yet ought I to promi&longs;e another benefit to my &longs;elfe,

<lb/>namely, of attaining the knowledge of the truth, by hearing my

<lb/>Fallacyes confuted, and true demon&longs;trations produced by tho&longs;e

<lb/>of the contrary opinion.</s>

<s>And to proceed with the greate&longs;t plainne&longs;s and per&longs;picuity that

<lb/>I can po&longs;&longs;ible, it is, I conceive, nece&longs;&longs;ary, fir&longs;t of all to declare

<lb/>what is the true, intrin&longs;ecall, and totall Cau&longs;e, of the a&longs;cending of

<lb/>&longs;ome Sollid Bodyes in the Water, and therein floating; or on the

<lb/>contrary, of their &longs;inking. </s><s>and &longs;o much the rather in a&longs;much as I

<lb/>cannot &longs;atisfie my &longs;elfe in that which <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hath left written on

<lb/>this Subject.</s>

<s><margin.target id="marg1402"></margin.target>The cau&longs;e of the

<lb/>Natation & &longs;ub</s>

<s>I &longs;ay then the Cau&longs;e why &longs;ome Sollid Bodyes de&longs;cend to the

<pb pagenum="405"/>Bottom of Water, is the exce&longs;&longs;e of their Gravity, above the

<lb/>Gravity of the Water; and on the contrary, the exce&longs;s of the

<lb/>Waters Gravity above the Gravity of tho&longs;e, is the Cau&longs;e that others

<lb/>do not de&longs;cend, rather that they ri&longs;e from the Bottom, and a&longs;cend

<lb/>to the Surface. </s><s>This was &longs;ubtilly demon&longs;trated by <emph type="italics"/>Archimedes<emph.end type="italics"/> in

<lb/>his Book Of the NATATION of BODIES: Conferred afterwards

<lb/>by a very grave Author, but, if I erre not invi&longs;ibly, as below for

<lb/>defence of him, I &longs;hall endeavour to prove.</s>

<s><margin.target id="marg1403"></margin.target>mer&longs;ion of Sol

<lb/>ids in the Wa

<s>I, with a different Method, and by other meanes, will endeavour

<lb/>to demon&longs;trate the &longs;ame, reducing the Cau&longs;es of &longs;uch Effects to

<lb/>more intrin&longs;ecall and immediate Principles, in which al&longs;o are di&longs;co

<lb/>vered the Cau&longs;es of &longs;ome admirable and almo&longs;t incredible Acci

<lb/>dents, as that would be, that a very little quantity of Water, &longs;hould

<lb/>be able, with its &longs;mall weight, to rai&longs;e and &longs;u&longs;tain a Solid Body, an

<lb/>hundred or a thou&longs;and times heavier than it.</s>

<s>And becau&longs;e demon&longs;trative Order &longs;o requires, I &longs;hall define cer

<lb/>tain Termes, and afterwards explain &longs;ome Propo&longs;itions, of which,

<lb/>as of things true and obvious, I may make u&longs;e of to my pre&longs;ent pur

<lb/>po&longs;e.</s>

<s>DEFINITION I.</s>

<s><emph type="italics"/>I then call equally Grave<emph.end type="italics"/> in &longs;pecie, <emph type="italics"/>tho&longs;e Matters

<lb/>of which equall Ma&longs;&longs;es weigh equally.<emph.end type="italics"/></s>

<s>As if for example, two Balls, one of Wax, and the other of &longs;ome

<lb/>Wood of equall Ma&longs;&longs;e, were al&longs;o equall in Weight, we &longs;ay, that

<lb/>&longs;uch Wood, and the Wax are <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> equally grave.</s>

<s>DEFINITION II.</s>

<s><emph type="italics"/>But equally grave in Ab&longs;olute Gravity, we call two

<lb/>Sollids, weighing equally, though of Ma&longs;s they be

<lb/>unequall.<emph.end type="italics"/></s>

<s>As for example, a Ma&longs;s of Lead, and another of Wood, that

<lb/>weigh each ten pounds, I call equall in Ab&longs;olute Gravity, though

<lb/>the Ma&longs;s of the Wood be much greater then that of the Lead.</s>

<s><emph type="italics"/>And, con&longs;equently, le&longs;s Grave<emph.end type="italics"/> in &longs;pecie.</s>

<s>DEFINITION III.</s>

<s><emph type="italics"/>I call a Matter more Grave<emph.end type="italics"/> in &longs;pecie <emph type="italics"/>than another, of

<lb/>which a Ma&longs;s, equall to a Ma&longs;s of the other, &longs;hall

<lb/>weigh more.<emph.end type="italics"/></s>

<s>And &longs;o I &longs;ay, that Lead is more grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than Tinn, becau&longs;e

<lb/>if you take of them two equall Ma&longs;&longs;es, that of the Lead weigheth

<s>DEFINITION IV.</s>

<s><emph type="italics"/>But I call that Body more grave ab&longs;olutely than this, if

<lb/>that weigh more than this, without any re&longs;pect had to

<lb/>the Ma&longs;&longs;es.<emph.end type="italics"/></s>

<s>And thus a great piece of Wood is &longs;aid to weigh more than a

<lb/>little lump of Lead, though the Lead be <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> more heavy than

<lb/>the Wood. </s><s>And the &longs;ame is to be under&longs;tood of the le&longs;s grave <emph type="italics"/>in

<lb/>&longs;pecie,<emph.end type="italics"/> and the le&longs;s grave ab&longs;olutely.</s>

<s>The&longs;e Termes defined, I take from the Mechanicks two Princi

<lb/>ples: the fir&longs;t is, that</s>

<s>AXIOME. I.</s>

<s><emph type="italics"/>Weights ab&longs;olutely equall, moved with equall Velocity,

<lb/>are of equall Force and Moment in their operations.<emph.end type="italics"/></s>

<s><emph type="italics"/>DEFINITION V.<emph.end type="italics"/></s>

<s>Moment, among&longs;t Mechanicians, &longs;igrifieth that

<lb/>Vertue, that Force, or that Efficacy, with which

<lb/>the Mover moves, and the Moveable re&longs;i&longs;ts.</s>

<s><emph type="italics"/>Which Vertue dependes not only on the &longs;imple Gravity, but on the

<lb/>Velocity of the Motion, and on the diver&longs;e Inclinations of the Spaces

<lb/>along which the Motion is made: For a de&longs;cending Weight makes a

<lb/>greater<emph.end type="italics"/> Impetus <emph type="italics"/>in a Space much declining, than in one le&longs;s declining;

<lb/>and in &longs;umme, what ever is the occa&longs;ion of &longs;uch Vertue, it ever retaines

<lb/>the name of<emph.end type="italics"/> Moment; <emph type="italics"/>nor in my Judgement, is this &longs;ence new in our

<lb/>Idiome, for, if I mistake not, I think we often &longs;ay; This is a weighty

<lb/>bu&longs;ine&longs;&longs;e, but the other is of &longs;mall moment: and we con&longs;ider lighter mat

<lb/>ters and let pa&longs;s tho&longs;e of Moment; a Metaphor, I &longs;uppo&longs;e, taken from

<lb/>the Mechanicks.<emph.end type="italics"/></s>

<s>As for example, two weights equall in ab&longs;olute Gravity, being

<lb/>put into a Ballance of equall Arms, they &longs;tand in <emph type="italics"/>Equilibrium,<emph.end type="italics"/> nei

<lb/>ther one going down, nor the other up: becau&longs;e the equality of the

<lb/>Di&longs;tances of both, from the Centre on which the Ballance is &longs;uppor

<lb/>ted, and about which it moves, cau&longs;eth that tho&longs;e weights, the &longs;aid

<lb/>Ballance moving, &longs;hall in the &longs;ame Time move equall Spaces, that is,

<lb/>&longs;hall move with equall Velocity, &longs;o that there is no rea&longs;on for which

<pb pagenum="407"/>this Weight &longs;hould de&longs;cend more than that, or that more than this;

<lb/>and therefore they make an <emph type="italics"/>Equilibrium,<emph.end type="italics"/> and their Moments continue

<lb/>of &longs;emblable and equall Vertue.</s>

<s>The &longs;econd Principle is; That</s>

<s>AXIOME II.</s>

<s><emph type="italics"/>The Moment and Force of the Gravity, is encrea&longs;ed by

<lb/>the Velocity of the Motion.<emph.end type="italics"/></s>

<s>So that Weights ab&longs;olutely equall, but conjoyned with Velocity

<lb/>unequall, are of Force, Moment and Vertue unequall: and the

<lb/>more potent, the more &longs;wift, according to the proportion of the Ve

<lb/>locity of the one, to the Velocity of the other. </s><s>Of this we have a

<lb/>very pertinent example in the Balance or Stiliard of unequall Arms,

<lb/>at which Weights ab&longs;olutely equall being &longs;u&longs;pended, they do not

<lb/>weigh down, and gravitate equally, but that which is at a greater

<lb/>di&longs;tance from the Centre, about which the Beam moves, de&longs;cends,

<lb/>rai&longs;ing the other, and the Motion of this which a&longs;cends is &longs;low, and

<lb/>the other &longs;wift: and &longs;uch is the Force and Vertue, which from the

<lb/>Velocity of the Mover, is conferred on the Moveable, which receives

<lb/>it, that it can exqui&longs;itely compen&longs;ate, as much more Weight added to

<lb/>the other &longs;lower Moveable: &longs;o that if of the Arms of the Balance,

<lb/>one were ten times as long as the other, whereupon in the Beames

<lb/>moving about the Centre, the end of that would go ten times as far

<lb/>as the end of this, a Weight &longs;u&longs;pended at the greater di&longs;tance, may

<lb/>&longs;u&longs;tain and poy&longs;e another ten times more grave ab&longs;olutely than it:

<lb/>and that becau&longs;e the Stiliard moving, the le&longs;&longs;er Weight &longs;hall move

<lb/>ten times fa&longs;ter than the bigger. </s><s>It ought alwayes therefore to be

<lb/>under&longs;tood, that Motions are according to the &longs;ame Inclinations,

<lb/>namely, that if one of the Moveables move perpendicularly to the

<lb/>Horizon, then the other makes its Motion by the like Perpendicular;

<lb/>and if the Motion of one were to be made Horizontally; that then

<lb/>the other is made along the &longs;ame Horizontall plain: and in &longs;umme,

<lb/>alwayes both in like Inclinations. </s><s>This proportion between the

<lb/>Gravity and Velocity is found in all Mechanicall In&longs;truments: and

<lb/>is con&longs;idered by <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> as a Principle in his <emph type="italics"/>Mechanicall Que&longs;tions<emph.end type="italics"/>;

<lb/>whereupon we al&longs;o may take it for a true A&longs;&longs;umption, That</s>

<s>AXIOME III.</s>

<s><emph type="italics"/>Weights ab&longs;olutely unequall, do alternately counterpoy&longs;e

<lb/>and become of equall Moments, as oft as their Gravi

<lb/>ties, with contrary proportion, an&longs;wer to the Velocity of

<lb/>their Motions.<emph.end type="italics"/></s>

<s>That is to &longs;ay, that by how much the one is le&longs;s grave than the other,

<lb/>by &longs;o much is it in a con&longs;titution of moving more &longs;wiftly than that.</s>

<s>Having prefatically explicated the&longs;e things, we may begin to en

<lb/>quire, what Bodyes tho&longs;e are which totally &longs;ubmerge in Water, and

<lb/>go to the Bottom, and which tho&longs;e that by con&longs;traint float on the

<lb/>top, &longs;o that being thru&longs;t by violence under Water, they return to

<lb/>&longs;wim, with one part of their Ma&longs;s vi&longs;ible above the Surface of the

<lb/>Water: and this we will do by con&longs;idering the re&longs;pective operati

<lb/>on of the &longs;aid Solids, and of Water: Which operation followes

<lb/>the Submer&longs;ion and &longs;inking; and this it is, That in the Submer&longs;ion

<lb/>that the Solid maketh, being depre&longs;&longs;ed downwards by its proper

<lb/>Gravity, it comes to drive away the water from the place where it

<lb/>&longs;ucce&longs;&longs;ively &longs;ubenters, and the water repul&longs;ed ri&longs;eth and a&longs;cends

<lb/>above its fir&longs;t levell, to which A&longs;cent on the other &longs;ide it, as being a

<lb/>grave Body of its own nature, re&longs;i&longs;ts: And becau&longs;e the de&longs;cending

<lb/>Solid more and more immerging, greater and greater quantity of

<lb/>Water a&longs;cends, till the whole Sollid be &longs;ubmerged; its nece&longs;&longs;ary to

<lb/>compare the Moments of the Re&longs;i&longs;tance of the water to A&longs;cen&longs;ion,

<lb/>with the Moments of the pre&longs;&longs;ive Gravity of the Solid: And if the

<lb/>Moments of the Re&longs;i&longs;tance of the water, &longs;hall equalize the Moments

<lb/>of the Solid, before its totall Immer&longs;ion; in this ca&longs;e doubtle&longs;s there

<lb/>&longs;hall be made an <emph type="italics"/>Equilibrium,<emph.end type="italics"/> nor &longs;hall the Body &longs;ink any farther.

<lb/></s><s>But if the Moment of the Solid, &longs;hall alwayes exceed the Moments

<lb/>wherewith the repul&longs;ed water &longs;ucce&longs;&longs;ively makes Re&longs;i&longs;tance, that

<lb/>Solid &longs;hall not only wholly &longs;ubmerge under water, but &longs;hall de&longs;cend

<lb/>to the Bottom. </s><s>But if, la&longs;tly, in the in&longs;tant of totall Submer&longs;ion,

<lb/>the equality &longs;hall be made between the Moments of the prement

<lb/>Solid, and the re&longs;i&longs;ting Water; then &longs;hall re&longs;t en&longs;ue, and the &longs;aid

<lb/>Solid &longs;hall be able to re&longs;t indifferently, in what&longs;oever part of the

<lb/>water. </s><s>By this time is manife&longs;t the nece&longs;&longs;ity of comparing the

<lb/>Gravity of the water, and of the Solid; and this compari&longs;on might

<lb/>at fir&longs;t &longs;ight &longs;eem &longs;ufficient to conclude and determine which are the

<lb/>Solids that float a-top, and which tho&longs;e that &longs;ink to the Bottom in the

<lb/>water, a&longs;&longs;erting that tho&longs;e &longs;hall float which are le&longs;&longs;e grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/>

<lb/>than the water, and tho&longs;e &longs;ubmerge, which are <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> more grave.

<lb/></s><s>For it &longs;eems in appearance, that the Sollid in &longs;inking continually,

<lb/>rai&longs;eth &longs;o much Water in Ma&longs;s, as an&longs;wers to the parts of its own

<lb/>Bulk &longs;ubmerged: whereupon it is impo&longs;&longs;ible, that a Solid le&longs;s grave

<lb/><emph type="italics"/>in &longs;pecie,<emph.end type="italics"/> than water, &longs;hould wholly &longs;ink, as being unable to rai&longs;e a

<lb/>weight greater than its own, and &longs;uch would a Ma&longs;s of water equall

<lb/>to its own Ma&longs;s be. </s><s>And likewi&longs;e it &longs;eems nece&longs;&longs;ary, that the graver

<lb/>Solids do go to the Bottom, as being of a Force more than &longs;ufficient

<lb/>for the rai&longs;ing a Ma&longs;&longs;e of water, equall to its own, though inferiour

<lb/>in weight. </s><s>Neverthele&longs;s the bu&longs;ine&longs;s &longs;ucceeds otherwi&longs;e: and

<pb pagenum="409"/>though the Conclu&longs;ions are true, yet are the Cau&longs;es thus a&longs;&longs;igned

<lb/>deficient, nor is it true, that the Solid in &longs;ubmerging, rai&longs;eth and

<lb/>repul&longs;eth Ma&longs;&longs;es of Water, equall to the parts of it &longs;elf &longs;ubmerged;

<lb/>but the Water repul&longs;ed, is alwayes le&longs;s than the parts of the Solid

<lb/>&longs;ubmerged: and &longs;o much the more by how much the Ve&longs;&longs;ell in

<lb/>which the Water is contained is narrower: in &longs;uch manner that it

<lb/>hinders not, but that a Solid may &longs;ubmerge all under Water, with

<lb/>out rai&longs;ing &longs;o much Water in Ma&longs;s, as would equall the tenth or

<lb/>twentieth part of its own Bulk: like as on the contrary, a very

<lb/>&longs;mall quantity of Water, may rai&longs;e a very great Solid Ma&longs;s, though

<lb/>&longs;uch Solid &longs;hould weigh ab&longs;olutely a hundred times as much, or

<lb/>more, than the &longs;aid Water, if &longs;o be that the Matter of that &longs;ame

<lb/>Solid be <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> le&longs;s grave than the Water. </s><s>And thus a great

<lb/>Beam, as &longs;uppo&longs;e of a 1000 weight, may be rai&longs;ed and born afloat

<lb/>by Water, which weighs not 50: and this happens when the Mo

<lb/>ment of the Water is compen&longs;ated by the Velocity of its Motion.</s>

<s><margin.target id="marg1404"></margin.target>How the &longs;ub

<lb/>mer&longs;ion of So

<lb/>lids in the Wa

<lb/>ter, is effected.</s>

<s><margin.target id="marg1405"></margin.target>What Solids

<lb/>&longs;hall float on the

<lb/>Water.</s>

<s><margin.target id="marg1406"></margin.target>What Solids

<lb/>&longs;hall &longs;inke to the

<lb/>botome.</s>

<s><margin.target id="marg1407"></margin.target>What Solids

<lb/>&longs;hall re&longs;t in all

<lb/>places of the Wa

<s><margin.target id="marg1408"></margin.target>The Gravitie of

<lb/>the Water and

<lb/><emph type="italics"/>S<emph.end type="italics"/>olid mu&longs;t be

<lb/>compared in all

<lb/>Problems, of Na

<lb/>tation of Bodies.</s>

<s><margin.target id="marg1409"></margin.target>The water re

<lb/>pul&longs;ed is ever le&longs;s

<lb/>than the parts of

<lb/>the Sollid &longs;ub

<lb/>merged.</s>

<s><margin.target id="marg1410"></margin.target><emph type="italics"/>A<emph.end type="italics"/> &longs;mall quantity

<lb/>of water, may

<lb/>float a very

<lb/>great Solid Ma&longs;s.</s>

<s>But becau&longs;e &longs;uch things, propounded thus in ab&longs;tract, are &longs;ome

<lb/>what difficult to be comprehended, it would be good to demon&longs;trate

<lb/>them by particular examples; and for facility of demon&longs;tration, we

<lb/>will &longs;uppo&longs;e the Ve&longs;&longs;els in which we are to put the Water, and place

<lb/>the Solids, to be inviron'd and included with &longs;ides erected perpendi

<lb/>cular to the Plane of the Horizon, and the Solid that is to be put

<lb/>into &longs;uch ve&longs;&longs;ell to be either a &longs;treight Cylinder, or el&longs;e an upright

<lb/>Pri&longs;me</s>

<s><emph type="italics"/>The which propo&longs;ed and declared, I proceed to demonstrate the truth

<lb/>of what hath been hinted, forming the en&longs;uing Theoreme.<emph.end type="italics"/></s>

<s><emph type="italics"/>THEOREME I.<emph.end type="italics"/></s>

<s>The Ma&longs;s of the Water whicha&longs;cends in the &longs;ub

<lb/>merging of a Solid, Pri&longs;me or Cylinder, or that

<lb/>aba&longs;eth in taking it out, is le&longs;s than the Ma&longs;s of

<lb/>the &longs;aid Solid, &longs;o depre&longs;&longs;ed or advanced: and

<lb/>hath to it the &longs;ame proportion, that the Surface

<lb/>of the Water circumfu&longs;ing the Solid, hath to the

<lb/>&longs;ame circumfu&longs;ed Surface, together with the Ba&longs;e

<lb/>of the Solid.</s>

<s><margin.target id="marg1411"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he Proportion

<lb/>of the water rai

<lb/>&longs;ed to the <emph type="italics"/>S<emph.end type="italics"/>olid

<lb/>&longs;ubmerged.</s>

<s><emph type="italics"/>Let the Ve&longs;&longs;ell be A B C D, and in it the Water rai&longs;ed up to the

<lb/>Levell E F G, before the Solid Pri&longs;me H I K be therein immerged;

<lb/>but after that it is depre&longs;&longs;ed under Water, let the Water be rai&longs;ed as

<lb/>high as the Levell L M, the Solid H I K &longs;hall then be all under Water,

<lb/>and the Ma&longs;s of the elevated Water &longs;hall be L G, which is le&longs;s than the<emph.end type="italics"/>

<lb/><emph type="italics"/>Ma&longs;&longs;e of the Solid depre&longs;&longs;ed, namely of

<lb/>H I K, being equall to the only part E I K,

<lb/>which is contained under the fir&longs;t Levell

<lb/>E F G. </s><s>Which is manife&longs;t, becau&longs;e if

<lb/>the Solid H I K be taken out, the Water

<lb/>I G &longs;hall return into the place occupied by

<lb/>the Ma&longs;s E I K, where it was continuate be

<lb/>fore the &longs;ubmer&longs;ion of the Pri&longs;me. </s><s>And

<lb/>the Ma&longs;s L G being equall to the Ma&longs;s

<lb/>E K: adde thereto the Ma&longs;s E N, and it

<lb/>&longs;hall be the whole Ma&longs;s E M, compo&longs;ed of the parts of the Pri&longs;me E N,

<lb/>and of the Water N F, equall to the whole Solid H I K: And, there

<lb/>fore, the Ma&longs;s L G &longs;hall have the &longs;ame proportion to E M, as to the

<lb/>Ma&longs;s H I K: But the Ma&longs;s L G hath the &longs;ame proportion to the Ma&longs;s

<lb/>E M, as the Surface L M hath to the Surface M H: Therefore it is ma

<lb/>nife&longs;t, that the Ma&longs;s of Water repul&longs;ed L G, is in proportion to the Ma&longs;s

<lb/>of the Solid &longs;ubmerged H I K; as the Surface L M, namely, that of the

<lb/>Water ambient about the Sollid, to the whole Surface H M, compounded

<lb/>of the &longs;aid ambient water, and the Ba&longs;e of the Pri&longs;me H N. </s><s>But if we

<lb/>&longs;uppo&longs;e the fir&longs;t Levell of the Water the according to the Surface H M,

<lb/>and the Pri&longs;me allready &longs;ubmerged H I K; and after to be taken out and

<lb/>rai&longs;ed to E A O, and the Water to be faln from the fir&longs;t Levell H L M as

<lb/>low as E F G; It is manife&longs;t, that the Pri&longs;me E A O being the &longs;ame with

<lb/>H I K, its &longs;uperiour part H O, &longs;hall be equall to the inferiour E I K:

<lb/>and remove the common part E N, and, con&longs;equently, the Ma&longs;s of the

<lb/>Water L G is equall to the Ma&longs;s H O; and, therefore, le&longs;s than the

<lb/>Solid, which is without the Water, namely, the whole Pri&longs;me E A O, to

<lb/>which likewi&longs;e, the &longs;aid Ma&longs;s of Water abated L G, hath the &longs;ame propor

<lb/>tion, that the Surface of the Waters circumfu&longs;ed L M hath to the &longs;ame

<lb/>circumfu&longs;ed Surface, together with the Ba&longs;e of the Pri&longs;me A O: which

<lb/>hath the &longs;ame demon&longs;tration with the former ca&longs;e above.<emph.end type="italics"/></s>

<s><emph type="italics"/>And from hence is inferred, that the Ma&longs;s of the Water, that ri&longs;eth in

<lb/>the immer&longs;ion of the Solid, or that ebbeth in elevating it, is not equall to

<lb/>all the Ma&longs;s of the Solid, which is &longs;ubmerged or elevated, but to that

<lb/>part only, which in the immer&longs;ion is under the fir&longs;t Levell of the Water,

<lb/>and in the elevation remaines above the fir&longs;t Levell: Which is that

<lb/>which was to be demon&longs;trated. </s><s>We will now pur&longs;ue the things that

<lb/>remain.<emph.end type="italics"/></s>

<s>And fir&longs;t we will demon&longs;trate that,</s>

<s>THEOREME II.</s>

<s><emph type="italics"/>When in one of the above &longs;aid Ve&longs;&longs;els, of what ever<emph.end type="italics"/>

<lb/><emph type="italics"/>breadth, whether wide or narrow, there is placed &longs;uch

<lb/>a Pri&longs;me or Cylinder, inviron'd with Water, if we ele

<lb/>vate that Solid perpendicularly, the Water circumfu

<lb/>&longs;ed &longs;hall abate, and the Abatement of the Water,

<lb/>&longs;hall have the &longs;ame proportion to the Elevation of the

<lb/>Pri&longs;me, as one of the Ba&longs;es of the Pri&longs;me, hath to

<lb/>the Surface of the Water Circumfu&longs;ed.<emph.end type="italics"/></s>

<s><margin.target id="marg1412"></margin.target>The proportion

<lb/>of the water aba

<lb/>ted, to the Solid

<lb/>rai&longs;ed.</s>

<s>Imagine in the Ve&longs;&longs;ell, as is afore&longs;aid, the

<lb/>Pri&longs;me A C D B to be placed, and in the

<lb/>re&longs;t of the Space the Water to be dif

<lb/>fu&longs;ed as far as the Levell E A: and rai

<lb/>&longs;ing the Solid, let it be transferred to

<lb/>G M, and let the Water be aba&longs;ed from

<lb/>E A to N O: I &longs;ay, that the de&longs;cent of

<lb/>the Water, mea&longs;ured by the Line A O,

<lb/>hath the &longs;ame proportion to the ri&longs;e of the

<lb/>Pri&longs;me, mea&longs;ured by the Line G A, as the Ba&longs;e of the Solid G H

<lb/>hath to the Surface of the Water N O. </s><s>The which is manife&longs;t:

<lb/>becau&longs;e the Ma&longs;s of the Solid G A B H, rai&longs;ed above the fir&longs;t Levell

<lb/>E A B, is equall to the Ma&longs;s of Water that is aba&longs;ed E N O A.

<lb/>Therefore, E N O A and G A B H are two equall Pri&longs;mes; for of

<lb/>equall Pri&longs;mes, the Ba&longs;es an&longs;wer contrarily to their heights: There

<lb/>fore, as the Altitude A O is to the Altitude A G, &longs;o is the Superfi

<lb/>cies or Ba&longs;e G H to the Surface of the Water N O. </s><s>If therefore,

<lb/>for example, a Pillar were erected in a wa&longs;te Pond full of Water,

<lb/>or el&longs;e in a Well, capable of little more then the Ma&longs;s of the &longs;aid

<lb/>Pillar, in elevating the &longs;aid Pillar, and taking it out of the Water,

<lb/>according as it ri&longs;eth, the Water that invirons it will gradually abate,

<lb/>and the aba&longs;ement of the Water at the in&longs;tant of lifting out the

<lb/>Pillar, &longs;hall have the &longs;ame proportion, that the thickne&longs;s of the Pillar

<lb/>hath to the exce&longs;s of the breadth of the &longs;aid Pond or Well, above

<lb/>the thickne&longs;s of the &longs;aid Pillar: &longs;o that if the breadth of the Well

<lb/>were an eighth part larger than the thickne&longs;s of the Pillar, and the

<lb/>breadth of the Pond twenty five times as great as the &longs;aid thickne&longs;s,

<lb/>in the Pillars a&longs;cending one foot, the water in the Well &longs;hall de&longs;cend

<lb/>&longs;even foot, and that in the Pond only 1/25 of a foot.</s>

<s><margin.target id="marg1413"></margin.target>Why a Solid

<lb/>le&longs;s grave <emph type="italics"/>in &longs;pe

<lb/>cie<emph.end type="italics"/> than water,

<lb/>&longs;tayeth not un

<lb/>der water, in ve

<lb/>ry &longs;mall depthst.</s>

<s>This Demon&longs;trated, it will not be difficult to &longs;hew the true

<lb/>cau&longs;e, how it comes to pa&longs;s, that,</s>

<s>THEOREME III.</s>

<s><emph type="italics"/>A Pri&longs;me or regular Cylinder, of a &longs;ub&longs;tance &longs;pecifically

<lb/>le&longs;s grave than Water, if it &longs;hould be totally &longs;ubmerged

<lb/>in Water, &longs;tayes not underneath, but ri&longs;eth, though the

<lb/>Water circumfu&longs;ed be very little, and in ab&longs;olute

<lb/>Gravity, never &longs;o much inferiour to the Gravity of the

<lb/>&longs;aid Pri&longs;me.<emph.end type="italics"/></s>

<s>Let then the Pri&longs;me A E F B, be put into the Ve&longs;&longs;ell C D F B, the

<lb/>&longs;ame being le&longs;s grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than the Water: and let the

<lb/>Water infu&longs;ed ri&longs;e to the height of the Pri&longs;me: I &longs;ay, that the

<lb/>Pri&longs;me left at liberty, it &longs;hall ri&longs;e, being born up

<lb/>by the Water circumfu&longs;ed C D E A. </s><s>For the

<lb/>Water C E being &longs;pecifically more grave than

<lb/>the Solid A F, the ab&longs;olute weight of the water

<lb/>C E, &longs;hall have greater proportion to the ab&longs;o

<lb/>lute weight of the Pri&longs;me A F, than the Ma&longs;s

<lb/>C E hath to the Ma&longs;s A F (in regard the Ma&longs;s

<lb/>hath the &longs;ame proportion to the Ma&longs;s, that the

<lb/>weight ab&longs;olute hath to the weight ab&longs;olute,

<lb/>in ca&longs;e the Ma&longs;&longs;es are of the &longs;ame Gravity <emph type="italics"/>in &longs;pecie.<emph.end type="italics"/>) But

<lb/>the Ma&longs;s C E is to the Ma&longs;s A F, as the Surface of the water A C, is

<lb/>to the Superficies, or Ba&longs;e of the Pri&longs;me A B; which is the &longs;ame pro

<lb/>portion as the a&longs;cent of the Pri&longs;me when it ri&longs;eth, hath to the de&longs;cent

<lb/>of the water circumfu&longs;ed C E.</s>

<s>Therefore, the ab&longs;olute Gravity of the water C E, hath greater

<lb/>proportion to the ab&longs;olute Gravity of the Pri&longs;me A F; than the

<lb/>A&longs;cent of the Pri&longs;me A F, hath to the de&longs;cent of the &longs;aid

<lb/>water C E. </s><s>The Moment, therefore, compounded of the ab&longs;olute

<lb/>Gravity of the water C E, and of the Velocity of its de&longs;cent, whil&longs;t

<lb/>it forceably repul&longs;eth and rai&longs;eth the Solid A F, is greater than the

<lb/>Moment compounded of the ab&longs;olute Gravity of the Pri&longs;me A F, and

<lb/>of the Tardity of its a&longs;cent, with which Moment it contra&longs;ts and re

<lb/>fi&longs;ts the repul&longs;e and violence done it by the Moment of the water:

<lb/>Therefore, the Pri&longs;me &longs;hall be rai&longs;ed.

<s><margin.target id="marg1414"></margin.target>The Proportion

<lb/>according to

<lb/>which the Sub

<lb/>mer&longs;ion & Na

<lb/>tation of Solids

<s>It followes, now, that we proceed forward to demon&longs;trate more

<lb/>particularly, how much &longs;uch Solids &longs;hall be inferiour in Gravity to

<lb/>the water elevated; namely, what part of them &longs;hall re&longs;t &longs;ubmerged,

<lb/>and what &longs;hall be vi&longs;ible above the Surface of the water: but fir&longs;t

<lb/>it is nece&longs;&longs;ary to demon&longs;trate the &longs;ub&longs;equent Lemma.</s>

<s>LEMMA I.</s>

<s><emph type="italics"/>The ab&longs;olute Gravities of Solids, have a proportion com-<emph.end type="italics"/></s>

<lb/><emph type="italics"/>pounded of the proportions of their &longs;pecificall Gravities,

<lb/>and of their Ma&longs;&longs;es.<emph.end type="italics"/></s>

<s><margin.target id="marg1415"></margin.target>The ab&longs;olute

<lb/>Gravity of So

<lb/>lids, are in a pro

<lb/>portion com

<lb/>pounded of their

<lb/>Specifick Gravi

<lb/>ties, and of their

<lb/>Ma&longs;&longs;es.</s>

<s>Let A and B be two Solids. </s><s>I &longs;ay, that the Ab&longs;olute Gravity

<lb/>of A, hath to the Ab&longs;olute Gravity of B, a proportion com

<lb/>pounded of the proportions of the &longs;pecificall Gravity of A, to

<lb/>the Specificall Gravity of B, and of the Ma&longs;s

<lb/>A to the Ma&longs;s B. </s><s>Let the Line D have the

<lb/>&longs;ame proportion to E, that the &longs;pecifick

<lb/>Gravity of A, hath to the &longs;pecifick Gravity

<lb/>of B; and let E be to F, as the Ma&longs;s A to the

<lb/>Ma&longs;s B: It is manife&longs;t, that the proportion

<lb/>of D to F, is compounded of the proportions

<lb/>D and E; and E and F. </s><s>It is requi&longs;ite,

<lb/>therefore, to demon&longs;trate, that as D is to F, &longs;o the ab&longs;olute Gravity

<lb/>of A, is to the ab&longs;olute Gravity of B. </s><s>Take the Solid C, equall in

<lb/>Ma&longs;s to the Solid A, and of the &longs;ame Gravity <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> with the Solid

<lb/>B. Becau&longs;e, therefore, A and C are equall in Ma&longs;s, the ab&longs;olute

<lb/>Gravity of A, &longs;hall have to the ab&longs;olute Gravity of C, the &longs;ame pro

<lb/>portion, as the &longs;pecificall Gravity of A, hath to the &longs;pecificall Gravity

<lb/>of C, or of B, which is the &longs;ame <emph type="italics"/>in &longs;pecie<emph.end type="italics"/>; that is, as D is to E. And, be

<lb/>cau&longs;e, C and B are of the &longs;ame Gravity <emph type="italics"/>in &longs;pecie,<emph.end type="italics"/> it &longs;hall be, that as

<lb/>the ab&longs;olute weight of C, is to the ab&longs;olute weight of B, &longs;o the Ma&longs;s

<lb/>C, or the Ma&longs;s A, is to the Ma&longs;s B; that is, as the Line E to the Line

<lb/>F. </s><s>As therefore, the ab&longs;olute Gravity of A, is to the ab&longs;olute

<lb/>Gravity of C, &longs;o is the Line D to the Line E: and, as the ab&longs;olute

<lb/>Gravity of C, is to the ab&longs;olute Gravity of B, &longs;o is the Line E to the

<lb/>Line F: Therefore, by Equality of proportion, the ab&longs;olute Gra

<lb/>vity of A, is to the ab&longs;olute Gravity of B, as the Line D to the

<lb/>Line F: which was to be demon&longs;trated. </s><s>I proceed now to demon

<lb/>&longs;trate, how that,</s>

<s>THEOREME IV.

<s><margin.target id="marg1416"></margin.target>The proportion

<lb/>of water requi

<lb/>&longs;ite to make a

<lb/>Solid &longs;wim.</s>

<s><emph type="italics"/>If a Solid, Cylinder, or Pri&longs;me, le&longs;&longs;e grave &longs;pecifically

<lb/>than the Water, being put into a Ve&longs;&longs;el, as above, of

<lb/>what&longs;oever greatne&longs;&longs;e, and the Water, be afterwards

<lb/>infu&longs;ed, the Solid &longs;hall re&longs;t in the bottom, unrai&longs;ed, till

<lb/>the Water arrive to that part of the Altitude, of the

<lb/>&longs;aid Pri&longs;me, to which its whole Altitude hath the

<lb/>&longs;ame proportion, that the Specificall Gravity of the

<lb/>Water, hath to the Specificall Gravity of the &longs;aid

<lb/>Solid: but infu&longs;ing more Water, the Solid &longs;hall a&longs;cend.<emph.end type="italics"/></s>

<s>Let the Ve&longs;&longs;ell be M L G N of any bigne&longs;s, and let there be pla

<lb/>ced in it the Solid Pri&longs;me D F G E, le&longs;s grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than the

<lb/>water; and look what proportion the <emph type="italics"/>S<emph.end type="italics"/>pecificall Gravity of

<lb/>the water, hath to that of the Pri&longs;me, &longs;uch let the Altitude D F, have

<lb/>to the Altitude F B. </s><s>I &longs;ay, that infu&longs;ing water to the Altitude F B,

<lb/>the Solid D G &longs;hall not float, but &longs;hall &longs;tand in <emph type="italics"/>Equilibrium,<emph.end type="italics"/> &longs;o, that

<lb/>that every little quantity of water, that is infu&longs;ed, &longs;hall rai&longs;e it. </s><s>Let

<lb/>the water, therefore, be infu&longs;ed to the Levell A B C, and, becau&longs;e

<lb/>the Specifick Gravity of the Solid D G, is to the Specifick Gravity of

<lb/>the water, as the altitude B F is to the altitude F D; that is, as the Ma&longs;s

<lb/>B G to the Ma&longs;s G D; as the proportion of the Ma&longs;s B G is to the

<lb/>Ma&longs;s G D, as the proportion of the Ma&longs;s G D is to the Ma&longs;s A F, they

<lb/>compo&longs;e the Proportion of the Ma&longs;s B G to the Ma&longs;s A F. Therefore,

<lb/>the Ma&longs;s B G is to the Ma&longs;s A F, in a proportion compounded of the

<lb/>proportions of the Specifick Gravity of the Solid G D, to the Speci

<lb/>fick Gravity of the water, and of the Ma&longs;s G D

<lb/>to the Ma&longs;s A F: But the &longs;ame proportions

<lb/>of the Specifick Gravity of G D, to the Specifick

<lb/>Gravity of the water, and of the Ma&longs;s G D to

<lb/>the Ma&longs;s A F, do al&longs;o by the precedent <emph type="italics"/>Lemma,<emph.end type="italics"/>

<lb/>compound the proportion of the ab&longs;olute Gra

<lb/>vity of the Solid D G, to the ab&longs;olute Gravity

<lb/>of the Ma&longs;s of the water A F: Therefore,

<lb/>as the Ma&longs;s B G is to the Ma&longs;s A F, &longs;o is the

<lb/>Ab&longs;olute Gravity of the Solid D G, to the Ab

<lb/>&longs;olute Gravity of the Ma&longs;s of the water A F. </s><s>But as the Ma&longs;s B G

<lb/>is to the Ma&longs;s A F; &longs;o is the Ba&longs;e of the Pri&longs;me D E, to the Surface

<lb/>of the water AB; and &longs;o is the de&longs;cent of the water A B, to the

<lb/>Elevation of the Pri&longs;me D G; Therefore, the de&longs;cent of the

<pb pagenum="415"/>water is to the elevation of the Pri&longs;me, as the ab&longs;olute Gravity of

<lb/>the Pri&longs;me, is to the ab&longs;olute Gravity of the water: Therefore, the

<lb/>Moment re&longs;ulting from the ab&longs;olute Gravity of the water A F, and

<lb/>the Velocity of the Motion of declination, with which Moment it

<lb/>forceth the Pri&longs;me D G, to ri&longs;e and a&longs;cend, is equall to the Moment

<lb/>that re&longs;ults from the ab&longs;olute Gravity of the Pri&longs;me D G, and from

<lb/>the Velocity of the Motion, wherewith being rai&longs;ed, it would a&longs;cend:

<lb/>with which Moment it re&longs;i&longs;ts its being rai&longs;ed: becau&longs;e, therefore,

<lb/>&longs;uch Moments are equall, there &longs;hall be an <emph type="italics"/>Equilibrium<emph.end type="italics"/> between the

<lb/>water and the Solid. </s><s>And, it is manife&longs;t, that putting a little more

<lb/>water unto the other A F, it will increa&longs;e the Gravity and Moment,

<lb/>whereupon the Pri&longs;me D G, &longs;hall be overcome, and elevated till that

<lb/>the only part B F remaines &longs;ubmerged. </s><s>Which is that that was to

<lb/>be demon&longs;trated.</s>

<s>COROLLARY I.</s>

<s><emph type="italics"/>By what hath been demon&longs;trated, it is manife&longs;t, that Solids le&longs;s grave<emph.end type="italics"/></s>

<lb/>in &longs;pecie <emph type="italics"/>than the water, &longs;ubmerge only &longs;o far, that as much water in

<lb/>Ma&longs;s, as is the part of the Solid &longs;ubmerged, doth weigh ab&longs;olutely as

<lb/>much as the whole Solid.<emph.end type="italics"/></s>

<s><margin.target id="marg1417"></margin.target><emph type="italics"/>H<emph.end type="italics"/>ow far Solids

<lb/>le&longs;s grave <emph type="italics"/>in &longs;pe

<lb/>cie<emph.end type="italics"/> than water,

<lb/>do &longs;ubmerge.</s>

<s>For, it being &longs;uppo&longs;ed, that the Specificall Gravity of the water,

<lb/>is to the Specificall Gravity of the Pri&longs;me D G, as the Altitude

<lb/>D F, is to the Altitude F B; that is, as the Solid D G is to the

<lb/>Solid B G; we might ea&longs;ily demon&longs;trate, that as much water in Ma&longs;s

<lb/>as is equall to the Solid B G, doth weigh ab&longs;olutely as much as the

<lb/>whole Solid D G; For, by the <emph type="italics"/>Lemma<emph.end type="italics"/> foregoing, the Ab&longs;olute

<lb/>Gravity of a Ma&longs;s of water, equall to the Ma&longs;s B G, hath to the Ab

<lb/>&longs;olute Gravity of the Pri&longs;me D G, a proportion compounded of the

<lb/>proportions, of the Ma&longs;s B G to the Ma&longs;s G D, and of the Specifick

<lb/>Gravit 7 of the water, to the Specifick Gravity of the Pri&longs;me: But

<lb/>the Gravity <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> of the water, to the Gravity <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> of the

<lb/>Pri&longs;me, is &longs;uppo&longs;ed to be as the Ma&longs;s G D to the Ma&longs;s G B. There

<lb/>fore, the Ab&longs;olute Gravity of a Ma&longs;s of water, equall to the Ma&longs;s

<lb/>B G, is to the Ab&longs;olute Gravity of the Solid D G, in a proportion

<lb/>compounded of the proportions, of the Ma&longs;s B G to the Ma&longs;s G D,

<lb/>and of the Ma&longs;s D G to the Ma&longs;s G B; which is a proportion of

<lb/>equalitie. </s><s>The Ab&longs;olute Gravity, therefore, of a Ma&longs;s of Water

<lb/>equall to the part of the Ma&longs;s of the Pri&longs;me B G, is equall to the Ab

<lb/>&longs;olute Gravity of the whole Solid D G.</s>

<s>COROLLARY II.

<s><margin.target id="marg1418"></margin.target><emph type="italics"/>A<emph.end type="italics"/> Rule to equi

<lb/>librate <emph type="italics"/>S<emph.end type="italics"/>olids in

<lb/>the water.</s>

<s><emph type="italics"/>It followes, moreover, that a Solid le&longs;s grave than the water, being put

<lb/>into a Ve&longs;&longs;ell of any imaginable greatne&longs;s, and water being circumfu&longs;ed

<lb/>about it to &longs;uch a height, that as much water in Ma&longs;s, as is the part of

<lb/>the Solid &longs;ubmerged, doth/> weigh ab&longs;olutely as much as the whole Solid;

<lb/>it &longs;hall by that water be ju&longs;tly &longs;u&longs;tained, be the circumfu&longs;ed Water in

<lb/>quantity greater or le&longs;&longs;er.<emph.end type="italics"/></s>

<s>For, if the Cylinder or Pri&longs;me M, le&longs;s grave than the water, <emph type="italics"/>v.

<lb/></s><s>gra.<emph.end type="italics"/> in Sub&longs;equiteriall proportion, &longs;hall be put into the capaci

<lb/>ous Ve&longs;&longs;ell A B C D, and the water rai&longs;ed about it, to three

<lb/>quarters of its height, namely, to its Levell A D: it &longs;hall be &longs;u&longs;tained

<lb/>and exactly poy&longs;ed in <emph type="italics"/>Equi

<lb/>librium.<emph.end type="italics"/> The &longs;ame will hap

<lb/>pen, if the Ve&longs;&longs;ell E N S F

<lb/>were very &longs;mall, &longs;o, that be

<lb/>tween the Ve&longs;&longs;ell and the So

<lb/>lid M, there were but a very

<lb/>narrow &longs;pace, and only capable of &longs;o much water, as the hundredth

<lb/>part of the Ma&longs;s M, by which it &longs;hould be likewi&longs;e rai&longs;ed and erected,

<lb/>as before it had been elevated to three fourths of the height of the

<lb/>Solid: which to many at the fir&longs;t &longs;ight, may &longs;eem a notable Paradox,

<lb/>and beget a conceit, that the Demon&longs;tration of the&longs;e effects, were

<lb/>&longs;ophi&longs;ticall and fallacious: but, for tho&longs;e who &longs;o repute it, the Ex

<lb/>periment is a means that may fully &longs;atisfie them. </s><s>But he that &longs;hall

<lb/>but comprehend of what Importance Velocity of Motion is, and how

<lb/>it exactly compen&longs;ates the defect and want of Gravity, will cea&longs;e to

<lb/>wonder, in con&longs;idering that at the elevation of the Solid M, the great

<lb/>Ma&longs;s of water A B C D abateth very little, but the little Ma&longs;s of

<lb/>water E N S F decrea&longs;eth very much, and in an in&longs;tant, as the Solid

<lb/>M before did li&longs;e, howbeit for a very &longs;hort &longs;pace: Whereupon the

<lb/>Moment, compounded of the &longs;mall Ab&longs;olute Gravity of the water

<lb/>E N S F, and of its great Velocity in ebbing, equalizeth the Force and

<lb/>and Moment, that re&longs;ults from the compo&longs;icion of the immen&longs;e Gra

<lb/>vity of the water A B C D, with its great &longs;lowne&longs;&longs;e of ebbing;

<lb/>&longs;ince that in the Elevation of the Sollid M, the aba&longs;ement of the le&longs;</s>

<lb/>&longs;er water E S, is performed ju&longs;t &longs;o much more &longs;wiftly than the great

<lb/>Ma&longs;s of water A C, as this is more in Ma&longs;s than that which we thus

<lb/>demon&longs;trate.</s>

<s><margin.target id="marg1419"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he proportion

<lb/>according to

<lb/>which water ri

<lb/>&longs;eth and falls in

<lb/>different Ve&longs;&longs;els

<lb/>at the Immer&longs;i

<lb/>on and Elevati

<lb/>on of <emph type="italics"/>s<emph.end type="italics"/>olids.</s>

<s>In the ri&longs;ing of the Solid M, its elevation hath the &longs;ame proportion

<lb/>to the circumfu&longs;ed water E N S F, that the Surface of the &longs;aid water,

<lb/>hath to the Superficies or Ba&longs;e of the &longs;aid Solid M; which Ba&longs;e hath

<lb/>the &longs;ame proportion to the Surface of the water A D, that the aba&longs;e

<pb pagenum="417"/>ment or ebbing of the water A C, hath to the ri&longs;e or elevation of

<lb/>the &longs;aid Solid M. Therefore, by Perturbation of proportion, in the

<lb/>a&longs;cent of the &longs;aid Solid M, the aba&longs;ement of the water A B C D, to

<lb/>the aba&longs;ement of the water E N S F, hath the &longs;ame proportion, that the

<lb/>Surface of the water E F, hath to the Surface of the water A D;

<lb/>that is, that the whole Ma&longs;s of the water E N S F, hath to the whole

<lb/>Ma&longs;s A B C D, being equally high: It is manife&longs;t, therefore, that

<lb/>in the expul&longs;ion and elevation of the Solid M, the water E N S F

<lb/>&longs;hall exceed in Velocity of <emph type="italics"/>M<emph.end type="italics"/>otion the water A B C D, a&longs;much as it

<lb/>on the other &longs;ide is exceeded by that in quantity: whereupon their

<lb/>Moments in &longs;uch operations, are mutually equall.</s>

<s><emph type="italics"/>And, for ampler confirmation, and clearer explication of this, let us

<lb/>con&longs;ider the pre&longs;ent Figure, (which if I be not deceived, may &longs;erve to

<lb/>detect the errors of &longs;ome Practick Mechanitians, who upon a fal&longs;e founda

<lb/>tion &longs;ome times attempt impo&longs;&longs;ible enterprizes,) in which, unto the large

<lb/>Ve&longs;&longs;ell E I D F, the narrow Funnell or Pipe I C A B is continued, and &longs;up

<lb/>po&longs;e water infu&longs;ed into them, unto the Levell L G H, which water &longs;hall

<lb/>re&longs;t in this po&longs;ition, not without admiration in &longs;ome, who cannot conceive<emph.end type="italics"/>

<lb/><emph type="italics"/>how it can be, that the heavie charge of the great

<lb/>Ma&longs;s of water G D, pre&longs;&longs;ing downwards, &longs;hould

<lb/>not elevate and repul&longs;e the little quantity of the

<lb/>other, contained in the Funnell or Pipe C L, by

<lb/>which the de&longs;cent of it is re&longs;isted and hindered:

<lb/>But &longs;uch wonder &longs;hall cea&longs;e, if we begin to &longs;uppo&longs;e

<lb/>the water G D to be aba&longs;ed only to Q D, and

<lb/>&longs;hall afterwards con&longs;ider, what the water C L

<lb/>hath done, which to give place to the other, which

<lb/>is de&longs;cended from the Levell G H, to the Levell

<lb/>Q O, &longs;hall of nece&longs;&longs;ity have a&longs;cended in the &longs;ame

<lb/>time, from the Levell Lunto A B. </s><s>And the

<lb/>a&longs;cent L B, &longs;hall be &longs;o much greater than the de

<lb/>&longs;cent G Q, by how much the breadth of the Ve&longs;&longs;ell

<lb/>G D, is greater than that of the Funnell I C;

<lb/>which, in &longs;umme, is as much as the water G D,

<lb/>is more than the water L C: but in regard that the Moment of the Velocity

<lb/>of the Motion, in one Moveable, compen&longs;ates that of the Gravity of ano

<lb/>ther, what wonder is it, if the &longs;wift a&longs;cent of the le&longs;&longs;er Water C L, &longs;hall

<lb/>re&longs;i&longs;t the &longs;low de&longs;cent of the greater G D<emph.end type="italics"/>?</s>

<s>The &longs;ame, therefore, happens in this operation, as in the Stilliard,

<lb/>in which a weight of two pounds counterpoy&longs;eth an other of 200,

<lb/>asoften as that &longs;hall move in the &longs;ame time, a &longs;pace 100 times great

<lb/>er than this: which falleth out when one Arme of the Beam is an

<pb pagenum="418"/>hundred times as long as the other. </s><s>Let the erroneous opinion o

<lb/>tho&longs;e therefore cea&longs;e, who hold that a Ship is better, and ea&longs;ter born

<lb/>up in a great abundance of water, then in a le&longs;&longs;er quantity, (<emph type="italics"/>this was

<lb/>believed by<emph.end type="italics"/> Ari&longs;totle <emph type="italics"/>in his Problems, Sect. </s><s>23, Probl.<emph.end type="italics"/> 2.) it being or

<lb/>the contrary true, that its po&longs;&longs;ible, that a Ship may as well float in

<lb/>ten Tun of water, as in an Ocean.

<s><margin.target id="marg1420"></margin.target>A &longs;hip flotes as

<lb/>well in ten Tun

<lb/>of water as in an

<lb/>Ocean.</s>

<s><margin.target id="marg1421"></margin.target>A Solid &longs;peci

<lb/>fiaclly graver

<lb/>than the water,

<lb/>cannot be born

<lb/>up by any quan

<s>But following our matter, I &longs;ay, that by what hath been hitherto

<lb/>demon&longs;trated, we may under&longs;tand how, that</s>

<s>COROLLARY III.</s>

<s><emph type="italics"/>One of the above named Solids, when more grave<emph.end type="italics"/> in &longs;pecie <emph type="italics"/>than the water,

<lb/>can never be &longs;u&longs;tained, by any whatever quantity of it.<emph.end type="italics"/></s>

<s>For having &longs;een how that the Moment wherewith &longs;uch a Solid

<lb/>as grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> as the water, contra&longs;ts with the Moment of any Ma&longs;s

<lb/>of water what&longs;oever, is able to retain it, even to its totall Submer&longs;ion:

<lb/>without its ever a&longs;cending; it remaineth, manife&longs;t, that the water is

<lb/>far le&longs;s able to rai&longs;e it up, when it exceeds the &longs;ame <emph type="italics"/>in &longs;pecie<emph.end type="italics"/>: &longs;o,

<lb/>that though you infu&longs;e water till its totall Submer&longs;ion, it &longs;hall &longs;till

<lb/>&longs;tay at the Bottome, and with &longs;uch Gravity, and Re&longs;i&longs;tance to Eleva

<lb/>tion, as is the exce&longs;s of its Ab&longs;olute Gravity, above the Ab&longs;olute Gra

<lb/>vity of a Ma&longs;s equall to it, made of water, or of a Matter <emph type="italics"/>in &longs;pecie<emph.end type="italics"/>

<lb/>equally grave with the water: and, though you &longs;hould moreover

<lb/>adde never &longs;o much water above the Levell of that which equalizeth

<lb/>the Altitude of the Solid, it &longs;hall not, for all that, encrea&longs;e the Pre&longs;&longs;ion

<lb/>or Gravitation, of the parts circumfu&longs;ed about the &longs;aid Solid, by

<lb/>which greater pre&longs;&longs;ion, it might come to be repul&longs;ed, becau&longs;e, the

<lb/>Re&longs;i&longs;tance is not made, but only by tho&longs;e parts of the water, which

<lb/>at the Motion of the &longs;aid Solid do al&longs;o move, and the&longs;e are tho&longs;e

<lb/>only, which are comprehended by the two Superficies equidi&longs;tant to

<lb/>the Horizon, and their parallels, that comprehend the Altitude of the

<lb/>Solid immerged in the water.</s>

<s>I conceive, I have by this time &longs;ufficiently declared and opened

<lb/>the way to the contemplation of the true, intrin&longs;ecall and proper

<lb/>Cau&longs;es of diver&longs;e Motions, and of the Re&longs;t of many Solid Bodies in

<lb/>diver&longs;e <emph type="italics"/>Mediums,<emph.end type="italics"/> and particularly in the water, &longs;hewing how all ii

<lb/>effect, depend on the mutuall exce&longs;&longs;es of the Gravity of the Movea

<lb/>bles and of the <emph type="italics"/>Mediums<emph.end type="italics"/>: and, that which did highly import, re

<lb/>moving the Objection, which peradventure would have begotter

<lb/>much doubting, and &longs;cruple in &longs;ome, about the verity of my Con

<lb/>clu&longs;ion, namely, how that notwith&longs;tanding, that the exce&longs;s of the

<lb/>Gravity of the water, above the Gravity of the Solid, demitted into

<lb/>it, be the cau&longs;e of its floating and ri&longs;ing from the Bottom to the Sur

<lb/>face, yet a quantity of water, that weighs not ten pounds, can rai&longs;e

<pb pagenum="419"/>Solid that weighs above 100 pounds: in that we have demon&longs;tra

<lb/>ted, That it &longs;ufficeth, that &longs;uch difference be found between the

<lb/>Specificall Gravities of the <emph type="italics"/>Mediums<emph.end type="italics"/> and Moveables, let the particular

<lb/>and ab&longs;olute Gravities be what they will: in&longs;omuch, that a Solid,

<lb/>provided that it be Specifically le&longs;s grave than the water, although

<lb/>its ab&longs;olute weight were 1000 pounds, yet may it be born up and

<lb/>elevated by ten pounds of water, and le&longs;s: and on the contrary, a

<lb/>nother Solid, &longs;o that it be Specifically more grave than the water,

<lb/>though in ab&longs;olute Gravity it were not above a pound, yet all the

<lb/>water in the Sea, cannot rai&longs;e it from the Bottom, or float it. </s><s>This

<lb/>&longs;ufficeth me, for my pre&longs;ent occa&longs;ion, to have, by the above declared

<lb/>Examples, di&longs;covered and demon&longs;trated, without extending &longs;uch

<lb/>matters farther, and, as I might have done, into a long Treati&longs;e:

<lb/>yea, but that there was a nece&longs;&longs;ity of re&longs;olving the above propo&longs;ed

<lb/>doubt, I &longs;hould have contented my &longs;elf with that only, which is

<lb/>demon&longs;trated by <emph type="italics"/>Archimedes,<emph.end type="italics"/> in his fir&longs;t Book <emph type="italics"/>De In&longs;identibus hu

<lb/>mido<emph.end type="italics"/>: where in generall termes he infers and confirms the &longs;ame </s>

<lb/>Conclu&longs;ions, namely, that Solids (<emph type="italics"/>a<emph.end type="italics"/>) le&longs;s grave than water, &longs;wim or

<lb/>float upon it, the (<emph type="italics"/>b<emph.end type="italics"/>) more grave go to the Bottom, and the (<emph type="italics"/>c<emph.end type="italics"/>) e

<lb/>qually grave re&longs;t indifferently in all places, yea, though they &longs;hould

<lb/>be wholly under water.</s>

<s><margin.target id="marg1422"></margin.target><emph type="italics"/>Of Natation<emph.end type="italics"/></s>

<s><margin.target id="marg1424"></margin.target>(b) <emph type="italics"/>Id. </s><s>Lib. </s><s>1.

<s><margin.target id="marg1425"></margin.target>(c) <emph type="italics"/>Id. </s><s>Lib. 1.

<s>But, becau&longs;e that this Doctrine of <emph type="italics"/>Archimedes,<emph.end type="italics"/> peru&longs;ed, tran&longs;cri

<lb/>bed and examined by <emph type="italics"/>Signor France&longs;co Buonamico,<emph.end type="italics"/> in his <emph type="italics"/>fifth Book

<lb/>of Motion, Chap.<emph.end type="italics"/> 29, and afterwards by him confuted, might by the

<lb/>Authority of &longs;o renowned, and famous a Philo&longs;opher, be rendered

<lb/>dubious, and &longs;u&longs;pected of fal&longs;ity; I have judged it nece&longs;&longs;ary to de

<lb/>fend it, if I am able &longs;o to do, and to clear <emph type="italics"/>Archimedes,<emph.end type="italics"/> from tho&longs;e

<lb/>cen&longs;ures, with which he appeareth to be charged. <emph type="italics"/>Buonamico<emph.end type="italics"/> re

<lb/>jecteth the Doctrine of <emph type="italics"/>Archimedes,<emph.end type="italics"/> fir&longs;t, as not con&longs;entaneous with

<lb/>the Opinion of <emph type="italics"/>Aristotle,<emph.end type="italics"/> adding, that it was a &longs;trange thing to him,

<lb/>that the Water &longs;hould exceed the Earth in Gravity, &longs;eeing on the

<lb/>contrary, that the Gravity of water, increa&longs;eth, by means of the parti

<lb/>cipation of Earth. </s><s>And he &longs;ubjoyns pre&longs;ently after, that he was

<lb/>not &longs;atisfied with the Rea&longs;ons of <emph type="italics"/>Archimedes,<emph.end type="italics"/> as not being able with

<lb/>that Doctrine, to a&longs;&longs;ign the cau&longs;e whence it comes, that a Boat and

<lb/>a Ve&longs;&longs;ell, which otherwi&longs;e, floats above the water, doth &longs;ink to the

<lb/>Bottom, if once it be filled with water; that by rea&longs;on of the e

<lb/>quality of Gravity, between the water within it, and the other water

<lb/>without, it &longs;hould &longs;tay a top; but yet, neverthele&longs;s, we &longs;ee it to go to

<lb/>the Bottom.

<s><margin.target id="marg1426"></margin.target>The <emph type="italics"/>Authors<emph.end type="italics"/>

<lb/>defence of <emph type="italics"/>Ar

<lb/>chimedes<emph.end type="italics"/> his Do

<lb/>ctrine, again&longs;t

<lb/>the oppo&longs;itions

<lb/>of <emph type="italics"/>Buonamico.<emph.end type="italics"/></s>

<s><margin.target id="marg1427"></margin.target>His fir&longs;t Objecti

<lb/>on again&longs;t the

<lb/>Doctrine of <emph type="italics"/>Ar

<lb/>chimedes.<emph.end type="italics"/></s>

<s><margin.target id="marg1428"></margin.target>His Second Ob

<lb/>jection.</s>

<s><margin.target id="marg1429"></margin.target>His third Obje

<lb/>ction.</s>

<s><margin.target id="marg1430"></margin.target>His &longs;ourth Ob

<lb/>jection.</s>

<s>He farther addes, that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> had clearly confuted the Ancients,

<lb/>who &longs;aid, that light Bodies moved upwards, driven by the impul&longs;e </s>

<lb/>of the more grave Ambient: which if it were &longs;o, it &longs;hould &longs;eem of

<lb/>nece&longs;&longs;ity to follow, that all naturall Bodies are by nature heavy,

<pb pagenum="420"/>and none light: For that the &longs;ame would befall the Fire and Air,

<lb/>if put in the Bottom of the water. </s><s>And, howbeit, <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> grants

<lb/>a Pul&longs;ion in the Elements, by which the Earth is reduced into a Sphe

<lb/>ricall Figure, yet neverthele&longs;s, in his judgement, it is not &longs;uch that it

<lb/>can remove grave Bodies from their naturall places, but rather, that

<lb/>it &longs;end them toward the Centre, to which (as he &longs;omewhat ob&longs;curely

<lb/>continues to &longs;ay,) the water principally moves, if it in the interim

<lb/>meet not with &longs;omething that re&longs;i&longs;ts it, and, by its Gravity, thru&longs;ts

<lb/>it out of its place: in which ca&longs;e, if it cannot directly, yet at lea&longs;t

<lb/>as well as it can, it tends to the Centre: but it happens, that light

<lb/>Bodies by &longs;uch Impul&longs;ion, do all a&longs;cend upward: but this properly

<lb/>they have by nature, as al&longs;o, that other of &longs;wimming. </s><s>He concludes,

<lb/>la&longs;tly, that he concurs with <emph type="italics"/>Archimedes<emph.end type="italics"/> in his Conclu&longs;ions; but not

<lb/>in the Cau&longs;es, which he would referre to the facile and difficult Sepa

<lb/>ration of the <emph type="italics"/>Medium,<emph.end type="italics"/> and to the predominance of the Elements, &longs;o

<lb/>that when the Moveable &longs;uperates the power of the <emph type="italics"/>Medium<emph.end type="italics"/>; as for

<lb/>example, Lead doth the Continuity of water, it &longs;hall move thorow it,

<lb/>el&longs;e not.</s>

<s><margin.target id="marg1431"></margin.target>The <emph type="italics"/>Ancients<emph.end type="italics"/>

<lb/>denved <emph type="italics"/>Ao&longs;olute<emph.end type="italics"/>

<lb/>Levity.</s>

<s><margin.target id="marg1432"></margin.target>The cau&longs;es of

<lb/>Natation & Sub

<lb/>mer&longs;ion, accord

<lb/>ing to the Peri

<lb/>pateticks.</s>

<s>This is all that I have been able to collect, as produced again&longs;t

<lb/><emph type="italics"/>Archimedes<emph.end type="italics"/> by <emph type="italics"/>Signor Buonamico<emph.end type="italics"/>: who hath not well ob&longs;erved the

<lb/>Principles and Suppo&longs;itions of <emph type="italics"/>Archimedes<emph.end type="italics"/>; which yet mu&longs;t be

<lb/>fal&longs;e, if the Doctrine be fal&longs;e, which depends upon them; but is

<lb/>contented to alledge therein &longs;ome Inconveniences, and &longs;ome Repug

<lb/>nances to the Doctrine and Opinion of <emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/> In an&longs;wer to which

<lb/>Objections, I &longs;ay, fir&longs;t, That the being of <emph type="italics"/>Archimedes<emph.end type="italics"/> Doctrine, &longs;im

<lb/>ply different from the Doctrine of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> ought not to move any

<lb/>to &longs;u&longs;pect it, there being no cau&longs;e, why the Authority of this &longs;hould

<lb/>be preferred to the Authority of the other: but, becau&longs;e, where the

<lb/>decrees of Nature are indifferently expo&longs;ed to the intellectuall eyes of

<lb/>each, the Authority of the one and the other, lo&longs;eth all anthentical

<lb/>ne&longs;s of Per&longs;wa&longs;ion, the ab&longs;olute power re&longs;iding in Rea&longs;on; therefore

<lb/>I pa&longs;s to that which he alledgeth in the &longs;econd place, as an ab&longs;urd con

<lb/>&longs;equent of the Doctrine of <emph type="italics"/>Archimedes,<emph.end type="italics"/> namely, That water &longs;hould

<lb/>be more grave than Earth. </s><s>But I really find not, that ever <emph type="italics"/>Archi

<lb/>medes<emph.end type="italics"/> &longs;aid &longs;uch a thing, or that it can be rationally deduced from his

<lb/>Conclu&longs;ions: and if that were manife&longs;t unto me, I verily believe, I

<lb/>&longs;hould renounce his Doctrine, as mo&longs;t erroneous. </s><s>Perhapsthis Dedu

<lb/>ction of <emph type="italics"/>Buonamico,<emph.end type="italics"/> is founded upon that which he citeth of the Ve

<lb/>&longs;&longs;el, which &longs;wims as long as its voyd of water, but once full it &longs;inks to

<lb/>the Bottom, and under&longs;tanding it of a Ve&longs;&longs;el of Earth, he infers again&longs;t

<lb/><emph type="italics"/>Archimedes<emph.end type="italics"/> thus: Thou &longs;ay&longs;t that the Solids which &longs;wim, are le&longs;s grave

<lb/>than water: this Ve&longs;&longs;ell &longs;wimmeth: therefore, this Ve&longs;&longs;ell is le&longs;&longs;e grave

<lb/>than water. </s><s>If this be the Illation. </s><s>I ea&longs;ily an&longs;wer, granting that this

<lb/>Ve&longs;&longs;ell is le&longs;&longs;e grave than water, and denying the other con&longs;equence,

<pb pagenum="421"/>namely, that Earth is le&longs;s Grave than Water. </s><s>The Ve&longs;&longs;el that &longs;wims

<lb/>occupieth in the water, not only a place equall to the Ma&longs;s of the

<lb/>Earth, of which it is formed; but equall to the Earth and to the Air

<lb/>together, contained in its concavity. </s><s>And, if &longs;uch a Ma&longs;s compoun

<lb/>ded of Earth and Air, &longs;hall be le&longs;s grave than &longs;uch another quantity

<lb/>of water, it &longs;hall &longs;wim, and &longs;hall accord with the Doctrine of <emph type="italics"/>Archi

<lb/>medes<emph.end type="italics"/>; but if, again, removing the Air, the Ve&longs;&longs;ell &longs;hall be filled

<lb/>with water, &longs;o that the Solid put in the water, be nothing but

<lb/>Earth, nor occupieth other place, than that which is only po&longs;&longs;e&longs;t by

<lb/>Earth, it &longs;hall then go to the Bottom, by rea&longs;on that the Earth is

<lb/>heavier than the water: and this corre&longs;ponds well with the meaning

<lb/>of <emph type="italics"/>Archimedes.<emph.end type="italics"/> See the &longs;ame effect illu&longs;trated, with &longs;uch another

<lb/>Experiment, In pre&longs;&longs;ing a Viall Gla&longs;s to the Bottom of the water,

<lb/>when it is full of Air, it will meet with great re&longs;i&longs;tance, becau&longs;e it is

<lb/>not the Gla&longs;s alone, that is pre&longs;&longs;ed under water, but together with

<lb/>the Gla&longs;s a great Ma&longs;s of Air, and &longs;uch, that if you &longs;hould take as

<lb/>much water, as the Ma&longs;s of the Gla&longs;s, and of the Air contained in it,

<lb/>you would have a weight much greater than that of the Viall, and of

<lb/>its Air: and, therefore, it will not &longs;ubmerge without great violence:

<lb/>but if we demit only the Gla&longs;s into the water, which &longs;hall be when

<lb/>you &longs;hall fill the Gla&longs;s with water, then &longs;hall the Gla&longs;s de&longs;cend to

<lb/>the Bottom; as &longs;uperiour in Gravity to the water.</s>

<s><margin.target id="marg1433"></margin.target>The Authors an

<lb/>&longs;wer to the fir&longs;t

<lb/>Objection.</s>

<s><margin.target id="marg1434"></margin.target>The Authors an

<lb/>&longs;wer to the &longs;e

<lb/>cond Objection.</s>

<s>Returning, therefore, to our fir&longs;t purpo&longs;e; I &longs;ay, that Earth is

<lb/>more grave than water, and that therefore, a Solid of Earth goeth to

<lb/>the bottom of it; but one may po&longs;&longs;ibly make a compo&longs;ition of Earth

<lb/>and Air, which &longs;hall be le&longs;s grave than a like Ma&longs;s of Water; and

<lb/>this &longs;hall &longs;wim: and yet both this and the other experiment &longs;hall

<lb/>very well accord with the Doctrine of <emph type="italics"/>Archimedes.<emph.end type="italics"/> But becau&longs;e that

<lb/>in my judgment it hath nothing of difficulty in it, I will not po&longs;itive

<lb/>ly affirme that <emph type="italics"/>Signor Buonamico,<emph.end type="italics"/> would by &longs;uch a di&longs;cour&longs;e object

<lb/>unto <emph type="italics"/>Archimedes<emph.end type="italics"/> the ab&longs;urdity of inferring by his doctrine, that Earth

<lb/>was le&longs;s grave than Water, though I know not how to conceive what

<lb/>other accident he could have induced thence.</s>

<s>Perhaps &longs;uch a Probleme (in my judgement fal&longs;e) was read by

<lb/><emph type="italics"/>Signor Buonamico<emph.end type="italics"/> in &longs;ome other Author, by whom peradventure it

<lb/>was attributed as a &longs;ingular propertie, of &longs;ome particular Water, and

<lb/>&longs;o comes now to be u&longs;ed with a double errour in confutation of <emph type="italics"/>Ar

<lb/>chimedes,<emph.end type="italics"/> &longs;ince he &longs;aith no &longs;uch thing, nor by him that did &longs;ay it was it

<lb/>meant of the common Element of Water.</s>

<s>The third difficulty in the doctrine of <emph type="italics"/>Archimedes<emph.end type="italics"/> was, that he

<lb/>could not render a rea&longs;on whence it aro&longs;e, that a piece of Wood,

<lb/>and a Ve&longs;&longs;ell of Wood, which otherwi&longs;e floats, goeth to the bottom,

<lb/>if filled with Water. <emph type="italics"/>Signor Buonamico<emph.end type="italics"/> hath &longs;uppo&longs;ed that a Ver&longs;&longs;ell

<lb/>of Wood, and of Wood that by nature &longs;wims, as before is &longs;aid,

<pb pagenum="422"/>goes to the bottom, if it be filled with water; of which he in the fol

<lb/>lowing Chapter, which is the 30 of the fifth Book copiou&longs;ly di&longs;cour&longs;

<lb/>eth: but I (&longs;peaking alwayes without diminution of his &longs;ingular

<lb/>Learning) dare in defence of <emph type="italics"/>Archimedes<emph.end type="italics"/> deny this experiment, being

<lb/>certain that a piece of Wood which by its nature &longs;inks not in Water,

<lb/>&longs;hall not &longs;inke though it be turned and converted into the forme of a

<lb/>ny Ve&longs;&longs;ell what&longs;oever, and then filled with Water: and he that would

<lb/>readily &longs;ee the Experiment in &longs;ome other tractable Matter, and that is

<lb/>ea&longs;ily reduced into &longs;everal Figures, may take pure Wax, and ma

<lb/>king it fir&longs;t into a Ball or other &longs;olid Figure, let him adde to it &longs;o

<lb/>much Lead as &longs;hall ju&longs;t carry it to the bottome, &longs;o that being a graine

<lb/>le&longs;s it could not be able to &longs;inke it, and making it afterwards into

<lb/>the forme of a Di&longs;h, and filling it with Water, he &longs;hall finde that with

<lb/>out the &longs;aid Lead it &longs;hall not &longs;inke, and that with the Lead it &longs;hall de

<lb/>&longs;cend with much &longs;lowne&longs;s: & in &longs;hort he &longs;hall &longs;atisfie him&longs;elf, that the

<lb/>Water included makes no alteration. </s><s>I &longs;ay not all this while, but that

<lb/>its po&longs;&longs;ible of Wood to make Barkes, which being filled with water,

<lb/>&longs;inke; but that proceeds not through its Gravity, encrea&longs;ed by the

<lb/>Water, but rather from the Nailes and other Iron Workes, &longs;o that

<lb/>it no longer hath a Body le&longs;s grave than Water, but one mixt of Iron

<lb/>and Wood, more grave than a like Ma&longs;&longs;e of Water. </s><s>Therefore let

<lb/><emph type="italics"/>Signor Buonamico<emph.end type="italics"/> de&longs;i&longs;t from de&longs;iring a rea&longs;on of an effect, that is

<lb/>not in nature: yea if the &longs;inking of the Woodden Ve&longs;&longs;ell when its full

<lb/>of Water, may call in que&longs;tion the Doctrine of <emph type="italics"/>Archimedes,<emph.end type="italics"/> which

<lb/>he would not have you to follow, is on the contrary con&longs;onant and a

<lb/>greeable to the Doctrine of the Peripateticks, &longs;ince it aptly a&longs;&longs;ignes a

<lb/>rea&longs;on why &longs;uch a Ve&longs;&longs;ell mu&longs;t, when its full of Water, de&longs;cend to the

<lb/>bottom; converting the Argument the other way, we may with

<lb/>&longs;afety &longs;ay that the Doctrine of <emph type="italics"/>Archimedes<emph.end type="italics"/> is true, &longs;ince it aptly agre

<lb/>eth with true experiments, and que&longs;tion the other, who&longs;e Deducti

<lb/>ons are fa&longs;tened upon etroneou&longs;s Conclu&longs;ions. </s><s>As for the other point

<lb/>hinted in this &longs;ame In&longs;tance, where it &longs;eemes that <emph type="italics"/>Benonamico<emph.end type="italics"/> under

<lb/>&longs;tands the &longs;ame not only of a piece of wood, &longs;haped in the forme of a

<lb/>Ve&longs;&longs;ell, but al&longs;o of ma&longs;&longs;ie Wood, which filled, <emph type="italics"/>&longs;cilicet,<emph.end type="italics"/> as I believe, he

<lb/>would &longs;ay, &longs;oaked and &longs;teeped in Water, goes finally to the bottom

<lb/>that happens in &longs;ome poro&longs;e Woods, which, while their Poro&longs;ity is re

<lb/>pleni&longs;hed with Air, or other Matter le&longs;s grave than Water, are Ma&longs;

<lb/>&longs;es &longs;pecificially le&longs;s grave than the &longs;aid Water, like as is that Viall of

<lb/>Gla&longs;s while&longs;t it is full of Air: but when, &longs;uch light Matter depart

<lb/>ing, there &longs;ucceedeth Water into the &longs;ame Poro&longs;ities and Cavities,

<lb/>there re&longs;ults a compound of Water and Gla&longs;s more grave than a like

<lb/>Ma&longs;s of Water: but the exce&longs;s of its Gravity con&longs;i&longs;ts in the Matter

<lb/>of the Gla&longs;s, and not in the Water, which cannot be graver than it

<lb/>&longs;elf: &longs;o that which remaines of the Wood, the Air of its Cavi

<pb pagenum="423"/>ties departing, if it &longs;hall be more grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than Water, fil but its

<lb/>Poro&longs;ities with Water, and you &longs;hal have a Compo&longs;t of Water and

<lb/>of Wood more grave than Water, but not by vertue of the Water re

<lb/>ceived into and imbibed by the Poro&longs;ities, but of that Matter of the

<lb/>Wood which remains when the Air is departed: and being &longs;uch it

<lb/>&longs;hall, according to the Doctrine of <emph type="italics"/>Archimedes,<emph.end type="italics"/> goe to the bottom,

<lb/>like as before, according to the &longs;ame Doctrine it did &longs;wim.</s>

<s><margin.target id="marg1435"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he Authors an

<lb/>&longs;wer to the third

<lb/>Objection.</s>

<s>As to that finally which pre&longs;ents it &longs;elf in the fourth place, namely,

<lb/>that the <emph type="italics"/>Ancients<emph.end type="italics"/> have been heretofore confuted by <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> who

<lb/>denying Po&longs;itive and Ab&longs;olute Levity, and truely e&longs;teeming all Bo

<lb/>dies to be grave, &longs;aid, that that which moved upward was driven by

<lb/>the circumambient Air, and therefore that al&longs;o the Doctrine of

<lb/><emph type="italics"/>Archimedes,<emph.end type="italics"/> as an adherent to &longs;uch an Opinion was con

<lb/>victed and confuted: I an&longs;wer fir&longs;t, that <emph type="italics"/>Signor Buonamico<emph.end type="italics"/> in my

<lb/>judgement hath impo&longs;ed upon <emph type="italics"/>Archimedes,<emph.end type="italics"/> and deduced from his

<lb/>words more than ever he intended by them, or may from his Propo

<lb/>&longs;itions be collected, in regard that <emph type="italics"/>Archimedes<emph.end type="italics"/> neither denies, nor ad

<lb/>mitteth Po&longs;itive Levity, nor doth he &longs;o much as mention it: &longs;o that

<lb/>much le&longs;s ought <emph type="italics"/>Buonamico<emph.end type="italics"/> to inferre, that he hath denyed that it

<lb/>might be the Cau&longs;e and Principle of the A&longs;cen&longs;ion of Fire, and other

<lb/>Light Bodies: having but only demon&longs;trated, that Solid Bodies

<lb/>more grave than Water de&longs;cend in it, according to the exce&longs;s of their

<lb/>Gravity above the Gravity of that, he demon&longs;trates likewi&longs;e, how the

<lb/>le&longs;s grave a&longs;cend in the &longs;ame Water, accordng to its exce&longs;s of Gra

<lb/>ty, above the Gravity of them. </s><s>So that the mo&longs;t that can be gather

<lb/>ed from the Dem on&longs;tration of <emph type="italics"/>Archimedes<emph.end type="italics"/> is, that like as the exce&longs;s

<lb/>of the Gravity of the Moveable above the Gravity of the Water, is

<lb/>the Cau&longs;e that it de&longs;cends therein, &longs;o the exce&longs;s of the Gravity of

<lb/>the water above that of the Moveable, is a &longs;ufficient Cau&longs;e why it de&longs;

<lb/>cends not, but rather betakes it &longs;elf to &longs;wim: not enquiring whe

<lb/>ther of moving upwards there is, or is not any other Cau&longs;e contrary

<lb/>to Gravity: nor doth <emph type="italics"/>Archimedes<emph.end type="italics"/> di&longs;cour&longs;e le&longs;s properly than if one

<lb/>&longs;hould &longs;ay: If the South Winde &longs;hall a&longs;&longs;ault the Barke with greater

<lb/><emph type="italics"/>Impetus<emph.end type="italics"/> than is the violence with which the Streame of the River car

<lb/>ries it towards the South, the motion of it &longs;hall be towards the North:

<lb/>but if the <emph type="italics"/>Impetus<emph.end type="italics"/> of the Water &longs;hall overcome that of the Winde, its

<lb/>motion &longs;hall be towards the South. </s><s>The di&longs;cour&longs;e is excellent and

<lb/>would be unworthily contradicted by &longs;uch as &longs;hould oppo&longs;e it, &longs;aying:

<lb/>Thou mi&longs;-alledge&longs;t as Cau&longs;e of the motion of the Bark towards the

<lb/>South, the <emph type="italics"/>Impetus<emph.end type="italics"/> of the Stream of the Water above that of the

<lb/>South Winde; mi&longs;-alledge&longs;t I &longs;ay, for it is the Force of the North

<lb/>Winde oppo&longs;ite to the South, that is able to drive the Bark towards

<lb/>the South. </s><s>Such an Objection would be &longs;uperfluous, becau&longs;e he which

<lb/>alledgeth for Cau&longs;e of the Motion the &longs;tream of the Water, denies not

<pb pagenum="424"/>but that the Winde oppo&longs;ite to the South may do the &longs;ame, but only

<lb/>affirmeth that the force of the Water prevailing over the South

<lb/>Wind, the Bark &longs;hall move towards the South: and &longs;aith no more

<lb/>than is true. </s><s>And ju&longs;t thus when <emph type="italics"/>Archimedes<emph.end type="italics"/> &longs;aith, that the Gravity

<lb/>of the Water prevailing over that by which the moveable de&longs;cends to

<lb/>the Bottom, &longs;uch moveable &longs;hall be rai&longs;ed from the Bottom to the Sur

<lb/>face alledgeth a very true Cau&longs;e of &longs;uch an Accident, nor doth he af

<lb/>firm or deny that there is, or is not, a vertue contrary to Gravity, called

<lb/>by &longs;ome Levity, that hath al&longs;o a power of moving &longs;ome Matters up

<lb/>wards. </s><s>Let therefore the Weapons of <emph type="italics"/>Signor Buonamico<emph.end type="italics"/> be directed a

<lb/>gain&longs;t <emph type="italics"/>Plato,<emph.end type="italics"/> and other <emph type="italics"/>Ancients,<emph.end type="italics"/> who totally denying <emph type="italics"/>Levity,<emph.end type="italics"/> and taking

<lb/>all Bodies to be grave, &longs;ay that the Motion upwards is made, not

<lb/>from an intrin&longs;ecal Principle of the Moveable, but only by the Im

<lb/>pul&longs;e of the <emph type="italics"/>Medium<emph.end type="italics"/>; and let <emph type="italics"/>Archimedes<emph.end type="italics"/> and his Doctrine e&longs;cape

<lb/>him, &longs;ince he hath given him no Cau&longs;e of quarelling with him

<lb/>But if this Apologie, produced in defence of <emph type="italics"/>Archimedes,<emph.end type="italics"/> &longs;hould &longs;een

<lb/>to &longs;ome in&longs;ufficient to free him from the Objections and Arguments

<lb/>produced by <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> again&longs;t <emph type="italics"/>Plato,<emph.end type="italics"/> and the other <emph type="italics"/>Ancients,<emph.end type="italics"/> as if they

<lb/>did al&longs;o fight again&longs;t <emph type="italics"/>Archimedes,<emph.end type="italics"/> alledging the Impul&longs;e of the Water

<lb/>as the Cau&longs;e of the &longs;wimming of &longs;ome Bodies le&longs;s grave than it, I would

<lb/>not que&longs;tion, but that I &longs;hould be able to maintaine the Doctrine of

<lb/><emph type="italics"/>Plato<emph.end type="italics"/> and tho&longs;e others to be mo&longs;t true, who ab&longs;olutely deny Levity,

<lb/>and affirm no other Intrin&longs;ecal Principle of Motion to be in Elemen

<lb/>tary Bodies &longs;ave only that towards the Centre of the Earth, nor no

<lb/>other Cau&longs;e of moving upwards, &longs;peaking of that which hath the re

<lb/>&longs;emblance of natural Motion, but only the repul&longs;e of the <emph type="italics"/>Medium,<emph.end type="italics"/> &longs;luid,

<lb/>and exceeding the Gravity of the Moveable: and as to the Rea&longs;ons

<lb/>of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> on the contrary, I believe that I could be able fully to

<lb/>an&longs;wer them, and I would a&longs;&longs;ay to do it, if it were ab&longs;olutely nece&longs;&longs;a

<lb/>ry to the pre&longs;ent Matter, or were it not too long a Digre&longs;&longs;ion for this

<lb/>&longs;hort Treati&longs;e. </s><s>I will only &longs;ay, that if there were in &longs;ome of our Elle

<lb/>mentary Bodies an Intrin&longs;ecall Principle and Naturall Inclination

<lb/>to &longs;hun the Centre of the Earth, and to move towards the Concave

<lb/>of the Moon, &longs;uch Bodies, without doubt, would more &longs;wiftly a&longs;cend

<lb/>through tho&longs;e <emph type="italics"/>Mediums<emph.end type="italics"/> that lea&longs;t oppo&longs;e the Velocity of the Moveable,

<lb/>and the&longs;e are the more tenuous and &longs;ubtle; as is, for example, the

<lb/>Air in compari&longs;on of the Water, we daily proving that we can with

<lb/>farre more expeditious Velocity move a Hand or a Board to and a

<lb/>gain in one than in the other: neverthele&longs;s, we never could finde any

<lb/>Body, that did not a&longs;cend much more &longs;wiftly in the water than in the

<lb/>Air. </s><s>Yea of Bodies which we &longs;ee continually to a&longs;cend in the Water,

<lb/>there is none that having arrived to the confines of the Air, do not whol

<lb/>ly lo&longs;e their Motion; even the Air it &longs;elf, which ri&longs;ing with great Ce

<lb/>lerity through the Water, being once come to its Region it lo&longs;eth all</s>

<s><margin.target id="marg1436"></margin.target>The Authors

<lb/>an&longs;wer to the

<lb/>fourth Object

<s><margin.target id="marg1437"></margin.target>Of Natation,

<s><margin.target id="marg1438"></margin.target>Of Natation,

<s><margin.target id="marg1439"></margin.target><emph type="italics"/>Plato<emph.end type="italics"/> denyeth

<lb/>Po&longs;itive Levi

<s><margin.target id="marg1440"></margin.target>The Authors

<lb/>defence of the

<lb/>doctrine of <emph type="italics"/>Plato<emph.end type="italics"/>

<lb/>and the <emph type="italics"/>Ancients,<emph.end type="italics"/>

<lb/>who ab&longs;olutely

<lb/>deny Levity:</s>

<s><margin.target id="marg1441"></margin.target>According to

<lb/><emph type="italics"/>Plato<emph.end type="italics"/> there is no

<lb/>Principle of the

<lb/>Motion of de

<lb/>&longs;cent in Naturall

<lb/>Bodies, &longs;ave that

<lb/>to the Centre.</s>

<s><margin.target id="marg1442"></margin.target>No cau&longs;e of

<lb/>the motion of

<lb/><emph type="italics"/>A<emph.end type="italics"/> cent, &longs;ave the

<lb/>Impul&longs;e of the

<lb/><emph type="italics"/>Medium,<emph.end type="italics"/> exceed

<lb/>ing the Move

<lb/>able in Gravi

<s><margin.target id="marg1443"></margin.target>Bodies a&longs;cend

<lb/>much &longs;wifter in

<lb/>the Water, than

<s><margin.target id="marg1444"></margin.target>All Bodies a&longs;

<lb/>cending through

<lb/>Water, lo&longs;e

<lb/>their Motion,

<lb/>comming to the

<lb/>confines of the

<s>And, howbeit, Experience &longs;hewes, that the Bodies, &longs;ucce&longs;&longs;ively

<lb/>le&longs;s grave, do mo&longs;t expeditiou&longs;ly a&longs;cend in water, it cannot be doubt

<lb/>ed, but that the Ignean Exhalations do a&longs;cend more &longs;wiftly

<lb/>through the water, than doth the Air: which Air is &longs;een by Experi

<lb/>ence to a&longs;cend more &longs;wiftly through the Water, than the Fiery Exha

<lb/>lations through the Air: Therefore, we mu&longs;t of nece&longs;&longs;ity conclude,

<lb/>that the &longs;aid Exhalations do much more expeditiou&longs;ly a&longs;cend through

<lb/>the Water, than through the Air; and that, con&longs;equently, they are

<lb/>moved by the Impul&longs;e of the Ambient <emph type="italics"/>Medium,<emph.end type="italics"/> and not by an intrin

<lb/>&longs;ick Principle that is in them, of avoiding the Centre of the Earth;

<lb/>to which other grave Bodies tend.</s>

<s><margin.target id="marg1445"></margin.target>The lighter

<lb/>Bodies al&longs;end

<lb/>more &longs;wiftly

<lb/>through Water.</s>

<s><margin.target id="marg1446"></margin.target>Fiery Exhalati

<lb/>ons ascend tho

<lb/>row the Water

<lb/>more &longs;wiftly

<lb/>than doth the

<lb/>Air; & the Air

<lb/>a&longs;cends more

<lb/>&longs;wiftly thorow

<lb/>the Water, than

<lb/><emph type="italics"/>F<emph.end type="italics"/>ire thorow the

<s>To that which for a finall conclu&longs;ion, <emph type="italics"/>Signor Buonamico<emph.end type="italics"/> produceth

<lb/>of going about to reduce the de&longs;cending or not de&longs;cending, to the

<lb/>ea&longs;ie and unea&longs;ie Divi&longs;ion of the <emph type="italics"/>Medium,<emph.end type="italics"/> and to the predominancy

<lb/>of the Elements: I an&longs;wer, as to the fir&longs;t part, that that cannot in any

<lb/>manner be admitted as a Cau&longs;e, being that in none of the Fluid

<lb/><emph type="italics"/>Mediums,<emph.end type="italics"/> as the Air, the Water, and other Liquids, there is any

<lb/>Re&longs;i&longs;tance again&longs;t Divi&longs;ion, but all by every the lea&longs;t Force, are di

<lb/>vided and penetrated, as I will anon demon&longs;trate: &longs;o, that of &longs;uch

<lb/>Re&longs;i&longs;tance of Divi&longs;ion there can be no Act, &longs;ince it &longs;elf is not in be

<lb/>ing. </s><s>As to the other part, I &longs;ay, that the predominancy of the Ele

<lb/>ments in Moveables, is to be con&longs;idered, as far as to the exce&longs;&longs;e or

<lb/>defect of Gravity, in relation to the <emph type="italics"/>Medium<emph.end type="italics"/>: for in that Action,

<lb/>the Elements operate not, but only, &longs;o far as they are grave or light:

<lb/>therefore, to &longs;ay that the Wood of the Firre &longs;inks not, becau&longs;e Air

<lb/>predominateth in it, is no more than to &longs;ay, becau&longs;e it is le&longs;s grave

<lb/>than the Water. </s><s>Yea, even the immediate Cau&longs;e, is its being le&longs;s

<lb/>grave than the Water: and it being under the predominancy of the

<lb/>Air, is the Cau&longs;e of its le&longs;s Gravity: Therefore, he that alledgeth the

<lb/>predominancy of the Element for a Cau&longs;e, brings the Cau&longs;e of the

<lb/>Cau&longs;e, and not the neere&longs;t and immediate Cau&longs;e. </s><s>Now, who knows

<lb/>not that the true Cau&longs;e is the immediate, and not the mediate?

<lb/>Moreover, he that alledgeth Gravity, brings a Cau&longs;e mo&longs;t per&longs;picuous

<lb/>to Sence: The cau&longs;e we may very ea&longs;ily a&longs;&longs;ertain our &longs;elves;

<lb/>whether Ebony, for example, and Firre, be more or le&longs;s grave than

<lb/>water: but whether Earth or Air predominates in them, who &longs;hall

<lb/>make that manife&longs;t? </s><s>Certainly, no Experiment can better do it

<lb/>than to ob&longs;erve whether they &longs;wim or &longs;ink. </s><s>So, that he who knows,

<lb/>not whether &longs;uch a Solid &longs;wims, unle&longs;s when he knows that Air pre

<lb/>dominates in it, knows not whether it &longs;wim, unle&longs;s he &longs;ees it &longs;wim,

<lb/>for then he knows that it &longs;wims, when he knows that it is Air that

<lb/>predominates, but knows not that Air hath the predominance, unle&longs;s

<lb/>he &longs;ees it &longs;wim: therefore, he knows not if it &longs;wims, till &longs;uch time

<lb/>as he hath &longs;een it &longs;wim.</s>

<s><margin.target id="marg1447"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he Authors

<lb/>confutation of

<lb/>the Peripateticks

<lb/>Cau&longs;es of Nata

<lb/>tion & Submer&longs;i

<s><margin.target id="marg1448"></margin.target>Water & other

<lb/>fluids void of

<lb/>Re&longs;i&longs;tance a

<lb/>gain&longs;t Divi&longs;ion.</s>

<s><margin.target id="marg1449"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he predomi

<lb/>nancy of Ele

<lb/>ments in Move

<lb/>ables to be con

<lb/>&longs;idered only in

<lb/>relation to their

<lb/>excefs or defect

<lb/>of Gravity in

<lb/>reference to the

<lb/><emph type="italics"/>Medium.<emph.end type="italics"/></s>

<s><margin.target id="marg1450"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he immedi

<lb/>ate Cau&longs;e of Na

<lb/>tation is that the

<lb/>Moveable is le&longs;s

<lb/>grave than the

<lb/>Water.</s>

<s><margin.target id="marg1451"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he <emph type="italics"/>P<emph.end type="italics"/>eripate

<lb/>ticks alledge for

<lb/>the rea&longs;on of

<lb/>Natation the

<lb/>Cau&longs;e of the

<lb/>Cau&longs;e.</s>

<s><margin.target id="marg1452"></margin.target>Gravity a

<lb/>Cau&longs;e mo&longs;t per

<lb/>&longs;picuous to

<lb/>&longs;ence:</s>

<s>Let us not then de&longs;pi&longs;e tho&longs;e Hints, though very dark, which

<lb/>Rea&longs;on, after &longs;ome contemplation, offereth to our Intelligence, and

<lb/>lets be content to be taught by <emph type="italics"/>Archimedes,<emph.end type="italics"/> that then any Body &longs;hall

<lb/>&longs;ubmerge in water, when it &longs;hall be &longs;pecifically more grave than it

<lb/>and that if it &longs;hall be le&longs;s grave, it &longs;hall of nece&longs;&longs;ity &longs;wim, and

<lb/>that it will re&longs;t indifferently in any place under water, if its Gravity

<lb/>be perfectly like to that of the water.

<s><margin.target id="marg1453"></margin.target>Lib 1. of Na

<lb/>tation Prop. </s><s>7.</s>

<s><margin.target id="marg1454"></margin.target>Id. </s><s>Lib. 1.

<s><margin.target id="marg1455"></margin.target>Id. </s><s>Lib. </s><s>1:

<s>The&longs;e things explained and proved, I come to con&longs;ider that which

<lb/>offers it &longs;elf, touching what the Diver&longs;ity of figure given unto the

<lb/>&longs;aid Moveable hath to do with the&longs;e Motions and Re&longs;ts; and pro

<lb/>ceed to affirme, that,</s>

<s>THEOREME V.</s>

<s><emph type="italics"/>The diver&longs;ity of Figures given to this or that Solid<emph.end type="italics"/></s>

<lb/><emph type="italics"/>cannot any way be a Cau&longs;e of its ab&longs;olute Sinking or

<lb/>Swimming.<emph.end type="italics"/></s>

<s><margin.target id="marg1456"></margin.target>Diver&longs;ity of

<lb/>Figure no Cau&longs;e

<lb/>of its ab&longs;olute

<lb/>Natation or Sub

<lb/>mer&longs;ion.</s>

<s>So that if a Solid being formed, for example, into a Spherical

<lb/>Figure, doth &longs;ink or &longs;wim in the water, I &longs;ay, that being formed

<lb/>into any other Figure, the &longs;ame figure in the &longs;ame water, &longs;hall

<lb/>&longs;ink or &longs;wim: nor can &longs;uch its Motion by the Expan&longs;ion or by o

<lb/>ther mutation of Figure, be impeded or taken away.

<s><margin.target id="marg1457"></margin.target>The Expan&longs;i

<lb/>on of <emph type="italics"/>F<emph.end type="italics"/>igure, re

<lb/>tards the Veloci

<lb/>ty of the a&longs;cent

<lb/>or de&longs;cent of the

<lb/>Moveable in the

<lb/>water; but doth

<lb/>not deprive it of

<lb/>all Motion.</s>

<s>The Expan&longs;ion of the Figure may indeed retard its Velocity, a&longs;

<lb/>well of a&longs;cent as de&longs;cent, and more and more according as the &longs;aid Fi

<lb/>gure is reduced to a greater breadth and thinne&longs;s: but that it may bere

<lb/>duced to &longs;uch a form as that that &longs;ame matter be wholly hindred from

<lb/>moving in the &longs;ame water, that I hold to be impo&longs;&longs;ible. </s><s>In this I have

<lb/>met with great contradictors, who producing &longs;ome Experiments, and

<lb/>in perticular a thin Board of Ebony, and a Ball of the &longs;ame Wood

<lb/>and &longs;hewing how the Ball in Water de&longs;cended to the bottom, and

<lb/>the Board being put lightly upon the Water &longs;ubmerged not, but re&longs;t

<lb/>ed; have held, and with the Authority of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> confirmed them

<lb/>&longs;elves in their Opinions, that the Cau&longs;e of that Re&longs;t was the breadth

<lb/>of the Figure, u able by its &longs;mall weight to pierce and penetrate the

<lb/>Re&longs;i&longs;tance of the Waters Cra&longs;&longs;itude, which Re&longs;i&longs;tance is readily o

<lb/>vercome by the other Sphericall Figure.</s>

<s>This is the Principal point in the pre&longs;ent Que&longs;tion, in which I per

<lb/>&longs;wade my &longs;elf to be on the right &longs;ide.</s>

<s>Therefore, beginning to inve&longs;tigate with the examination of ex

<lb/>qui&longs;ite Experiments that really the Figure doth not a jot alter the de&longs;

<lb/>cent or A&longs;cent of the &longs;ame Solids, and having already demon&longs;tra

<lb/>ted that the greater or le&longs;s Gravity of the Solid in relation to the Gra

<lb/>vity of the <emph type="italics"/>Medium<emph.end type="italics"/> is the cau&longs;e of De&longs;cent or A&longs;cent: when ever we

<pb pagenum="427"/>would make proof of that, which about this Effect the diver&longs;ity of Fi

<lb/>gure worketh, its nece&longs;&longs;ary to make the Experiment with Matter

<lb/>wherein variety of Gravities hath no place. </s><s>For making u&longs;e of Mat

<lb/>ters which may be different in their Specifical Gravities, and meeting

<lb/>with varieties of effects of A&longs;cending and De&longs;cending, we &longs;hall al

<lb/>wayes be left un&longs;atisfied whether that diver&longs;ity derive it &longs;elf really

<lb/>from the &longs;ole Figure, or el&longs;e from the divers Gravity al&longs;o. </s><s>We may

<lb/>remedy this by takeing one only Matter, that is tractable and ea&longs;ily

<lb/>reduceable into every &longs;ort of Figure. </s><s>Moreover, it wil be an excellent

<lb/>expedient to take a kinde of Matter, exactly alike in Gravity unto the

<lb/>Water: for that Matter, as far as pertaines to the Gravity, is in

<lb/>different either to A&longs;cend or De&longs;cend; &longs;o that we may pre&longs;ently ob

<lb/>&longs;erve any the lea&longs;t difference that derives it &longs;elf from the diver&longs;ity of

<lb/>Figure.</s>

<s>Now to do this, Wax is mo&longs;t apt, which, be&longs;ides its incapacity of </s>

<lb/>receiveing any &longs;en&longs;ible alteration from its imbibing of Water, is duct

<lb/>ile or pliant, and the &longs;ame piece is ea&longs;ily reduceable into all Figures:

<lb/>and being <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> a very incon&longs;iderable matter inferiour in Gravity

<lb/>to the Water, by mixing therewith a little of the fileings of Lead it is

<lb/>reduced to a Gravity exactly equall to that of the Water.</s>

<s><margin.target id="marg1458"></margin.target>An Experi

<lb/>ment in Wax,

<lb/>that proveth Fi

<lb/>gute to have no

<lb/>Operation in

<lb/>Natation & Sub

<lb/>mer&longs;ion.</s>

<s>This Matter prepared, and, for example, a Ball being made there

<lb/>of as bigge as an Orange or biger, and that made &longs;o grave as to

<lb/>&longs;ink to the bottom, but &longs;o lightly, that takeing thence one only Grain

<lb/>of Lead, it returnes to the top, and being added, it &longs;ubmergeth to

<lb/>the bottom, let the &longs;ame Wax afterwards be made into a very broad

<lb/>and thin Flake or Cake; and then, returning to make the &longs;ame Ex

<lb/>periment, you &longs;hall &longs;ee that it being put to the bottom, it &longs;hall, with the

<lb/>Grain of Lead re&longs;t below, and that Grain deducted, it &longs;hall a&longs;cend to

<lb/>the very Surface, and added again it &longs;hall dive to the bottom. </s><s>And

<lb/>this &longs;ame effect &longs;hall happen alwaies in all &longs;ort of Figures, as wel re

<lb/>gular as irregular: nor &longs;hall you ever finde any that will &longs;wim with

<lb/>out the removall of the Grain of Lead, or &longs;inke to the bottom unle&longs;s

<lb/>it be added: and, in &longs;hort, about the going or not going to the Bot

<lb/>tom, you &longs;hall di&longs;cover no diver&longs;ity, although, indeed, you &longs;hall about

<lb/>the quick and &longs;low de&longs;cent: for the more expatiated and di&longs;tended

<lb/>Figures move more &longs;lowly a&longs;wel in the diveing to the bottom as in

<lb/>the ri&longs;ing to the top; and the other more contracted and compact Fi

<lb/>gures, more &longs;peedily. </s><s>Now I know not what may be expected from

<lb/>the diver&longs;ity of Figures, if the mo&longs;t contrary to one another operate

<lb/>not &longs;o much as doth a very &longs;mall Grain of Lead, added or removed.</s>

<s>Me thinkes I hear &longs;ome of the Adver&longs;aries to rai&longs;e a doubt upon

<lb/>my produced Experiment. </s><s>And fir&longs;t, that they offer to my con&longs;idera

<lb/>tion, that the Figure, as a Figure &longs;imply, and disjunct from the Matter

<lb/>workes not any effect, but requires to be conjoyned with the Matter

<pb pagenum="428"/>and, furthermore, not with every Matter, but with tho&longs;e only,

<lb/>wherewith it may be able ro execute the de&longs;ired operation. </s><s>Like

<lb/>as we &longs;ee it verified by Experience, that the Acute and &longs;harp Angle is

<lb/>more apt to cut, than the Obtu&longs;e; yet alwaies provided, that both

<lb/>the one and the other, be joyned with a Matter apt to cut, as for

<lb/>example, with Steel. </s><s>Therefore, a Knife with a fine and &longs;harp

<lb/>edge, cuts Bread or Wood with much ea&longs;e, which it will not do, if

<lb/>the edge be blunt and thick: but he that will in&longs;tead of Steel, take

<lb/>Wax, and mould it into a Knife, undoubtedly &longs;hall never know the

<lb/>effects of &longs;harp and blunt edges: becau&longs;e neither of them will cut,

<lb/>the Wax being unable by rea&longs;on of its flexibility, to overcome the

<lb/>hardne&longs;s of the Wood and Bread. </s><s>And, therefore, applying the

<lb/>like di&longs;cour&longs;e to our purpo&longs;e, they &longs;ay, that the difference of Figure

<lb/>will &longs;hew different effects, touching Natation and Submer&longs;ion, but

<lb/>not conjoyned with any kind of Matter, but only with tho&longs;e Matters

<lb/>which, by their Gravity, are apt to re&longs;i&longs;t the Velocity of the water,

<lb/>whence he that would elect for the Matter, Cork or other light wood

<lb/>unable, through its Levity, to &longs;uperate the Cra&longs;&longs;itude of the water,

<lb/>and of that Matter &longs;hould forme Solids of divers Figures, woulld in

<lb/>vain &longs;eek to find out what operation Figure hath in Natation or Sub

<lb/>mer&longs;ion; becau&longs;e all would &longs;wim, and that not through any property

<lb/>of this or that Figure, but through the debility of the Matter, want

<lb/>ing &longs;o much Gravity, as is requi&longs;ite to &longs;uperate and overcome the

<lb/>Den&longs;ity and Cra&longs;&longs;itude of the water.</s>

<s><margin.target id="marg1459"></margin.target>An objection a

<lb/>gain&longs;t the Expe

<lb/>riment in Wax.</s>

<s>Its needfull, therefore, if wee would &longs;ee the effect wrought by the

<lb/>Diver&longs;ity of Figure, fir&longs;t to make choice of a Matter of its nature

<lb/>apt to penetrate the Cra&longs;&longs;itude of the water. </s><s>And, for this effect,

<lb/>they have made choice of &longs;uch a Matter, as fit, that being readily re

<lb/>duced into Sphericall Figure, goes to the Bottom; and it is Ebony

<lb/>of which they afterwards making a &longs;mall Board or Splinter, as thin as

<lb/>a Lath, have illu&longs;trated how that this, put upon the Surface of the

<lb/>water, re&longs;ts there without de&longs;cending to the Bottom: and making, on

<lb/>the other&longs;ide, of the &longs;ame wood a Ball, no le&longs;s than a hazell Nut,

<lb/>they &longs;hew, that this &longs;wims not, but de&longs;cendes. </s><s>From which Experi

<lb/>ment, they think they may frankly conclude, that the Breadth ofthe

<lb/>Figure in the flat Lath or Board, is the cau&longs;e of its not de&longs;cendingto

<lb/>the Bottom, fora&longs;much as a Ball of the &longs;ame Matter, not different

<lb/>from the Board in any thing but in Figure, &longs;ubmergeth in the &longs;ame

<lb/>water to the Bottom. </s><s>The di&longs;cour&longs;e and the Experiment hath really

<lb/>&longs;o much of probability and likely hood of truth in it, that it would be

<lb/>no wonder, if many per&longs;waded by a certain cur&longs;ory ob&longs;ervation,

<lb/>&longs;hould yield credit to it; neverthele&longs;s, I think I am able to di&longs;cover,

<lb/>how that it is not free from falacy.</s>

<s><margin.target id="marg1460"></margin.target>An Experi

<lb/>ment in Ebany,

<lb/>brought to di&longs;

<lb/>prove the Expe

<lb/>timent in Wax.</s>

<s>Beginning, therefore, to examine one by one, all the particulars that

<pb pagenum="429"/>have been produced, I &longs;ay, that Figures, as &longs;imple Figures, not only

<lb/>operate not in naturall things, but neither are they ever &longs;eperated

<lb/>from the Corporeall &longs;ub&longs;tance: nor have I ever alledged them &longs;tript

<lb/>of &longs;en&longs;ible Matter, like as al&longs;o I freely admit, that in our endeavour

<lb/>ing to examine the Diver&longs;ity of Accidents, dependant upon the va

<lb/>riety of Figures, it is nece&longs;&longs;ary to apply them to Matters, which ob

<lb/>&longs;truct not the various operations of tho&longs;e various Figures: and I ad

<lb/>mit and grant, that I &longs;hould do very ill, if I would experiment the in

<lb/>fluence of Acutene&longs;&longs;e of edge with a Knife of Wax, applying it to cut

<lb/>an Oak, becau&longs;e there is no Acutene&longs;s in Wax able to cut that

<lb/>very hard wood. </s><s>But yet &longs;uch an Experiment of this Knife, would

<lb/>not be be&longs;ides the purpo&longs;e, to cut curded Milk, or other very yielding

<lb/>Matter: yea, in &longs;uch like Matters, the Wax is more commodious

<lb/>than Steel; for finding the diver&longs;ity depending upon Angles, more or

<lb/>le&longs;s Acute, for that Milk is indifferently cut with a Rai&longs;or, and with

<lb/>a Knife, that hath a blunt edge. </s><s>It needs, therefore, that regard be

<lb/>had, not only to the hardne&longs;s, &longs;olidity or Gravity of Bodies, which

<lb/>under divers figures, are to divide and penetrate &longs;ome Matters, but it

<lb/>forceth al&longs;o, that regard be had, on the other &longs;ide, to the Re&longs;i&longs;tance

<lb/>of the Matters, to be divided and penetrated. </s><s>But &longs;ince I have in

<lb/>making the Experiment concerning our Conte&longs;t, cho&longs;en a Matter

<lb/>which penetrates the Re&longs;i&longs;tance of the water; and in all figures de&longs;

<lb/>cendes to the Bottome, the Adver&longs;aries can charge me with no defect;

<lb/>yea, I have propounded &longs;o much a more excellent Method than they,

<lb/>in as much as I have removed all other Cau&longs;es, of de&longs;cending or

<lb/>not de&longs;cending to the Bottom, and retained the only &longs;ole and pure

<lb/>variety of Figures, demon&longs;trating that the &longs;ame Figures all de&longs;cende

<lb/>with the only alteration of a Grain in weight: which Grain being

<lb/>removed, they return to float and &longs;wim; it is not true, therefore,

<lb/>(re&longs;uming the Example by them introduced) that I have gon about

<lb/>to experiment the efficacy of Acutene&longs;s, in cutting with Matters un

<lb/>able to cut, but with Matters proportioned to our occa&longs;ion; &longs;ince

<lb/>they are &longs;ubjected to no other variety, then that alone which depends

<lb/>on the Figure more or le&longs;s a cute.

<s><margin.target id="marg1461"></margin.target>Figure is un

<lb/>&longs;eperable from

<lb/>Corporeall Sub

<lb/>&longs;tance.</s>

<s><margin.target id="marg1462"></margin.target>The an&longs;wer to

<lb/>the Objection a

<lb/>gain&longs;t the Expe

<lb/>riment of the

<s>But let us proceed a little farther, and ob&longs;erve, how that indeed

<lb/>the Con&longs;ideration, which, they &longs;ay, ought to be had about the Election

<lb/>of the Matter, to the end, that it may be proportionate for the ma

<lb/>king of our experiment, is needle&longs;ly introduced, declaring by the ex

<lb/>ample of Cutting, that like as Acutene&longs;s is in&longs;ufficient to cut, unle&longs;s

<lb/>when it is in a Matter hard and apt to &longs;uperate the Re&longs;i&longs;tance of the

<lb/>wood or other Matter, which we intend to cut; &longs;o the aptitude of

<lb/>de&longs;cending or notde&longs;cending in water, ought and can only be known

<lb/>in tho&longs;e Matters, that are able to overcome the Renitence, and &longs;upe

<lb/>rate the Cra&longs;&longs;itude of the water. </s><s>Unto which, I &longs;ay, that to make

<lb/>di&longs;tinction and election, more of this than of that Matter, on which to

<pb pagenum="430"/>impre&longs;s the Figures for cutting or penetrating this or that Body,

<lb/>as the &longs;olidity or obduratene&longs;s of the &longs;aid Bodies &longs;hall be greater

<lb/>or le&longs;s, is very nece&longs;&longs;ary: but withall I &longs;ubjoyn, that &longs;uch di&longs;tinct

<lb/>ion, election and caution would be &longs;uperfluous and unprofitable, if

<lb/>the Body to be cut or penetrated, &longs;hould have no Re&longs;i&longs;tance, or

<lb/>&longs;hould not at all with&longs;tand the Cutting or Penitration: and if the

<lb/>Knife were to be u&longs;ed in cutting a Mi&longs;t or Smoak, one of Paper

<lb/>would be equally &longs;erviceable with one of <emph type="italics"/>Dama&longs;cus<emph.end type="italics"/> Steel: and &longs;o

<lb/>by rea&longs;on the water hath not any Re&longs;i&longs;tance again&longs;t the Penitration

<lb/>of any Solid Body, all choice of Matter is &longs;uperfluous and needle&longs;s,

<lb/>and the Election which I &longs;aid above to have been well made of a

<lb/>Matter reciprocall in Gravity to water, was not becau&longs;e it was ne

<lb/>ce&longs;&longs;ary, for the overcoming of the cra&longs;&longs;iitude of the water, but its

<lb/>Gravity, with which only it re&longs;i&longs;ts the &longs;inking of Solid Bodies: and

<lb/>for what concerneth the Re&longs;i&longs;tance of the cra&longs;&longs;itude, if we narrowly

<lb/>con&longs;ider it, we &longs;hall find that all Solid Bodies, as well tho&longs;e that

<lb/>&longs;ink, as tho&longs;e that &longs;wim, are indifferently accomodated and apt to

<lb/>bring us to the knowledge of the truth in que&longs;tion. </s><s>Nor will I

<lb/>be frighted out of the belief of the&longs;e Conclu&longs;ions, by the Experi

<lb/>ments which may be produced again&longs;t me, of many &longs;everall Woods,

<lb/>Corks, Galls, and, moreover, of &longs;ubtle &longs;lates and plates of all &longs;orts

<lb/>of Stone and Mettall, apt by means of their Naturall Gravity, to

<lb/>move towards the Centre of the Earth, the which, neverthele&longs;s, be

<lb/>ing impotent, either through the Figure (as the Adver&longs;aries thinke)

<lb/>or through Levity, to break and penetrate the Continuity of the

<lb/>parts of the water, and to di&longs;tract its union, do continue to &longs;wimm

<lb/>without &longs;ubmerging in the lea&longs;t: nor on the other &longs;ide, &longs;hall the

<lb/>Authority of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> move me, who in more than one place, a&longs;&longs;ir

<lb/>meth the contrary to this, which Experience &longs;hews me.</s>

<s><margin.target id="marg1463"></margin.target>No Solid of

<lb/>&longs;uch Levity, nor

<lb/>of &longs;uch Figure,

<lb/>but that it doth

<lb/>penetrate the

<lb/>Cra&longs;&longs;itude of

<lb/>the Water.</s>

<s>I return, therefore, to a&longs;&longs;ert, that there is not any Solid of &longs;uch

<lb/>Levity, nor of &longs;uch Figure, that being put upon the water, doth not

<lb/>divide and penetrate its Cra&longs;&longs;itude: yea if any with a more per

<lb/>&longs;picatious eye, &longs;hall return to ob&longs;erve more exactly the thin Boards

<lb/>of Wood, he &longs;hall &longs;ee them to be with part of their thickne&longs;s under </s>

<lb/>water, and not only with their inferiour Superficies, to ki&longs;&longs;e the

<lb/>Superiour of the water, as they of nece&longs;&longs;ity mu&longs;t have believed, who

<lb/>have &longs;aid, that &longs;uch Boards &longs;ubmerge not, as not being able to di

<lb/>vide the Tenacity of the parts of the water: and, moreover, he

<lb/>&longs;hall &longs;ee, that &longs;ubtle &longs;hivers of Ebony, Stone or Metall, when they

<lb/>float, have not only broak the Continuity of the water, but are with

<lb/>all their thickne&longs;s, under the Surface of it; and more and more,

<lb/>according as the Matters are more grave: &longs;o that a thin Plate of

<lb/>Lead, &longs;hall be lower than the Surface of the circumfu&longs;ed water, by

<lb/>at lea&longs;t twelve times the thickne&longs;s of the Plate, and Gold &longs;hall dive

<pb pagenum="431"/>below the Levell of the water, almo&longs;t twenty times the thickne&longs;s

<lb/>of the Plate, as I &longs;hall anon declare.</s>

<s><margin.target id="marg1464"></margin.target>Bodies of all

<lb/>Figures, laid up

<lb/>on the water, do

<lb/>penetrate its

<lb/>Cra&longs;&longs;itude, and

<lb/>in what propor

<s>But let us proceed to evince, that the water yields and &longs;ufters it

<lb/>&longs;elf to be penetrated by every the lighte&longs;t Body; and therewithall

<lb/>demon&longs;trate, how, even by Matters that &longs;ubmerge not, we may

<lb/>come to know that Figure operates nothing about the going or

<lb/>not going to the Bottom, &longs;eeing that the water &longs;uffers it &longs;elf to be

<lb/>penetrated equally by every Figure.</s>

<s>Make a Cone, or a Piramis of Cypre&longs;s, of Firre, or of other

<lb/>Wood of like Gravity, or of pure Wax, and let its height be &longs;ome

<lb/>what great, namely a handfull, or more, and put it into the water

<lb/>with the Ba&longs;e downwards: fir&longs;t, you &longs;hall &longs;ee that it will penetrate

<lb/>the water, nor &longs;hall it be at all impeded by the largene&longs;s of the Ba&longs;e,

<lb/>nor yet &longs;hall it &longs;ink all under water, but the part towards the point

<lb/>&longs;hall lye above it: by which &longs;hall be manife&longs;t, fir&longs;t, that that Solid

<lb/>forbeares not to &longs;ink out of an inabillity to divide the Continuity

<lb/>of the water, having already divided it with its broad part, that in

<lb/>the opinion of the Adver&longs;aries is the le&longs;s apt to make the divi&longs;ion.

<lb/></s><s>The Piramid being thus fixed, note what part of it &longs;hall be &longs;ub

<lb/>merged, and revert it afterwards with the point downwards, and

<lb/>you &longs;hall &longs;ee that it &longs;hall not dive into the water more than before,

<lb/>but if you ob&longs;erve how far it &longs;hall &longs;ink, every per&longs;on expert in

<lb/>Geometry, may mea&longs;ure, that tho&longs;e parts that remain out of the

<lb/>water, both in the one and in the other Experiment are equall to

<lb/>an hair: whence he may manife&longs;tly conclude, that the acute Figure

<lb/>which &longs;eemed mo&longs;t apt to part and penetrate the water, doth not

<lb/>part or penetrate it more than the large and &longs;pacious.</s>

<s><margin.target id="marg1465"></margin.target>The Experi

<lb/>ment of a Cone,

<lb/>demitted with

<lb/>its Ba&longs;e, and af

<lb/>ter with its

<lb/>Point down

<lb/>wards.</s>

<s>And he that would have a more ea&longs;ie Experiment, let him take

<lb/>two Cylinders of the &longs;ame Matter, one long and &longs;mall, and the o

<lb/>ther &longs;hert, but very broad, and let him put them in the water, not

<lb/>di&longs;tended, but erect and endways: he &longs;hall &longs;ee, if he diligently

<lb/>mea&longs;ure the parts of the one and of the other, that in each of them

<lb/>the part &longs;ubmerged, retains exactly the &longs;ame proportion to that

<lb/>out of the water, and that no greater part is &longs;ubmerged of that

<lb/>long and &longs;mall one, than of the other more &longs;pacious and broad:

<lb/>howbeit, this re&longs;ts upon a very large, and that upon a very little

<lb/>Superficies of water: therefore the diver&longs;ity of Figure, occa&longs;ioneth

<lb/>neither facility, nor difficulty, in parting and penetrating the Con

<lb/>tinuity of the water; and, con&longs;equently, cannot be the Cau&longs;e of the

<lb/>Natation or Submer&longs;ion. </s><s>He may likewi&longs;e di&longs;cover the non

<lb/>operating of variety of Figures, in ari&longs;ing from the Bottom of the

<lb/>water, towards the Surface, by taking Wax, and tempering it with

<lb/>a competent quantity of the filings of Lead, &longs;o that it may become

<lb/>a con&longs;iderable matter graver than the water: then let him make

<pb pagenum="432"/>it into a Ball, and thru&longs;t it unto the Bottom of the water; and

<lb/>fa&longs;ten to it as much Cork, or other light matter, as ju&longs;t &longs;erveth to

<lb/>rai&longs;e it, and draw it towards the Surface: for afterwards changing

<lb/>the &longs;ame Wax into a thin Cake, or into any other Figure, that

<lb/>&longs;ame Cork &longs;hall rai&longs;e it in the &longs;ame manner to a hair.</s>

<s>This &longs;ilenceth not my Antagoni&longs;ts, but they &longs;ay, that all the

<lb/>di&longs;cour&longs;e hitherto made by me little importeth to them, and that it

<lb/>&longs;erves their turn, that they have demon&longs;trated in one only parti

<lb/>cular, and in what matter, and under what Figure plea&longs;eth them,

<lb/>namely, in a Board and in a Ball of Ebony, that this put in the

<lb/>water, de&longs;cends to the Bottom, and that &longs;tays atop to &longs;wim:

<lb/>and the Matter being the &longs;ame, and the two Bodies differing in no

<lb/>thing but in Figure, they affirm, that they have with all per&longs;picuity

<lb/>demon&longs;trated and &longs;en&longs;ibly manife&longs;ted what they undertook; and

<lb/>la&longs;tly, that they have obtained their intent. </s><s>Neverthele&longs;s, I believe,

<lb/>and thinke, I can demon&longs;trate, that that &longs;ame Experiment proveth

<lb/>nothing again&longs;t my Conclu&longs;ion.</s>

<s>And fir&longs;t, it is fal&longs;e, that the Ball de&longs;cends, and the Board not:

<lb/>for the Board &longs;hall al&longs;o de&longs;cend, if you do to both the Figures, as

<lb/>the words of our Que&longs;tion requireth; that is, if you put them both

<lb/>into the water.

<s><margin.target id="marg1466"></margin.target>In Experi

<lb/>ments of Nata

<lb/>tion, the Solid

<lb/>is to be put into,

<lb/>not upon the

<lb/>water.</s>

<s><margin.target id="marg1467"></margin.target>The Que&longs;tion

<lb/>of Natation &longs;ta

<s><emph type="italics"/>The words were the&longs;e. </s><s>That the Antagoni&longs;ts having an opinion, that

<lb/>the Figure would alter the Solid Bodies, in relation to the de&longs;cending

<lb/>or not de&longs;cending, a&longs;cending or not a&longs;cending in the &longs;ame<emph.end type="italics"/> Medium, <emph type="italics"/>as<emph.end type="italics"/>

<lb/>v. </s><s>gr. <emph type="italics"/>in the &longs;ame water, in &longs;uch &longs;ort, that, for Example, a Solid that

<lb/>being of a Sphericall Figure, &longs;hall de&longs;cend to the Bottom, being reduced

<lb/>into &longs;ome other Figure, &longs;hall not de&longs;cend: I holding the contrary, do

<lb/>affirm, that a Corporeall Solid Body, which reduced into a Sphericall Fi

<lb/>gure, or any other, &longs;hall go to the Bottom, &longs;hall do the like under what&longs;oever

<lb/>other Figure, &c.<emph.end type="italics"/></s>

<s>But to be in the water, implies to be placed in the water, and by </s>

<lb/><emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> own Definition of place, to be placed, importeth to be in

<lb/>vironed by the Superficies of the Ambient Body, therefore, then

<lb/>&longs;hall the two Figures be in the water, when the Superficies of the

<lb/>water, &longs;hall imbrace and inviron them: but when the Adver&longs;aries

<lb/>&longs;hew the Board of Ebony not de&longs;cending to the Bottom, they put it

<lb/>not into the water, but upon the water, where being by a certain im

<lb/>pediment (as by and by we will &longs;hew) retained, it is invironed, part

<lb/>by water, and part by air, which thing is contrary to our agreement,

<lb/>that was, that the Bodies &longs;hould be in the water, and not part in

<lb/>water, and part in air.</s>

<s><margin.target id="marg1468"></margin.target>Place defined

<lb/>according to

<lb/><emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/></s>

<s><emph type="italics"/>The which is again made manifest, by the que&longs;tions being put as well

<lb/>about the things which go to the Bottom, as tho&longs;e which ari&longs;e from the

<lb/>Bottom to &longs;wimme, and who &longs;ees not that things placed in the Bottom,

<lb/>mu&longs;t have water about them.<emph.end type="italics"/></s>

<s>It is now to be noted, that the Board of Ebany and the Ball, put

<lb/><emph type="italics"/>into<emph.end type="italics"/> the water, both &longs;ink, but the Ball more &longs;wiftly, and the Board

<lb/>more &longs;lowly; and &longs;lower and &longs;lower, according as it &longs;hall be more

<lb/>broad and thin, and of this Tardity the breadth of the Figure is the

<lb/>true Cau&longs;e: But the&longs;e broad Boards that &longs;lowly de&longs;cend, are the

<lb/>&longs;ame, that being put lightly upon the water, do &longs;wimm: Therefore,

<lb/>if that were true which the Adver&longs;aries affirm, the &longs;ame numerical

<lb/>Figure, would in the &longs;ame numericall water, cau&longs;e one while Re&longs;t, and

<lb/>another while Tardity of Motion, which is impo&longs;&longs;ible: for every per

<lb/>ticular Figure which de&longs;cends to the Bottom, hath of nece&longs;&longs;ity its own

<lb/>determinate Tardity and &longs;lowne&longs;s, proper and naturall unto it, accor

<lb/>ding to which it moveth, &longs;o that every other Tardity, greater or le&longs;&longs;er

<lb/>is improper to its nature: if, therefore, a Board, as &longs;uppo&longs;e of a foot

<lb/>&longs;quare, de&longs;cendeth naturally with &longs;ix degrees of Tardity, it is impo&longs;&longs;i

<lb/>ble, that it &longs;hould de&longs;cend with ten or twenty, unle&longs;s &longs;ome new impe

<lb/>diment do arre&longs;t it. </s><s>Much le&longs;s can it, by rea&longs;on of the &longs;ame Figure

<lb/>re&longs;t, and wholly cea&longs;e to move; but it is nece&longs;&longs;ary, that when ever it

<lb/>re&longs;teth, there do &longs;ome greater impediment intervene than the breadth

<lb/>of the Figure. </s><s>Therefore, it mu&longs;t be &longs;omewhat el&longs;e, and not the Fi

<lb/>gure, that &longs;tayeth the Board of Ebany above water, of which Eigure

<lb/>the only Effect is the retardment of the Motion, according to which

<lb/>it de&longs;cendeth more &longs;lowly than the Ball. </s><s>Let it be confe&longs;&longs;ed, there

<lb/>fore, rationally di&longs;cour&longs;ing, that the true and &longs;ole Cau&longs;e of the Ebanys

<lb/>going to the Bottom, is the exce&longs;s of its Gravity above the Gravity of

<lb/>the water: and the Cau&longs;e of the greater or le&longs;s Tardity, the breadth

<lb/>of this Figure, or the contractedne&longs;s of that: but of its Re&longs;t, it can

<lb/>by no means be allowed, that the quallity of the Figure, is the Cau&longs;e

<lb/>thereof: a&longs;well, becau&longs;e, making the Tardity greater, according as

<lb/>the Figure more dilateth, there cannot be &longs;o immen&longs;e a Dilatation, to

<lb/>which there may not be found a corre&longs;pondent immence Tardity.

<lb/></s><s>without redu&longs;ing it to Nullity of Motion; as, becau&longs;e the Figures

<lb/>produced by the Antagoni&longs;ts for effecters of Re&longs;t, are the &longs;elf &longs;ame

<lb/>that do al&longs;o go to the Bottom.

<s><margin.target id="marg1469"></margin.target>The con&longs;utati

<lb/>on of the Expe

<lb/>riment in the

<lb/>Ebany.</s>

<s><margin.target id="marg1470"></margin.target>Every perticular

<lb/>Figure hath its

<lb/>own peculiat

<lb/>Tardity.</s>

<s><margin.target id="marg1471"></margin.target>* The Figure &

<lb/>Re&longs;i&longs;tance of

<lb/>the Medium a

<lb/>gain&longs;t Divi&longs;ion,

<lb/>have nothing to

<lb/>do with the Ef

<lb/>fect of Natation

<lb/>or Submer&longs;ion,

<lb/>by an Experi

<lb/>ment in Wall

<s>I will not omit another rea&longs;on, founded al&longs;o upon Experience, and

<lb/>if I deceive not my &longs;elf, manife&longs;tly concluding, how that the Intro

<lb/>ducton of the breadth or amplitude of Figure, and the Re&longs;i&longs;tance of

<lb/>the water again&longs;t penetration, have nothing to do in the Effect of de

<lb/>&longs;cending, or a&longs;cending, or re&longs;ting in the water. ^{*}Take a piece of wood

<lb/>or other Matter, of which a Ball a&longs;cends from the Bottom of the water

<pb pagenum="434"/>to the Surface, more &longs;lowly than a Ball of Ebony of the &longs;ame bigne&longs;&longs;e,

<lb/>&longs;o that it is manife&longs;t, that the Ball of Ebony more readily divideth the

<lb/>water in de&longs;cending, than the other in a&longs;cending; as for Example, let

<lb/>the Wood be Walnut-tree. </s><s>Then take a Board of Walnut-tree, like

<lb/>and equall to that of Ebony of the Antagoni&longs;ts, which &longs;wims; and if

<lb/>it be true, that this floats above water, by rea&longs;on of the Figure, unable

<lb/>through its breadth, to pierce the Cra&longs;&longs;itude of the &longs;ame, the other of

<lb/>Wallnut-tree, without all que&longs;tion, being thru&longs;t unto the Bottom, will

<lb/>&longs;tay there, as le&longs;s apt, through the &longs;ame impediment of Figure, to di

<lb/>vide the &longs;aid Re&longs;i&longs;tance of the water. </s><s>But if we &longs;hall find, and by

<lb/>experience &longs;ee, that not only the thin Board, but every other Figure

<lb/>of the &longs;ame Wallnut-tree will return to float, as undoubtedly we &longs;hall,

<lb/>then I mu&longs;t de&longs;ier my oppo&longs;ers to forbear to attribute the floating of

<lb/>the Ebony, unto the Figure of the Board, in regard that the Re&longs;i&longs;tance

<lb/>of the water is the &longs;ame, as well to the a&longs;cent, as to the de&longs;cent, and the

<lb/>force of the Wallnut-trees a&longs;cen&longs;ion, is le&longs;&longs;e than the Ebonys force in

<lb/>going to the Bottom.</s>

<s>Nay, I will &longs;ay more, that if we &longs;hall con&longs;ider Gold in compari&longs;on

<lb/>of water, we &longs;hall find, that it exceeds it in Gravity almo&longs;t twenty times,

<lb/>&longs;o that the Force and Impetus, wherewith a Ball of Gold goes to the

<lb/>Bottom, is very great. </s><s>On the contrary, there want not matters, as

<lb/>Virgins Wax, and &longs;ome Woods, which are not above a fiftieth part le&longs;s

<lb/>grave than water, whereupon their A&longs;cen&longs;ion therein is very &longs;low, and

<lb/>a thou&longs;and times weaker than the <emph type="italics"/>Impetus<emph.end type="italics"/> of the Golds de&longs;cent: yet

<lb/>notwith&longs;tanding, a plate of Gold &longs;wims without de&longs;cending to the

<lb/>Bottom, and, on the contrary, we cannot make a Cake of Wax, or thin

<lb/>Board of Wood, which put in the Bottom of the Water, &longs;hall re&longs;t there

<lb/>without a&longs;cending. </s><s>Now if the Figure can ob&longs;truct the Penetration,

<lb/>and impede the de&longs;cent of Gold, that hath &longs;o great an <emph type="italics"/>Impetus,<emph.end type="italics"/> how

<lb/>can it choo&longs;e but &longs;uffice to re&longs;i&longs;t the &longs;ame Penetration of the other mat

<lb/>ter in a&longs;cending, when as it hath &longs;carce a thou&longs;andth part of the <emph type="italics"/>Impetus<emph.end type="italics"/>

<lb/>that the Gold hath in de&longs;cending? </s><s>Its therefore, nece&longs;&longs;ary, that that

<lb/>which &longs;u&longs;pends the thin Plate of Gold, or Board of Ebony, upon the

<lb/>water, be &longs;ome thing that is wanting to the other Cakes and Boards of

<lb/>Matters le&longs;s grave than the water; &longs;ince that being put to the Bottom,

<lb/>and left at liberty, they ri&longs;e up to the Surface, without any ob&longs;truction:

<lb/>But they want not for flatne&longs;s and breadth of Figure: Therefore, the

<lb/>&longs;paciou&longs;ne&longs;&longs;e of the Figure, is not that which makes the Gold and Ebony

<lb/>to &longs;wim.</s>

<s><margin.target id="marg1472"></margin.target>An Experi

<lb/>ment in Gold, to

<lb/>prove the non

<lb/>operating of Fi

<lb/>gure in Natation

<lb/>and Submer&longs;ion.</s>

<s>And, becau&longs;e, that the exce&longs;s of their Gravity above the Gravity of

<lb/>the water, is que&longs;tionle&longs;s the Cau&longs;e of the &longs;inking of the flat piece of

<lb/>Ebony, and the thin Plate of Gold, when they go to the Bottom, there

<lb/>fore, of nece&longs;&longs;ity, when they float, the Cau&longs;e of their &longs;taying above

<lb/>water, proceeds from Levity, which in that ca&longs;e, by &longs;ome Accident,

<pb pagenum="435"/>peradventure not hitherto ob&longs;erved, cometh to meet with the &longs;aid

<lb/>Board, rendering it no longer as it was before, whil&longs;t it did fink more

<lb/>ponderous than the water, but le&longs;s.</s>

<s>Now, let us return to take the thin Plate of Gold, or of Silver, or the

<lb/>thin Board of Ebony, and let us lay it lightly upon the water, &longs;o that it

<lb/>&longs;tay there without &longs;inking, and diligently ob&longs;erve its effect. </s><s>And

<lb/>fir&longs;t, &longs;ee how fal&longs;e the a&longs;&longs;ertion of <emph type="italics"/>Aristotle,<emph.end type="italics"/> and our oponents is, to wit,

<lb/>that it &longs;tayeth above water, through its unability to pierce and pene

<lb/>trate the Re&longs;i&longs;tance of the waters Cra&longs;&longs;itude: for it will manife&longs;tly

<lb/>appear, not only that the &longs;aid Plates have penetrated the water, but

<lb/>al&longs;o that they are a con&longs;iderable matter lower than the Surface of the

<lb/>&longs;ame, the which continueth eminent, and maketh as it were a Rampert

<lb/>on all &longs;ides, round about the &longs;aid Plates, the profundity of which they

<lb/>&longs;tay &longs;wimming: and, according as the &longs;aid Plates &longs;hall be more grave

<lb/>than the water, two, four, ten or twenty times, it is nece&longs;&longs;ary, that

<lb/>their Superficies do &longs;tay below the univer&longs;all Surface of the water, &longs;o

<lb/>much more, than the thickne&longs;s of tho&longs;e Plates, as we &longs;hal more di&longs;tinctly

<lb/>&longs;hew anon. </s><s>In the mean &longs;pace, for the more ea&longs;ie under&longs;tanding of what

<lb/>I &longs;ay, ob&longs;erve with me a little the pre&longs;ent

<lb/>Scheme: in which let us &longs;uppo&longs;e the Surface

<lb/>of the water to be di&longs;tended, according to the

<lb/>Lines F L D B, upon which if one &longs;hall put a

<lb/>board of matter &longs;pecifically more grave than

<lb/>water, but &longs;o lightly that it &longs;ubmetge not, it

<lb/>&longs;hall not re&longs;t any thing above, but &longs;hall enter with its whole thickne&longs;s

<lb/>into the water: and, moreover, &longs;hall &longs;ink al&longs;o, as we &longs;ee by the Board

<lb/>A I, O I, who&longs;e breadth is wholly &longs;unk into the water, the little Ram

<lb/>perts of water L A and D O incompa&longs;&longs;ing it, who&longs;e Superficies is no

<lb/>tably higher than the Superficies of the Board. </s><s>See now whether it be

<lb/>true, that the &longs;aid Board goes not to the Bottom, as being of Figure

<lb/>unapt to penetrate the Cra&longs;&longs;itude of the water.</s>

<s>But, if it hath already penetrated, and overcome the Continuity of

<lb/>the water, & is of its own nature more grave than the &longs;aid water, why

<lb/>doth it not proceed in its &longs;inking, but &longs;top and &longs;u&longs;pend its &longs;elf within

<lb/>that little dimple or cavitie, which with its pondero&longs;ity it hath made in

<lb/>the water? </s><s>I an&longs;wer; becau&longs;e that in &longs;ubmerging it &longs;elf, &longs;o far as till its

<lb/>Superficies come to the Levell with that of the water, it lo&longs;eth a part

<lb/>of its Gravity, and lo&longs;eth the re&longs;t of it as it &longs;ubmergeth & de&longs;cends be

<lb/>neath the Surface of the water, which maketh Ramperts and Banks

<lb/>round about it, and it &longs;u&longs;taines this lo&longs;s by means of its drawing after it,

<lb/>and carrying along with it, the Air that is above it, and by Contact ad

<lb/>herent to it, which Air &longs;ucceeds to fill the Cavity that is invironed by

<lb/>the Ramperts of water: &longs;o that that which in this ca&longs;e de&longs;cends and is

<lb/>placed in the water, is not only the Board of Ebony or Plate of Iron,

<pb pagenum="436"/>but a compo&longs;ition of Ebony and Air, from which re&longs;ulteth a Solid

<lb/>no longer &longs;uperiour in Gravity to the water, as was the &longs;imple Ebony,

<lb/>or the &longs;imple Gold. </s><s>And, if we exactly con&longs;ider, what, and how

<lb/>great the Solid is, that in this Experiment enters into the water, and

<lb/>contra&longs;ts with the Gravity of the &longs;ame, it will be found to be all that

<lb/>which we find to be beneath the Surface of the water, the which is

<lb/>an aggregate and Compound of a Board of Ebony, and of almo&longs;t

<lb/>the like quantity of Air, or a Ma&longs;s compounded of a Plate of Lead,

<lb/>and ten or twelve times as much Air. </s><s>But, Genrlemen, you that

<lb/>are my Antagoni&longs;ts in our Que&longs;tion, we require the Identity of

<lb/>Matter, and the alteration only of the Figure; therefore, you mu&longs;t

<lb/>remove that Air, which being conjoyned with the Board, makes it

<lb/>become another Body le&longs;s grave than the Water, and put only the

<lb/>Ebony into the Water, and you &longs;hall certainly &longs;ee the Board de&longs;cend

<lb/>to the Bottom; and, if that do not happen, you have got the day.

<lb/>And to &longs;eperate the Air from the Ebony, there needs no more but

<lb/>only to bath the Superficies of the &longs;aid Board with the &longs;ame Water:

<lb/>for the Water being thus interpo&longs;ed between the Board and the Air,

<lb/>the other circumfu&longs;ed Water &longs;hall run together without any impedi

<lb/>ment, and &longs;hall receive into it the &longs;ole and bare Ebony, as it was to do.</s>

<s><margin.target id="marg1473"></margin.target>Why &longs;olids

<lb/>having penitra

<lb/>ted the Water,

<lb/>do not proceed

<lb/>to a totail Sub

<lb/>mer&longs;ion.</s>

<s><margin.target id="marg1474"></margin.target>How to &longs;epe

<lb/>rate the Air from

<lb/>Solids in demit

<lb/>ting them into

<lb/>the water.</s>

<s>But, me thinks I hear &longs;ome of the Adver&longs;aries cunningly oppo&longs;ing

<lb/>this, and telling me, that they will not yield, by any means, that

<lb/>their Board be wetted, becau&longs;e the weight added thereto by the

<lb/>Water, by making it heavier than it was before, draws it to the

<lb/>Bottom, and that the addition of new weight is contrary to our a

<lb/>greement, which was, that the Matter be the &longs;ame.</s>

<s>To this, I an&longs;wer, fir&longs;t; that treating of the operation of Figure

<lb/>in Bodies put into the Water, none can &longs;uppo&longs;e them to be put into

<lb/>the Water without being wet; nor do I de&longs;ire more to be done to

<lb/>the Board, then I will give you leave to do to the Ball. </s><s>Moreover,

<lb/>it is untrue, that the Board &longs;inks by vertue of the new Weight added

<lb/>to it by the Water, in the &longs;ingle and &longs;light bathing of it: for I will

<lb/>put ten or twenty drops of Water upon the &longs;ame Board, whil&longs;t it is

<lb/>&longs;u&longs;tained upon the water, which drops, becau&longs;e not conjoyned with

<lb/>the other Water circumfu&longs;ed, &longs;hall not &longs;o encrea&longs;e the weight of it, as

<lb/>to make it &longs;ink: but if the Board being taken out, and all the water

<lb/>wiped off that was added thereto, I &longs;hould bath all its Superficies

<lb/>with one only very &longs;mall drop, and put it again upon the water, with

<lb/>out doubt it &longs;hall &longs;ink, the other Water running to cover it, not be

<lb/>ing retained by the &longs;uperiour Air; which Air by the interpo&longs;ition of

<lb/>the thin vail of water, that takes away its Contiguity unto the Ebony,

<lb/>&longs;hall without Renitence be &longs;eperated, nor doth it in the lea&longs;t oppo&longs;e

<lb/>the &longs;ucce&longs;&longs;ion of the other Water: but rather, to &longs;peak better, it

<lb/>&longs;hall de&longs;cend freely; becau&longs;e it &longs;hall be all invironed and covered

<pb pagenum="437"/>with water, as &longs;oon as its &longs;uperiour Superficies, before vailed with

<lb/>water, doth arrive to the Levell of the univer&longs;all Surface of the &longs;aid

<lb/>water. </s><s>To &longs;ay, in the next place, that water can encrea&longs;e the weight

<lb/>of things that are demitted into it, is mo&longs;t fal&longs;e, for water hath no

<lb/>Gravity in water, &longs;ince it de&longs;cends not: yea, if we would well con&longs;i

<lb/>der what any immen&longs;e Ma&longs;s of water doth put upon a grave Body;

<lb/>that is placed in it, we &longs;hall find experimentally, that it, on the con

<lb/>trary, will rather in a great part demini&longs;h the weight of it, and that

<lb/>we may be able to lift an huge Stone from the Bottom of the water,

<lb/>which the water being removed, we are not able to &longs;tir. </s><s>Nor let

<lb/>them tell me by way of reply, that although the &longs;uperpo&longs;ed water

<lb/>augment not the Gravity of things that are in it, yet it increa&longs;eth the

<lb/>pondero&longs;ity of tho&longs;e that &longs;wim, and are part in the water and part

<lb/>in the Air, as is &longs;een, for Example, in a Bra&longs;s Ketle, which whil&longs;t it

<lb/>is empty of water, and repleni&longs;hed only with Air &longs;hall &longs;wim, but

<lb/>pouring of Water therein, it &longs;hall become &longs;o grave, that it &longs;hall &longs;ink

<lb/>to the Bottom, and that by rea&longs;on of the new weight added thereto.

<lb/></s><s>To this I will return an&longs;wer, as above, that the Gravity of the

<lb/>Water, contained in the Ve&longs;&longs;el is not that which &longs;inks it to the Bot

<lb/>tom, but the proper Gravity of the Bra&longs;s, &longs;uperiour to the Specificall

<lb/>Gravity of the Water: for if the Ve&longs;&longs;el were le&longs;s grave than

<lb/>water, the Ocean would not &longs;uffice to &longs;ubmerge it. </s><s>And, give me

<lb/>leave to repeat it again, as the fundamentall and principall point in

<lb/>this Ca&longs;e, that the Air contained in this Ve&longs;&longs;el before the infu&longs;ion of

<lb/>the Water, was that which kept it a-float, &longs;ince that there was made

<lb/>of it, and of the Bra&longs;s, a Compo&longs;ition le&longs;s grave than an equall quanti

<lb/>ty of Water: and the place that the Ve&longs;&longs;el occupyeth in the

<lb/>Water whil&longs;t it floats, is not equall to the Bra&longs;s alone, but to the

<lb/>Bra&longs;s and to the Air together, which filleth that part of the Ve&longs;&longs;el

<lb/>that is below the Levell of the water: Moreover, when the Water

<lb/>is infu&longs;ed, the Air is removed, and there is a compo&longs;ition made of

<lb/>Bra&longs;s and of water, more grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than the &longs;imple water, but

<lb/>not by vertue of the water infu&longs;ed, as having greater Specifick

<lb/>Gravity than the other water, but through the proper Gravity of

<lb/>the Bra&longs;s, and through the alienation of the Air. </s><s>Now, as he that

<lb/>&longs;hould &longs;ay that Bra&longs;s, that by its nature goes to the Bottom, being

<lb/>formed into the Figure of a Ketle, acquireth from that Figure a

<lb/>vertue of lying in the Water without &longs;inking, would &longs;ay that which

<lb/>is fal&longs;e; becau&longs;e that Bra&longs;s fa&longs;hioned into any whatever Figure,

<lb/>goeth always to the Bottom, provided, that that which is put into the

<lb/>water be &longs;imple Bra&longs;s; and it is not the Figure of the Ve&longs;&longs;el that

<lb/>makes the Bra&longs;s to float, but it is becau&longs;e that that is not purely

<lb/>Bra&longs;s which is put into the water, but an aggregate of Bra&longs;s and of

<lb/>Air: &longs;o is it neither more nor le&longs;s fal&longs;e, that a thin Plate of Bra&longs;s

<pb pagenum="438"/>or of Ebony, &longs;wims by vertue of its dilated & broad Figure: for the

<lb/>truth is, that it bares up without &longs;ubmerging, becau&longs;e that that which

<lb/>is put in the water, is not pure Bra&longs;s or &longs;imple Ebony, but an ag

<lb/>gregate of Bra&longs;s and Air, or of Ebony and Air. </s><s>And, this is not

<lb/>contrary unto my Conclu&longs;ion, the which, (having many a time &longs;een

<lb/>Ve&longs;&longs;els of Mettall, and thin pieces of diver&longs;e grave Matters float, by

<lb/>vertue of the Air conjoyned with them) did affirm, That Figure

<lb/>was not the Cau&longs;e of the Natation or Submer&longs;ion of &longs;uch Solids as

<lb/>were placed in the water. </s><s>Nay more, I cannot omit, but mu&longs;t tell

<lb/>my Antagoni&longs;ts, that this new conceit of denying that the Superfi

<lb/>cies of the Board &longs;hould be bathed, may beget in a third per&longs;on an

<lb/>opinion of a poverty of Arguments of defence on their part, &longs;ince

<lb/>that &longs;uch bathing was never in&longs;i&longs;ted upon by them in the beginning

<lb/>of our Di&longs;pute, and was not que&longs;tioned in the lea&longs;t, being that the

<lb/>Originall of the di&longs;cour&longs;e aro&longs;e upon the &longs;wiming of Flakes of Ice,

<lb/>wherein it would be &longs;implicity to require that their Superficies might

<lb/>bedry: be&longs;ides, that whether the&longs;e pieces of Ice be wet or dry they

<lb/>alwayes &longs;wim, and as the Adver&longs;aries &longs;ay, by rea&longs;on of the Figure. </s>

<s><margin.target id="marg1475"></margin.target>Water hath

<lb/>no Gravity in

<lb/>Water.</s>

<s><margin.target id="marg1476"></margin.target>Water de

<lb/>mini&longs;heth the

<lb/>Gravity of So

<lb/>lids immerged

<lb/>therein.</s>

<s><margin.target id="marg1477"></margin.target>The Experi

<lb/>ment of a Bra&longs;s

<lb/>Ketle &longs;wiming

<lb/>when empty, &

<lb/>&longs;inking when

<lb/>full, alledged to

<lb/>prove that water

<lb/>gravitates in

<lb/>water, an&longs;wered.</s>

<s><margin.target id="marg1478"></margin.target>An Ocean &longs;uf

<lb/>ficeth not to

<lb/>&longs;ink a Ve&longs;&longs;el &longs;pe

<lb/>cifically le&longs;s

<lb/>grave than wa

<s><margin.target id="marg1479"></margin.target>Air, the Cau&longs;e

<lb/>of the Natation

<lb/>of empty Ve&longs;&longs;els

<lb/>of Matters gra

<lb/>ver <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than

<lb/>the water.</s>

<s><margin.target id="marg1480"></margin.target>Neither Figure,

<lb/>nor the breadth

<lb/>of Figure, is the

<lb/>Cau&longs;e of Nata

<s>Some peradventure, by way of defence, may &longs;ay, that wetting the

<lb/>Board of Ebony, and that in the &longs;uperiour Superficies, it would,

<lb/>though of it &longs;elf unable to pierce and penetrate the water, be born

<lb/>downwards, if not by the weight of the additionall water, at lea&longs;t

<lb/>by that de&longs;ire and propen&longs;ion that the &longs;uperiour parts of the water

<lb/>have to re-unite and rejoyn them&longs;elves: by the Motion of which

<lb/>parts, the &longs;aid Board cometh in a certain manner, to be depre&longs;&longs;ed

<lb/>downwards.

<s><margin.target id="marg1481"></margin.target>The Bathed

<lb/>Solid de&longs;cends

<lb/>not out of any

<lb/>affectation of u

<lb/>nion in the upper

<lb/>parts of the wa

<s>This weak Refuge will be removed, if we do but con&longs;ider, that

<lb/>the repugnancy of the inferiour parts of the water, is as great against

<lb/>Di&longs;-union, as the Inclination of its &longs;uperiour parts is to union: nor can

<lb/>the uper unite them&longs;elves without depre&longs;&longs;ing the board, nor can it

<lb/>de&longs;cend without di&longs;uniting the parts of the nether Water: &longs;o that

<lb/>it doth follow, by nece&longs;&longs;ary con&longs;equence, that for tho&longs;e re&longs;pects, it &longs;hall

<lb/>not de&longs;cend. </s><s>Moreover, the &longs;ame that may be &longs;aid of the upper

<lb/>parts of the water, may with equall rea&longs;on be &longs;aid of the nethe,

<lb/>namely, that de&longs;iring to unite, they &longs;hall force the &longs;aid Board

<lb/>upwards.</s>

<s>Happily, &longs;ome of the&longs;e Gentlemen that di&longs;&longs;ent from me, will won

<lb/>der, that I affirm, that the contiguous &longs;uperiour Air is able to &longs;u&longs;tain

<lb/>that Plate of <emph type="italics"/>B<emph.end type="italics"/>ra&longs;s or of Silver, that &longs;tayeth above water; as if I

<lb/>would in a certain &longs;ence allow the Air, a kind of Magnetick vertue

<lb/>of &longs;u&longs;taining the grave <emph type="italics"/>B<emph.end type="italics"/>odies, with which it is contiguous. </s><s>To &longs;a

<lb/>tis&longs;ie all I may, to all doubts, I have been con&longs;idering how by &longs;ome

<lb/>other &longs;en&longs;ible Experiment I might demon&longs;trate, how truly that little

<lb/>contiguous and &longs;uperiour Air &longs;u&longs;taines tho&longs;e Solids, which being by

<pb pagenum="439"/>nature apt to de&longs;cend to the Bottom, being placed lightly on the water

<lb/>&longs;ubmerge not, unle&longs;s they be fir&longs;t thorowly bathed; and have found,

<lb/>that one of the&longs;e Bodies having de&longs;cended to the Bottom, by conveigh

<lb/>ing to it (without touching it in the lea&longs;t) a little Air, which conjoyneth

<lb/>with the top of the &longs;ame; it becometh &longs;ufficient, not only, as before to

<lb/>&longs;u&longs;tain it, but al&longs;o to rai&longs;e it, and to carry it back to the top, where it

<lb/>&longs;tays and abideth in the &longs;ame manner, till &longs;uch time, as the a&longs;&longs;i&longs;tance

<lb/>of the conjoyned Air is taken away. </s><s>And to this effect, I have taken a

<lb/>Ball of Wax, and made it with a little Lead, &longs;o grave, that it lea&longs;urely

<lb/>de&longs;cends to the Bottom, making with all its Superficies very &longs;mooth and

<lb/>pollite: and this being put gently into the water, almo&longs;t wholly &longs;ub

<lb/>mergeth, there remaining vi&longs;&longs;ible only a little of the very top, the which

<lb/>solong as it is conjoyned with the Air, &longs;hall retain the Ball a-top, but

<lb/>the Contiguity of the Air taken away by wetting it, it &longs;hall de&longs;cend to

<lb/>the Bottom and there remain. </s><s>Now to make it by vertue of the Air, that

<lb/>before &longs;u&longs;tained it to return again to the top, and &longs;tay there, thru&longs;t into

<lb/>the water a Gla&longs;s rever&longs;ed with the mouth downwards, the which &longs;hall

<lb/>carry with it the Air it contains, and move this towards the Ball, aba&longs;ing

<lb/>it till &longs;uch time that you &longs;ee, by the tran&longs;parency of the Gla&longs;s, that the

<lb/>contained Air do arrive to the &longs;ummity of the <emph type="italics"/>B<emph.end type="italics"/>all: then gently with

<lb/>draw the Gla&longs;s upwards, and you &longs;hall &longs;ee the <emph type="italics"/>B<emph.end type="italics"/>all to ri&longs;e, and afterwards

<lb/>stay on the top of the water, if you carefully part the Gla&longs;s and the water

<lb/>without overmuch commoving and di&longs;turbing it. </s><s>There is, therefore, a

<lb/>certain affinity between the Air and other <emph type="italics"/>B<emph.end type="italics"/>odies, which holds them uni

<lb/>ed, &longs;o, that they &longs;eperate not without a kind of violence. </s><s>The &longs;ame

<lb/>likewi&longs;e is &longs;een in the water; for if we &longs;hall wholly &longs;ubmerge &longs;ome <emph type="italics"/>B<emph.end type="italics"/>ody

<lb/>in it, &longs;o that it be thorowly bathed, in the drawing of it afterwards gent

<lb/>ly out again, we &longs;hall &longs;ee the water follow it, and ri&longs;e notably above its

<lb/>Surface, before it &longs;eperates from it. </s><s>Solid <emph type="italics"/>B<emph.end type="italics"/>odies, al&longs;o, if they be equall

<lb/>and alike in Superficies, &longs;o, that they make an exact Contact without

<lb/>the interpo&longs;ition of the lea&longs;t Air, that may part them in the &longs;eperation

<lb/>and yield untill that the ambient <emph type="italics"/>Medium<emph.end type="italics"/> &longs;ucceeds to repleni&longs;h the place,

<lb/>do hold very firmly conjoyned, and are not to be &longs;eperated without great

<lb/>force but, becau&longs;e, the Air, Water, and other Liquids, very expedi

<lb/>tiou&longs;ly &longs;hape them&longs;elves to contact with any Solid <emph type="italics"/>B<emph.end type="italics"/>odies, &longs;o that their

<lb/>Superficies do exqui&longs;itely adopt them&longs;elves to that of the Solids, without

<lb/>any thing remaining between them, therefore, the effect of this Con

<lb/>junction and Adherence is more manife&longs;tly and frequently ob&longs;erved in

<lb/>them, than in hard and inflexible <emph type="italics"/>B<emph.end type="italics"/>odies, who&longs;e Superficies do very rate

<lb/>ly conjoyn with exactne&longs;s of Contact. </s><s>This is therefore that Magne

<lb/>tick vertue, which with firm Connection conjoyneth all Bodies, that do

<lb/>touch without the interpo&longs;ition of flexible fluids; and, who knows, but

<lb/>that that a Contact, when it is very exact, may be a &longs;ufficient Cau&longs;e of

<lb/>the Union and Continuity of the parts of a naturall <emph type="italics"/>B<emph.end type="italics"/>ody?</s>

<s><margin.target id="marg1482"></margin.target><emph type="italics"/>A<emph.end type="italics"/> Magneti&longs;me in

<lb/>the <emph type="italics"/>A<emph.end type="italics"/>ir, by which

<lb/>it bears up tho&longs;e

<lb/>Solids in the wa

<lb/>ter, that are con

<lb/>tiguous with it.</s>

<s><margin.target id="marg1483"></margin.target>The Effect of

<lb/>the Airs Conti

<lb/>guity in the Na

<lb/>tation of Solids.</s>

<s><margin.target id="marg1484"></margin.target>The force of

<lb/>Contact.</s>

<s><margin.target id="marg1485"></margin.target><emph type="italics"/>A<emph.end type="italics"/>n affectati

<lb/>on of Conjunct

<lb/>ion betwixt So

<lb/>lids and the Air

<lb/>contiguous to

<s><margin.target id="marg1486"></margin.target>The like affect

<lb/>ation of Con

<lb/>junction be

<lb/>twixt Solids &

<lb/>the water.</s>

<s><margin.target id="marg1487"></margin.target>Al&longs;o the like

<lb/>affectation and

<lb/>Conjunction be

<lb/>twixt Solids

<lb/>them&longs;eives.</s>

<s><margin.target id="marg1488"></margin.target>Contact may

<lb/>be the Cau&longs;e of

<lb/>the Continuity

<lb/>of Naturall Bo

<s>Now, pur&longs;uing my purpo&longs;e, I &longs;ay; that it needs not, that we have

<lb/>recour&longs;e to the Tenacity, that the parts of the water have among&longs;t them

<lb/>&longs;elves, by which they re&longs;i&longs;t and oppo&longs;e Divi&longs;ion, Di&longs;traction, and Seper

<lb/>ration, becau&longs;e there is no &longs;uch Coherence and Re&longs;i&longs;tance of Divi&longs;ion

<lb/>for if there were, it would be no le&longs;s in the internall parts than in tho&longs;e

<lb/>nearer the &longs;uperiour or externall Surface, &longs;o that the &longs;ame Board, find

<lb/>ing alwayes the &longs;ame Re&longs;i&longs;tance and Renitence, would no le&longs;s &longs;top in

<lb/>the middle of the water than about the Surface, which is fal&longs;e. More

<lb/></s><s>over, what Re&longs;i&longs;tance can we place in the Continuity of the water

<lb/>if we &longs;ee that it is impo&longs;&longs;ible to &longs;ind any Body of what&longs;oever Matter

<lb/>Figure or Magnitude, which being put into the water, &longs;hall be ob&longs;tructed

<lb/>and impeded by the Tenacity of the parts of the water to one another

<lb/>&longs;o, but that it is moved upwards or downwards, according as the Cau&longs;e

<lb/>of their Motion tran&longs;ports it? </s><s>And, what greater proof of it can we de

<lb/>&longs;ier, than that which we daily &longs;ee in Muddy waters, which being put into

<lb/>Ve&longs;&longs;els to be drunk, and being, after &longs;ome hours &longs;etling, &longs;till, as we &longs;ay

<lb/>thick in the end, after four or &longs;ix dayes they are wholly &longs;etled, and be

<lb/>come pure and clear? </s><s>Nor can their Re&longs;i&longs;tance of Penetration &longs;tay tho&longs;e

<lb/>impalpable and in&longs;en&longs;ible Atomes of Sand, which by rea&longs;on of their

<lb/>exceeding &longs;mall force, &longs;pend &longs;ix dayes in de&longs;cending the &longs;pace of half

<s><margin.target id="marg1489"></margin.target><emph type="italics"/>T<emph.end type="italics"/>he &longs;ettlement

<lb/>of <emph type="italics"/>M<emph.end type="italics"/>uddy Wa

<lb/>ter, proveth that

<lb/>that Element

<lb/>hath no aver&longs;i

<lb/>on to Divi&longs;ion.</s>

<s><emph type="italics"/>Nor let them &longs;ay, that the &longs;eeing of &longs;uch &longs;mall Bodies, con&longs;ume &longs;ix dayes in

<lb/>de&longs;cending &longs;o little a way, is a &longs;ufficient Argument of the Waters Re&longs;i&longs;tance

<lb/>of Divi&longs;ion; becau&longs;e that is no re&longs;i&longs;ting of Divi&longs;ion, but a retarding of<emph.end type="italics"/>

<lb/><emph type="italics"/>Motion; and it would be &longs;implicity to &longs;ay, that a thing oppo&longs;eth Divi&longs;ion

<lb/>and that in the &longs;ame in&longs;tant, it permits it &longs;elf to be divided: nor doth the

<lb/>Retardation of Motion at all favour the Adver&longs;aries cau&longs;e, for that they are

<lb/>to in&longs;tance in a thing that wholly prohibiteth Motion, and procureth Re&longs;t;

<lb/>it is nece&longs;&longs;ary, therefore, to find out Bodies that &longs;tay in the water, if one would

<lb/>&longs;hew its repugnancy to Divi&longs;ion, and not &longs;uch as move in it, howbeit

<lb/>&longs;lowly.<emph.end type="italics"/></s>

<s><margin.target id="marg1490"></margin.target>Water cannot

<lb/>oppo&longs;e divi&longs;ion,

<lb/>and at the &longs;ame

<lb/>time permit it

<lb/>&longs;elf to be divi

<s>What then is this Cra&longs;&longs;itude of the water, with which it re&longs;i&longs;teth Di

<lb/>vi&longs;ion? </s><s>What, I be&longs;eech you, &longs;hould it be, if we (as we have &longs;aid above)

<lb/>with all diligence attempting the reduction of a Matter into &longs;o like a

<lb/>Gravity with the water, that forming it into a dilated Plate it re&longs;ts &longs;u&longs;

<lb/>pended as we have &longs;aid, between the two waters, it be impo&longs;&longs;ible to

<lb/>effect it, though we bring them to &longs;uch an Equiponderance, that as

<lb/>much Lead as the fourth part of a Grain of Mu&longs;terd-&longs;eed, added to the

<lb/>&longs;ame expanded Plate, that in Air [<emph type="italics"/>i. </s><s>e. </s><s>out of the water<emph.end type="italics"/>] &longs;hall weigh four

<lb/>or fix pounds, &longs;inketh it to the Bottom, and being &longs;ub&longs;tracted, it a&longs;cends

<lb/>to the Surface of the water? </s><s>I cannot &longs;ee, (if what I &longs;ay be true, as it is

<lb/>mo&longs;t certain) what minute vertue and force we can po&longs;&longs;ibly find or ima

<lb/>gine, to which the Re&longs;i&longs;tance of the water again&longs;t Divi&longs;ion and Penetra

<pb pagenum="441"/>tion is not inferiour; whereupon, we mu&longs;t of nece&longs;&longs;ity conclude

<lb/>that it is nothing: becan&longs;e, if it were of any &longs;en&longs;ible power, &longs;ome

<lb/>large Plate might be found or compounded of a Matter alike in Gra

<lb/>vity to the water, which not only would &longs;tay between the two wa

<lb/>ters; but, moreover, &longs;hould not be able to de&longs;cend or a&longs;cend with

<lb/>out notable force. </s><s>We may likewi&longs;e collect the &longs;ame from an o

<lb/>ther Experiment, &longs;hewing that the Water gives way al&longs;o in the &longs;ame

<lb/>manner to tran&longs;ver&longs;all Divi&longs;ion; for if in a &longs;etled and &longs;tanding water

<lb/>we &longs;hould place any great Ma&longs;s that goeth not to the bottom, draw

<lb/>ing it with a &longs;ingle (Womans) Hair, we might carry it from place to

<lb/>place without any oppo&longs;ition, and this whatever Figure it hath,

<lb/>though that it po&longs;&longs;e&longs;s a great &longs;pace of water, as for in&longs;tance, a great

<lb/>Beam would do moved &longs;ide-ways. </s><s>Perhaps &longs;ome might oppo&longs;e me

<lb/>and &longs;ay, that if the Re&longs;i&longs;tance of water again&longs;t Divi&longs;ion, as I affirm,

<lb/>were nothing; Ships &longs;hould not need &longs;uch a force of Oars and Sayles

<lb/>for the moving of them from place to place in a tranquile Sea, or

<lb/>&longs;tanding Lake. </s><s>To him that &longs;hould make &longs;uch an objection, I would

<lb/>reply, that the water contra&longs;teth not again&longs;t, nor &longs;imply re&longs;i&longs;teth

<lb/>Divi&longs;ion, but a &longs;udden Divi&longs;ion, and with &longs;o much greater Reni

<lb/>tence, by how much greater the Velocity is: and the Cau&longs;e of this

<lb/>Re&longs;i&longs;tance depends not on Cra&longs;&longs;itude, or any other thing that ab&longs;o

<lb/>lutely oppo&longs;eth Divi&longs;ion, but becau&longs;e that the parts of the water

<lb/>divided, in giving way to that Solid that is moved in it, are them

<lb/>&longs;elves al&longs;o nece&longs;&longs;itated locally to move, &longs;ome to the one &longs;ide, and &longs;ome

<lb/>to the other, and &longs;ome downwards: and this mu&longs;t no le&longs;s be done

<lb/>by the waves before the Ship, or other Body &longs;wimming through the

<lb/>water, than by the po&longs;teriour and &longs;ub&longs;equent; becau&longs;e, the Ship

<lb/>proceeding forwards, to make it &longs;elf a way to receive its Bulk, it is

<lb/>requi&longs;ite, that with the Prow it repul&longs;e the adjacent parts of the

<lb/>water, as well on one hand as on the other, and that it move them

<lb/>as much tran&longs;ver&longs;ly, as is the half of the breadth of the Hull: and

<lb/>the like removall mu&longs;t tho&longs;e waves make, that &longs;ucceeding the Poump

<lb/>do run from the remoter parts of the Ship towards tho&longs;e of the

<lb/>middle, &longs;ucce&longs;&longs;ively to repleni&longs;h the places, which the Ship in ad

<lb/>vancing forwards, goeth, leaving vacant. </s><s>Now, becau&longs;e, all Moti

<lb/>tions are made in Time, and the longer in greater time: and it being

<lb/>moreover true, that tho&longs;e Bodies that in a certain time are moved

<lb/>by a certain power &longs;uch a certain &longs;pace, &longs;hall not be moved the &longs;ame

<lb/>&longs;pace, and in a &longs;horter Time, unle&longs;s by a greater Power: therefore,

<lb/>the broader Ships move &longs;lower than the narrower, being put on by

<lb/>an equall Force: and the &longs;ame Ve&longs;&longs;el requires &longs;o much greater

<lb/>force of Wind, or Oars, the fa&longs;ter it is to move.</s>

<s><margin.target id="marg1491"></margin.target>An hair will

<lb/>draw a great

<lb/>Ma&longs;s thorow the

<lb/>Water; which

<lb/>proveth, that it

<lb/>hath no Re&longs;i&longs;t

<lb/>ance again&longs;t

<lb/>tran&longs;ver&longs;all Di

<lb/>vi&longs;ion.</s>

<s><margin.target id="marg1492"></margin.target>How &longs;hips are

<lb/>moved in the

<lb/>water.</s>

<s><margin.target id="marg1493"></margin.target>Bodies moved

<lb/>a certain &longs;pace in

<lb/>a certain Time,

<lb/>by a certain

<lb/>power, cannot be

<lb/>moved the

<lb/>&longs;ame &longs;pace, and

<lb/>in a &longs;horter time,

<lb/>but by a greater

<lb/>power.</s>

<s><emph type="italics"/>But yet for all this, any great Ma&longs;s &longs;wimming in a &longs;tanding Lake, may

<lb/>be moved by any petit force; only it is true, that a le&longs;&longs;er force more

<lb/>&longs;lowly moves it: but if the waters Re&longs;i&longs;tance of Divi&longs;ion, were in any

<lb/>manner &longs;en&longs;ible, it would follow, that the &longs;aid Ma&longs;s, &longs;hould, notwith

<lb/>&longs;tanding the percu&longs;&longs;ion of &longs;ome &longs;en&longs;ible force, continue immoveable, which is<emph.end type="italics"/>

<lb/><emph type="italics"/>not &longs;o. </s><s>Yea, I will &longs;ay farther, that &longs;hould we retire our &longs;elves into the

<lb/>more internall contemplation of the Nature of water and other Fluids,

<lb/>perhaps we &longs;hould di&longs;cover the Con&longs;titution of their parts to be &longs;uch, that

<lb/>they not only do not oppo&longs;e Divi&longs;ion, but that they have not any thing in

<lb/>them to be divided: &longs;o that the Re&longs;i&longs;tance that is ob&longs;erved in moving<emph.end type="italics"/>

<lb/><emph type="italics"/>through the water, is like to that which we meet with in pa&longs;&longs;ing through

<lb/>a great Throng of People, wherein we find impediment, and not by any

<lb/>difficulty in the Divi&longs;ion, for that none of tho&longs;e per&longs;ons are divided

<lb/>whereof the Croud is compo&longs;ed, but only in moving of tho&longs;e per&longs;ons &longs;ide

<lb/>ways which were before divided and disjoyned: and thus we find

<lb/>Re&longs;i&longs;tance in thru&longs;ting a Stick into an heap of Sand, not becau&longs;e any part

<lb/>of the Sand is to be cut in pieces, but only to be moved and rai&longs;ed. two <emph.end type="italics"/>

<lb/><emph type="italics"/>manners of Penetration, therefore, offer them&longs;elves to us, one in Bodies,

<lb/>who&longs;e parts were continuall, and here Divi&longs;ion &longs;eemeth nece&longs;&longs;ary; the <emph.end type="italics"/>

<lb/><emph type="italics"/>other in the aggregates of parts not continuall, but contiguous only, and

<lb/>here there is no nece&longs;&longs;ity of dividing but of moving only. </s><s>Now, I am

<lb/>not well re&longs;olved, whether water and other Fluids may be e&longs;teemed to

<lb/>be of parts continuall or contiguous only; yet I find my &longs;elf indeed incli<emph.end type="italics"/>

<lb/><emph type="italics"/>ned to think that they are rather contiguous (if there be in Naturno

<lb/>other manner of aggregating, than by the union, or by the touching of the

<lb/>extreams:) and I am induced thereto by the great difference that I &longs;ee >

<lb/>between the Conjunction of the parts of an hard or Solid Body, and the<emph.end type="italics"/>

<lb/><emph type="italics"/>Conjunction of the &longs;ame parts when the &longs;ame Body &longs;hall be made Liquid

<lb/>and Fluid: for if, for example, I take a Ma&longs;s of Silver or other Solid

<lb/>and hard Mettall, I &longs;hall in dividing it into two parts, find not only the <emph.end type="italics"/>

<lb/><emph type="italics"/>re&longs;i&longs;tance that is found in the moving of it only, but an other incomparably

<lb/>greater, dependent on that vertue, whatever it be, which holds the parts

<lb/>united: and &longs;o if we would divide again tho&longs;e two parts into other two

<lb/>and &longs;ucce&longs;&longs;ively into others and others, we &longs;hould &longs;till find a like Re&longs;i&longs;t

<lb/>ance, but ever le&longs;s by how much &longs;maller the parts to be divided &longs;hall be;

<lb/>but if, la&longs;tly, employing mo&longs;t &longs;ubtile and acute In&longs;truments, &longs;uch as are

<lb/>the mo&longs;t tenuous parts of the Fire, we &longs;hall re&longs;olve it (perhaps) into its

<lb/>la&longs;t and lea&longs;t Particles, there &longs;hall not be left in them any longer either

<lb/>Re&longs;i&longs;tance of Divi&longs;ion, or &longs;o much as a capacity of being farther divi

<lb/>ded, e&longs;pecially by In&longs;truments more gro&longs;&longs;e than the acuities of Fire: and

<lb/>what Knife or Ra&longs;or put into well melted Silver can we finde, that will

<lb/>divide a thing which &longs;urpa&longs;&longs;eth the &longs;eparating power of Fire? </s><s>Certainly

<lb/>none: becau&longs;e either the whole &longs;hall be reduced to the mo&longs;t minute and

<lb/>ultimate Divi&longs;ions, or if there remain parts capable &longs;till of other Suddi<emph.end type="italics"/>

<pb pagenum="443"/><emph type="italics"/>divi&longs;ions, they cannot receive them, but only from acuter Divi&longs;ors than

<lb/>Fire; but a Stick or Rod of Iron, moved in the melted Met all, is not

<lb/>&longs;uch a one. </s><s>Of a like Con&longs;titution and Con&longs;i&longs;tence, I account the parts<emph.end type="italics"/>

<lb/><emph type="italics"/>of Water, and other Liquids to be, namely, incapable of Divi&longs;ion by

<lb/>rea&longs;on of their Temtity; or if not ab&longs;olutely indivi&longs;ible, yet at lea&longs;t

<lb/>not to be divided by a Board, or other Solid Body, palpable unto the

<lb/>band, the Sector being alwayes required to be more &longs;harp than the Solid

<lb/>to be cut. </s><s>Solid Bodies, therefore, do only move, and not divide the<emph.end type="italics"/>

<lb/><emph type="italics"/>Water, when put into it; who&longs;e parts being before divided to the ex

<lb/>treame&longs;t minuity, and therefore capable of being moved, either many of

<lb/>them at once, or few, or very few, they &longs;oon give place to every &longs;mall Cor

<lb/>pu&longs;cle, that de&longs;cends in the &longs;ame: for that, it being little and light, de

<lb/>&longs;cending in the Air, and arriving to the Surface of the Water, it meets

<lb/>with Particles of Water more &longs;mall, and of le&longs;s Re&longs;i&longs;tance again&longs;t

<lb/>Motion and Extru&longs;ion, than is its own prement and extru&longs;ive force,

<lb/>whereupon it &longs;ubmergeth, and moveth &longs;uch a portion of them, as is pro

<lb/>portionate to its Power. </s><s>There is not, therefore, any Re&longs;i&longs;tance in

<lb/>Water again&longs;t Divi&longs;ion, nay, there is not in it any divi&longs;ible parts. </s><s>I

<lb/>adde, moreover, that in ca&longs;e yet there &longs;bould be any &longs;mall Re&longs;i&longs;tance<emph.end type="italics"/>

<lb/><emph type="italics"/>found (which is ab&longs;olutely fal&longs;e) haply in attempting with an Hair to

<lb/>move a very great natant Machine, or in e&longs;&longs;aying by the addition of one

<lb/>&longs;mall Grain of Lead to &longs;ink, or by removall of it to rai&longs;e a very broad

<lb/>Plate of Matter, equall in Gravity with Water, (which likewi&longs;e will

<lb/>not happen, in ca&longs;e we proceed with dexterity) we may ob&longs;erve that that

<lb/>Re&longs;i&longs;tance is a very different thing from that which the Adver&longs;aries pro

<lb/>duce for the Cau&longs;e of the Natation of the Plate of Lead or Board of Ebo

<lb/>ny, for that one may make a Board of Ebony, which being put upon the

<lb/>Water &longs;wimmeth, and cannot be &longs;ubmerged, no not by the addition of an

<lb/>bundred Grains of Lead put upon the &longs;ame, and afterwards being ba

<lb/>thed, not only &longs;inks, though the &longs;aid Lead be taken away, but though

<lb/>moreover a quantity of Cork, or of &longs;ome other light Body fa&longs;tened to it,

<lb/>&longs;ufficeth not to hinder it from &longs;inking unto the bottome: &longs;o that you

<lb/>&longs;ee, that although it were granted that there is a certain &longs;mall Re&longs;i&longs;t

<lb/>ance of Divi&longs;ion found in the &longs;ubstance of the Water, yet this hath no

<lb/>thing to do with that Cau&longs;e which &longs;upports the Board above the Water,

<lb/>with a Re&longs;i&longs;tance an hundred times greater than that which men can

<lb/>find in the parts of the Water: nor let them tell me, that only the Sur-<emph.end type="italics"/>

<lb/><emph type="italics"/>face of the Water hath &longs;uch Re&longs;i&longs;tance, and not the internall parts, or

<lb/>that &longs;uch Re&longs;i&longs;tance is found greate&longs;t in the beginning of the Submer&longs;ion,

<lb/>as it al&longs;o &longs;eems that in the beginning, Motion meets with greater oppo&longs;iti

<lb/>on, than in the continuance of it; becau&longs;e, fir&longs;t, I will permit, that the<emph.end type="italics"/>

<lb/><emph type="italics"/>Water be &longs;tirred, and that the &longs;uperiour parts be mingled with the mid

<lb/>dle, and inferiour parts, or that tho&longs;e above be wholly removed, and

<lb/>tho&longs;e in the middle only made u&longs;e off, and yet you &longs;hall &longs;ee the effect for<emph.end type="italics"/>

<pb pagenum="444"/><emph type="italics"/>all that, to be still the &longs;ame: Moreover, that Hair which draws a

<lb/>Beam through the Water, is likewi&longs;e to divide the upperparts, and is

<lb/>al&longs;o to begin the Motion, and yet it begins it, and yet it divides it: and

<lb/>finally, let the Board of Ebony be put in the midway, betwixt the bottome

<lb/>and the top of the Water, and let it there for a while be &longs;u&longs;pended and

<lb/>&longs;etled, and afterwards let it be left at liberty, and it will instantly begin

<lb/>its Motion, and will continue it unto the bottome. </s><s>Nay, more, the Board

<lb/>&longs;o &longs;oon as it is dimitted upon the Water, hath not only begun to move

<lb/>and divide it, but is for a good &longs;pace dimerged into it.<emph.end type="italics"/></s>

<s><margin.target id="marg1494"></margin.target>The parts of

<lb/>Liquids, &longs;o farte

<lb/>from re&longs;i&longs;ting

<lb/>Divi&longs;ion, that

<lb/>they contain not

<lb/>any thing that

<lb/>may be divided.</s>

<s><margin.target id="marg1495"></margin.target>The Re&longs;i&longs;t

<lb/>ance a Solid

<lb/>findeth in mo

<lb/>ving through

<lb/>the water, like

<lb/>to that we meet

<lb/>with in pa&longs;&longs;ing

<lb/>through a

<lb/>throng of peo

<s><margin.target id="marg1496"></margin.target>Or in thru&longs;t

<lb/>ing a Stick into

<s><margin.target id="marg1497"></margin.target>Two kinds of

<lb/>Penetration, one

<lb/>in Bodies conti

<lb/>nuall, the other

<lb/>in Bodies only

<lb/>contiguous.</s>

<s><margin.target id="marg1498"></margin.target>Water con&longs;i&longs;ts

<lb/>not of continu

<lb/>all, but only

<lb/>of contiguous

<lb/>parts.</s>

<s><margin.target id="marg1499"></margin.target><emph type="italics"/>Set what &longs;atis

<lb/>faction he hath

<lb/>given, as to this

<lb/>point, in Lib. de

<s><margin.target id="marg1500"></margin.target>Great differ

<lb/>ence betwixt the

<lb/>Conjunction of

<lb/>the parts of a Bo

<lb/>dy when Solid,

<lb/>and when fluid.</s>

<s><margin.target id="marg1501"></margin.target>Water con&longs;i&longs;ts

<lb/>of parts that ad

<lb/>mit of no fat

<lb/>ther divi&longs;ion.</s>

<s><margin.target id="marg1502"></margin.target>Solids dimit

<lb/>ted into the wa

<lb/>ter, do onely

<lb/>move, and not

<lb/>divide it.</s>

<s><margin.target id="marg1503"></margin.target>If there were

<lb/>any Re&longs;i&longs;tance

<lb/>of Divi&longs;ion in

<lb/>water, it mu&longs;t

<lb/>needs be &longs;mall,

<lb/>in that it is over

<lb/>come by an

<lb/>Hair, a Grain of

<lb/>Lead, or a &longs;light

<lb/>bathing of the

<lb/>Solid.</s>

<s><margin.target id="marg1504"></margin.target>The uper parts

<lb/>of the Water, do

<lb/>no more re&longs;i&longs;t

<lb/>Divi&longs;ion, than

<lb/>the middle or

<lb/>lowe&longs;t parts.</s>

<s><margin.target id="marg1505"></margin.target>Waters Re

<lb/>&longs;i&longs;tance of divi

<lb/>&longs;ion, not greater

<lb/>in the begin

<lb/>ning of the Sub

<lb/>mer&longs;ion.</s>

<s>Let us receive it, therefore, for a true and undoubted Conclu&longs;i

<lb/>on, That the Water hath not any Renitence again&longs;t &longs;imple Divi&longs;i

<lb/>on, and that it is not po&longs;&longs;ible to find any Solid Body, be it of what

<lb/>Figure it will, which being put into the Water, its Motion upwards

<lb/>or downwards, according as it exceedeth, or &longs;hall be exceeded by

<lb/>the Water in Gravity (although &longs;uch exce&longs;&longs;e and difference be in

<lb/>&longs;en&longs;ible) &longs;hall be prohibited, and taken away, by the Cra&longs;&longs;itude of

<lb/>the &longs;aid Water. </s><s>When, therefore, we &longs;ee the Board of Ebony, or

<lb/>of other Matter, more grave than the Water, to &longs;tay in the Con

<lb/>fines of the Water and Air, without &longs;ubmerging, we mu&longs;t have re

<lb/>cour&longs;e to &longs;ome other Originall, for the inve&longs;ting the Cau&longs;e of that

<lb/>Effect, than to the breadth of the Figure, unable to overcome the

<lb/>Renitence with which the Water oppo&longs;eth Divi&longs;ion, &longs;ince there is

<lb/>no Re&longs;i&longs;tance; and from that which is not in being, we can expect

<lb/>no Action. </s><s>It remains mo&longs;t true, therefore, as we have &longs;aid before, that

<lb/>this &longs;o &longs;ucceds, for that that which in &longs;uch manner put upon the wa

<lb/>ter, not the &longs;ame Body with that which is put <emph type="italics"/>into<emph.end type="italics"/> the Water: becau&longs;e

<lb/>this which is put <emph type="italics"/>into<emph.end type="italics"/> the Water, is the pure Board of Ebony, which

<lb/>for that it is more grave than the Water, &longs;inketh, and that which is

<lb/>put <emph type="italics"/>upon<emph.end type="italics"/> the Water, is a Compo&longs;ition of Ebony, and of &longs;o much

<lb/>Air, that both together are &longs;pecifically le&longs;s grave than the Water,

<lb/>and therefore they do not de&longs;cend.</s>

<s>I will farther confirm this which I &longs;ay. </s><s>Gentlemen, my Antago

<lb/>ni&longs;ts, we are agreed, that the exce&longs;s or defect of the Gravity of the

<lb/>Solid, unto the Gravity of the Water, is the true and proper Cau&longs;e

<lb/>of Natation or Submer&longs;ion.

<s><margin.target id="marg1506"></margin.target>Great Caution

<lb/>to be had in ex

<lb/>perimenting the

<lb/>operation of Fi

<lb/>gure in Natati

<s>Now, if you will &longs;hew that be&longs;ides the former Cau&longs;e, there is ano

<lb/>ther which is &longs;o powerfull, that it can hinder and remove the Sub

<lb/>mer&longs;ion of tho&longs;e very Solids, that by their Gravity &longs;ink, and if you

<lb/>will &longs;ay, that this is the breadth or amplene&longs;s of Figure, you are ob

<lb/>lieged, when ever you would &longs;hew &longs;uch an Experiment, fir&longs;t to make

<lb/>the circum&longs;tances certain, that that Solid which you put into the

<lb/>Water, be not le&longs;s grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than it, for if you &longs;hould not do &longs;o

<lb/>any one might with rea&longs;on &longs;ay, that not the Figure, but the Levity

<lb/>was the cau&longs;e of that Natation. </s><s>But I &longs;ay, that when you &longs;hall di

<pb pagenum="445"/>mit a Board of Ebony into the Water, you do not put therein a Solid

<lb/>more grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than the Water, but one lighter, for be &longs;ides the

<lb/>Ebony, there is in the Water a Ma&longs;s of Air, united with the Ebony,

<lb/>and &longs;uch, and &longs;o light, that of both there re&longs;ults a Compo&longs;ition le&longs;s

<lb/>grave than the Water: See, therefore, that you remove the Air, and

<lb/>put the Ebony alone into the Water, for &longs;o you &longs;hall immerge a So

<lb/>lid more grave then the Water, and if this &longs;hall not go to the Bottom,

<lb/>you have well Philo&longs;ophized, and I ill.</s>

<s>Now, &longs;ince we have found the true Cau&longs;e of the Natation of tho&longs;e

<lb/>Bodies, which otherwi&longs;e as being graver than the Water, would de

<lb/>&longs;cend to the bottom, I think, that for the perfect and di&longs;tinct know

<lb/>ledge of this bu&longs;ine&longs;s, it would be good to proceed in a way of di&longs;

<lb/>covering demon&longs;tratively tho&longs;e particular Accidents that do attend

<lb/>the&longs;e effects, and,</s>

<s>PROBL. I.</s>

<s><emph type="italics"/>To finde what proportion &longs;everall Figures of different<emph.end type="italics"/></s>

<lb/><emph type="italics"/>Matters ought to have, unto the Gravity of the

<lb/>Water, that &longs;o they may be able by vertue of the

<lb/>Contigucus Air to &longs;tay afloat.<emph.end type="italics"/></s>

<s><margin.target id="marg1507"></margin.target>To finde the

<lb/>proportion Fi

<lb/>gures ought to

<lb/>have to the wa

<lb/>ters Gravity,

<lb/>that by help of

<lb/>the contiguous

<lb/>Air, they may

<lb/>&longs;wim.</s>

<s>Let, therefore, for better illu&longs;tration, D F N E be a Ve&longs;&longs;ell,

<lb/>wherein the water is contained, and &longs;uppo&longs;e a Plate or Board,

<lb/>who&longs;e thickne&longs;s is comprehended between the Lines I C and

<lb/>O S, and let it be of Matter exceeding the water in Gravity, &longs;o that

<lb/>being put upon the water, it dimergeth and aba&longs;eth below the Levell

<lb/>of the &longs;aid water, leaving the little Banks A I and B C, which are at

<lb/>the greate&longs;t height they can be, &longs;o that if the Plate I S &longs;hould but

<lb/>de&longs;cend any little &longs;pace farther, the little Banks or Ramparts would

<lb/>no longer con&longs;i&longs;t, but expul&longs;ing the Air A I C B, they would dif

<lb/>fu&longs;e them&longs;elves over the Superficies I C, and

<lb/>would &longs;ubmerge the Plate. </s><s>The height AIBC

<lb/>is therefore the greate&longs;t profundity that the

<lb/>little <emph type="italics"/>B<emph.end type="italics"/>anks of water admit of. </s><s>Now I &longs;ay,

<lb/>that from this, and from the proportion in Gra

<lb/>vity, that the Matter of the Plate hath to the

<lb/>water, we may ea&longs;ily &longs;inde of what thickne&longs;s, at mo&longs;t, we may make

<lb/>the &longs;aid Plates, to the end, they may be able to bear up above water:

<lb/>for if the Matter of the Plate or <emph type="italics"/>B<emph.end type="italics"/>oard I S were, for Example, as

<lb/>heavy again as the water, a <emph type="italics"/>B<emph.end type="italics"/>oard of that Matter &longs;hall be, at the mo&longs;t

<lb/>of a thickne&longs;s equall to the greate&longs;t height of the <emph type="italics"/>B<emph.end type="italics"/>anks, that is, as

<lb/>thick as A I is high: which we will thus demon&longs;trate. </s><s>Lot the So

<lb/>lid I S be donble in Gravity to the water, and let it be a regular

<pb pagenum="446"/>Pri&longs;me, or Cylinder, to wit, that hath its two flat Superficies, &longs;uperi

<lb/>our and inferiour, alike and equall, and at Right Angles with the o

<lb/>ther laterall Superficies, and let its thickne&longs;s I O be equall to the

<lb/>greate&longs;t Altitude of the Banks of water: I &longs;ay, that if it be put upon

<lb/>the water, it will not &longs;ubmerge: for the Altitude

<lb/>A I being equall to the Altitude I O, the Ma&longs;s

<lb/>of the Air A B C I &longs;hall be equall to the Ma&longs;s of

<lb/>the Solid C I O S: and the whole Ma&longs;s A O S B

<lb/>double to the Ma&longs;s I S; And &longs;ince the Ma&longs;s

<lb/>of the Air A C, neither encrea&longs;eth nor dimi

<lb/>ni&longs;heth the Gravity of the Ma&longs;s I S, and the Solid I S was &longs;uppo&longs;ed

<lb/>double in Gravity to the water; Therefore as much water as the

<lb/>Ma&longs;s &longs;ubmerged A O S B, compounded of the Air A I C B, and of

<lb/>the Solid I O S C, weighs ju&longs;t as much as the &longs;ame &longs;ubmerged Ma&longs;s

<lb/>A O S B: but when &longs;uch a Ma&longs;s of water, as is the &longs;ubmerged part of

<lb/>the Solid, weighs as much as the &longs;aid Solid, it de&longs;cends not farther,

<lb/>but re&longs;teth, as by <emph type="italics"/>(a) Archimedes,<emph.end type="italics"/> and above by us, hath been de>

<lb/>mon&longs;trated: Therefore, I S &longs;hall de&longs;cend no farther, but &longs;hall re&longs;t.

<lb/>And if the Solid I S &longs;hall be Se&longs;quialter in Gravity to the water, it

<lb/>&longs;hall float, as long as its thickne&longs;s be not above twice as much as the

<lb/>greate&longs;t Altitude of the Ramparts of water, that is, of A I. </s><s>For I S

<lb/>being Se&longs;quialter in Gravity to the water, and the Altitude O I

<lb/>being double to I A, the Solid &longs;ubmerged A O S B, &longs;hall be al&longs;o

<lb/>Se&longs;quialter in Ma&longs;s to the Solid I S. </s><s>And becau&longs;e the Air A C,

<lb/>neither increa&longs;eth nor dimini&longs;heth the pondero&longs;ity of the Solid I S:

<lb/>Therefore, as much water in quantity as the &longs;ubmerged Ma&longs;s AOSB,

<lb/>weighs as much as the &longs;aid Ma&longs;s &longs;ubmerged: And, therefore, that

<lb/>Ma&longs;s &longs;hall re&longs;t. </s><s>And briefly in generall.</s>

<s><margin.target id="marg1508"></margin.target>Of Natation

<s>THEOREME. VI.</s>

<s><emph type="italics"/>When ever the exce&longs;s of the Gravity of the Solid above<emph.end type="italics"/>

<lb/><emph type="italics"/>the Gravity of the Water, &longs;hall have the &longs;ame pro

<lb/>portion to the Gravity of the Water, that the Alti

<lb/>tude of the Rampart, hath to the thickne&longs;s of the

<lb/>Solid, that Solid &longs;hall not &longs;ink, but being never &longs;o lit

<lb/>tle thicker it &longs;hall.<emph.end type="italics"/></s>

<s><margin.target id="marg1509"></margin.target>The proporti

<lb/>on of the great

<lb/>e&longs;t thickne&longs;s of

<lb/>Solids, beyond

<lb/>which encrea

<lb/>&longs;ed they &longs;ink.</s>

<s>Let the Solid I S be &longs;uperior in Gravity to the water, and of &longs;uch

<lb/>thickne&longs;s, that the Altitude of the Rampart A I, be in proporti

<lb/>on to the thickne&longs;s of the Solid I O, as the exce&longs;s of the Gravi

<lb/>ty of the &longs;aid Solid I S, above the Gravity of a Ma&longs;s of water equall

<lb/>to the Ma&longs;s I S, is to the Gravity of the Ma&longs;s of water equall to the

<pb pagenum="447"/>Ma&longs;s I S. </s><s>I &longs;ay, that the Solid I S &longs;hall not

<lb/>&longs;inke, but being never &longs;o little thicker it &longs;hall

<lb/>go to the bottom: For being that as A I is

<lb/>to I O, &longs;o is the Exce&longs;s of the Gravity of the

<lb/>Solid I S, above the Gravity of a Ma&longs;s of water

<lb/>equall to the Ma&longs;s I S, to the Gravity of the

<lb/>&longs;aid Ma&longs;s of water: Therefore, compounding, as A O is to O I, &longs;o

<lb/>&longs;hall the Gravity of the Solid I S, be to the Gravity of a Ma&longs;s of water

<lb/>equall to the Ma&longs;s I S: And, converting, as I O is to O A, &longs;o &longs;hall the

<lb/>Gravity of a Ma&longs;s of water equall to the Ma&longs;s I S, be to the Gravity

<lb/>of the Solid I S: But as I O is to O A, &longs;o is a Ma&longs;s of water I S, to a

<lb/>Ma&longs;s of water equall to the Ma&longs;s A B S O: and &longs;o is the Gravity of

<lb/>a Ma&longs;s of water I S, to the Gravity of a Ma&longs;s of water A S: Therefore

<lb/>as the Gravity of a Ma&longs;s of water, equall to the Ma&longs;s I S, is to the

<lb/>Gravity of the Solid I S, &longs;o is the &longs;ame Gravity of a Ma&longs;s of water

<lb/>I S, to the Gravity of a Ma&longs;s of Water A S: Therefore the Gra

<lb/>vity of the Solid I S, is equall to the Gravity of a Ma&longs;s of water e

<lb/>quall to the Ma&longs;s A S: But the Gravity of the Solid I S, is the &longs;ame

<lb/>with the Gravity of the Solid A S, compounded of the Solid I S,

<lb/>and of the Air A B C I. </s><s>Therefore the whole compounded Solid

<lb/>A O S B, weighs as much as the water that would be compri&longs;ed in the

<lb/>place of the &longs;aid Compound A O S B: And, therefore, it &longs;hall make

<lb/>an <emph type="italics"/>Equilibrium<emph.end type="italics"/> and re&longs;t, and that &longs;ame Solid I O S C &longs;hall &longs;inke no

<lb/>farther. </s><s>But if its thickne&longs;s I O &longs;hould be increa&longs;ed, it would be ne

<lb/>ce&longs;&longs;ary al&longs;o to encrea&longs;e the Altitude of the Rampart A I, to main

<lb/>tain the due proportion: But by what hath been &longs;uppo&longs;ed, the Alti

<lb/>tude of the Rampart A I, is the greate&longs;t that the Nature of the

<lb/>Water and Air do admit, without the waters repul&longs;ing the Air ad

<lb/>herent to the Superficies of the Solid I C, and po&longs;&longs;e&longs;&longs;ing the &longs;pace

<lb/>A I C B: Therefore, a Solid of greater thickne&longs;s than I O, and of the

<lb/>&longs;ame Matter with the Solid I S, &longs;hall not re&longs;t without &longs;ubmerging,

<lb/>but &longs;hall de&longs;cend to the bottome: which was to be demon&longs;trated.

<lb/></s><s>In con&longs;equence of this that hath been demon&longs;trated, &longs;undry and va

<lb/>rious Conclu&longs;ions may be gathered, by which the truth of my prin

<lb/>cipall Propo&longs;ition comes to be more and more confirmed, and the

<lb/>imperfection of all former Argumentations touching the pre&longs;ent

<lb/>Que&longs;tion cometh to be di&longs;covered.</s>

<s><emph type="italics"/>And fir&longs;t we gather from the things demonstrated, that,<emph.end type="italics"/></s>

<s>THEOREME VII.

<s><margin.target id="marg1510"></margin.target>The heavie&longs;t

<lb/>Bodies may

<lb/>&longs;wimme.</s>

<s><emph type="italics"/>All Matters, how heavy &longs;oever, even to Gold it &longs;elf, the

<lb/>heavie&longs;t of all Bodies, known by us, may float upon

<lb/>the Water.<emph.end type="italics"/></s>

<s>Becau&longs;e its Gravity being con&longs;idered to be almo&longs;t twenty times

<lb/>greater than that of the water, and, moreover, the greate&longs;t Alti

<lb/>tude that the Rampart of water can be extended to, without break

<lb/>ing the Contiguity of the Air, adherent to the Surface of the Solid,

<lb/>that is put upon the water being predetermined, if we &longs;hould make

<lb/>a Plate of Gold &longs;o thin, that it exceeds not the nineteenth part ofthe

<lb/>Altitude of the &longs;aid Rampart, this put lightly upon the water &longs;hall

<lb/>re&longs;t, without going to the bottom: and if Ebony &longs;hall chance to be

<lb/>in &longs;e&longs;qui&longs;eptimall proportion more grave than the water, the greate&longs;t

<lb/>thickne&longs;s that can be allowed to a Board of Ebony, &longs;o that it may be

<lb/>able to &longs;tay above water without &longs;inking, would be &longs;eaven times

<lb/>more than the height of the Rampart Tinn, <emph type="italics"/>v. </s><s>gr.<emph.end type="italics"/> eight times more

<lb/>grave than water, &longs;hall &longs;wimm as oft as the thickne&longs;s of its Plate,</s>

<lb/>exceeds not the 7th part of the Altitude of the Rampart.</s>

<s><margin.target id="marg1511"></margin.target><emph type="italics"/>He el&longs;ewhere

<lb/>cites this as a

<lb/>Propo&longs;ition, there

<lb/>fore I make it of

<lb/>that number.<emph.end type="italics"/></s>

<s>And here I will not omit to note, as a &longs;econd Corrollary dependent

<lb/>upon the things demon&longs;trated, that,</s>

<s>THEOREME VIII.

<s><margin.target id="marg1512"></margin.target>Natation and

<lb/>Submer&longs;ion, col

<lb/>lected from the

<lb/>thickne&longs;s, exclu

<lb/>ding the length

<lb/>and breadth of

<lb/>Plates.</s>

<s><emph type="italics"/>The Expan&longs;ion of Figure not only is not the Cau&longs;e of the

<lb/>Natation of tho&longs;e grave Bodies, which otherwi&longs;e

<lb/>do &longs;ubmerge, but al&longs;o the determining what be tho&longs;e

<lb/>Boards of Ebony, or Plates of Iron or Gold that will

<lb/>&longs;wimme, depends not on it, rather that &longs;ame determina

<lb/>tion is to be collected from the only thickne&longs;s of tho&longs;e

<lb/>Figures of Ebony or Gold, wholly excluding the con

<lb/>&longs;ideration of length and breadth, as having no way

<lb/>any &longs;hare in this Effect.<emph.end type="italics"/></s>

<s>It hath already been manife&longs;ted, that the only cau&longs;e of the Nata

<lb/>tion of the &longs;aid Plates, is the reduction of them to be le&longs;s grave

<lb/>than the water, by means of the connexion of that Air, which de

<lb/>&longs;cendeth together with them, and po&longs;&longs;e&longs;&longs;eth place in the water;

<lb/>which place &longs;o occupyed, if before the circumfu&longs;ed water diffu&longs;eth

<lb/>it &longs;elf to fill it, it be capable of as much water, as &longs;hall weigh equall

<lb/>with the Plate, the Plate &longs;hall remain &longs;u&longs;pended, and &longs;inke no

<lb/>farther.</s>

<s>Now let us &longs;ee on which of the&longs;e three dimen&longs;ions of the Solid

<lb/>depends the terminating, what and how much the Ma&longs;s of that ought

<lb/>to be, that &longs;o the a&longs;&longs;i&longs;tance of the Air contiguous unto it, may &longs;uffice

<lb/>to render it &longs;pecifically le&longs;s grave than the water, whereupon it may

<lb/>re&longs;t without Submer&longs;ion. </s><s>It &longs;hall undoubtedly be found, that the

<lb/>length and breadth have not any thing to do in the &longs;aid determina

<lb/>tion, but only the height, or if you will the thickne&longs;s: for, if we take

<lb/>a Plate or Board, as for Example, of Ebony, who&longs;e Altitude hath

<lb/>unto the greate&longs;t po&longs;&longs;ible Altitude of the Rampart, the proportion

<lb/>above declared, for which cau&longs;e it &longs;wims indeed, but yet not if we

<lb/>never &longs;o little increa&longs;e its thickne&longs;s; I &longs;ay, that retaining its thick

<lb/>ne&longs;s, and encrea&longs;ing its Superficies to twice, four times, or ten times

<lb/>its bigne&longs;s, or dmini&longs;ning it by dividing it into four, or &longs;ix, or

<lb/>twenty, or a hundred parts, it &longs;hall &longs;till in the &longs;ame manner continue

<lb/>to float: but encrea&longs;ing its thickne&longs;s only a Hairs breadth, it will

<lb/>alwaies &longs;ubmerge, although we &longs;hould multiply the Superficies a

<lb/>hundred and a hundred times. </s><s>Now fora&longs;much as that this is a

<lb/>Cau&longs;e, which being added, we adde al&longs;o the Effect, and being remo

<lb/>ved, it is removed; and by augmenting or le&longs;&longs;ening the length or

<lb/>breadth in any manner, the effect of going, or not going to the bot

<lb/>tom, is not added or removed: I conclude, that the greatne&longs;s and

<lb/>&longs;malne&longs;s of the Superficies hath no influence upon the Natation or

<lb/>Submer&longs;ion. </s><s>And that the proportion of the Altitude of the Ram

<lb/>parts of Water, to the Altitude of the Solid, being con&longs;tituted in

<lb/>the manner afore&longs;aid, the greatne&longs;s or &longs;malne&longs;s of the Superficies,

<lb/>makes not any variation, is manife&longs;t from that which hath been above

<lb/>demon&longs;trated, and from this, that, <emph type="italics"/>The Pri&longs;ms and Cylinders which<emph.end type="italics"/></s>

<lb/><emph type="italics"/>have the &longs;ame Ba&longs;e, are in proportion to one another as their heights:<emph.end type="italics"/>

<lb/>Whence Cylinders or Prifmes, namely, the Board, be they great or

<lb/>little, &longs;o that they be all of equall thickne&longs;s, have the &longs;ame proportion

<lb/>to their Conterminall Air, which hath for Ba&longs;e the &longs;aid Superficies of

<lb/>the Board, and for height the Ramparts of water; &longs;o that alwayes

<lb/>of that Air, and of the Board, Solids are compounded, that in Gravity

<lb/>equall a Ma&longs;s of water equall to the Ma&longs;s of the Solids, compounded

<lb/>of Air, and of the Board: whereupon all the &longs;aid Solids do in the

<lb/>&longs;ame manner continue afloat. </s><s>We will conclude in the third place,

<s><margin.target id="marg1513"></margin.target>Pri&longs;mes and

<lb/>Cylinders ha

<lb/>ving the &longs;ame

<lb/>Ba&longs;e, are to one

<lb/>another as their

<lb/>heights.</s>

<s>THEOREME. IX.

<s><margin.target id="marg1514"></margin.target>All Figures

<lb/>of all Matters,

<lb/>float by hep of

<lb/>the Rampart re

<lb/>pleni&longs;hed with

<lb/>Air, and &longs;ome

<lb/>but only touch

<lb/>the water.</s>

<s><emph type="italics"/>All &longs;orts of Figures of what&longs;oever Matter, albeit more

<lb/>grave than the Water, do by Benefit of the &longs;aid Ram

<lb/>part, not only float, but &longs;ome Figures, though of the

<lb/>grave&longs;t Matter, do &longs;tay wholly above Water, wetting

<lb/>only the inferiour Surface that toucheth the Water.<emph.end type="italics"/></s>

<s>And the&longs;e &longs;hall be all Figures, which from the inferiour Ba&longs;e up

<lb/>wards, grow le&longs;&longs;er and le&longs;&longs;er; the which we &longs;hall exemplifie for

<lb/>this time in Piramides or Cones, of which Figures the pa&longs;&longs;ions sre

<lb/>common. </s><s>We will demon&longs;trate therefore, that,</s>

<s><emph type="italics"/>It is po&longs;&longs;ible to form a Piramide, of any what&longs;oever Matter propo&longs;ed,

<lb/>which being put with its Ba&longs;e upon the Water, re&longs;ts not only without

<lb/>&longs;ubmerging, but without wetting it more then its Ba&longs;e.<emph.end type="italics"/></s>

<s>For the explication of which it is requi&longs;ite, that we fir&longs;t demon&longs;trate

<lb/>the &longs;ub&longs;equent Lemma, namely, that,</s>

<s>LEMMA II.</s>

<s><emph type="italics"/>Solids who&longs;e Ma&longs;&longs;es an&longs;wer in proportion contrarily to<emph.end type="italics"/></s>

<lb/><emph type="italics"/>their Specificall Gravities, are equall in Ab&longs;olute

<lb/>Gravities.<emph.end type="italics"/></s>

<s><margin.target id="marg1515"></margin.target>Solids who&longs;e

<lb/>Ma&longs;&longs;es are in

<lb/>contrary pro

<lb/>portion to their

<lb/>Specifick Gra

<lb/>vities, are equall

<lb/>in ab&longs;olute Gra

<s>Let A C and B be two Solids, and let the Ma&longs;s A C be to the

<lb/>Ma&longs;s B, as the Specificall Gravity of the Solid B, is to the Speci

<lb/>ficall Gravity of the Solid A C: I &longs;ay, the Solids A C and B are

<lb/>equall in ab&longs;olute weight, that is, equally grave. For

<lb/>if the Ma&longs;s A C be equall to the Ma&longs;s B, then, by the

<lb/>A&longs;&longs;umption, the Specificall Gravity of B, &longs;hall be e

<lb/>quall to the Specificall Gravity of A C, and being e

<lb/>quall in Ma&longs;s, and of the &longs;ame Specificall Gravity they

<lb/>&longs;hall ab&longs;olutely weigh one as much as another. </s><s>But

<lb/>if their Ma&longs;&longs;es &longs;hall be unequall, let the Ma&longs;s A C be greater, and in it

<lb/>take the part C, equall to the Ma&longs;s B. And, becau&longs;e the Ma&longs;&longs;es B

<lb/>and C are equall; the Ab&longs;olute weight of B, &longs;hall have the &longs;ame pro

<lb/>portion to the Ab&longs;olute weight of C, that the Specificall Gravity of

<lb/>B, hath to the Specificall Gravity of C; or of C A, which is the

<lb/>&longs;ame <emph type="italics"/>in &longs;pecie<emph.end type="italics"/>: But look what proportion the Specificall Gravity of

<lb/>B, hath to the Specificall Gravity of C A, the like proportion, by the

<lb/>A&longs;&longs;umption, hath the Ma&longs;s C A, to the Ma&longs;s B; that is, to the Ma&longs;s C:

<pb pagenum="451"/>Therefore, the ab&longs;olute weight of B, to the ab&longs;olute weight of C, is

<lb/>as the Ma&longs;s A C to the Ma&longs;s <emph type="italics"/>C<emph.end type="italics"/>: But as the Ma&longs;s AC, is to the Ma&longs;s C,

<lb/>&longs;o is the ab&longs;olute weight of A C, to the ab&longs;olute weight of C: There

<lb/>fore the ab&longs;olute weight of B, hath the &longs;ame proportion to the ab&longs;o

<lb/>lute weight of C, that the ab&longs;olute weight of A C, hath to the ab

<lb/>&longs;olute weight of C: Therefore, the two Solids A C and B are equall

<lb/>in ab&longs;olute Gravity: which was to be demon&longs;trated. </s><s>Having de

<lb/>mon&longs;trated this, I &longs;ay,</s>

<s>THEOREME X.</s>

<s><emph type="italics"/>That it is po&longs;&longs;ible of any a&longs;&longs;igned Matter, to form a Pi-<emph.end type="italics"/>

<lb/><emph type="italics"/>ramide or Cone upon any Ba&longs;e, which being put upon

<lb/>the Water &longs;hall not &longs;ubmerge, nor wet any more than

<lb/>its Ba&longs;e.<emph.end type="italics"/></s>

<s><margin.target id="marg1516"></margin.target>There may be

<lb/>Cones and Pira

<lb/>mides of any

<lb/><emph type="italics"/>M<emph.end type="italics"/>atter, which

<lb/>demittedinto the

<lb/>water, re&longs;t only

<lb/>their Ba&longs;es.</s>

<s>Let the greate&longs;t po&longs;&longs;ible Altitude of the Rampart be the Line D B,

<lb/>and the Diameter of the Ba&longs;e of the Cone to be made of any Mat

<lb/>ter a&longs;&longs;igned B C, at right angles to D B: And as the Specificall Gravity

<lb/>of the Matter of the Piramide or Cone to be made, is to the Specificall

<lb/>Gravity of the water, &longs;o let the Altitude of the

<lb/>Rampart D B, be to the third part of the Piramide

<lb/>or Cone A B C, de&longs;cribed upon the Ba&longs;e, who&longs;e

<lb/>Diameter is B C: I &longs;ay, that the &longs;aid Cone A B C,

<lb/>and any other Cone, lower then the &longs;ame, &longs;hall re&longs;t

<lb/>upon the Surface of the water B C without &longs;inking.

<lb/></s><s>Draw D F parallel to B C, and &longs;uppo&longs;e the Pri&longs;me

<lb/>or Cylinder E C, which &longs;hall be tripple to the Cone

<lb/>A B C. And, becau&longs;e the Cylinder D C hath the &longs;ame proportion

<lb/>to the Cylinder C E, that the Altitude D B, hath to the Altitude B E:

<lb/>But the Cylinder C E, is to the Cone A B C, as the Altitude E B is to

<lb/>the third part of the Altitude of the Cone: Therefore, by Equality of

<lb/>proportion, the Cylinder D C is to the Cone A B C, as D B is to the

<lb/>third part of the Altitude B E: But as D B is to the third part of B E,

<lb/>&longs;o is the Specificall Gravity of the Cone A B C, to the Specificall Gra

<lb/>vity of the water: Therefore, as the Ma&longs;s of the Solid D C, is to the

<lb/>Ma&longs;s of the Cone A <emph type="italics"/>B<emph.end type="italics"/> C, &longs;o is the Specificall Gravity of the &longs;aid Cone,

<lb/>to the Specificall Gravity of the water: Therefore, by the precedent

<lb/>Lemma, the Cone A B C weighs in ab&longs;olute Gravity as much as a

<lb/>Ma&longs;s of Water equall to the Ma&longs;s D C: But the water which by the

<lb/>impo&longs;ition of the Cone A B C, is driven out of its place, is as much

<lb/>as would preci&longs;ely lie in the place D C, and is equall in weight to the

<lb/>Cone that di&longs;placeth it: Therefore, there &longs;hall be an <emph type="italics"/>Equilibrium,<emph.end type="italics"/>

<lb/>and the Cone &longs;hall re&longs;t without farther &longs;ubmerging. </s><s>And its ma

<lb/>nife&longs;t,</s>

<s>COROLARY I.

<s><margin.target id="marg1517"></margin.target>Among&longs;t Cones

<lb/>of the &longs;ame Ba&longs;e,

<lb/>tho&longs;e of lea&longs;t Al

<lb/>titude &longs;hall &longs;ink

<lb/>the lea&longs;t.</s>

<s><emph type="italics"/>That making upon the &longs;ame Ba&longs;is, a Cone of a le&longs;s Altitude, it &longs;hall be

<lb/>al&longs;o le&longs;s grave, and &longs;hall &longs;o much the more re&longs;t without Submer&longs;ion.<emph.end type="italics"/></s>

<s>COROLARY II.</s>

<s><emph type="italics"/>It is manife&longs;t, al&longs;o, that one may make Cones and Piramids of any Matter <emph.end type="italics"/></s>

<lb/><emph type="italics"/>what&longs;oever, more grave than the water, which being put into the

<lb/>water, with the Apix or Point downwards, re&longs;t without Submer&longs;ion. <emph.end type="italics"/></s>

<s><margin.target id="marg1518"></margin.target>There may be

<lb/>Cones and Pira

<lb/>mides of any

<lb/>Matter, which

<lb/>demitted with

<lb/>the Point down

<lb/>wards do float a

<s>Becau&longs;e if we rea&longs;&longs;ume what hath been above demon&longs;trated, of

<lb/>Pri&longs;ms and Cylinders, and that on Ba&longs;es equall to tho&longs;e of the

<lb/>&longs;aid Cylinders, we make Cones of the &longs;ame Matter, and thrree

<lb/>times as high as the Cylinders, they &longs;hall re&longs;t afloat, for that in Ma&longs;s

<lb/>and Gravity they &longs;hall be equall to tho&longs;e Cylinders, and by having

<lb/>their Ba&longs;es equall to tho&longs;e of the Cylinders, they &longs;hall leave equall

<lb/>Ma&longs;&longs;es of Air included within the Ramparts. </s><s>This, which for Exam

<lb/>ple &longs;ake hath been demon&longs;trated, in Pri&longs;ms, Cylinders, Cones and

<lb/>Piramids, might be proved in all other Solid Figures, but it would

<lb/>require a whole Volume (&longs;uch is the multitude and variety of their

<lb/>Symptoms and Accidents) to comprehend the particuler demon&longs;tration

<lb/>of them all, and of their &longs;everall Segments: but I will to avoid prolixity

<lb/>in the pre&longs;ent Di&longs;cour&longs;e, content my &longs;elf, that by what I have declared

<lb/>every one of ordinary Capacity may comprehend, that there is not

<lb/>any Matter &longs;o grave, no not Gold it &longs;elf, of which one may not form

<lb/>all &longs;orts of Figures, which by vertue of the &longs;uperiour Air adherent to

<lb/>them, and not by the Waters Re&longs;i&longs;tance of Penetration, do remain

<lb/>afloat, &longs;o that they &longs;ink not. </s><s>Nay, farther, I will &longs;hew, for removing

<lb/>that Error, that,</s>

<s>THEOREME XI.

<s><margin.target id="marg1519"></margin.target>A Piramide or

<lb/>Cone, demitted

<lb/>with the Point

<lb/>downwards &longs;hal

<lb/>&longs;wim, with its

<lb/>Ba&longs;e downward

<lb/>&longs;hall &longs;ink.</s>

<s><emph type="italics"/>A Piramide or Cone put into the Water, with the Point

<lb/>downward &longs;hall &longs;wimme, and the &longs;ame put with the

<lb/>Ba&longs;e downwards &longs;hall &longs;inke, and it &longs;hall be impo&longs;&longs;ible

<lb/>to make it float.<emph.end type="italics"/></s>

<s>Now the quite contrary would happen, if the difficulty of Pene

<lb/>trating the water, were that which had hindred the de&longs;cent, for

<lb/>that the &longs;aid Cone is far apter to pierce and penetrate with its &longs;harp

<lb/>Point, than with its broad and &longs;pacious Ba&longs;e.</s>

<s>And, to demon&longs;trate this, let the Cone be <emph type="italics"/>A B C,<emph.end type="italics"/> twice as grave

<lb/>as the water, and let its height be tripple to the height of the Rampart

<lb/><emph type="italics"/>D A E C<emph.end type="italics"/>: I &longs;ay, fir&longs;t, that being put lightly into the water with the

<pb pagenum="453"/>Point downwards, it &longs;hall not de&longs;cend to the bot

<lb/>tom: for the Aeriall Cylinder contained betwixt

<lb/>the Ramparts <emph type="italics"/>D A C E,<emph.end type="italics"/> is equall in Ma&longs;s to the

<lb/>Cone <emph type="italics"/>A B C<emph.end type="italics"/>; &longs;o that the whole Ma&longs;s of the Solid

<lb/>compounded of the Air <emph type="italics"/>D A C E,<emph.end type="italics"/> and of the Cone

<lb/><emph type="italics"/>A B C,<emph.end type="italics"/> &longs;hall be double to the Cone <emph type="italics"/>A C B:<emph.end type="italics"/> And,

<lb/>becau&longs;e the Cone <emph type="italics"/>A B C<emph.end type="italics"/> is &longs;uppo&longs;ed to be of Matter double in Gra

<lb/>vity to the water, therefore as much water as the whole Ma&longs;&longs;e

<lb/><emph type="italics"/>D A B C E,<emph.end type="italics"/> placed beneath the Levell of the water, weighs as much

<lb/>as the Cone <emph type="italics"/>A B C<emph.end type="italics"/>: and, therefore, there &longs;hall be an <emph type="italics"/>Equilibrium,<emph.end type="italics"/>

<lb/>and the Cone <emph type="italics"/>A B C<emph.end type="italics"/> &longs;hall de&longs;cend no lower. </s><s>Now, I &longs;ay farther,

<lb/>that the &longs;ame Cone placed with the Ba&longs;e downwards, &longs;hall &longs;ink to

<lb/>the bottom, without any po&longs;&longs;ibility of returning again, by any means

<lb/>to &longs;wimme.</s>

<s>Let, therefore, the Cone be <emph type="italics"/>A B D,<emph.end type="italics"/> double in Gravity to the

<lb/>water, and let its height be tripple the height

<lb/>of the Rampart of water L B: It is already

<lb/>manife&longs;t, that it &longs;hall not &longs;tay wholly out of

<lb/>the water, becau&longs;e the Cylinder being com

<lb/>prehended betwixt the Ramparts <emph type="italics"/>L B D P,<emph.end type="italics"/>

<lb/>equall to the Cone <emph type="italics"/>A B D,<emph.end type="italics"/> and the Matter of

<lb/>the Cone, beig double in Gravity to the

<lb/>water, it is evident that the weight of the &longs;aid

<lb/>Cone &longs;hall be double to the weight of the Ma&longs;s of water equall to the

<lb/>Cylinder <emph type="italics"/>L B D P<emph.end type="italics"/>: Therefore it &longs;hall not re&longs;t in this &longs;tate, but

<lb/>&longs;hall de&longs;cend.</s>

<s>COROLARY I.</s>

<s><emph type="italics"/>I &longs;ay farther; that much le&longs;&longs;e &longs;hall the &longs;aid Cone stay afloat, if one<emph.end type="italics"/></s>

<lb/><emph type="italics"/>immerge a part thereof.<emph.end type="italics"/></s>

<s><margin.target id="marg1520"></margin.target>Much le&longs;s &longs;hall

<lb/>the &longs;aid Cone

<lb/>&longs;wim, if one im

<lb/>merge a part

<lb/>thereof.</s>

<s>Which you may &longs;ee, comparing with the water as well the part

<lb/>that &longs;hall immerge as the other above water. </s><s>Let us therefore

<lb/>of the Cone A B D, &longs;ubmergeth part N T O S, and advance the

<lb/>Point N S F above water. </s><s>The Altitude of the Cone F N S, &longs;hall

<lb/>either be more than half the whole Altitude of the Cone F T O, or

<lb/>it &longs;hall not be more: if it &longs;hall be more than half, the Cone F N S

<lb/>&longs;hall be more than half of the Cylinder E N S C: for the Altitude

<lb/>of the Cone F N S, &longs;hall be more than Se&longs;quialter of the Altitude

<lb/>of the Cylinder E N S C: And, becau&longs;e the Matter of the Cone is

<lb/>&longs;uppo&longs;ed to be double in Specificall Gravity to the water, the water

<lb/>which would be contained within the Rampart E N S C, would be

<lb/>le&longs;s grave ab&longs;olutely than the Cone F N S; &longs;o that the whole Cone

<lb/>F N S cannot be &longs;u&longs;tained by the Rampart: But the part immerged

<lb/>N T O S, by being double in Specificall Gravity to the water, &longs;hall

<pb pagenum="454"/>tend to the bottom: Therefore, the whole <emph type="italics"/>C<emph.end type="italics"/>one F T O, as well in

<lb/>re&longs;pect of the part &longs;ubmerged, as the part above water &longs;hall de

<lb/>&longs;cend to the bottom. </s><s>But if the Altitude of the Point F N S, &longs;hall

<lb/>be half the Altitude of the whole Cone F T O, the &longs;ame Altitude of

<lb/>the &longs;aid <emph type="italics"/>C<emph.end type="italics"/>one F N S &longs;hall be Se&longs;quialter to the Altitude E N: and,

<lb/>therefore, E N S C &longs;hall be double to the Cone F N S; and as much

<lb/>water in Ma&longs;s as the <emph type="italics"/>C<emph.end type="italics"/>ylinder E N S C, would weigh as much as the

<lb/>part of the <emph type="italics"/>C<emph.end type="italics"/>one F N S. But, becau&longs;e the other immerged part

<lb/>N T O S, is double in Gravity to the water, a Ma&longs;s of water equall

<lb/>to that compounded of the <emph type="italics"/>C<emph.end type="italics"/>ylinder E N S C, and of the Solid N T O S,

<lb/>&longs;hall weigh le&longs;s than the <emph type="italics"/>C<emph.end type="italics"/>one F T O, by as much as the weight of

<lb/>a Ma&longs;s of water equall to the Solid N T O S: Therefore, the <emph type="italics"/>C<emph.end type="italics"/>one

<lb/>&longs;ha l al&longs;o de&longs;cend. </s><s>Again, becau&longs;e the Solid N T O S, is &longs;eptuple

<lb/>to the <emph type="italics"/>C<emph.end type="italics"/>one F N S, to which the <emph type="italics"/>C<emph.end type="italics"/>ylinder E S is double, the propor

<lb/>tion of the Solid N T O S, &longs;hall be to the <emph type="italics"/>C<emph.end type="italics"/>ylinder E N S C, as &longs;eaven

<lb/>to two: Therefore, the whole Solid compounded of the <emph type="italics"/>C<emph.end type="italics"/>ylinder

<lb/>E N S C, and of the Solid N T O S, is much le&longs;s than double the

<lb/>Solid N T O S: Therefore, the &longs;ingle Solid N T O S, is much graver

<lb/>than a Ma&longs;s of water equall to the Ma&longs;s, compounded of the <emph type="italics"/>C<emph.end type="italics"/>y

<lb/>linder E N S C, and of N T O S.</s>

<s>COROLARY II.

<s><margin.target id="marg1521"></margin.target>Part of the

<lb/>Cones towards

<lb/>the Cu&longs;pis remo

<lb/>ved, it &longs;hall &longs;till

<lb/>&longs;ink.</s>

<s><emph type="italics"/>From whence it followeth, that though one &longs;hould remove and take a

<lb/>way the part of the Cone F N S, the &longs;ole remainder N T O S would

<lb/>go to the bottom.<emph.end type="italics"/></s>

<s>COROLARY III.</s>

<s><emph type="italics"/>And if we &longs;hould more depre&longs;s the Cone F T O, it would be &longs;o much the<emph.end type="italics"/></s>

<lb/><emph type="italics"/>more impo&longs;&longs;ible that it &longs;hould &longs;u&longs;tain it &longs;elf afloat, the part &longs;ubmerged

<lb/>N T O S &longs;till encrea&longs;ing, and the Ma&longs;s of Air contained in the Rampart

<lb/>dimini&longs;hing, which ever grows le&longs;s, the more the Cone &longs;ubmergeth.<emph.end type="italics"/></s>

<s><margin.target id="marg1522"></margin.target>The more the

<lb/>Cone is immer

<lb/>ged, the more

<lb/>impo&longs;&longs;ible is its

<lb/>floating.</s>

<s>That Cone, therefore, that with its Ba&longs;e upwards, and its

<lb/><emph type="italics"/>Cu&longs;pis<emph.end type="italics"/> downwards doth &longs;wimme, being dimitted with its Ba&longs;e

<lb/>downward mu&longs;t of nece&longs;&longs;ity &longs;inke. </s><s>They have argued farre

<lb/>from the truth, therefore, who have a&longs;cribed the cau&longs;e of Natation

<lb/>to waters re&longs;i&longs;tance of Divi&longs;ion, as to a pa&longs;&longs;ive principle, and to the

<lb/>breadth of the Figure, with which the divi&longs;ion is to be made, as the

<lb/>Efficient.</s>

<s>I come in the fourth place, to collect and conclude the rea&longs;on of

<lb/>that which I have propo&longs;ed to the Adver&longs;aries, namely,</s>

<s>THE OREME XII.</s>

<s><emph type="italics"/>That it is po&longs;&longs;ible to fo m Solid Bodies, of what Figure<emph.end type="italics"/>

<lb/><emph type="italics"/>and greatne&longs;s &longs;oever, that of their own Nature goe

<lb/>to the Bottome; But by the help of the Air con

<lb/>tained in the Rampart, re&longs;t without &longs;ubmerging.<emph.end type="italics"/></s>

<s><margin.target id="marg1523"></margin.target>Solids of any

<lb/>Figure & great

<lb/>ne&longs;&longs;e, that natu

<lb/>rally &longs;ink, may

<lb/>by help of the

<lb/>Air in the Ram

<lb/>part &longs;wimme.</s>

<s>The truth of this Propo&longs;ition is &longs;ufficiently manife&longs;t in all tho&longs;e

<lb/>Solid Figures, that determine in their uppermo&longs;t part in a plane

<lb/>Superficies: for making &longs;uch Figures of &longs;ome Matter &longs;pecifi

<lb/>cally as grave as the water, putting them into the water, &longs;o that the

<lb/>whole Ma&longs;s be covered, it is manife&longs;t, that they &longs;hall re&longs;t in all

<lb/>places, provided, that &longs;uch a Matter equall in weight to the water,

<lb/>may be exactly adju&longs;ted: and they &longs;hall by con&longs;equence, re&longs;t or

<lb/>lie even with the Levell of the water, without making any Rampart.

<lb/></s><s>If, therefore, in re&longs;pect of the Matter, &longs;uch Figures are apt to re&longs;t

<lb/>without &longs;ubmerging, though deprived of the help of the Rampart,

<lb/>it is manife&longs;t, that they may admit &longs;o much encrea&longs;e of Gravity,

<lb/>(without encrea&longs;ing their Ma&longs;&longs;es) as is the weight of as much water

<lb/>as would be contained within the Rampart, that is made about their

<lb/>upper plane Surface: by the help of which being &longs;u&longs;tained, they

<lb/>&longs;hall re&longs;t afloat, but being bathed, they &longs;hall de&longs;cend, having been

<lb/>made graver than the water. </s><s>In Figures, therefore, that determine

<lb/>above in a plane, we may cleerly comprehend, that the Rampart

<lb/>added or removed, may prohibit or permit the de&longs;cent: but in tho&longs;e

<lb/>Figures that go le&longs;&longs;ening upwards towards the top, &longs;ome Per&longs;ons

<lb/>may, and that not without much &longs;eeming Rea&longs;on, doubt whether

<lb/>the &longs;ame may be done, and e&longs;pecially by tho&longs;e which terminate in a

<lb/>very acute Point, &longs;uch as are your Cones and &longs;mall Piramids. </s><s>Touch

<lb/>ing the&longs;e, therefore, as more dubious than the re&longs;t, I will endeavour

<lb/>to demon&longs;trate, that they al&longs;o lie under the &longs;ame Accident of going,

<lb/>or not going to the Bottom, be they of any whatever bigne&longs;s. </s><s>Let

<lb/>therefore the Cone be A B D, made of a matter

<lb/>&longs;pecifically as grave as the water; it is manife&longs;t

<lb/>that being put all under water, it &longs;hall re&longs;t in

<lb/>all places (alwayes provided, that it &longs;hall weigh

<lb/>exactly as much as the water, which is almo&longs;t

<lb/>impo&longs;&longs;ible to effect) and that any &longs;mall weight

<lb/>being added to it, it &longs;hall &longs;ink to the bottom:

<lb/>but if it &longs;hall de&longs;cend downwards gently, I &longs;ay,

<lb/>that it &longs;hall make the Rampart E S T O, and

<lb/>that there &longs;hall &longs;tay out of the water the point A S T, tripple in

<lb/>height to the Rampart E S: which is manife&longs;t, for the Matter of the

<pb pagenum="456"/>Cone weighing equally with the water, the part &longs;ubmerged S B D T,

<lb/>becomes indifferent to move downwards or upwards; and the Cone

<lb/><emph type="italics"/>A S T,<emph.end type="italics"/> being equall in Ma&longs;s to the water that would be contained in

<lb/>the concave of the Rampart <emph type="italics"/>E S T O,<emph.end type="italics"/> &longs;hall be al&longs;o equall unto it in

<lb/>Gravity: and, therefore, there &longs;hall be a perfect <emph type="italics"/>Equilibrium,<emph.end type="italics"/> and,

<lb/>con&longs;equently, a Re&longs;t. </s><s>Now here ari&longs;eth a doubt, whether the

<lb/>Cone <emph type="italics"/>A B D<emph.end type="italics"/> may be made heavier, in &longs;uch &longs;ort, that when it is put

<lb/>wholly under water, it goes to the bottom, but yet not in &longs;uch &longs;ort,

<lb/>as to take from the Rampart the vertue of &longs;u&longs;taining it that it &longs;ink not,

<lb/>and, the rea&longs;on of the doubt is this: that although at &longs;uch time as

<lb/>the Cone <emph type="italics"/>A B D<emph.end type="italics"/> is &longs;pecifically as grave as the water, the Rampart

<lb/><emph type="italics"/>E S T O<emph.end type="italics"/> &longs;u&longs;taines it, not only when the point <emph type="italics"/>A S T<emph.end type="italics"/> is tripple in

<lb/>height to the Altitude of the Rampart <emph type="italics"/>E S,<emph.end type="italics"/> but al&longs;o when a le&longs;&longs;er

<lb/>part is above water; [for although in the De&longs;cent of the Cone the

<lb/>Point <emph type="italics"/>A S T<emph.end type="italics"/> by little and little dimini&longs;heth, and &longs;o likewi&longs;e the

<lb/>Rampart <emph type="italics"/>E S T O,<emph.end type="italics"/> yet the Point dimini&longs;heth in

<lb/>greater proportion than the Rampart, in that

<lb/>it dimini&longs;heth according to all the three Di

<lb/>men&longs;ions, but the Rampart according to two

<lb/>only, the Altitude &longs;till remaining the &longs;ame;

<lb/>or, if you will, becau&longs;e the Cone <emph type="italics"/>S T<emph.end type="italics"/> goes di

<lb/>mini&longs;hing, according to the proportion of the

<lb/>cubes of the Lines that do &longs;ucce&longs;&longs;ively become

<lb/>the Diameters of the Ba&longs;es of emergent Cones,

<lb/>and the Ramparts dimini&longs;h according to the proportion of the

<lb/>Squares of the &longs;ame Lines; whereupon the proportions of the Points

<lb/>are alwayes Se&longs;quialter of the proportions of the Cylinders, con

<lb/>tained within the Rampart; &longs;o that if, for Example, the height of

<lb/>the emergent Point were double, or equall to the height of the

<lb/>Rampart, in the&longs;e ca&longs;es, the Cylinder contained within the Ram

<lb/>part, would be much greater than the &longs;aid Point, becau&longs;e it would be

<lb/>either &longs;e&longs;quialter or tripple, by rea&longs;on of which it would perhaps

<lb/>&longs;erve over and above to fu&longs;tain the whole Cone, &longs;ince the part &longs;ub

<lb/>merged would no longer weigh any thing;] yet, neverthele&longs;s, when

<lb/>any Gravity is added to the whole Ma&longs;s of the Cone, &longs;o that al&longs;o the

<lb/>part &longs;ubmerged is not without &longs;ome exce&longs;&longs;e of Gravity above the

<lb/>Gravity of the water, it is not manife&longs;t, whether the Cylinder con

<lb/>tained within the Rampart, in the de&longs;cent that the Cone &longs;hall make,

<lb/>can be reduced to &longs;uch a proportion unto the emergent Point, and to

<lb/>&longs;uch an exce&longs;&longs;e of Ma&longs;s above the Ma&longs;s of it, as to compen&longs;ate the

<lb/>exce&longs;&longs;e of the Cones Specificall Gravity above the Gravity of the wa

<lb/>ter: and the Scruple ari&longs;eth, becau&longs;e that howbeit in the de&longs;cent

<lb/>made by the Cone, the emergent Point <emph type="italics"/>A S T<emph.end type="italics"/> dimini&longs;heth, whereby

<lb/>there is al&longs;o a diminution of the exce&longs;s of the Cones Gravity above

<pb pagenum="459"/>the Gravity of the water, yet the ca&longs;e &longs;tands &longs;o, that the Rampart

<lb/>doth al&longs;o contract it &longs;elf, and the Cylinder contained in it doth de

<lb/>mini&longs;h. </s><s>Neverthele&longs;s it &longs;hall be demon&longs;trated, how that the Cone

<lb/><emph type="italics"/>A B D<emph.end type="italics"/> being of any &longs;uppo&longs;ed bigne&longs;&longs;e, and made at the fir&longs;t of a

<lb/>Matter exactly equall in Gravity to the Water, if there may

<lb/>be affixed to it &longs;ome Weight, by means of which it may de&longs;cend to

<lb/>the bottom, when &longs;ubmerged under water, it may al&longs;o by vertue of

<lb/>the Rampart &longs;tay above without &longs;inking.</s>

<s>Let, therefore, the Cone <emph type="italics"/>A B D<emph.end type="italics"/> be of any &longs;uppo&longs;ed greatne&longs;&longs;e,

<lb/>and alike in &longs;pecificall Gravity to the water. </s><s>It is manife&longs;t, that

<lb/>being put lightly into the water, it &longs;hall re&longs;t without de&longs;cending;

<lb/>and it &longs;hall advance above water, the Point

<lb/><emph type="italics"/>AS T,<emph.end type="italics"/> tripple in height to the height of the

<lb/>Rampart <emph type="italics"/>E S<emph.end type="italics"/>: Now, &longs;uppo&longs;e the Cone <emph type="italics"/>A B D<emph.end type="italics"/>

<lb/>more depre&longs;&longs;ed, &longs;o that it advance above wa

<lb/>ter, only the Point <emph type="italics"/>A I R,<emph.end type="italics"/> higher by half than

<lb/>the Point <emph type="italics"/>A S T,<emph.end type="italics"/> with the Rampart about it

<lb/><emph type="italics"/>C I R N.<emph.end type="italics"/> And, becau&longs;e, the Cone <emph type="italics"/>A B D<emph.end type="italics"/> is

<lb/>is to the cube of the Line <emph type="italics"/>I R,<emph.end type="italics"/> but the Cylin

<lb/>der <emph type="italics"/>E S T O,<emph.end type="italics"/> is to the Cylinder <emph type="italics"/>C I R N,<emph.end type="italics"/> as the Square of <emph type="italics"/>S T<emph.end type="italics"/> to

<lb/>the Square of <emph type="italics"/>I R,<emph.end type="italics"/> the Cone <emph type="italics"/>A S T<emph.end type="italics"/> &longs;hall be Octuple to the Cone

<lb/><emph type="italics"/>A I R,<emph.end type="italics"/> and the Cylinder <emph type="italics"/>E S T O,<emph.end type="italics"/> quadruple to the Cylinder <emph type="italics"/>C I R N<emph.end type="italics"/>:

<lb/>But the Cone <emph type="italics"/>A S T,<emph.end type="italics"/> is equall to the Cylinder E <emph type="italics"/>S T O<emph.end type="italics"/>: Therefore,

<lb/>the Cylinder <emph type="italics"/>C I R N,<emph.end type="italics"/> &longs;hall be double to the Cone <emph type="italics"/>A I R:<emph.end type="italics"/> and the

<lb/>water which might be contained in the Rampart <emph type="italics"/>C I R N,<emph.end type="italics"/> would be

<lb/>double in Ma&longs;s and in Weight to the Cone <emph type="italics"/>A I R,<emph.end type="italics"/> and, therefore,

<lb/>would be able to &longs;u&longs;tain the double of the Weight of the Cone <emph type="italics"/>AIR<emph.end type="italics"/>:

<lb/>Therefore, if to the whole Cone <emph type="italics"/>A B D,<emph.end type="italics"/> there be added as much

<lb/>Weight as the Gravity of the Cone <emph type="italics"/>A I R,<emph.end type="italics"/> that is to &longs;ay, the eighth

<lb/>part of the weight of the Cone <emph type="italics"/>A S T,<emph.end type="italics"/> it al&longs;o &longs;hall be &longs;u&longs;tained by

<lb/>the Rampart <emph type="italics"/>C I R N,<emph.end type="italics"/> but without that it &longs;hall go to the bottome:

<lb/>the Cone <emph type="italics"/>A B D,<emph.end type="italics"/> being, by the addition of the eighth part of the

<lb/>weight of the Cone <emph type="italics"/>A S T,<emph.end type="italics"/> made &longs;pecifically more grave than the

<lb/>water. </s><s>But if the Altitude of the Cone <emph type="italics"/>A I R,<emph.end type="italics"/> were two thirds

<lb/>of the Altitude of the Cone <emph type="italics"/>A S T,<emph.end type="italics"/> the Cone <emph type="italics"/>A S T<emph.end type="italics"/> would be to the

<lb/>Cone <emph type="italics"/>A I R,<emph.end type="italics"/> as twenty &longs;even to eight; and the Cylinder <emph type="italics"/>E S T O,<emph.end type="italics"/> to

<lb/>the Cylinder <emph type="italics"/>C I R N,<emph.end type="italics"/> as nine to four, that is, as twenty &longs;even to

<lb/>twelve; and, therefore, the Cylinder <emph type="italics"/>C I R N,<emph.end type="italics"/> to the Cone <emph type="italics"/>A I R,<emph.end type="italics"/>

<lb/>as twelve to eight; and the exce&longs;s of the Cylinder <emph type="italics"/>C I R N,<emph.end type="italics"/> above

<lb/>the Cone <emph type="italics"/>A I R,<emph.end type="italics"/> to the Cone <emph type="italics"/>A S T,<emph.end type="italics"/> as four to twenty &longs;even: there

<lb/>fore if to the Cone <emph type="italics"/>A B D<emph.end type="italics"/> be added &longs;o much weight as is the four

<lb/>twenty &longs;evenths of the weight of the Cone <emph type="italics"/>A S T,<emph.end type="italics"/> which is a little

<lb/>more then its &longs;eventh part, it al&longs;o &longs;hall continue to &longs;wimme, and

<pb pagenum="460"/>the height of the emergent Point &longs;hall be double to the height of the

<lb/>Rampart. </s><s>This that hath been demon&longs;trated in Cones, exactly holds

<lb/>in Piramides, although the one or the other &longs;hould be very &longs;harp in

<lb/>their Point or Cu&longs;pis: From whence we conclude, that the &longs;ame

<lb/>Accident &longs;hall &longs;o much the more ea&longs;ily happen in all other Figures,

<lb/>by how much the le&longs;s &longs;harp the Tops &longs;hall be, in which they deter

<lb/>mine, being a&longs;&longs;i&longs;ted by more &longs;pacious Ramparts.</s>

<s><margin.target id="marg1524"></margin.target>Natatiou ea&longs;i

<lb/>e&longs;t effected in

<lb/>Figures broad

<lb/>toward the top.</s>

<s>THEOREME XIII.

<s><margin.target id="marg1525"></margin.target>All Figures &longs;ink

<lb/>or &longs;wim, upon

<lb/>bathing or not

<lb/>bathing of their

<s><emph type="italics"/>All Figures, therefore, of whatever greatne&longs;&longs;e, may

<lb/>go, and not go, to the Bottom, according as their Sumi

<lb/>ties or Tops &longs;hall be bathed or not bathed.<emph.end type="italics"/></s>

<s>And this Accident being common to all &longs;orts of Figures, without

<lb/>exception of &longs;o much as one. </s><s>Figure hath, therefore, no part

<lb/>in the production of this Effect, of &longs;ometimes &longs;inking, and &longs;ome

<lb/>times again not &longs;inking, but only the being &longs;ometimes conjoyned

<lb/>to, and &longs;ometimes &longs;eperated from, the &longs;upereminent Air: which

<lb/>cau&longs;e, in fine, who &longs;o &longs;hall rightly, and, as we &longs;ay, with both his

<lb/>Eyes, con&longs;ider this bu&longs;ine&longs;s, will find that it is reduced to, yea, that

<lb/>it really is the &longs;ame with, the true, Naturall and primary cau&longs;e of

<lb/>Natation or Submer&longs;ion; to wit, the exce&longs;s or deficiency of the

<lb/>Gravity of the water, in relation to the Gravity of that Solid Mag

<lb/>nitude, that is demitted into the water. </s><s>For like as a Plate of Lead,

<lb/>as thick as the back of a Knife, which being put into the water by it

<lb/>&longs;elf alone goes to the bottom, if upon it you fa&longs;ten a piece of Cork

<lb/>four fingers thick, doth continue afloat, for that now the Solid that

<lb/>is demitted in the water, is not, as before, more grave than the water,

<lb/>but le&longs;s, &longs;o the Board of Ebony, of its own nature more grave than

<lb/>water; and, therefore, de&longs;cending to the bottom, when it is demit

<lb/>ted by it &longs;elf alone into the water, if it &longs;hall be put upon the water,

<lb/>conjoyned with an Expanded vail of Air, that together with the

<lb/>Ebony doth de&longs;cend, and that it be &longs;uch, as that it doth make with

<lb/>it a compound le&longs;s grave than &longs;o much water in Ma&longs;s, as equalleth

<lb/>the Ma&longs;s already &longs;ubmerged and depre&longs;&longs;ed beneath the Levell of the

<lb/>waters Surface, it &longs;hall not de&longs;cend any farther, but &longs;hall re&longs;t, for

<lb/>no other than the univer&longs;all and mo&longs;t common cau&longs;e, which is that

<lb/>Solid Magnitudes, le&longs;s grave <emph type="italics"/>in&longs;pecie<emph.end type="italics"/> than the water, go not to the

<lb/>bottom.</s>

<s>So that if one &longs;hould take a Plate of Lead, as for Example, a finger

<lb/>thick, and an handfull broad every way, and &longs;hould attempt to make

<lb/>it &longs;wimme, with putting it lightly on the water, he would lo&longs;e his

<lb/>Labour, becau&longs;e that if it &longs;hould be depre&longs;&longs;ed an Hairs breadth be

<pb pagenum="461"/>yond the po&longs;&longs;ible Altitude of the Ramparts of water, it would dive

<lb/>and &longs;ink; but if whil&longs;t it is going downwards, one &longs;hould make

<lb/>certain Banks or Ramparts about it, that &longs;hould hinder the do fu&longs;ion

<lb/>of the water upon the &longs;aid Plate, the which Banks &longs;hould ri&longs;e &longs;o

<lb/>high, as that they might be able to contain as much water, as &longs;hould

<lb/>weigh equally with the &longs;aid Plate, it would, without all Que&longs;tion,

<lb/>de&longs;cend no lower, but would re&longs;t, as being &longs;u&longs;tained by vertue of

<lb/>the Air contained within the afore&longs;aid Ramparts: and, in &longs;hort,

<lb/>there would be a Ve&longs;&longs;ell by this means formed with the bottom of

<lb/>Lead. </s><s>But if the thinne&longs;s of the Lead &longs;hall be &longs;uch, that a very

<lb/>&longs;mall height of Rampart would &longs;uffice to contain &longs;o much Air, as might

<lb/>keep it afloat, it &longs;hall al&longs;o re&longs;t without the Artificiall Banks or Ram

<lb/>parts, but yet not without the Air, becau&longs;e the Air by it &longs;elf makes

<lb/>Banks &longs;ufficient for a &longs;mall height, to re&longs;i&longs;t the Superfu&longs;ion of the

<lb/>water: &longs;o that that which in this ca&longs;e &longs;wimmes, is as it were a

<lb/>Ve&longs;&longs;ell filled with Air, by vertue of which it continueth afloat.</s>

<s>I will, in the la&longs;t place, with an other Experimeut, attempt to

<lb/>remove all difficulties, if &longs;o be there &longs;hould yet be any doubt le&longs;t in

<lb/>any one, touching the opperation of this ^{*}Continuity of the Air, with </s>

<lb/>the thin Plate which &longs;wims, and afterwards put an end to this part of

<lb/>my di&longs;cour&longs;e.</s>

<s><margin.target id="marg1526"></margin.target>*Or rather Cor

<lb/>tiguity,</s>

<s>I &longs;uppo&longs;e my &longs;elf to be que&longs;tioning with &longs;ome of my Oponents.</s>

<s>Whether Figure have any influence upon the encrea&longs;e or diminu

<lb/>tion of the Re&longs;i&longs;tance in any Weight again&longs;t its being rai&longs;ed in the

<lb/>Air, and I &longs;uppo&longs;e, that I am to maintain the Affirmative, a&longs;&longs;ert

<lb/>ing that a Ma&longs;s of Lead, reduced to the Figure of a Ball, &longs;hall be

<lb/>rai&longs;ed with le&longs;s force, then if the &longs;ame had been made into a thinne

<lb/>and broad Plate, becau&longs;e that it in this &longs;pacious Figure, hath a great

<lb/>quantity of Air to penetrate, and in that other, more compacted and

<lb/>contracted very little: and to demon&longs;trate the truth of &longs;uch my O

<lb/>pinion, I will hang in a &longs;mall thred fir&longs;t the Ball or Bullet, and put

<lb/>that into the water, tying the thred that upholds it to one end of

<lb/>the Ballance that I hold in the Air, and to the other end I by degrees

<lb/>adde &longs;o much Weight, till that at la&longs;t it brings up the Ball of Lead

<lb/>out of the water: to do which, &longs;uppo&longs;e a Gravity of thirty Ounces

<lb/>&longs;ufficeth; I afcerwards reduce the &longs;aid Lead into a flat and thinne

<lb/>Plate, the which I likewi&longs;e put into the water, &longs;u&longs;pended by three

<lb/>threds, which hold it parallel to the Surface of the water, and put

<lb/>ting in the &longs;ame manner, Weights to the other end, till &longs;uch time as

<lb/>the Place comes to be rai&longs;ed and drawn out of the water: I finde

<lb/>that thirty &longs;ix ounces will not &longs;uffice to &longs;eperate it from the water,

<lb/>and rai&longs;e it thorow the Air: and arguing from this Experiment, I af

<lb/>firm, that I have fully demon&longs;trated the truth of my Propo&longs;ition.

<lb/></s><s>He re my Oponents de&longs;ires me to look down, &longs;hewing me a thing

<pb pagenum="462"/>which I had not before ob&longs;erved, to wit, that in the A&longs;cent of the

<lb/>Plate out of the water, it draws after it another Plate <emph type="italics"/>(if I may &longs;o

<lb/>call it)<emph.end type="italics"/> of water, which before it divides and parts from the inferiour

<lb/>Surface of the Plate of Lead, is rai&longs;ed above the Levell of the other

<lb/>water, more than the thickne&longs;s of the back of a Knife: Then he

<lb/>goeth to repeat the Experiment with the Ball, and makes me &longs;ee,

<lb/>that it is but a very &longs;mall quantity of water, which cleaves to its

<lb/>compacted and contracted Figure: and then he &longs;ubjoynes, that its

<lb/>no wonder, if in &longs;eperating the thinne and broad Plate from the

<lb/>water, we meet with much greater Re&longs;i&longs;tance, than in &longs;eperating the

<lb/>Ball, &longs;ince together with the Plate, we are to rai&longs;e a great quantity of

<lb/>water, which occurreth not in the Ball: He telleth me moreover,

<lb/>how that our Que&longs;tion is, whether the Re&longs;i&longs;tance of Elevation be

<lb/>greater in a dilated Plate of Lead, than in a Ball, and not whether

<lb/>more re&longs;i&longs;teth a Plate of Lead with a great quantity of water, or a

<lb/>Ball with a very little water: He &longs;heweth me in the clo&longs;e, that the

<lb/>putting the Plate and the Ball fir&longs;t into the water, to make proofe

<lb/>thereby of their Re&longs;i&longs;tance in the Air, is be&longs;ides our ca&longs;e, which

<lb/>treats of Elivating in the Air, and of things placed in the Air, and

<lb/>not of the Re&longs;i&longs;tance that is made in the Confines of the Air and

<lb/>water, and by things which are part in Air and part in water: and

<lb/>la&longs;tly, they make me feel with my hand, that when the thinne Plate

<lb/>is in the Air, and free from the weight of the water, it is rai&longs;ed with

<lb/>the very &longs;ame Force that rai&longs;eth the Ball. </s><s>Seeing, and under&longs;tand

<lb/>ing the&longs;e things, I know not what to do, unle&longs;s to grant my &longs;elf con

<lb/>vinced, and to thank &longs;uch a Friend, for having made me to &longs;ee that

<lb/>which I never till then ob&longs;erved: and, being adverti&longs;ed by this &longs;ame

<lb/>Accident, to tell my Adver&longs;aries, that our Que&longs;tion is, whether a

<lb/>Board and a Ball of Ebony, equally go to the bottom in water, and

<lb/>not a Ball of Ebony and a Board of Ebony, joyned with another

<lb/>flat Body of Air: and, farthermore, that we &longs;peak of &longs;inking, and

<lb/>not &longs;inking to the bottom, in water, and not of that which happeneth

<lb/>in the Confines of the water and Air to Bodies that be part in the

<lb/>Air, and part in the water; nor much le&longs;s do we treat of the greater

<lb/>or le&longs;&longs;er Force requi&longs;ite in &longs;eperating this or that Body from the Air;

<lb/>not omitting to tell them, in the la&longs;t place, that the Air doth re&longs;i&longs;t,

<lb/>and gravitate downwards in the water, ju&longs;t &longs;o much as the water (if

<lb/>I may &longs;o &longs;peak) gravitates and re&longs;i&longs;ts upwards in the Air, and that the

<lb/>&longs;ame force is required to &longs;inke a Bladder under water, that is full of

<lb/>Air, as to rai&longs;e it in the Air, being full of water, removing the con

<lb/>&longs;ideration of the weight of that Filme or Skinne, and confidering the

<lb/>water and the Air only. </s><s>And it is likewi&longs;e true, that the &longs;ame Force

<lb/>is required to &longs;ink a Cup or &longs;uch like Ve&longs;&longs;ell under water, whil&longs;t it is

<lb/>full of Air, as to rai&longs;e it above the Superficies of the water, keeping

<pb pagenum="463"/>it with the mouth downwards; whil&longs;t it is full of water, which is

<lb/>con&longs;trained in the &longs;ame manner to follow the Cup which contains it,

<lb/>and to ri&longs;e above the other water into the Region of the Air, as the

<lb/>Air is forced to follow the &longs;ame Ve&longs;&longs;ell under the Surface of the wa

<lb/>ter, till that in this ca&longs;e the water, &longs;urmounting the brimme of the

<lb/>Cup, breaks in, driving thence the Air, and in that ca&longs;e, the &longs;aid

<lb/>brimme coming out of the water, and arriving to the Confines of the

<lb/>Air, the water falls down, and the Air &longs;ub-enters to fill the cavity of

<lb/>the Cup: upon which en&longs;ues, that he no le&longs;s tran&longs;gre&longs;&longs;es the Arti

<lb/>cles of the <emph type="italics"/>Convention,<emph.end type="italics"/> who produceth a Plate conjoyned with much

<lb/>Air, to &longs;ee if it de &longs;eend to the bottom in water, then he that makes

<lb/>proof of the Re&longs;i&longs;tance again&longs;t Elevation in Air with a Plate of Lead,

<lb/>joyned with a like quantity of water.</s>

<s><margin.target id="marg1527"></margin.target>An Experi

<lb/>ment of the op

<lb/>peration of Fi

<lb/>gures, in en

<lb/>crea&longs;ing or le&longs;

<lb/>&longs;ening of the

<lb/>Airs Re&longs;i&longs;tance

<lb/>of Divi&longs;ion.</s>

<s>I have &longs;aid all that I could at pre&longs;ent think of, to maintain the

<lb/>A&longs;&longs;ertion I have undertook. </s><s>It remains, that I examine that which

<lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> hath writ of this matter towards the end of his Book <emph type="italics"/>De Cælo<emph.end type="italics"/>;

<lb/>wherein I &longs;hall note two things: the one that it being true as hath

<lb/>been demon&longs;trated, that Figure hath nothing to do about the moving

<lb/>or not moving it &longs;elf upwards or downwards, it &longs;eemes that <emph type="italics"/>Aristotle<emph.end type="italics"/>

<lb/>at his fir&longs;t falling upon this Sp. </s><s>culation, was of the &longs;ame opinion, as

<lb/>in my opinion may be collected from the examination of his words.

<lb/></s><s>Tis true, indeed, that in e&longs;&longs;aying afterwards to render a rea&longs;on of

<lb/>&longs;uch effect, as not having in my conceit hit upon the right, (which

<lb/>in the &longs;econd place I will examine) it &longs;eems that he is brought to

<lb/>admit the largene&longs;&longs;e of Figure, to be intere&longs;&longs;ed in this operation.

<lb/></s><s>As to the fir&longs;t particuler, hear the preci&longs;e words of <emph type="italics"/>Aristotle.<emph.end type="italics"/></s>

<s><margin.target id="marg1528"></margin.target><emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> opi

<lb/>nion touching

<lb/>the Operation

<lb/>of Figure ex

<lb/>amined.</s>

<s><margin.target id="marg1529"></margin.target><emph type="italics"/>Ari&longs;tot de Cælo,<emph.end type="italics"/>

<lb/>Lib. 4. Cap.

66.</s>

<s><emph type="italics"/>Figures are not the Cau&longs;es of moving &longs;imply upwards or downwards,<emph.end type="italics"/>

<lb/><emph type="italics"/>but of moving more &longs;lowly or &longs;wiftly, and by what means this comes to

<lb/>pa&longs;s, it is not difficult to &longs;ee.<emph.end type="italics"/></s>

<s><margin.target id="marg1530"></margin.target><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> makes

<lb/>not Figure the

<lb/>cau&longs;e of Motion

<lb/>ab&longs;olutely, but

<lb/>of &longs;wi&longs;t or &longs;low

<lb/>motion,</s>

<s>Here fir&longs;t I note, that the terms being four, which fall under the

<lb/>pre&longs;ent con&longs;ideration, namely, Motion, Re&longs;t, Slowly and Swiftly:

<lb/>And <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> naming Figures as Cau&longs;es of Tardity and Velocity, ex

<lb/>cluding them from being the Cau&longs;e of ab&longs;olute and &longs;imple Motion,

<lb/>it &longs;eems nece&longs;&longs;ary, that he exclude them on the other &longs;ide, from being

<lb/>the Cau&longs;e of Re&longs;t, &longs;o that his meaning is this. </s><s>Figures are not the

<lb/>Cau&longs;es of moving or not moving ab&longs;olutely, but of moving quickly

<lb/>or &longs;lowly: and, here, if any &longs;hould &longs;ay the mind of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> is to

<lb/>exclude Figures from being Cau&longs;es of Motion, but yet not from

<lb/>being Cau&longs;es of Re&longs;t, &longs;o that the &longs;ence would be to remove from

<lb/>Figures, there being the Cau&longs;es of moving &longs;imply, but yet not there

<lb/>being Cau&longs;es of Re&longs;t, I would demand, whether we ought with

<lb/><emph type="italics"/>Aristotle<emph.end type="italics"/> to under&longs;tand, that all Figures univer&longs;ally, are, in &longs;ome

<lb/>manner, the cau&longs;es of Re&longs;t in tho&longs;e Bodies, which otherwi&longs;e would

<lb/>move, or el&longs;e &longs;ome particular Figures only, as for Example, broad

<pb pagenum="464"/>and thinne Figures: If all indifferently, then every Body &longs;hall re&longs;t:

<lb/>becau&longs;e every Body hath &longs;ome Figure, which is fal&longs;e: but if &longs;ome

<lb/>particular Figures only may be in &longs;ome manner a Cau&longs;e of Re&longs;t, as,

<lb/>for Example, the broad, then the others would be in &longs;ome manner

<lb/>the Cau&longs;es of Motion: for if from &longs;eeing &longs;ome Bodies of a contracted

<lb/>Figure move, which after dilated into Plates re&longs;t, may be inferred,

<lb/>that the Amplitude of Figure hath a part in the Cau&longs;e of that Re&longs;t;

<lb/>&longs;o from &longs;eeing &longs;uch like Figures re&longs;t, which afterwards contracted

<lb/>move, it may with the &longs;ame rea&longs;on be affirmed, that the united and

<lb/>contracted Figure, hath a part in cau&longs;ing Motion, as the remover of

<lb/>that which impeded it: The which again is directly oppo&longs;ite to what

<lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;aith, namely, that Figures are not the Cau&longs;es of Motion.

<lb/></s><s>Be&longs;ides, if <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> had admitted and not excluded Figures from be

<lb/>ing Cau&longs;es of not moving in &longs;ome Bodies, which moulded into ano

<lb/>ther Figure would move, he would have impertinently propounded

<lb/>in a dubitative manner, in the words immediately following, whence

<lb/>it is, that the large and thinne Plates of Lead or Iron, re&longs;t upon the

<lb/>water, &longs;ince the Cau&longs;e was apparent, namely, the Amplitude of

<lb/>Figure. </s><s>Let us conclude, therefore, that the meaning of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>

<lb/>in this place is to affirm, that Figures are not the Cau&longs;es of ab&longs;olutely

<lb/>moving or not moving, but only of moving &longs;wiftly or &longs;lowly: which

<lb/>we ought the rather to believe, in regard it is indeed a me&longs;t true con

<lb/>ceipt and opinion. </s><s>Now the mird of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> being &longs;uch, and ap

<lb/>pearing by con&longs;equence, rather contrary at the fir&longs;t &longs;ight, then fa

<lb/>vourable to the a&longs;&longs;ertion of the Oponents, it is nece&longs;&longs;ary, that their

<lb/>Interpretation be not exactly the &longs;ame with that, but &longs;uch, as being

<lb/>in part under&longs;tood by &longs;ome of them, and in part by others, was &longs;et

<lb/>down: and it may ea&longs;ily be indeed &longs;o, being an Interpretation

<lb/>con&longs;onent to the &longs;ence of the more famous Interpretors, which is,

<lb/>that the Adverbe <emph type="italics"/>Simply<emph.end type="italics"/> or <emph type="italics"/>Ab&longs;olutely,<emph.end type="italics"/> put in the Text, orght not to

<lb/>be joyned to the Verbe to <emph type="italics"/>Move,<emph.end type="italics"/> but with the Noun <emph type="italics"/>Cau&longs;es<emph.end type="italics"/>: &longs;o that

<lb/>the purport of <emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> words, is to affirm, That Figures are not the

<lb/>Cau&longs;es ab&longs;olutely of moving or not moving, but yet are Cau&longs;es <emph type="italics"/>Se

<lb/>cundum quid, viz<emph.end type="italics"/> in &longs;ome &longs;ort; by which means, they are called

<lb/>Auxiliary and Concomitant Cau&longs;es: and this Propo&longs;ition is received

<lb/>and a&longs;&longs;erted as true by <emph type="italics"/>Signor Buonamico Lib.<emph.end type="italics"/> 5. <emph type="italics"/>Cap.<emph.end type="italics"/> 28. where he

<lb/>thus writes. <emph type="italics"/>There are other Cau&longs;es concomitant, by which &longs;ome

<lb/>things float, and others &longs;ink, among which the Figures of Bodies hath

<lb/>the fir&longs;t place,<emph.end type="italics"/> &c.</s>

<s><margin.target id="marg1531"></margin.target>Lib. 4. Cap.

<s>Concerning this Propo&longs;ition, I meet with many doubts and diffi

<lb/>culties, for which me thinks the words of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> are not capable of

<lb/>&longs;uch a con&longs;truction and &longs;ence, and the difficulties are the&longs;e.</s>

<s>Fir&longs;t in the order and di&longs;po&longs;ure of the words of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> the par

<lb/>ticle <emph type="italics"/>Simpliciter,<emph.end type="italics"/> or if you will <emph type="italics"/>ab&longs;oluté,<emph.end type="italics"/> is conjoyned with the Verb

<pb pagenum="465"/><emph type="italics"/>to move,<emph.end type="italics"/> and &longs;eperated from the Noun <emph type="italics"/>Cau&longs;es,<emph.end type="italics"/> the which is a great

<lb/>pre&longs;umption in my favour, &longs;eeing that the writing and the Text

<lb/>&longs;aith, Figures are not the Cau&longs;e of moving &longs;imply upwards or

<lb/>downwards, but of quicker or &longs;lower Motion: and, &longs;aith not,

<lb/>Figures are not &longs;imply the Cau&longs;es of moving upwards or down

<lb/>wards, and when the words of a Text receive, tran&longs;po&longs;ed, a &longs;ence

<lb/>different from that which they found, taken in the order wherein

<lb/>the Author di&longs;po&longs;eth them, it is not convenient to inverte them.

<lb/></s><s>And who will affirm that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> de&longs;iring to write a Propo&longs;ition,

<lb/>would di&longs;po&longs;e the words in &longs;uch &longs;ort, that they &longs;hould import a

<lb/>different, nay, a contrary &longs;ence? </s><s>contrary, I &longs;ay, becau&longs;e under

<lb/>&longs;tood as they are written; they &longs;ay, that Figures are not the

<lb/>Cau&longs;es of Motion, but inverted, they &longs;ay, that Figures are the

<lb/>Cau&longs;es of Motion, &c.</s>

<s>Moreover, if the intent of <emph type="italics"/>Aristotle<emph.end type="italics"/> had been to &longs;ay, that Figures

<lb/>are not &longs;imply the Cau&longs;es of moving upwards or downwards, but

<lb/>only Cau&longs;es <emph type="italics"/>Secundum quid,<emph.end type="italics"/> he would not have adjoyned tho&longs;e

<lb/>words, <emph type="italics"/>but they are Cau&longs;es of the more &longs;wift or &longs;low Motion<emph.end type="italics"/>; yea, the

<lb/>&longs;ubjoining this would have been not only &longs;uperfluous but fal&longs;e, for

<lb/>that the whole tenour of the Propo&longs;ition would import thus much.

<lb/></s><s>Figures are not the ab&longs;olute Cau&longs;es of moving upwards or down

<lb/>wards, but are the ab&longs;olute Cau&longs;e of the &longs;wift or &longs;low Motion;

<lb/>which is not true: becau&longs;e the primary Cau&longs;es of greater or le&longs;&longs;er

<lb/>Velocity, are by <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in the 4th of his <emph type="italics"/>Phy&longs;icks, Text.<emph.end type="italics"/> 71. attri

<lb/>buted to the greater or le&longs;&longs;er Gravity of Moveables, compared a

<lb/>mong them&longs;elves, and to the greater or le&longs;&longs;er Re&longs;i&longs;tance of the

<lb/><emph type="italics"/>Medium's,<emph.end type="italics"/> depending on their greater or le&longs;s Cra&longs;&longs;itude: and the&longs;e

<lb/>are in&longs;erted by <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> as the primary Cau&longs;es; and the&longs;e two only

<lb/>are in that place nominated: and Figure comes afterwards to be

<lb/>con&longs;idered, <emph type="italics"/>Text.<emph.end type="italics"/> 74. rather as an In&longs;trumentall Cau&longs;e of the force

<lb/>of the Gravity, the which divides either with the Figure, or with

<lb/>the <emph type="italics"/>Impetus<emph.end type="italics"/>; and, indeed, Figure by it &longs;elf without the force of

<lb/>Gravity or Levity, would opperate nothing.</s>

<s>Iadde, that if <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> had an opinion that Figure had been in

<lb/>&longs;ome &longs;ort the Cau&longs;e of moving or not moving, the inqui&longs;ition

<lb/>which he makes immediately in a doubtfull manner, whence it

<lb/>comes, that a Plate of Lead flotes, would have been impertinent;

<lb/>for if but ju&longs;t before he had &longs;aid, that Figure was in a certain &longs;ort

<lb/>the Cau&longs;e of moving or not moving, he needed not to call in

<lb/>Que&longs;tion, by what Cau&longs;e the Plate of Lead &longs;wims, and then a&longs;cri

<lb/>bing the Cau&longs;e to its Figure; and framing a di&longs;cour&longs;e in this manner.

<lb/></s><s>Figure is a Cau&longs;e <emph type="italics"/>Secundum quid<emph.end type="italics"/> of not &longs;inking: but, now, if it be

<lb/>doubted, for what Cau&longs;e a thin Plate of Lead goes not to the bottom;

<lb/>it &longs;hall be an&longs;wered, that that proceeds from its Figure: a di&longs;cour&longs;e

<pb pagenum="466"/>which would be indecent in a Child, much more in <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>; For

<lb/>where is the occa&longs;ion of doubting? </s><s>And who &longs;ees not, that if <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>

<lb/>had held, that Figure was in &longs;ome &longs;ort a Cau&longs;e of Natation, he

<lb/>would without the lea&longs;t He&longs;itation have writ; That Figure is in a

<lb/>certain &longs;ort the Cau&longs;e of Natation, and therefore the Plate of Lead

<lb/>in re&longs;pect of its large and expatiated Figure &longs;wims; but if we take

<lb/>the propo&longs;ition of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> as I &longs;ay, and as it is writte n, and as in

<lb/>deed it is true, the en&longs;uing words come in very oppo&longs;itely, as well in

<lb/>the introduction of &longs;wift and &longs;low, as in the que&longs;tion, which very

<lb/>pertinently offers it &longs;elf, and would &longs;ay thus much.</s>

<s>Figures are not the Cau&longs;e of moving or not moving &longs;imply up

<lb/>wards or downwards, but of moving more quickly or &longs;lowly: But if

<lb/>it be &longs;o, the Cau&longs;e is doubtfull, whence it proceeds, that a Plate of

<lb/>Lead or of Iron broad and thin doth &longs;wim, &c. </s><s>And the occa&longs;ion of

<lb/>the doubt is obvious, becau&longs;e it &longs;eems at the fir&longs;t glance, that the

<lb/>Figure is the Cau&longs;e of this Natation, &longs;ince the &longs;ame Lead, or a le&longs;s

<lb/>quantity, but in another Figure, goes to the bottom, and we have

<lb/>already affirmed, that the Figure hath no &longs;hare in this effect.</s>

<s>La&longs;tly, if the intent of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in this place had been to &longs;ay,

<lb/>that Figures, although not ab&longs;olutely, are at lea&longs;t in &longs;ome mea&longs;ure

<lb/>the Cau&longs;e of moving or not moving: I would have it con&longs;idered,

<lb/>that he names no le&longs;s the Motion upwards, than the other down

<lb/>wards: and becau&longs;e in exemplifying it afterwards, he produceth

<lb/>no other Experiments than of a Plate of Lead, and Board of Ebony,

<lb/>Matters that of their own Nature go to the bottom, but by vertue

<lb/>(as our Adver&longs;aries &longs;ay) of their Figure, re&longs;t afloat; it is &longs;it that

<lb/>they &longs;hould produce &longs;ome other Experiment of tho&longs;e Matters, which

<lb/>by their Nature &longs;wims, but retained by their Figure re&longs;t at the

<lb/>bottom. </s><s>But &longs;ince this is impo&longs;&longs;ible to be done, we conclude, that

<lb/><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in this place, hath not attributed any action to the Figure

<lb/>of &longs;imply moving or not moving.</s>

<s>But though he hath exqui&longs;itely Philo&longs;ophiz'd, in inve&longs;tigating

<lb/>the &longs;olution of the doubts he propo&longs;eth, yet will I not undertake

<lb/>to maintain, rather various difficulties, that pre&longs;ent them&longs;elves

<lb/>unto me, give me occa&longs;ion of &longs;u&longs;pecting that he hath not entirely

<lb/>di&longs;plaid unto us, the true Cau&longs;e of the pre&longs;ent Conclu&longs;ion: which

<lb/>difficulties I will propound one by one, ready to change opinion,

<lb/>when ever I am &longs;hewed, that the Truth is different from what I &longs;ay;

<lb/>to the confe&longs;&longs;ion whereof I am much more inclinable than to contra

<lb/>diction.

<s><margin.target id="marg1532"></margin.target><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> erred

<lb/>in affirming a

<lb/>Needle dimitted

<lb/>long wayes to

<lb/>&longs;ink.</s>

<s><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> having propounded the Que&longs;tion, whence it proceeds,

<lb/>that broad Plates of Iron or Lead, float or &longs;wim; he addeth (as

<lb/>it were &longs;trengthening the occa&longs;ion of doubting) fora&longs;much as other

<lb/>things, le&longs;s, and le&longs;s grave, be they round or long, as for in&longs;tance a

<pb pagenum="467"/>Needle go to the bottom. </s><s>Now I here doubt, or rather am certain,

<lb/>that a Needle put lightly upon the water, re&longs;ts afloat, no le&longs;s than the

<lb/>thin Plates of Iron or Lead. </s><s>I cannot believe, albeit it hath been

<lb/>told me, that &longs;ome to defend <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;hould &longs;ay, that he intends a

<lb/>Needle demitted not longwayes but endwayes, and with the Point

<lb/>downwards; neverthele&longs;s, not to leave them &longs;o much as this, though

<lb/>very weak refuge, and which in my judgement <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf

<lb/>would refu&longs;e, I &longs;ay it ought to be under&longs;tood, that the Needle mu&longs;t

<lb/>be demitted, according to the Dimen&longs;ion named by <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> which

<lb/>is the length: becau&longs;e, if any other Dimen&longs;ion than that which is

<lb/>named, might or ought to be taken, I would &longs;ay, that even the Plates

<lb/>of Iron and Lead, &longs;ink to the bottom, if they be put into the water

<lb/>edgewayes and not flatwayes. </s><s>But becau&longs;e <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;aith, broad

<lb/>Figures go not to the bottom, it is to be under&longs;tood, being demitted

<lb/>broadwayes: and, therefore, when he &longs;aith, long Figures as a

<lb/>Needle, albeit light, re&longs;t not afloat, it ought to be under&longs;tood of

<lb/>them when demitted longwayes.</s>

<s><emph type="italics"/>Morcover, to &longs;ay that<emph.end type="italics"/> Ari&longs;totle <emph type="italics"/>is to be under&longs;tood of the Needle de

<lb/>mitted with the Point downwards, is to father upon him a great imper

<lb/>tinency; for in this place he &longs;aith, that little Particles of Lead or Iron,

<lb/>if they be round or long as a Needle, do &longs;ink to the bottome; &longs;o that by

<lb/>his Opinion, a Particle or &longs;mall Grain of Iron cannot &longs;wim: and if he

<lb/>thus believed, what a great folly would it be to &longs;ubjoyn, that neither

<lb/>would a Needle demitted endwayes &longs;wim? </s><s>And what other is &longs;uch a

<lb/>Needle, but many &longs;uch like Graines accumulated one upon another? </s><s>It

<lb/>was too unworthy of &longs;uch a man to &longs;ay, that one &longs;ingle Grain of Iron could

<lb/>not &longs;wim, and that neither can it &longs;wim, though you put a hundred more

<s>La&longs;tly, either <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> believed, that a Needle demitted long

<lb/>wayes upon the water, would &longs;wim, or he believed that it would

<lb/>not &longs;wim: If he believed it would not &longs;wim, he might well &longs;peak

<lb/>as indeed he did; but if he believed and knew that it would &longs;loat,

<lb/>why, together with the dubious Problem of the Natation of broad

<lb/>Figure, though of ponderous Matter, hath he not al&longs;o introduced

<lb/>the Que&longs;tion; whence it proceeds, that even long and &longs;lender Fi

<lb/>gures, howbeit of Iron or Lead do &longs;wim? </s><s>And the rather, for that

<lb/>the occa&longs;ion of doubting &longs;eems greater in long and narrow Figures,

<lb/>than in broad and thin, as from <emph type="italics"/>Aristotles<emph.end type="italics"/> not having doubted of it,

<lb/>is manife&longs;ted.</s>

<s>No le&longs;&longs;er an inconvenience would they fa&longs;ten upon <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> who

<lb/>in his defence &longs;hould &longs;ay, that he means a Needle pretty thick, and

<lb/>not a &longs;mall one; for take it for granted to be intended of a &longs;mall one

<pb pagenum="468"/>and it &longs;hall &longs;uffice to reply, that he believed that it would &longs;wim;

<lb/>and I will again charge him with having avoided a more wonderfull

<lb/>and intricate Probleme, and introduced the more facile and le&longs;s

<lb/>wonderfull.</s>

<s>We &longs;ay freely therefore; that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> did hold, that only the

<lb/>broad Figure did &longs;wim, but the long and &longs;lender, &longs;uch as a Needle,

<lb/>not. </s><s>The which neverthele&longs;s is fal&longs;e, as it is al&longs;o fal&longs;e in round

<lb/>Bodies: becau&longs;e, as from what hath been predemon&longs;trated, may be ga

<lb/>thered, little Balls of Lead and Iron, do in like manner &longs;wim.</s>

<s>He propo&longs;eth likewi&longs;e another Conclu&longs;ion, which likewi&longs;e &longs;eems </s>

<lb/>different from the truth, and it is, That &longs;ome things, by rea&longs;on of

<lb/>their littlene&longs;s fly in the Air, as the &longs;mall du&longs;t of the Earth, and the

<lb/>thin leaves of beaten Gold: but in my Opinion, Experience &longs;hews

<lb/>us, that that happens not only in the Air, but al&longs;o in the water, in

<lb/>which do de&longs;cend, even tho&longs;e Particles or Atomes of Earth, that

<lb/>di&longs;tur be it, who&longs;e minuity is &longs;uch, that they are not de&longs;ervable, &longs;ave

<lb/>only when they are many hundreds together. </s><s>Therefore, the du&longs;t

<lb/>of the Earth, and beaten Gold, do not any way &longs;u&longs;tain them&longs;elves

<lb/>in the Air, but de&longs;cend downwards, and only fly to and again in

<lb/>the &longs;ame, when &longs;trong Windes rai&longs;e them, or other agitations of the

<lb/>Air commove them: and this al&longs;o happens in the commotion of the

<lb/>water, which rai&longs;eth its Sand from the bottom, and makes it muddy.

<lb/></s><s>But <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> cannot mean this impediment of the commotion, of

<lb/>which he makes no mention, nor names other than the lightne&longs;s of

<lb/>&longs;uch Minutiæ or Atomes, and the Re&longs;i&longs;tance of the Cra&longs;&longs;itudes of the

<lb/>Water and Air, by which we &longs;ee, that he &longs;peakes of a calme, and

<lb/>not di&longs;turbed and agitated Air: but in that ca&longs;e, neither Gold nor

<lb/>Earth, be they never &longs;o &longs;mall, are &longs;u&longs;tained, but &longs;peedily de&longs;cend.

<s><margin.target id="marg1533"></margin.target><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> af

<lb/>fir meth &longs;ome

<lb/>Bodies volatile

<lb/>for their Minu

<s><margin.target id="marg1534"></margin.target><emph type="italics"/>Democritus<emph.end type="italics"/> pla

<lb/>ced the Cau&longs;e of

<lb/>Natation in

<lb/>certain &longs;iery A

<lb/>tomes.</s>

<s>He pa&longs;&longs;eth next to confute <emph type="italics"/>Democritus,<emph.end type="italics"/> which, by his Te&longs;timony

<lb/>would have it, that &longs;ome Fiery Atomes, which continually a&longs;cend

<lb/>through the water, do &longs;pring upwards, and &longs;u&longs;tain tho&longs;e grave Bodies,

<lb/>which are very broad, and that the narrow de&longs;cend to the bottom, </s>

<lb/>for that but a &longs;mall quantity of tho&longs;e Atomes, encounter and re&longs;i&longs;t

<s><margin.target id="marg1535"></margin.target><emph type="italics"/>Ari&longs;tot. </s><s>De C&oelig;lo<emph.end type="italics"/>

<lb/>lib.

4. cap.

<s>I &longs;ay, <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> confutes this po&longs;ition, &longs;aying, that that &longs;hould

<lb/>much more occurre in the Air, as the &longs;ame <emph type="italics"/>Democritus<emph.end type="italics"/> in&longs;tances a

<lb/>gain&longs;t him&longs;elf, but after he had moved the objection, he &longs;lightly re

<lb/>&longs;olves it, with &longs;aying, that tho&longs;e Corpu&longs;cles which a&longs;cend in the Air,

<lb/>make not their <emph type="italics"/>Impetus<emph.end type="italics"/> conjunctly. </s><s>Here I will not &longs;ay, that the

<lb/>rea&longs;on alledged by <emph type="italics"/>Democritus<emph.end type="italics"/> is true, but I will only &longs;ay, it &longs;eems

<lb/>in my judgement, that it is not wholly confuted by <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> whil&longs;t he

<lb/>&longs;aith, that were it true, that the calid a&longs;cending Atomes, &longs;hould

<lb/>&longs;u&longs;tain Bodies grave, but very broad, it would much more be done

<lb/>in the Air, than in Water, for that haply in the Opinion of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/>

<pb pagenum="469"/>the &longs;aid calid Atomes a&longs;cend with much greater Force and Velocity

<lb/>through the Air, than through the water. </s><s>And if this be &longs;o, as I veri

<lb/>ly believe it is, the Objection of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in my judgement &longs;eems to

<lb/>give occa&longs;ion of &longs;u&longs;pecting, that he may po&longs;&longs;ibly be deceived in more

<lb/>than one particular: Fir&longs;t, becau&longs;e tho&longs;e calid Atomes, (whether

<lb/>they be Fiery Corpu&longs;cles, or whether they be Exhalations, or in

<lb/>&longs;hort, whatever other matter they be, that a&longs;cends upwards through

<lb/>the Air) cannot be believed to mount fa&longs;ter through Air, than

<lb/>through water: but rather on the contrary, they peradventure move

<lb/>more impetuou&longs;ly through the water, than through the Air, as hath

<lb/>been in part demon&longs;trated above. </s><s>And here I cannot finde the rea

<lb/>&longs;on, why <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;eeing, that the de&longs;eending Motion of the &longs;ame

<lb/>Moveable, is more &longs;wift in Air, than in water, hath not adverti&longs;ed

<lb/>us, that from the contrary Motion, the contrary &longs;hould nece&longs;&longs;arily

<lb/>follow; to wit, that it is more &longs;wift in the water, than in the Air: for

<lb/>&longs;ince that the Moveable which de&longs;cendeth, moves &longs;wifter through

<lb/>the Air, than through the water, if we &longs;hould &longs;uppo&longs;e its Gravity

<lb/>gradually to dimini&longs;h, it would fir&longs;t become &longs;uch, that de&longs;cending

<lb/>&longs;wiftly through the Air, it would de&longs;cend but &longs;lowly through the

<lb/>water: and then again, it might be &longs;uch, that de&longs;cending in the

<lb/>Air, it &longs;hould a&longs;cend in the water: and being made yet le&longs;s grave,

<lb/>it &longs;hall a&longs;cend &longs;wiftly through the water, and yet de&longs;cend likewi&longs;e

<lb/>through the Air: and in &longs;hort, before it can begin to a&longs;cend, though

<lb/>but &longs;lowly through the Air, it &longs;hall a&longs;cend &longs;wiftly through the water:

<lb/>how then is it true, that a&longs;cending Moveables move &longs;wifter through

<lb/>the Air, than through the water?</s>

<s><margin.target id="marg1536"></margin.target><emph type="italics"/>Democritus<emph.end type="italics"/> con

<lb/>futed by <emph type="italics"/>Ari

<lb/>&longs;totle,<emph.end type="italics"/> text 43.</s>

<s><margin.target id="marg1537"></margin.target><emph type="italics"/>Ari&longs;totles<emph.end type="italics"/> con

<lb/>futation of <emph type="italics"/>De

<lb/>mocritus<emph.end type="italics"/> refuted

<lb/>by the Author.</s>

<s>That which hath made <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> believe, the Motion of A&longs;cent to be

<lb/>&longs;wifter in Air, than in water, was fir&longs;t, the having referred the

<lb/>Cau&longs;es of &longs;low and quick, as well in the Motion of A&longs;cent, as of

<lb/>De&longs;cent, only to the diver&longs;ity of the Figures of the Moveable, and to

<lb/>the more or le&longs;s Re&longs;i&longs;tance of the greater or le&longs;&longs;er Cra&longs;&longs;itude, or Ra

<lb/>rity of the <emph type="italics"/>Medium<emph.end type="italics"/>; not regarding the compari&longs;on of the Exce&longs;&longs;es

<lb/>of the Gravities of the Moveables, and of the <emph type="italics"/>Mediums<emph.end type="italics"/>: the which

<lb/>notwith&longs;tanding, is the mo&longs;t principal point in this affair: for if the

<lb/>augmentation and diminution of the Tardity or Velocity, &longs;hould

<lb/>have only re&longs;pect to the Den&longs;ity or Rarity of the <emph type="italics"/>Medium,<emph.end type="italics"/> every Body

<lb/>that de&longs;cends in Air, would de&longs;cend in water: becau&longs;e whatever

<lb/>difference is found between the Cra&longs;&longs;itude of the water, and that of

<lb/>the Air, may well be found between the Velocity of the &longs;ame Move

<lb/>able in the Air, and &longs;ome other Velocity: and this &longs;hould be its

<lb/>proper Velocity in the water, which is ab&longs;olutely fal&longs;e. </s><s>The other

<lb/>occa&longs;ion is, that he did believe, that like as there is a po&longs;itive and in

<lb/>trin&longs;ecall Quality, whereby Elementary Bodies have a propen&longs;ion

<lb/>of moving towards the Centre of the Earth, &longs;o there is another like

<pb pagenum="470"/>wi&longs;e intrin&longs;ecall, whereby &longs;ome of tho&longs;e Bodies have an <emph type="italics"/>Impetus<emph.end type="italics"/> of

<lb/>flying the Centre, and moving upwards: by Vertue of which in

<lb/>trin&longs;e call Principle, called by him Levity, the Moveables which have

<lb/>that &longs;ame Motion more ea&longs;ily penetrate the more &longs;ubtle <emph type="italics"/>Medium,<emph.end type="italics"/>

<lb/>than the more den&longs;e: but &longs;uch a Propo&longs;ition appears likewi&longs;e un

<lb/>certain, as I have above hinted in part, and as with Rea&longs;ons and

<lb/>Experiments, I could demon&longs;trate, did not the pre&longs;ent Argument im

<lb/>portune me, or could I di&longs;patch it in few words.</s>

<s><margin.target id="marg1538"></margin.target>Lib. 4. Cap.

5.</s>

<s>The Objection therefore of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> again&longs;t <emph type="italics"/>Democritus,<emph.end type="italics"/> whil&longs;t

<lb/>he &longs;aith, that if the Fiery a&longs;cending Atomes &longs;hould &longs;u&longs;tain Bodies

<lb/>grave, but of a di&longs;tended Figure, it would be more ob&longs;ervable in

<lb/>the Air than in the water, becau&longs;e &longs;uch Corpu&longs;cles move &longs;wifter in

<lb/>that, than in this, is not good; yea the contrary would evene, for

<lb/>that they a&longs;cend more &longs;lowly through the Air: and, be&longs;ides their

<lb/>moving &longs;lowly, they a&longs;cend, not united together, as in the water,

<lb/>but di&longs;continue, and, as we &longs;ay, &longs;catter: And, therefore, as

<lb/><emph type="italics"/>Democritus<emph.end type="italics"/> well replyes, re&longs;olving the in&longs;tance they make not their

<lb/>pu&longs;h or <emph type="italics"/>Impetus<emph.end type="italics"/> conjunctly.</s>

<s><emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> in the &longs;econd place, deceives him&longs;elf, whil&longs;t he will

<lb/>have the &longs;aid grave Bodies to be more ea&longs;ily &longs;u&longs;tained by the &longs;aid

<lb/>Fiery a&longs;cending Atomes in the Air than in the Water: not ob&longs;erv

<lb/>ing, that the &longs;aid Bodies are much more grave in that, than in this,

<lb/>and that &longs;uch a Body weighs ten pounds in the Air, which will not

<lb/>in the water weigh 1/2 an ounce; how can it then be more ea&longs;ily

<lb/>&longs;u&longs;tained in the Air, than in the Water?</s>

<s>Let us conclude, therefore, that <emph type="italics"/>Democritus<emph.end type="italics"/> hath in this particular

<lb/>better Philo&longs;ophated than <emph type="italics"/>Ari&longs;totle.<emph.end type="italics"/> But yet will not I affirm, that <emph type="italics"/>De-<emph.end type="italics"/>

<lb/><emph type="italics"/>mocritus<emph.end type="italics"/> hath rea&longs;on'd rightly, but I rather &longs;ay, that there is a ma

<lb/>nife&longs;t Experiment that overthrows his Rea&longs;on, and this it is, That

<lb/>if it were true, that calid a&longs;cending Atomes &longs;hould uphold a Body,

<lb/>that if they did not hinder, would go to the bottom, it would follow,

<lb/>that we may find a Matter very little &longs;uperiour in Gravity to the

<lb/>water, the which being reduced into a Ball, or other contracted

<lb/>Figure, &longs;hould go to the bottom, as encountring but few Fiery A

<lb/>tomes; and which being di&longs;tended afterwards into a dilated and

<lb/>thin Plate, &longs;hould come to be thru&longs;t upwards by the impul&longs;ion of a

<lb/>great Multitude of tho&longs;e Corpu&longs;cles, and at la&longs;t carried to the very

<lb/>Surface of the water: which wee &longs;ee not to happen; Experience

<lb/>&longs;hewing us, that a Body <emph type="italics"/>v. </s><s>gra.<emph.end type="italics"/> of a Sphericall Figure, which very

<lb/>hardly, and with very great lea&longs;ure goeth to the bottom, will re&longs;t

<lb/>there, and will al&longs;o de&longs;cend thither, being reduced into what&longs;oever

<lb/>other di&longs;tended Figure. </s><s>We mu&longs;t needs &longs;ay then, either that in the

<lb/>water, there are no &longs;uch a&longs;cending Fiery Atoms, or if that &longs;uch there

<lb/>be, that they are not able to rai&longs;e and lift up any Plate of a Matter,

<pb pagenum="471"/>that without them would go to the bottom: Of which two Pofitions,

<lb/>I e&longs;teem the &longs;econd to be true, under&longs;tanding it of water, con&longs;tituted

<lb/>in its naturall Coldne&longs;s. </s><s>But if we take a Ve&longs;&longs;el of Gla&longs;s, or Bra&longs;s,

<lb/>or any other hard matter, full of cold water, within which is put a

<lb/>Solid of a flat or concave Figure, but that in Gravity exceeds the

<lb/>water &longs;o little, that it goes &longs;lowly to the bottom; I &longs;ay, that putting

<lb/>&longs;ome burning Coals under the &longs;aid Ve&longs;&longs;el, as &longs;oon as the new Fiery

<lb/>Atomes &longs;hall have penetrated the &longs;ub&longs;tance of the Ve&longs;&longs;el, they &longs;hall

<lb/>without doubt, a&longs;cend through that of the water, and thru&longs;ting a

<lb/>gain&longs;t the fore&longs;aid Solid, they &longs;hall drive it to the Superficies, and

<lb/>there detain it, as long as the incur&longs;ions of the &longs;aid Corpu&longs;cles &longs;hall

<lb/>la&longs;t, which cea&longs;ing after the removall of the Fire, the Solid being a

<lb/>bandoned by its &longs;upporters, &longs;hall return to the bottom.</s>

<s><margin.target id="marg1539"></margin.target><emph type="italics"/>Democritus<emph.end type="italics"/> con

<lb/>futed by the

<lb/>Authour.</s>

<s>But <emph type="italics"/>Democritus<emph.end type="italics"/> notes, that this Caufe only takes place when we

<lb/>treat of rai&longs;ing and &longs;u&longs;taining of Plates of Matters, but very little

<lb/>heavier than the water, or extreamly thin: but in Matters very

<lb/>grave, and of &longs;ome thickne&longs;s, as Plates of Lead or other Mettal, that

<lb/>&longs;ame Effect wholly cea&longs;eth: In Te&longs;timony of which, let's ob&longs;erve

<lb/>that &longs;uch Plates, being rai&longs;ed by the Fiery Atomes, a&longs;cend through

<lb/>all the depth of the water, and &longs;top at the Confines of the Air, &longs;till

<lb/>&longs;taying under water: but the Plates of the Opponents &longs;tay not, but

<lb/>only when they have their upper Superficies dry, nor is there any

<lb/>means to be u&longs;ed, that when they are within the water, they may

<lb/>not &longs;ink to the bottom. </s><s>The cau&longs;e, therefore, of the Supernatation

<lb/>of the things of which <emph type="italics"/>Democritus<emph.end type="italics"/> &longs;peaks is one, and that of the Super

<lb/>natation of the things of which we &longs;peak is another. </s><s>But, returning

<lb/>to <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> methinks that he hath more weakly confuted <emph type="italics"/>Democritus,<emph.end type="italics"/>

<lb/>than <emph type="italics"/>Democritus<emph.end type="italics"/> him&longs;elf hath done: For <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> having propounded

<lb/>the Objection which he maketh again&longs;t him, and oppo&longs;ed him with

<lb/>&longs;aying, that if the calid a&longs;cendent Corpu&longs;cles were tho&longs;e that rai&longs;ed

<lb/>the thin Plate, much more then would &longs;uch a Solid be rai&longs;ed and

<lb/>born upwards through the Air, it &longs;heweth that the de&longs;ire in <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>

<lb/>to detect <emph type="italics"/>Democritus,<emph.end type="italics"/> was predominate over the exqui&longs;itene&longs;s of Solid

<lb/>Philo&longs;ophizing: which de&longs;ire of his he hath di&longs;covered in other oc

<lb/>ca&longs;ions, and that we may not digre&longs;s too far from this place, in the

<lb/>Text precedent to this Chapter which we have in hand; where he

<lb/>attempts to confute the &longs;ame <emph type="italics"/>Democritus,<emph.end type="italics"/> for that he, not content

<lb/>ing him&longs;elf with names only, had e&longs;&longs;ayed more particularly to de

<lb/>clare what things Gravity and Levity were; that is, the Cau&longs;es of

<lb/>de&longs;cending and a&longs;cending, (and had introduced Repletion and Va

<lb/>cuity) a&longs;cribing this to Fire, by which it moves upwards, and that to

<lb/>the Earth, by which it de&longs;cends; afterwards attributing to the

<lb/>Air more of Fire, and to the water more of Earth. </s><s>But <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/>

<lb/>de&longs;iring a po&longs;itive Cau&longs;e, even of a&longs;cending Motion, and not as <emph type="italics"/>Plato,<emph.end type="italics"/>

<pb pagenum="472"/>or the&longs;e others, a &longs;imple negation, or privation, &longs;uch as Vacuity

<lb/>would be in reference to Repletion, argueth again&longs;t <emph type="italics"/>Democritus<emph.end type="italics"/> and

<lb/>&longs;aith: If it be true, as you &longs;uppo&longs;e, then there &longs;hall be a great Ma&longs;s

<lb/>of water, which &longs;hall have more of Fire, than a &longs;mall Ma&longs;s of Air,

<lb/>and a great Ma&longs;s of Air, which &longs;hall have more of Earth than a lit

<lb/>tle Ma&longs;s of water, whereby it would en&longs;ue, that a great Ma&longs;s of Air,

<lb/>&longs;hould come more &longs;wiftly downwards, than a little quantity of

<lb/>water: But that is never in any ca&longs;e &longs;oever: Therefore <emph type="italics"/>Democritus<emph.end type="italics"/>

<lb/>di&longs;cour&longs;eth erroneou&longs;ly.</s>

<s><margin.target id="marg1540"></margin.target><emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;hews

<lb/>his de&longs;ire of

<lb/>finding <emph type="italics"/>Demo

<lb/>critus<emph.end type="italics"/> in an Er

<lb/>ror, to exceed

<lb/>that of di&longs;co

<lb/>veting Truth.</s>

<s><margin.target id="marg1541"></margin.target>Cap.

5. Text 41.</s>

<s>But in my opinion, the Doctrine of <emph type="italics"/>Democritus,<emph.end type="italics"/> is not by this alle

<lb/>gation overthrown, but if I erre not, the manner of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> deduction

<lb/>either concludes not, or if it do conclude any thing, it may with e

<lb/>quall force be re&longs;tored again&longs;t him&longs;elf. <emph type="italics"/>Democritus<emph.end type="italics"/> will grant to

<lb/><emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> that there may be a great Ma&longs;s of Air taken, which con

<lb/>tains more Earth, than a &longs;mall quantity of water, but yet will deny,

<lb/>that &longs;uch a Ma&longs;s of Air, &longs;hall go fa&longs;ter downwards than a little water,

<lb/>and that for many rea&longs;ons. </s><s>Fir&longs;t, becau&longs;e if the greater quantity

<lb/>of Earth, contained in the great Ma&longs;s of Air, ought to cau&longs;e a greater

<lb/>Velocity than a le&longs;s quantity of Earth, contained in a little quantity

<lb/>of water, it would be nece&longs;&longs;ary, fir&longs;t, that it were true, that a

<lb/>greater Ma&longs;s of pure Earth, &longs;hould move more &longs;wiftly than a le&longs;s:

<lb/>But this is fal&longs;e, though <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in many places affirms it to be true:

<lb/>becau&longs;e not the greater ab&longs;olute, but the greater &longs;pecificall Gravity,

<lb/>is the cau&longs;e of greater Velocity: nor doth a Ball of Wood, weigh

<lb/>ing ten pounds, de&longs;cend more &longs;wiftly than one weighing ten Ounces,

<lb/>and that is of the &longs;ame Matter: but indeed a Bullet of Lead of four

<lb/>Ounces, de&longs;cendeth more &longs;wiftly than a Ball of Wood of twenty

<lb/>Pounds: becau&longs;e the Lead is more grave <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> than the Wood.

<lb/></s><s>Therefore, its not nece&longs;&longs;ary, that a great Ma&longs;s of Air, by rea&longs;on of

<lb/>the much Earth contained in it, do de&longs;cend more &longs;wiftly than a little

<lb/>Ma&longs;s of water, but on the contrary, any what&longs;oever Ma&longs;s of water,

<lb/>&longs;hall move more &longs;wiftly than any other of Air, by rea&longs;on the partici

<lb/>pation of the terrene parts <emph type="italics"/>in &longs;pecie<emph.end type="italics"/> is greater in the water, than in the

<lb/>Air. </s><s>Let us note, in the &longs;econd place, how that in multiplying the

<lb/>Ma&longs;s of the Air, we not only multiply that which is therein of terrene,

<lb/>but its Fire al&longs;o: whence the Cau&longs;e of a&longs;cending, no le&longs;s encrea&longs;eth,

<lb/>by vertue of the Fire, than that of de&longs;cending on the account of its

<lb/>multiplied Earth. </s><s>It was requi&longs;ite in increa&longs;ing the greatne&longs;s of the

<lb/>Air, to multiply that which it hath of terrene only, leaving its Fire

<lb/>in its fir&longs;t &longs;tate, for then the terrene parts of the augmented Air,

<lb/>overcoming the terrene parts of the &longs;mall quantity of water, it might

<lb/>with more probability have been pretended, that the great quanti

<lb/>ty of Air, ought to de&longs;cend with a greater <emph type="italics"/>Impetus,<emph.end type="italics"/> than the little

<lb/>quantity of water.</s>

<s><margin.target id="marg1543"></margin.target>The greater

<lb/>Specificall, not

<lb/>the greater ab

<lb/>&longs;olute Gravity,

<lb/>is the Cau&longs;e of

<lb/>Velocity.</s>

<s><margin.target id="marg1544"></margin.target>Any Ma&longs;s of

<lb/>water &longs;hal move

<lb/>more &longs;wiftly,

<lb/>than any of Air,

<s>Therefore, the Fallacy lyes more in the Di&longs;cour&longs;e of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> than

<lb/>in that of <emph type="italics"/>Democritus,<emph.end type="italics"/> who with &longs;everall other Rea&longs;ons might oppo&longs;e

<lb/><emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> and alledge; If it be true, that the extreame Elements be

<lb/>one &longs;imply grave, and the other &longs;imply light, and that the mean

<lb/>Elements participate of the one, and of the other Nature; but the

<lb/>Air more of Levity, and the water more of Gravity, then there &longs;hall

<lb/>be a great Ma&longs;s of Air, who&longs;e Gravity &longs;hall exceed the Gravity of a

<lb/>little quantity of water; and therefore &longs;uch a Ma&longs;s of Air &longs;hall de

<lb/>&longs;cend more &longs;wiftly than that little water: But that is never &longs;een to

<lb/>occurr: Therefore its not true, that the mean Elements do partici

<lb/>pate of the one, and the other quality. </s><s>This argument is fallacious,

<lb/>no le&longs;s than the other again&longs;t <emph type="italics"/>Democritus.<emph.end type="italics"/></s>

<s>La&longs;tly, <emph type="italics"/>Aristotle<emph.end type="italics"/> having &longs;aid, that if the Po&longs;ition of <emph type="italics"/>Democritus<emph.end type="italics"/>

<lb/>were true, it would follow, that a great Ma&longs;s of Air &longs;hould move

<lb/>more &longs;wiftly than a &longs;mall Ma&longs;s of water, and afterwards &longs;ubjoyned,

<lb/>that that is never &longs;een in any Ca&longs;e: methinks others may become de

<lb/>&longs;irous to know of him in what place this &longs;hould evene, which he de

<lb/>duceth again&longs;t <emph type="italics"/>Democritus,<emph.end type="italics"/> and what Experiment teacheth us, that

<lb/>it never falls out &longs;o. </s><s>To &longs;uppo&longs;e to &longs;ee it in the Element of water,

<lb/>or in that of the Air is vain, becau&longs;e neither doth water through

<lb/>water, nor Air through Air move, nor would they ever by any

<lb/>whatever participation others a&longs;&longs;ign them, of Earth or of Fire: the

<lb/>Earth, in that it is not a Body fluid, and yielding to the mobility of

<lb/>other Bodies, is a mo&longs;t improper place and <emph type="italics"/>Medium<emph.end type="italics"/> for &longs;uch an Ex

<lb/>periment: <emph type="italics"/>Vacuum,<emph.end type="italics"/> according to the &longs;ame <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> him&longs;elf, there

<lb/>is none, and were there, nothing would move in it: there remaine

<lb/>the Region of Fire, but being &longs;o far di&longs;tant from us, what Experi

<lb/>ment can a&longs;&longs;ure us, or hath a&longs;&longs;ertained <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in &longs;uch &longs;ort, that he

<lb/>&longs;hould as of a thing mo&longs;t obvious to &longs;ence, affirm what he produ

<lb/>ceth in confutation of <emph type="italics"/>Democritus,<emph.end type="italics"/> to wit, that a great Ma&longs;s of Air,

<lb/>is moved no &longs;wifter than a little one of water? </s><s>But I will dwell no

<lb/>longer upon this matter, whereon I have &longs;poke &longs;ufficiently: but

<lb/>leaving <emph type="italics"/>Democritus,<emph.end type="italics"/> I return to the Text of <emph type="italics"/>Ari&longs;totle,<emph.end type="italics"/> wherein he

<lb/>goes about to render the true rea&longs;on, how it comes to pa&longs;s, that the

<lb/>thin Plates of Iron or Lead do &longs;wim on the water; and, moreover,

<lb/>that Gold it &longs;elf being beaten into thin Leaves, not only &longs;wims in

<lb/>water, but flyeth too and again in the Air. </s><s>He &longs;uppo&longs;eth that of

<lb/>Continualls, &longs;ome are ea&longs;ily divi&longs;ible, others not: and that of the

<lb/>ea&longs;ily divi&longs;ible, &longs;ome are more &longs;o, and &longs;ome le&longs;s: and the&longs;e he

<lb/>affirms we &longs;hould e&longs;teem the Cau&longs;es. </s><s>He addes that that is ea&longs;ily

<lb/>divi&longs;ible, which is well terminated, and the more the more divi&longs;ible,

<lb/>and that the Air is more &longs;o, than the water, and the water than the

<lb/>Earth. </s><s>And, la&longs;tly, he &longs;uppo&longs;eth that in each kind, the le&longs;&longs;e quan

<lb/>tity is ea&longs;lyer divided and broken than the greater.</s>

<s><margin.target id="marg1545"></margin.target><emph type="italics"/>De C&oelig;lo<emph.end type="italics"/> l. </s><s>4. c.

<s>Here I note, that the Conclu&longs;ions of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> in generall are all

<lb/>true, but methinks, that he applyeth them to particulars, in which

<lb/>they have no place, as indeed they have in others, as for Example,

<lb/>Wax is more ea&longs;ily divi&longs;ible than Lead, and Lead than Silver, in

<lb/>a&longs;much as Wax receives all the terms more ea&longs;iler than Lead, and

<lb/>Lead than Silver. </s><s>Its true, moreover, that a little quantity of Sil

<lb/>ver is ea&longs;lier divided than a great Ma&longs;s: and all the&longs;e Propo&longs;itions

<lb/>are true, becau&longs;e true it is, that in Silver, Lead and Wax, there

<lb/>is &longs;imply a Re&longs;i&longs;tance again&longs;t Divi&longs;ion, and where there is the ab&longs;o

<lb/>lute, there is al&longs;o the re&longs;pective. </s><s>But if as well in water as in Air,

<lb/>there be no Renitence again&longs;t &longs;imple Divi&longs;ion, how can we &longs;ay, that

<lb/>the water is ea&longs;lier divided than the Air? </s><s>We know not how to ex

<lb/>tricate our &longs;elves from the Equivocation: whereupon I return to

<lb/>an&longs;wer, that Re&longs;i&longs;tance of ab&longs;olute Divi&longs;ion is one thing, and Re

<lb/>&longs;i&longs;tance of Divi&longs;ion made with &longs;uch and &longs;uch Velocity is another.

<lb/></s><s>But to produce Re&longs;t, and to abate the Motion, the Re&longs;i&longs;tance of

<lb/>ab&longs;olute Divi&longs;ion is nece&longs;&longs;ary; and the Re&longs;i&longs;tance of &longs;peedy Di

<lb/>vi&longs;ion, cau&longs;eth not Re&longs;t, but &longs;lowne&longs;s of Motion. </s><s>But that as well

<lb/>in the Air, as in water, there is no Re&longs;i&longs;tance of &longs;imple Divi&longs;ion, is

<lb/>manife&longs;t, for that there is not found any Solid Body which divides

<lb/>not the Air, and al&longs;o the water: and that beaten Gold, or &longs;mall

<lb/>du&longs;t, are not able to &longs;uperate the Re&longs;i&longs;tance of the Air, is contrary

<lb/>to that which Experience &longs;hews us, for we &longs;ee Gold and Du&longs;t to go

<lb/>waving to and again in the Air, and at la&longs;t to de&longs;cend down

<lb/>wards, and to do the &longs;ame in the water, if it be put therein, and &longs;e

<lb/>parated from the Air. </s><s>And, becau&longs;e, as I &longs;ay, neither the water,

<lb/>nor the Air do re&longs;i&longs;t &longs;imple Divi&longs;ion, it cannot be &longs;aid, that the water

<lb/>re&longs;i&longs;ts more than the Air. </s><s>Nor let any object unto me, the Exam

<lb/>ple of mo&longs;t light Bodies, as a Feather, or a little of the pith of El

<lb/>der, or water-reed that divides the Air and not the water, and from

<lb/>this infer, that the Ait is ea&longs;lier divi&longs;ible than the water; for I &longs;ay

<lb/>unto them, that if they do well ob&longs;erve, they &longs;hall &longs;ee the &longs;ame

<lb/>Body likewi&longs;e divide the Continuity of the water, and &longs;ubmerge in

<lb/>part, and in &longs;uch a part, as that &longs;o much water in Ma&longs;s would weigh

<lb/>as much as the whole Solid. </s><s>And if they &longs;hal yet per&longs;i&longs;t in their doubt,

<lb/>that &longs;uch a Solid &longs;inks not through inability to divide the water, I will

<lb/>return them this reply, that if they put it under water, and then let it

<lb/>go, they &longs;hall &longs;ee it divide the water, and pre&longs;ently a&longs;cend with no le&longs;s

<lb/>celerity, than that with which it divided the Air in de&longs;cending: &longs;o that

<lb/>to &longs;ay that this Solid a&longs;cends in the Air, but that coming to the water,

<lb/>it cea&longs;eth its Motion, and therefore the water is more difficult to be

<lb/>divided, concludes nothing: for I, on the contrary, will propo&longs;e them

<lb/>a piece of Wood, or of Wax, which ri&longs;eth from the bottom of the

<lb/>water, and ea&longs;ily divides its Re&longs;i&longs;tance, which afterwards being arri

<pb pagenum="475"/>ved at the Air, &longs;tayeth there, and hardly toucheth it; whence I may

<lb/>aswell &longs;ay, that the water is more ea&longs;ier divided than the Air</s>

<s><margin.target id="marg1546"></margin.target><emph type="italics"/>Archimed. </s><s>De

<lb/>In&longs;ident, humi<emph.end type="italics"/> lib.

<lb/></s><s>2. prop.

1.</s>

<s>I will not on this occa&longs;ion forbear to give warning of another fal

<lb/>lacy of the&longs;e per&longs;ons, who attribute the rea&longs;on of &longs;inking or &longs;wimming

<lb/>to the greater or le&longs;&longs;e Re&longs;i&longs;tance of the Cra&longs;&longs;itude of the water again&longs;t

<lb/>Divi&longs;ion, making u&longs;e of the example of an Egg, which in &longs;weet water

<lb/>goeth to the bottom, but in &longs;alt water &longs;wims; and alledging for the

<lb/>cau&longs;e thereof, the faint Re&longs;i&longs;tance of fre&longs;h water again&longs;t Divi&longs;ion, and

<lb/>the &longs;trong Re&longs;i&longs;tance of &longs;alt water But if I mi&longs;take not, from the &longs;ame

<lb/>Experiment, we may aswell deduce the quite contrary; namely, that

<lb/>the fre&longs;h water is more den&longs;e, and the &longs;alt more tenuous and &longs;ubtle,

<lb/>&longs;ince an Egg from the bottom of &longs;alt water &longs;peedily a&longs;cends to the

<lb/>top, and divides its Re&longs;i&longs;tance, which it cannot do in the fre&longs;h, in who&longs;e

<lb/>bottom it &longs;tays, being unable to ri&longs;e upwards. </s><s>Into &longs;uch like perplex

<lb/>ities, do fal&longs;e Principles Lead men: but he that rightly Philo&longs;ophating,

<lb/>&longs;hall acknowledge the exce&longs;&longs;es of the Gravities of the Moveables and

<lb/>of the Mediums, to be the Cau&longs;es of tho&longs;e effects, will &longs;ay, that the

<lb/>Egg &longs;inks to the bottom in fre&longs;h water, for that it is more grave than

<lb/>it, and &longs;wimeth in the &longs;alt, for that its le&longs;s grave than it: and &longs;hall

<lb/>without any ab&longs;urdity, very &longs;olidly e&longs;tabli&longs;h his Conclu&longs;ions.</s>

<s>Therefore the rea&longs;on totally cea&longs;eth, that <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> &longs;ubjoyns in the

<lb/>Text &longs;aying; The things, therefore, which have great breadth remain

<lb/>above, becau&longs;e they comprehend much, and that which is greater,

<lb/>is not ea&longs;ily divided. </s><s>Such di&longs;cour&longs;ing cea&longs;eth, I &longs;ay, becau&longs;e its not

<lb/>true, that there is in water or in Air any Re&longs;i&longs;tance of Divi&longs;ion; be

<lb/>&longs;ides that the Plate of Lead when it &longs;tays, hath already divided and

<lb/>penetrated the Cra&longs;&longs;itude of the water, and profounded it &longs;elf ten or

<lb/>twelve times more than its own thickne&longs;s: be&longs;ides that &longs;uch Re&longs;i&longs;tance

<lb/>of Divi&longs;ion, were it &longs;uppo&longs;ed to be in the water, could not rationally

<lb/>be affirmed to be more in its &longs;uperiour parts than in the middle, and

<lb/>lower: but if there were any difference, the inferiour &longs;hould be the

<lb/>more den&longs;e, &longs;o that the Plate would be no le&longs;s unable to penetrate

<lb/>the lower, than the &longs;uperiour parts of the water; neverthele&longs;s we &longs;ee

<lb/>that no &longs;ooner do we wet the &longs;uperious Superficies of the Board or

<lb/>thin Piece of Wood, but it precipitatly, and without any reten&longs;ion,

<lb/>de&longs;cends to the bottom.</s>

<s>I believe not after all this, that any (thinking perhaps thereby to

<lb/>defend <emph type="italics"/>Aristotle<emph.end type="italics"/>) will &longs;ay, that it being true, that the much water re

<lb/>&longs;i&longs;ts more than the little, the &longs;aid Board being put lower de&longs;cendeth,

<lb/>becau&longs;e there remaineth a le&longs;s Ma&longs;s of water to be divided by it: be

<lb/>cau&longs;e if after the having &longs;een the &longs;ame Board &longs;wim in four Inches of

<lb/>water, and al&longs;o after that in the &longs;ame to &longs;ink, he &longs;hall try the &longs;ame

<lb/>Experiment upon a profundity of ten or twenty fathom water, he

<lb/>&longs;hall &longs;ee the very &longs;elf &longs;ame effect. </s><s>And here I will take occa&longs;ion to

<pb pagenum="476"/>remember, for the removall of an Error that is too common; That

<lb/>that Ship or other what&longs;oever Body, that on the depth of an hundred

<lb/>or a thou&longs;and fathom, &longs;wims with &longs;ubmerging only &longs;ix fathom of its

<lb/>own height, [<emph type="italics"/>or in the Sea dialect, that draws &longs;ix fathom water<emph.end type="italics"/>] &longs;hall

<lb/>&longs;wim in the &longs;ame manner in water, that hath but &longs;ix fathom and half

<lb/>an Inch of depth. </s><s>Nor do I on the other &longs;ide, think that it can be

<lb/>&longs;aid, that the &longs;uperiour parts of the water are the more den&longs;e, al

<lb/>though a mo&longs;t grave Authour hath e&longs;teemed the &longs;uperiour water in

<lb/>the Sea to be &longs;o, grounding his opinion upon its being more &longs;alt, than

<lb/>that at the bottom: but I doubt the Experiment, whether hitherto

<lb/>in taking the water from the bottom, the Ob&longs;ervatour did not light

<lb/>upon &longs;ome &longs;pring of fre&longs;h water there &longs;pouting up: but we plainly

<lb/>&longs;ee on the contrary, the fre&longs;h Waters of Rivers to dilate them&longs;elves

<lb/>for &longs;ome miles beyond their place of meeting with the &longs;alt water of

<lb/>the Sea, without de&longs;cending in it, or mixing with it, unle&longs;s by the

<lb/>intervention of &longs;ome commotion or turbulency of the Windes.</s>

<s><margin.target id="marg1548"></margin.target>A Ship that

<lb/>in 100 Fathome

<lb/>water draweth

<lb/>6 Fathome, &longs;hall

<lb/>float in 6 Fa

<lb/>thome and 1/2 an

<lb/>Inch of depth.</s>

<s>But returning to <emph type="italics"/>Aristotle,<emph.end type="italics"/> I &longs;ay, that the breadth of Figure hath

<lb/>nothing to do in this bu&longs;ine&longs;s more or le&longs;s, becau&longs;e the &longs;aid Plate of

<lb/>Lead, or other Matter, cut into long Slices, &longs;wim neither more nor

<lb/>le&longs;s; and the &longs;ame &longs;hall the Slices do, being cut anew into little

<lb/>pieces, becau&longs;e its not the breadth but the thickne&longs;s that operates in

<lb/>this bu&longs;ine&longs;s. </s><s>I &longs;ay farther, that in ca&longs;e it were really true, that the

<lb/>Renitence to Divi&longs;ion were the proper Cau&longs;e of &longs;wimming, the Fi

<lb/>gures more narrow and &longs;hort, would much better &longs;wim than the more

<lb/>&longs;pacious and broad, &longs;o that augmenting the breadth of the Figure,

<lb/>the facility of &longs;upernatation will be demini&longs;hed, and decrea&longs;ing, that

<lb/>this will encrea&longs;e.</s>

<s><margin.target id="marg1549"></margin.target>Thickne&longs;s not

<lb/>breadth of Fi

<lb/>gure to be re

<lb/>&longs;pected in Na

<lb/>tation.</s>

<s><margin.target id="marg1550"></margin.target>Were Reni

<lb/>tence the cau&longs;e

<lb/>of Natation,

<lb/>breadth of Fi

<lb/>gure would

<lb/>hinder the

<lb/>&longs;wiming of Bo

<s>And for declaration of what I &longs;ay, con&longs;ider that when a thin Plate

<lb/>of Lead de&longs;cends, dividing the water, the Divi&longs;ion and di&longs;continu

<lb/>ation is made between the parts of the water, invironing the perime

<lb/>ter or Circumference of the &longs;aid Plate, and according to the big

<lb/>ne&longs;s greater or le&longs;&longs;er of that circuit, it hath to divide a greater or

<lb/>le&longs;&longs;er quantity of water, &longs;o that if the circuit, &longs;uppo&longs;e of a Board,

<lb/>be ten Feet in &longs;inking it flatways, it is to make the &longs;eperation and

<lb/>divi&longs;ion, and to &longs;o &longs;peak, an inci&longs;&longs;ion upon ten Feet of water; and

<lb/>likewi&longs;e a le&longs;&longs;er Board that is four Feet in Perimeter, mu&longs;t make an

<lb/>ince&longs;&longs;ion of four Feet. </s><s>This granted, he that hath any knowledge

<lb/>in Geometry, will comprehend, not only that a Board &longs;awed in many

<lb/>long thin pieces, will much better float than when it was entire, but

<lb/>that all Figures, the more &longs;hort and narrow they be, &longs;hall &longs;o much the

<lb/>better &longs;wim. </s><s>Let the Board ABCD be, for Example, eight

<lb/>Palmes long, and five broad, its circuit &longs;hall be twenty &longs;ix Palmes;

<lb/>and &longs;o many mu&longs;t the ince&longs;&longs;ion be, which it &longs;hall make in the water to

<lb/>de&longs;cend therein: but if we do &longs;aw ir, as &longs;uppo&longs;e into eight little

<pb pagenum="469"/>pieces, according to the Lines E F, G H, <emph type="italics"/>&c.<emph.end type="italics"/> making &longs;even Segments,

<lb/>we mu&longs;t adde to the twenty &longs;ix Palmes of the circuit of the whole

<lb/>Board, &longs;eventy others; whereupon the eight little pieces &longs;o cut and

<lb/>&longs;eperated, have to cut ninty &longs;ix Palmes of water. </s><s>And, if moreover,

<lb/>we cur each of the &longs;aid pieces into five parts, re

<lb/>ducing them into Squares, to the circuit of ninty

<lb/>&longs;ix Palmes, with four cuts of eight Palmes apiece;

<lb/>we &longs;hall adde al&longs;o &longs;ixty four Palmes, whereupon

<lb/>the &longs;aid Squares to de&longs;cend in the water, mu&longs;t

<lb/>divide one hundred and &longs;ixty Palmes of water,

<lb/>but the Re&longs;i&longs;tance is much greater than that of

<lb/>twenty &longs;ix; therefore to the le&longs;&longs;er Superficies,

<lb/>we &longs;hall reduce them, &longs;o much the more ea&longs;ily

<lb/>will they float: and the &longs;ame will happen in all

<lb/>other Figures, who&longs;e Superficies are &longs;imular among&longs;t them&longs;elves, but

<lb/>different in bigne&longs;s: becau&longs;e the &longs;aid Superficies, being either demini

<lb/>&longs;hed or encrea&longs;ed, always dimini&longs;h or encrea&longs;e their Perimeters in

<lb/>&longs;ubduple proportion; to wit, the Re&longs;i&longs;tance that they find in pene

<lb/>trating the water; therefore the little pieces gradually &longs;wim, with more

<lb/>and more facility as their breadth is le&longs;&longs;ened.</s>

<s><emph type="italics"/>This is manife&longs;t; for keeping &longs;till the &longs;ame height of the Solid, with

<lb/>the &longs;ame proportion as the Ba&longs;e encrea&longs;eth or demini&longs;heth, doth the &longs;aid

<lb/>Solid al&longs;o encrea&longs;e or dimini&longs;h; whereupon the Solid more dimini&longs;hing

<lb/>than the Circuit, the Cau&longs;e of Submer&longs;ion more dimini&longs;heth than the Cau&longs;e

<lb/>of Natation: And on the contrary, the Solid more encrea&longs;ing than the

<lb/>Circuit, the Cau&longs;e of Submer&longs;ion encrea&longs;eth more, that of Natation

<lb/>le&longs;s.<emph.end type="italics"/></s>

<s>And this may all be dedueed out of the Doctrine of <emph type="italics"/>Ari&longs;totle<emph.end type="italics"/> a

<lb/>gain&longs;t his own Doctrine.</s>

<s>La&longs;tly, to that which we read in the latter part of the Text, that

<lb/>is to &longs;ay, that we mu&longs;t compare the Gravity of the Moveable with

<lb/>the Re&longs;i&longs;tance of the Medium again&longs;t Divi&longs;ion, becau&longs;e if the force of

<lb/>the Gravity exceed the Re&longs;i&longs;tance of the <emph type="italics"/>Medium,<emph.end type="italics"/> the Moveable will

<lb/>de&longs;cend, if not it will float. </s><s>I need not make any other an&longs;wer,

<lb/>but that which hath been already delivered; namely, that its not

<lb/>the Re&longs;i&longs;tance of ab&longs;olute Divi&longs;ion, (which neither is in Water nor

<lb/>Air) but the Gravity of the <emph type="italics"/>Medium<emph.end type="italics"/> that mu&longs;t be compared with the

<lb/>Gravity of the Moveables; and if that of the <emph type="italics"/>Medium<emph.end type="italics"/> be greater, the

<lb/>Moveable &longs;hall not de&longs;cend, nor &longs;o much as make a totall Submer&longs;ion,

<lb/>but a partiall only: becau&longs;e in the place which it would occupy in

<lb/>the water, there mu&longs;t not remain a Body that weighs le&longs;s than a like

<lb/>quantity of water: but if the Moveable be more grave, it &longs;hall de&longs;

<lb/>cend to the bottom, and po&longs;&longs;e&longs;s a place where it is more conformable

<pb/>

for it to remain, than another Body that is le&longs;s grave. </s><s>And this

<lb/>is the only true proper and ab&longs;olute Cau&longs;e of Natation and Sub

<lb/>mer&longs;ion, &longs;o that nothing el&longs;e hath part therein: and the Board of the

<lb/>Adver&longs;aries &longs;wimmeth, when it is conjoyned with as much Air,

<lb/>as, together with it, doth form a Body le&longs;s grave than &longs;o much water

<lb/>as would fill the place that the &longs;aid Compound occupyes in the

<lb/>water; but when they &longs;hall demit the &longs;imple Ebony into

<lb/>the water, according to the Tenour of our Que

<lb/>&longs;tion, it &longs;hall alwayes go to the bottom,

<lb/>though it were as thin as a

<lb/>Paper.</s>

<s><margin.target id="marg1551"></margin.target>Lib. 4. c. </s><s>6.

<s>Fir&longs;t, the weight <lb/>to be transferred from place to place; and &longs;econdly, the Force <lb/>and Power which &longs;hould move it; thirdly, the Di&longs;tance between <lb/>the one and the other Term of the Motion; Fourthly, the Time <lb/>in which that mutation is to be made: which Time becometh the <lb/>&longs;ame thing with the Dexterity, and Velocity of the Motion; we <lb/>determining that Motion to be more &longs;wift then another, which in <lb/>le&longs;&longs;e Time pa&longs;&longs;eth an equal Di&longs;tance.</s>

<s><emph type="italics"/>FINIS.<emph.end type="italics"/></s>

<s>Now, any determinate Re&longs;i&longs;tance and limited Force what&longs;oever <lb/>being a&longs;&longs;igned, and any Di&longs;tance given, there is no doubt to be <lb/>made, but that the given Force may carry the given Weight to the <lb/>determinate Di&longs;tance; for, although the Force were extream <lb/>&longs;mall, yet, by dividing the Weight into many &longs;mall parts, none <lb/>of which remain &longs;uperiour to the Force, and by transferring them <lb/>one by one, it &longs;hall at la&longs;t have carried the whole Weight to the <lb/>a&longs;&longs;igned Term: and yet one cannot at the end of the Work with <lb/>Rea&longs;on &longs;ay, that that great Weight hath been moved, and tran&longs;<lb/>ported by a Force le&longs;&longs;e then it &longs;elf, howbeit indeed it was done <lb/>by a Force, that many times reiterated that Motion, and that <lb/>Space, which &longs;hall have been mea&longs;ured but only once by the whole <lb/>Weight. </s>

<s>From whence it appears, that the Velocity of the Force <lb/>hath been as many times Superiour to the Re&longs;i&longs;tance of the weight, <lb/>as the &longs;aid Weight was &longs;uperiour to the Force; for that in the <lb/>&longs;ame Time that the moving Force hath many times mea&longs;ured the <lb/>intervall between the Terms of the Motion, the &longs;aid Moveable <lb/>happens to have pa&longs;t it onely once: nor therefore ought we to <lb/>affirm a great Re&longs;i&longs;tance to have been overcome by a &longs;mall Force, <lb/>contrary to the con&longs;titution of Nature. </s>

<s>Then onely may we &longs;ay <lb/>the Natural Con&longs;titution is overcome, when the le&longs;&longs;er Force tran&longs;<lb/>fers the greater Re&longs;i&longs;tance, with a Velocity of Motion like to that <pb xlink:href="070/01/003.jpg" pagenum="273"/>wherewith it &longs;elf doth move; which we affirm ab&longs;olutely to be <lb/>impo&longs;&longs;ible to be done with any Machine imaginable. </s>

<s>But becau&longs;e <lb/>it may &longs;ometimes come to pa&longs;&longs;e, that having but little Force, it is <lb/>required to move a great Weight all at once, without dividing it <lb/>in pieces, on this occa&longs;ion it will be necei&longs;ary to have recour&longs;e to <lb/>the Machine, by means whereof the propo&longs;ed Weight may be <lb/>transferred to the a&longs;&longs;igned Space by the Force given. </s>

<s>But yet <lb/>this doth not hinder, but that the &longs;ame Force is to move, mea&longs;uring <lb/>that &longs;ame Space, or another equall to it, as many &longs;everall times as <lb/>it is exceeded by the &longs;aid Weight. </s>

<s>So that in the end of the a<lb/>ction we &longs;hall &longs;ind that we have received from the Machine no <lb/>other benefit tnen only that of tran&longs;porting the &longs;aid Weight with <lb/>the given Force to the Term given, all at once. </s>

<s>Which Weight, <lb/>being divided into parts, would without any Machine have been <lb/>carried by the &longs;ame Force, in the &longs;ame Time, through the &longs;ame <lb/>Intervall. </s>

<s>And this ought to pa&longs;&longs;e for one of the benefits taken <lb/>from the Mechanicks: for indeed it frequently happens, that be<lb/>ing &longs;canted in Force but not Time, we are put upon moving great <lb/>Weights unitedly or in gro&longs;&longs;e: but he that &longs;hould hope, and at<lb/>tempt to do the &longs;ame by the help of Machines without increa&longs;e of <lb/>Tardity in the Moveable, would certainly be deceived, and would <lb/>declare his ignorance of the u&longs;e of Mechanick In&longs;truments, and <lb/>the rea&longs;on of their effects.</s>

<s>Another benefit is drawn from the In&longs;truments, which depend<lb/>eth on the place wherein the operation is to be made: for all In<lb/>&longs;truments cannot be made u&longs;e of in all places with equall conve<lb/>nience. </s>

<s>And &longs;o we &longs;ee (to explain our &longs;elves by an example) that <lb/>for drawing of Water out of a Well, we make u&longs;e of onely a <lb/>Rope and a Bucket fitted to receive and hold Water, wherewith <lb/>we draw up a determinate quantity of Water, in a certain Time, <lb/>with our limited &longs;trength: and he that &longs;hould think he could with <lb/>a Machine of what&longs;oever Force, with the &longs;ame &longs;trength, and in <lb/>the &longs;ame Time, take up a great quantity of Water, is in a gro&longs;&longs;e <lb/>Errour. </s>

<s>And he &longs;hall find him&longs;elf &longs;o much the more deceived, <lb/>the more he &longs;hall vary and multiply his Inventions: Yet never<lb/>thele&longs;&longs;e we &longs;ee Water drawn up with other Engines, as with a Pump <lb/>that drinks up Water in the Hold of Ships; where you mu&longs;t note <lb/>that the Pump was not imployed in tho&longs;e Offices, for that it draws <lb/>up more Water in the &longs;ame Time, and with the &longs;ame &longs;trength <lb/>then that which a bare Bucket would do, but becau&longs;e in that place <lb/>the u&longs;e of the Bucket or any &longs;uch like Ve&longs;&longs;el could not effect what <lb/>is de&longs;ired, namely to keep the Hold of the Ship quite dry from e<lb/>very little quantity of Water; which the Bucket cannot do, for <lb/>that it cannot dimerge and dive, where there is not a con&longs;iderable <lb/>depth of Water. </s>

<s>And thus we &longs;ee the Holds of Ships by the <pb xlink:href="070/01/004.jpg" pagenum="274"/>&longs;aid In&longs;trument kept dry, when Water cannot but onely oblique<lb/>ly be drawn up, which the ordinary u&longs;e of the Bucket would not <lb/>effect, which ri&longs;eth and de&longs;cends with its Rope perpendicu<lb/>larly.</s>

<s>The third is a greater benefit, haply, then all the re&longs;t that are <lb/>derived from Mechanick In&longs;truments, and re&longs;pects the a&longs;&longs;i&longs;tance <lb/>which is borrowed of &longs;ome Force exanimate, as of the &longs;tream of a <lb/>River, or el&longs;e animate, but of le&longs;&longs;e expence by far, then that which <lb/>would be nece&longs;&longs;ary for maintaining humane &longs;trength: as when to <lb/>turn Mills, we make u&longs;e of the Current of a River, or the &longs;trength <lb/>of a Hor&longs;e, to effect that, which would require the &longs;trength of five <lb/>or fix Men. </s>

<s>And this we may al&longs;o advantage our &longs;elves in rai&longs;ing <lb/>Water, or making other violent Motions, which mu&longs;t have been <lb/>done by Men, if there were no other helps; becau&longs;e with one &longs;ole <lb/>Ve&longs;&longs;el we may take Water, and rai&longs;e, and empty it where occa&longs;ion <lb/>requires; but becau&longs;e the Hor&longs;e, or &longs;uch other Mover wanteth <lb/>Rea&longs;on, and tho&longs;e In&longs;truments which are requi&longs;ite for holding and <lb/>emptying the Ve&longs;&longs;el in due time, returning again to fill it, and one<lb/>ly is endued with Force, therefore it's nece&longs;&longs;ary that the Mecha<lb/>nitian &longs;upply the naturall defect of that Mover, furni&longs;hing it with <lb/>&longs;uch devices and inventions, that with the &longs;ole application of it's <lb/>Force the defired effect may follow. </s>

<s>And therein is very great <lb/>advantage, not becau&longs;e that a Wheel or other Machine can enable <lb/>one to tran&longs;port the &longs;ame Weight with le&longs;&longs;e Force, and greater <lb/>Dexterity, or a greater Space than an equall Force, without tho&longs;e <lb/>In&longs;truments, but having Judgment and proper Organs, could have <lb/>done; but becau&longs;e that the &longs;tream of a River co&longs;teth little or <lb/>nothing, and the charge of keeping of an Hor&longs;e or other Bea&longs;t, <lb/>who&longs;e &longs;trength is greater then that of eight, or it may be more <lb/>Men, is far le&longs;&longs;e then what &longs;o many Men would be kept <lb/>for.</s>

<s>The&longs;e then are the benefits that may be derived from Mecha<lb/>nick In&longs;truments, and not tho&longs;e which ignorant Engineers dream <lb/>of, to their own di&longs;grace, and the abu&longs;e of &longs;o many Princes, <lb/>whil&longs;t they undertake impo&longs;&longs;ible enterprizes; of which, both <lb/>by the little which hath been hinted, and by the much which <lb/>&longs;hall be demon&longs;trated in the Progre&longs;&longs;e of this Treati&longs;e, we &longs;hall <lb/>come to a&longs;&longs;ure our &longs;elves, if we attentively heed that which &longs;hall <lb/>be &longs;poken.</s><pb xlink:href="070/01/005.jpg" pagenum="275"/>

<s>DEFINITIONS.</s>

<s>That which in all Demon&longs;trative Sciences is nece&longs;&longs;ary to be <lb/>ob&longs;erved, we ought al&longs;o to follow in this Di&longs;cour&longs;e, that is; <lb/>to propound the Definitions of the proper Terms of this <lb/>Art, and the primary Suppo&longs;itions, from which, as from &longs;eeds full <lb/>of fecundity, may of con&longs;equence &longs;pring and re&longs;ult the cau&longs;es, <lb/>and true Demon&longs;trations, of the Nature of all the Mechanick <lb/>Engines which are u&longs;ed, for the mo&longs;t part about the Motions of <lb/>Grave Matters, therefore we will determine, fir&longs;t, what is <emph type="italics"/>GRA<lb/>VITIE.<emph.end type="italics"/></s>

<s>We call <emph type="italics"/>GRAVITIE<emph.end type="italics"/> then, That propen&longs;ion of moving <lb/>naturally downwards, which is found in &longs;olid Bodies, cau&longs;ed by <lb/>the greater or le&longs;&longs;e quantity of matter, whereof they are con&longs;ti<lb/>tuted.</s>

<s><emph type="italics"/>MOMENT<emph.end type="italics"/> is the propen&longs;ion of de&longs;cending, cau&longs;ed not &longs;o <lb/>much by the Gravity of the moveable, as by the di&longs;po&longs;ure which <lb/>divers Grave Bodies have in relation to one another; by means of <lb/>whichMoment, we oft &longs;ee a Body le&longs;s Grave counterpoi&longs;e another <lb/>of greater Gravity: as in the Stiliard, a great Weight is rai&longs;ed by <lb/>a very &longs;mall counterpoi&longs;e, not through exce&longs;s of Gravity, but <lb/>through the remotene&longs;&longs;e from the point whereby the Beam is up<lb/>held, which conjoyned to the Gravity of the le&longs;&longs;er weight adds <lb/>thereunto Moment, and <emph type="italics"/>Impetus<emph.end type="italics"/> of de&longs;cending, wherewith the <lb/>Moment of the other greater Gravity may be exceeded. <emph type="italics"/>MO<lb/>MENT<emph.end type="italics"/> then is that IMPETUS of de&longs;cending, compounded <lb/>of Gravity, Po&longs;ition, and the like, whereby that propenfion may <lb/>be occa&longs;ioned</s>

<s>The <emph type="italics"/>CENTER<emph.end type="italics"/> of <emph type="italics"/>GRAVITY<emph.end type="italics"/> we define to be that point <lb/>in every Grave Body, about which con&longs;i&longs;t parts of equall Moment: <lb/>&longs;o that, imagining &longs;ome Grave Body to be &longs;u&longs;pended and &longs;u&longs;tain<lb/>ed by the &longs;aid point, the parts on the right hand will Equilibrate <lb/>tho&longs;e on the left, the Anteriour, the Po&longs;teriour, and tho&longs;e above <lb/>tho&longs;e below; &longs;o that be it in any what&longs;oever fite, and po&longs;ition, <lb/>provided it be &longs;u&longs;pended by the &longs;aid <emph type="italics"/>CENTER,<emph.end type="italics"/> it &longs;hall &longs;tand <lb/>&longs;till: and this is that point which would gladly unite with the <lb/>univer&longs;all Center of Grave Bodies, namely withthat of the Earth, <lb/>if it might thorow &longs;ome free <emph type="italics"/>Medium<emph.end type="italics"/> de&longs;cend thither. </s>

<s>From <lb/>whence we take the&longs;e Suppo&longs;itions.</s><pb xlink:href="070/01/006.jpg" pagenum="276"/>

<s>SUPPOSITIONS.</s>

<s>Any Grave Body, (as to what belongeth to it's proper ver<lb/>tue) moveth downwards, &longs;o that the Center of it's Gravity <lb/>never &longs;trayeth out of that Right Line which is produced <lb/>from the &longs;aid Center placed in the fir&longs;t Term of the Motion unto <lb/>the univer&longs;al Center of Grave Bodies. </s>

<s>Which is a Suppo&longs;ition <lb/>very manife&longs;t, becau&longs;e that &longs;ingle Center being obliged to endea<lb/>vour to unite with the common Center, it's nece&longs;&longs;ary, unle&longs;&longs;e &longs;ome <lb/>impediment intervene, that it go &longs;eeking it by the &longs;horte&longs;t Line, <lb/>which is the Right alone: And from hence may we &longs;econdarily <lb/>&longs;uppo&longs;e</s>

<s>Every Grave Body putteth the greate&longs;t &longs;tre&longs;&longs;e, and weigheth <lb/>mo&longs;t on the Center of it's Gravity, and to it, as to its proper &longs;eat, <lb/>all <emph type="italics"/>Impetus,<emph.end type="italics"/> all Pondero&longs;ity, and, in &longs;ome, all Moment hath re<lb/>cour&longs;e.</s>

<s>We la&longs;tly &longs;uppo&longs;e the Center of the Gravity of two Bodies e<lb/>qually Grave to be in the mid&longs;t of that Right Line which conjoyns <lb/>the &longs;aid two Centers; or that two equall weights, &longs;u&longs;pended in <lb/>equall di&longs;tence, &longs;hall have the point of <emph type="italics"/>Equilibrium<emph.end type="italics"/> in the common <lb/>Center, or meeting of tho&longs;e equal Di&longs;tances. </s>

<s>As for Example, <lb/>the Di&longs;tance C E being equall to the Di&longs;tance E D, and there be<lb/>ing by them two equall weights &longs;u&longs;pended, A and B, we &longs;uppo&longs;e <lb/>the point of <emph type="italics"/>Equilibrium<emph.end type="italics"/> to be in the point E, there being no <lb/>greater rea&longs;on for inclining to <lb/>one, then to the other part. </s>

<s>But <lb/><figure id="id.070.01.006.1.jpg" xlink:href="070/01/006/1.jpg"/><lb/>here is to be noted, that the Di<lb/>&longs;tances ought to be mea&longs;ured <lb/>with Perpendicular Lines, which <lb/>from the point of Su&longs;pen&longs;ion E, <lb/>fall on the Right Lines, that from <lb/>the Center of the Gravity of the <lb/>Weights A and B, are drawn to <lb/>the common Center of things <lb/>Grave; and therefore if the Di&longs;tance E D were tran&longs;ported into <lb/>E F, the weight B would not counterpoi&longs;e the weight A, becau&longs;e <lb/>drawing from the Centers of Gravity two Right Lines to the Cen<lb/>ter of the Earth, we &longs;hall &longs;ee that which cometh from the Center <lb/>of the Weight I, to be nearer to the Center E, then the other <lb/>produced from the Center of the weight A. </s>

<s>Therefore our &longs;aying <lb/>that equal Weights are &longs;u&longs;pended by [or at] equal Di&longs;tances, is <lb/>to be under&longs;tood to be meant when as the Right Lines that go from <lb/>their Centers & to &longs;eek out the common Center of Gravity, &longs;hall be <lb/>equidi&longs;ta nt from that Right Line, which is produced from the &longs;aid <pb xlink:href="070/01/007.jpg" pagenum="277"/>Term of tho&longs;e Di&longs;tances, that is from the point of Su&longs;pen&longs;ion, to <lb/>the &longs;ame Center of the Earrh.</s>

<s>The&longs;e things determined and &longs;uppo&longs;ed, we come to the explica<lb/>tion of a Principle, the mo&longs;t common and materiall of the greater <lb/>part of Mechanick In&longs;truments: demon&longs;trating, that unequall <lb/>Weights weigh equally when &longs;u&longs;pended by [or at] unequal Di&longs;tan<lb/>ces, which have contrary proportion to that which tho&longs;e weights <lb/>are found to have, See the Demon&longs;tration in the beginning of the <lb/>&longs;econd Dialogue of Local-Motions.</s>

<s><emph type="italics"/>Some Adverii&longs;ements about what hath been &longs;aid.<emph.end type="italics"/></s>

<s>Now being that Weights unequall come to acquire equall <lb/>Moment, by being alternately &longs;u&longs;pended at Di&longs;tances that <lb/>have the &longs;ame proportion with them; I think it not fit to <lb/>over pa&longs;&longs;e with &longs;ilence another congruicy and probability, which <lb/>may confirm the &longs;ame truth; for let the Ballance A B, be con&longs;ide<lb/>red, as it is divided into unequal parts in the point C, and let the <lb/>Weights be of the &longs;ame propor<lb/><figure id="id.070.01.007.1.jpg" xlink:href="070/01/007/1.jpg"/><lb/>tion that is between the Di&longs;tan<lb/>ces B C, and C A, alternately <lb/>&longs;u&longs;pended by the points A, and <lb/>B: It is already manife&longs;t, that <lb/>the one will counterpoi&longs;e the <lb/>other, and con&longs;equently, that <lb/>were there added to one of them <lb/>a very &longs;mall Moment of Gravity, it would preponderate, rai&longs;ing <lb/>the other, &longs;o that an in&longs;en&longs;ible Weight put to the Grave B, the <lb/>Ballance would move and de&longs;cend from the point B towards E, <lb/>and the other extream A would a&longs;cend into D, and in regard that <lb/>to weigh down B, every &longs;mall Gravity is &longs;ufficient, therefore not <lb/>keeping any accompt of this in&longs;en&longs;ible Moment, we will put no <lb/>difference between one Weights <emph type="italics"/>&longs;u&longs;taining,<emph.end type="italics"/> and one Weights <lb/><emph type="italics"/>moving<emph.end type="italics"/> another. </s>

<s>Now, let us con&longs;ider the Motion which the <lb/>Weight B makes, de&longs;cending into E, and that which the other <lb/>A makes in a&longs;cending into D, we &longs;hall without doubt find the <lb/>Space B E to be &longs;o much greater than the Space A D, as the Di<lb/>&longs;tance B C is greater than C A, forming in the Center C two an<lb/>gles D C A, and E C B, equall as being at the Cock, and con&longs;e<lb/>quently two Circumferences A D and B E alike; and to have the <lb/>&longs;ame proportion to one another, as have the Semidiameters B C, <lb/>and C A, by which they are de&longs;cribed: &longs;o that then the Velocity <lb/>of the Motion of the de&longs;cending Grave B cometh to be &longs;o much <lb/>Superiour to the Velocity of the other a&longs;cending Moveable A, as <lb/>the Gravity of this exceeds the Gravity of that; and it not being <pb xlink:href="070/01/008.jpg" pagenum="278"/>po&longs;&longs;ible that the Weight A &longs;hould be rai&longs;ed to D, although &longs;low<lb/>ly, unle&longs;&longs;e the other Weight B do move to E &longs;wiftly, it will not <lb/>be &longs;trange, or incon&longs;i&longs;tent with the Order of Nature, that the <lb/>Velocity of the Motion of the Grave B, do compen&longs;ate the greater <lb/>Re&longs;i&longs;tance of the Weight A, &longs;o long as it moveth &longs;lowly to D, <lb/>and the other de&longs;cendeth &longs;wiftly to E, and &longs;o on the contrary, <lb/>the Weight A being placed in the point D, and the other B in <lb/>the point E, it will not be unrea&longs;onable that that falling lea&longs;urely <lb/>to A, &longs;hould be able to rai&longs;e the other ha&longs;tily to B, recovering by <lb/>its Gravity what it had lo&longs;t by it's Tardity of Motion. </s>

<s>And by <lb/>this Di&longs;cour&longs;e we may come to know how the Velocity of the <lb/>Motion is able to encrea&longs;e Moment in the Moveable, according to <lb/>that &longs;ame proportion by which the &longs;aid Velocity of the Motion is <lb/>augmented.</s>

<s>There is al&longs;o another thing, before we proceed any farther, to <lb/>be confidered; and this is touching the Di&longs;tances, whereat, or <lb/>wherein Weights do hang: for it much imports how we are to <lb/>under&longs;tand Di&longs;tances equall, and unequall; and, in &longs;um, in what <lb/>manner they ought to be mea<lb/><figure id="id.070.01.008.1.jpg" xlink:href="070/01/008/1.jpg"/><lb/>&longs;ured: for that A B being the <lb/>Right Line, and two equall <lb/>Weights being &longs;u&longs;pended at <lb/>the very ends thereof, the point <lb/>C being taken in the mid&longs;t of <lb/>the &longs;aid Line, there &longs;hall be an <lb/><emph type="italics"/>Equilibrium<emph.end type="italics"/> upon the &longs;ame: <lb/>And the rea&longs;on is for that the <lb/>Di&longs;tance C B is equal to C A. <lb/></s>

<s>But if elevating the Line C B, moving it about the point C, it <lb/>&longs;hall be transferred into CD, &longs;o that the Ballance &longs;tand according <lb/>to the two Lines A C, and C D, the two equall Weights hanging <lb/>at the Terms A and D, &longs;hall no longer weigh equally on that <lb/>point C, becau&longs;e the di&longs;tance of the Weight placed in D, is made <lb/>le&longs;&longs;e then it was when it hanged in B. </s>

<s>For if we confider the Lines, <lb/>along [or by] which the &longs;aid Graves make their Impul&longs;e, and <lb/>would de&longs;cend, in ca&longs;e they were freely moved, there is no doubt <lb/>but that they would make or de&longs;cribe the Lines A G, D F, B H: <lb/>Therefore the Weight hanging on the point D, maketh it's Moment <lb/>and <emph type="italics"/>Impetus<emph.end type="italics"/> according to the Line D F: but when it hanged in <lb/>B, it made <emph type="italics"/>Impetus<emph.end type="italics"/> in the Line B H: and becau&longs;e the Line D F is <lb/>nearer to the Fulciment C, then is the Line B H Therefore we <lb/>are to under&longs;tand that the Weights hanging on the points A and D, <lb/>are not equi-di&longs;tant from the point C, as they be when they are <lb/>con&longs;tituted according to their Right Line A C B: And la&longs;tly, <lb/>we are to take notice, that the Di&longs;tance is to be mea&longs;ured by <pb xlink:href="070/01/009.jpg" pagenum="279"/>Lines, which fall at Right Angles on tho&longs;e whereon the Weights <lb/>hang, and would move, if &longs;o be they were permitted to de&longs;cend <lb/>freely.</s>

<s>Of the BALLANCE and LEAVER.</s>

<s>Having under&longs;tood by certain Demon&longs;tration, one of the <lb/>fir&longs;t Principles, from which, as from a plenti&longs;ul Fountain, <lb/>many of the Mechanical In&longs;truments are derived, we may <lb/>take occa&longs;ion without any difficulty to come to the knowledge of <lb/>the nature of them: and fir&longs;t &longs;peaking of the Stiliard, an In&longs;tru<lb/>ment of mo&longs;t ordinary u&longs;e, with which divers Merchandizes are <lb/>weighed, &longs;u&longs;taining them, though very heavy, with a very &longs;mall <lb/>counterpoi&longs;e, which is com<lb/>monly called the Roman or <lb/><figure id="id.070.01.009.1.jpg" xlink:href="070/01/009/1.jpg"/><lb/>Plummet, we &longs;hall prove that <lb/>there is no more to be done in <lb/>&longs;uch an operation, but to re<lb/>duce into act and practice <lb/>what hath been above contemplated. </s>

<s>For if we propo&longs;e the Bal<lb/>lance A B, who&longs;e Fulciment or Lanquet is in the point C, by <lb/>which, at the &longs;mall Di&longs;tance C A, hangeth the heavy Weight D, <lb/>and if along the other greater C B, (which we call the Needle of <lb/>the Stiliard) we &longs;hould &longs;uppo&longs;e the Roman F, though of but little <lb/>weight in compari&longs;on of the Grave Body D to be &longs;lipped to and <lb/>fro, it &longs;hall be pof&longs;ible to place it &longs;o remotely from the Lanquet C, <lb/>that the &longs;ame proportion may be found between the two Weights <lb/>D and F, as is between the Di&longs;tances F C, and C A: and then &longs;hall <lb/>an <emph type="italics"/>Equilibrium<emph.end type="italics"/> &longs;ucceed; unequall Weights hanging at Di&longs;tances <lb/>alternately proportional to them.</s>

<s>Nor is this In&longs;trument different from that other called <emph type="italics"/>Vectis,<emph.end type="italics"/><lb/><arrow.to.target n="marg1107"></arrow.to.target><lb/>and vulgarly the ^{*} Leaver, wherewith great Weights are moved <lb/>by &longs;mall Force; the application of which is according to the Fi<lb/>gure prefixed; wherein the Leaver <lb/>is repre&longs;ented by the Bar of wood <lb/>or other &longs;olid matter, <emph type="italics"/>B<emph.end type="italics"/> C D, let <lb/><figure id="id.070.01.009.2.jpg" xlink:href="070/01/009/2.jpg"/><lb/>the heavy Weight to be rai&longs;ed be <lb/>A, and let the &longs;teadfa&longs;t &longs;upport <lb/>or Fulciment on which the Leaver <lb/>re&longs;ts and moves be &longs;uppo&longs;ed to be <lb/>E, and putting one end of the <lb/>Leaver under the Weight A, as <lb/>may be &longs;een in the point C, en<lb/>crea&longs;ing the Weight or Force at the other end D, it will be able <lb/>to lift up the Weight A, though not much, whenever the Force in <pb xlink:href="070/01/010.jpg" pagenum="280"/>D hath the &longs;ame proportion to the Re&longs;i&longs;tance made by the Weight <lb/>A, in the point C: as the Di&longs;tance <emph type="italics"/>B<emph.end type="italics"/> C hath to the Di&longs;tance C D, <lb/>whereby it's clear, that the nearer the Fulciment E &longs;hall approach <lb/>to the Term B, encrea&longs;ing the proportion of the Di&longs;tance D C to <lb/>the Di&longs;tance C <emph type="italics"/>B,<emph.end type="italics"/> the more may one dimini&