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| author | Klaus Thoden <kthoden@mpiwg-berlin.mpg.de> |
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| date | Thu, 02 May 2013 11:08:12 +0200 |
| parents | 22d6a63640c6 |
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<?xml version="1.0"?> <archimedes xmlns:xlink="http://www.w3.org/1999/xlink" > <info> <author>Galilei, Galileo</author> <title>Discourse concerning the natation of bodies</title> <date>1663</date> <place>London</place> <translator>Thomas Salusbury</translator> <lang>en</lang> <cvs_file>galil_natat_074_en_1663.xml</cvs_file> <cvs_version></cvs_version> <locator>074.xml</locator> </info> <text> <front> <section> <pb></pb> <p type="head"> <s>A <lb></lb>DISCOURSE <lb></lb><emph type="italics"></emph>PRESENTED<emph.end type="italics"></emph.end><lb></lb>TO THE MOST SERENE <lb></lb>Don Coſimo II. <lb></lb>GREAT DUKE <lb></lb><emph type="italics"></emph>OF<emph.end type="italics"></emph.end><lb></lb>TUSCANY, <lb></lb>CONCERNING <lb></lb>The <emph type="italics"></emph>NATATION<emph.end type="italics"></emph.end> of BODIES Vpon, <lb></lb>And <emph type="italics"></emph>SUBMERSION<emph.end type="italics"></emph.end> In, <lb></lb>THE <lb></lb>WATER.</s></p><p type="head"> <s>By GALILEUS GALILEI: Philoſopher and <lb></lb>Mathematician, unto His moſt Serene Highneſſe.</s></p><p type="head"> <s>Engliſhed from the Second Edition of the ITALIAN, <lb></lb>compared with the Manuſcript Copies, and reduced <lb></lb>into PROPOSITIONS: <lb></lb>By <emph type="italics"></emph>THOMAS SALUSBURY,<emph.end type="italics"></emph.end> <expan abbr="Eſq;">Eſque</expan></s></p><p type="head"> <s><emph type="italics"></emph>LONDON<emph.end type="italics"></emph.end>: <lb></lb>Printed by WILLIAM LEYBOURN: <lb></lb><emph type="italics"></emph>M D C LXIII.<emph.end type="italics"></emph.end></s></p></section><section> <pb pagenum="401"></pb><p type="head"> <s>A DISCOVRSE <lb></lb>Preſented to the Moſt Serene DON COSIMO II. <lb></lb>GREATDUKE of <emph type="italics"></emph>TUSC ANY:<emph.end type="italics"></emph.end><lb></lb>CONCERNING<lb></lb><emph type="italics"></emph>The Natation of BODIES Upon, or Submerſion <lb></lb>In, the WATER.<emph.end type="italics"></emph.end></s> </p></section> </front> <body> <chap><p type="main"> <s>Conſidering (Moſt Serene Prince) that the <lb></lb>publiſhing this preſent Treatiſe, of ſo <lb></lb>different an Argument from that which <lb></lb><arrow.to.target n="marg1393"></arrow.to.target><lb></lb>many expect, and which according to the <lb></lb>intentions I propoſed in my ^{*} Aſtronomi<lb></lb>call <emph type="italics"></emph>Adviſo,<emph.end type="italics"></emph.end> I ſhould before this time <lb></lb>have put forth, might peradventure make <lb></lb>ſome thinke, either that I had wholly <lb></lb>relinquiſhed my farther imployment <lb></lb>about the new Celeſtiall Obſervations, <lb></lb>or that, at leaſt, I handled them very <lb></lb>remiſſely; I have judged fit to render an account, aſwell of my <lb></lb>deferring that, as of my writing, and publiſhing this treatiſe.</s></p><p type="margin"> <s><margin.target id="marg1393"></margin.target>His Nuncio Sl<lb></lb>derio.</s></p><p type="main"> <s>As to the firſt, the laſt diſcoveries of <emph type="italics"></emph>Saturn<emph.end type="italics"></emph.end> to be tricorporeall, and <lb></lb>of the mutations of Figure in <emph type="italics"></emph>Venus,<emph.end type="italics"></emph.end> like to thoſe that are ſeen in the <lb></lb>Moon, together with the Conſequents depending thereupon, have <lb></lb>not ſo much occaſioned the demur, as the inveſtigation of the times <lb></lb>of the Converſions of each of the Four Medicean Planets about <emph type="italics"></emph>Ju <lb></lb>piter,<emph.end type="italics"></emph.end> which I lighted upon in <emph type="italics"></emph>April<emph.end type="italics"></emph.end> the year paſt, 1611, at my being in <lb></lb><emph type="italics"></emph>Rome<emph.end type="italics"></emph.end>; where, in the end, I aſſertained my ſelfe, that the firſt and neereſt <lb></lb>to <emph type="italics"></emph>Jupiter,<emph.end type="italics"></emph.end> moved about 8 <emph type="italics"></emph>gr.<emph.end type="italics"></emph.end> & 29 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> of its Sphere in an houre, make <lb></lb>ing its whole revolution in one naturall day, and 18 hours, and almoſt <lb></lb>an halfe. </s><s>The ſecond moves in its Orbe 14 <emph type="italics"></emph>gr. </s><s>13 min.<emph.end type="italics"></emph.end> or very neer, <lb></lb>in an hour, and its compleat converſion is conſummate in 3 dayes, 13 <lb></lb>hours, and one third, or thereabouts. </s><s>The third paſſeth in an hour, <lb></lb>2 <emph type="italics"></emph>gr. </s><s>6 min.<emph.end type="italics"></emph.end> little more or leſs of its Circle, and meaſures it all in 7 <lb></lb>dayes, 4 hours, or very neer. </s><s>The fourth, and more remote than the <lb></lb>reſt, goes in one houre, o <emph type="italics"></emph>gr 54 min.<emph.end type="italics"></emph.end> and almoſt an halfe of its Sphere, <lb></lb>and finiſheth it all in 16 dayes, and very neer 18 hours. </s><s>But be <lb></lb>cauſe the exceſſive velocity of their returns or reſtitutions, requires a <lb></lb>moſt ſcrupulous preciſeneſſe to calculate their places, in times paſt <pb pagenum="402"></pb>and future, eſpecially if the time be for many Moneths or Years; I <lb></lb>am therefore forced, with other Obſervations, and more exact than <lb></lb>the former, and in times more remote from one another, to correct <lb></lb>the Tables of ſuch Motions, and limit them even to the ſhorteſt mo <lb></lb>ment: for ſuch exactneſſe my firſt Obſervations ſuffice not; not only <lb></lb>in regard of the ſhort intervals of Time, but becauſe I had not as then <lb></lb>found out a way to meaſure the diſtances between the ſaid Planets <lb></lb>by any Inſtrument: I Obſerved ſuch Intervals with ſimple relation <lb></lb>to the Diameter of the Body of <emph type="italics"></emph>Jupiter<emph.end type="italics"></emph.end>; taken, as we have ſaid, by <lb></lb>the eye, the which, though they admit not errors of above a Minute, <lb></lb>yet they ſuffice not for the determination of the exact greatneſs of the <lb></lb>Spheres of thoſe Stars. </s><s>But now that I have hit upon a way of ta <lb></lb>king ſuch meaſures without failing, ſcarce in a very few Seconds, I will <lb></lb>continue the obſervation to the very occultation of <emph type="italics"></emph>JVPITER,<emph.end type="italics"></emph.end> <lb></lb>which ſhall ſerve to bring us to the perfect knowledge of the Moti <lb></lb>ons, and Magnitudes of the Orbes of the ſaid Planets, together <lb></lb><arrow.to.target n="marg1394"></arrow.to.target> <lb></lb>alſo with ſome other conſequences thence ariſing. </s><s>I adde to theſe <lb></lb>things the obſervation of ſome obſcure Spots, which are diſcover <lb></lb>ed in the Solar Body, which changing, poſition in that, propounds <lb></lb>to our conſideration a great argument either that the Sun revolves in <lb></lb>it ſelfe, or that perhaps other Starts, in like manner as <emph type="italics"></emph>Venus<emph.end type="italics"></emph.end> and <lb></lb><emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> revolve about it, inviſible in other times, by reaſon of their <lb></lb>ſmall digreſſions, leſſe than that of <emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> and only viſible when <lb></lb>they interpoſe between the Sun and our eye, or elſe hint the truth <lb></lb>of both this and that; the certainty of which things ought not to be <lb></lb>contemned, nor omitted.</s></p><p type="margin"> <s><margin.target id="marg1394"></margin.target>The Authors <lb></lb>Obſervations of <lb></lb>the Solar Spots.</s></p><p type="main"> <s><emph type="italics"></emph>Continuall obſervation hath at laſt aſſured me that theſe Spots are <lb></lb>matters contiguous to the Body of the Sun, there continually produced <lb></lb>in great number, and afterwards diſſolved, ſome in a ſhorter, ſome in a <lb></lb>longer time, and to be by the Converſion or Revolution of the Sun in it <lb></lb>ſelfe, which in a Lunar Moneth, or thereabouts, finiſheth its Period, <lb></lb>caried about in a Circle, an accident great of it ſelfe, and greater for <lb></lb>its Conſequences.<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1395"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1395"></margin.target>The occaſion in <lb></lb>ducing the Au <lb></lb>thor to write <lb></lb>this Treatiſe.</s></p><p type="main"> <s>As to the other particular in the next place. ^{*} Many cauſes have <lb></lb>moved me to write the preſent Tract, the ſubject whereof, is the <lb></lb>Diſpute which I held ſome dayes ſince, with ſome learned men of <lb></lb>this City, about which, as your Highneſſe knows, have followed <lb></lb>many Diſcourſes: The principall of which Cauſes hath been the <lb></lb>Intimation of your Highneſſe, having commended to me Writing, <lb></lb>as a ſingular means to make true known from falſe, reall from appa <lb></lb>rent Reaſons, farr better than by Diſputing vocally, where the <lb></lb>one or the other, or very often both the Diſputants, through too <pb pagenum="403"></pb>greate heate, or exalting of the voyce, either are not underſtood, <lb></lb>or elſe being tranſported by oſtentation of not yeilding to one ano <lb></lb>ther, farr from the firſt Propoſition, with the novelty, of the <lb></lb>various Propoſals, confound both themſelves and their Auditors.</s></p><p type="main"> <s>Moreover, it ſeemed to me convenient to informe your High <lb></lb>neſſe of all the ſequell, concerning the Controverſie of which I <lb></lb>treat, as it hath been advertiſed often already by others: and becauſe <lb></lb>the Doctrine which I follow, in the diſcuſſion of the point in hand, <lb></lb>is different from that of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>; and interferes with his Principles, <lb></lb>I have conſidered that againſt the Authority of that moſt famous <lb></lb>Man, which amongſt many makes all ſuſpected that comes not from <lb></lb>the Schooles of the Peripateticks, its farr better to give ones Reaſons <lb></lb>by the Pen than by word of mouth and therfore I reſolved to write the <lb></lb>preſent diſcourſe: in which yet I hope to demonſtrate that it was not <lb></lb>out of capritiouſneſſe, or for that I had not read or underſtood <lb></lb><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> that I ſometimes ſwerve from his opinion, but becauſe <lb></lb>ſeverall Reaſons perſwade me to it, and the ſame <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath </s></p><p type="main"> <s><arrow.to.target n="marg1396"></arrow.to.target> <lb></lb>tought me to fix my judgment on that which is grounded upon <lb></lb>Reaſon, and not on the bare Authority of the Maſter; and it is <lb></lb>moſt certaine according to the ſentence of <emph type="italics"></emph>Alcinoos,<emph.end type="italics"></emph.end> that philoſopha <lb></lb><arrow.to.target n="marg1397"></arrow.to.target> <lb></lb>ting ſhould be free. </s><s>Nor is the reſolution of our Queſtion in my <lb></lb>judgment without ſome benefit to the Univerſall, foraſmuch as <lb></lb>treating whether the figure of Solids operates, or not, in their going, <lb></lb>or not going to the bottome in Water, in occurrences of building <lb></lb>Bridges or other Fabricks on the Water, which happen commonly <lb></lb>in affairs of grand import, it may be of great availe to know the <lb></lb>truth.</s></p><p type="margin"> <s><margin.target id="marg1396"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> prefers <lb></lb>Reaſon to the <lb></lb>Authority ofan <lb></lb>Author.</s></p><p type="margin"> <s><margin.target id="marg1397"></margin.target>The benefit of <lb></lb>this Argument.</s></p><p type="main"> <s>I ſay therfore, that being the laſt Summer in company with certain <lb></lb><arrow.to.target n="marg1398"></arrow.to.target> <lb></lb>Learned men, it was ſaid in the argumentation; That Condenſation <lb></lb>was the propriety of Cold, and there was alledged for inſtance, the <lb></lb>example of Ice: now I at that time ſaid, that, in my judgment, <lb></lb>the Ice ſhould be rather Water rarified than condenſed, and my <lb></lb><arrow.to.target n="marg1399"></arrow.to.target> <lb></lb>reaſon was, becauſe Condenſation begets diminution of Maſs, and <lb></lb>augmentation of gravity, and Rarifaction cauſeth greater Lightneſs, <lb></lb>and augmentarion of Maſſe: and Water in freezing, encreaſeth in <lb></lb>Maſſe, and the Ice made thereby is lighter than the Water on which <lb></lb>it ſwimmeth.</s></p><p type="margin"> <s><margin.target id="marg1398"></margin.target>Condenſation <lb></lb>the Propriety of <lb></lb>Cold, according <lb></lb>to the Peripate <lb></lb>ticks.</s></p><p type="margin"> <s><margin.target id="marg1399"></margin.target>Ice rather water <lb></lb>rarified, than <lb></lb>condenſed, and <lb></lb>why:</s></p><p type="main"> <s><emph type="italics"></emph>What I ſay, is manifeſt, becauſe, the medium ſubtracting from the <lb></lb>whole Gravity of Sollids the weight of ſuch another Maſſe of the ſaid<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1400"></arrow.to.target> <lb></lb><emph type="italics"></emph>Medium; was<emph.end type="italics"></emph.end> Archimedes <emph type="italics"></emph>proves in his ^{*} Firſt Booke<emph.end type="italics"></emph.end> De Inſidentibus <lb></lb>Humido; <emph type="italics"></emph>when ever the Maſſe of the ſaid Solid encreaſeth by Diſtraction, <lb></lb>the more ſhall the<emph.end type="italics"></emph.end> Medium <emph type="italics"></emph>detract from its entire Gravity; and leſſe, <lb></lb>when by Compreſſion it ſhall be condenſed and reduced to a leſſe Maſſe.<emph.end type="italics"></emph.end></s></p><p type="margin"> <pb pagenum="404"></pb> <s><margin.target id="marg1400"></margin.target>In lib: 1. of Na <lb></lb>tation of Bodies <lb></lb>Prop. </s><s>7.</s></p><p type="margin"> <s><margin.target id="marg1401"></margin.target>Figure operates <lb></lb>not in the Nata <lb></lb>tion of Sollids.</s></p><p type="main"> <s>It was anſwered me, that that proceeded not from the greater Levity; <lb></lb><arrow.to.target n="marg1401"></arrow.to.target> <lb></lb>but from the Figure, large and flat, which not being able to pene <lb></lb>trate the Reſiſtance of the Water, is the cauſe that it ſubmergeth not. <lb></lb></s><s>I replied, that any piece of Ice, of whatſoever Figure, ſwims upon <lb></lb>the Water, a manifeſt ſigne, that its being never ſo flat and broad, <lb></lb>hath not any part in its floating: and added, that it was a manifeſt <lb></lb>proofe hereof to ſee a piece of Ice of very broad Figure being thruſt <lb></lb>to the botome of the Water, ſuddenly return to flote atoppe, which <lb></lb>had it been more grave, and had its ſwimming proceeded from its <lb></lb>Forme, unable to penetrate the Reſiſtance of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> that <lb></lb>would be altogether impoſſible; I concluded therefore, that the Figure <lb></lb>was in ſort a Cauſe of the Natation or Submerſion of Bodies, <lb></lb>but the greater or leſſe Gravity in reſpect of the Water: and there <lb></lb>fore all Bodyes heavier than it of what Figure ſoever they be, indiffe <lb></lb>rently go to the bottome, and the lighter, though of any figure, float <lb></lb>indifferently on the top: and I ſuppoſe that thoſe which hold other <lb></lb>wiſe, were induced to that beliefe, by ſeeing how that diverſity <lb></lb>of Formes or Figures, greatly altereth the Veloſity, and Tardity <lb></lb>of Motion; ſo that Bodies of Figure broad and thin, deſcend <lb></lb>far more leaſurely into the Water, than thoſe of a more compacted <lb></lb>Figure, though both made of the ſame Matter: by which ſome <lb></lb>might be induced to believe that the Dilatation of the Figure might <lb></lb>reduce it to ſuch ampleneſſe that it ſhould not only retard but wholly <lb></lb>impede and take away the Motion, which I hold to be falſe. </s><s>Upon <lb></lb>this Concluſion, in many dayes diſcourſe, was ſpoken much, and <lb></lb>many things, and divers Experiments produced, of which your <lb></lb>Highneſſe heard, and ſaw ſome, and in this diſcourſe ſhall have <lb></lb>all that which hath been produced againſt my Aſſertion, and what <lb></lb>hath been ſuggeſted to my thoughts on this matter, and for con <lb></lb>firmation of my Concluſion: which if it ſhall ſuffice to remove that <lb></lb>(as I eſteem hitherto falſe) Opinion, I ſhall thinke I have not <lb></lb>unprofitably ſpent my paynes and time. </s><s>and although that come <lb></lb>not to paſſe, yet ought I to promiſe another benefit to my ſelfe, <lb></lb>namely, of attaining the knowledge of the truth, by hearing my <lb></lb>Fallacyes confuted, and true demonſtrations produced by thoſe <lb></lb>of the contrary opinion.</s></p><p type="main"> <s>And to proceed with the greateſt plainneſs and perſpicuity that <lb></lb>I can poſſible, it is, I conceive, neceſſary, firſt of all to declare <lb></lb>what is the true, intrinſecall, and totall Cauſe, of the aſcending of <lb></lb>ſome Sollid Bodyes in the Water, and therein floating; or on the <lb></lb>contrary, of their ſinking. </s><s>and ſo much the rather in aſmuch as I <lb></lb>cannot ſatisfie my ſelfe in that which <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath left written on <lb></lb>this Subject.</s></p><p type="margin"> <s><margin.target id="marg1402"></margin.target>The cauſe of the <lb></lb>Natation & ſub</s></p> <p type="main"> <s>I ſay then the Cauſe why ſome Sollid Bodyes deſcend to the <lb></lb><arrow.to.target n="marg1402"></arrow.to.target> <pb pagenum="405"></pb>Bottom of Water, is the exceſſe of their Gravity, above the <lb></lb><arrow.to.target n="marg1403"></arrow.to.target> <lb></lb>Gravity of the Water; and on the contrary, the exceſs of the <lb></lb>Waters Gravity above the Gravity of thoſe, is the Cauſe that others <lb></lb>do not deſcend, rather that they riſe from the Bottom, and aſcend <lb></lb>to the Surface. </s><s>This was ſubtilly demonſtrated by <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> in <lb></lb>his Book Of the NATATION of BODIES: Conferred afterwards <lb></lb>by a very grave Author, but, if I erre not inviſibly, as below for <lb></lb>defence of him, I ſhall endeavour to prove.</s></p><p type="margin"> <s><margin.target id="marg1403"></margin.target>merſion of Sol <lb></lb>ids in the Wa <lb></lb>ter.</s></p><p type="main"> <s>I, with a different Method, and by other meanes, will endeavour <lb></lb>to demonſtrate the ſame, reducing the Cauſes of ſuch Effects to <lb></lb>more intrinſecall and immediate Principles, in which alſo are diſco <lb></lb>vered the Cauſes of ſome admirable and almoſt incredible Acci <lb></lb>dents, as that would be, that a very little quantity of Water, ſhould <lb></lb>be able, with its ſmall weight, to raiſe and ſuſtain a Solid Body, an <lb></lb>hundred or a thouſand times heavier than it.</s></p><p type="main"> <s>And becauſe demonſtrative Order ſo requires, I ſhall define cer <lb></lb>tain Termes, and afterwards explain ſome Propoſitions, of which, <lb></lb>as of things true and obvious, I may make uſe of to my preſent pur <lb></lb>poſe.</s></p><p type="head"> <s>DEFINITION I.</s></p><p type="main"> <s><emph type="italics"></emph>I then call equally Grave<emph.end type="italics"></emph.end> in ſpecie, <emph type="italics"></emph>thoſe Matters <lb></lb>of which equall Maſſes weigh equally.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>As if for example, two Balls, one of Wax, and the other of ſome <lb></lb>Wood of equall Maſſe, were alſo equall in Weight, we ſay, that <lb></lb>ſuch Wood, and the Wax are <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> equally grave.</s></p><p type="head"> <s>DEFINITION II.</s></p><p type="main"> <s><emph type="italics"></emph>But equally grave in Abſolute Gravity, we call two <lb></lb>Sollids, weighing equally, though of Maſs they be <lb></lb>unequall.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>As for example, a Maſs of Lead, and another of Wood, that <lb></lb>weigh each ten pounds, I call equall in Abſolute Gravity, though <lb></lb>the Maſs of the Wood be much greater then that of the Lead.</s></p><p type="main"> <s><emph type="italics"></emph>And, conſequently, leſs Grave<emph.end type="italics"></emph.end> in ſpecie.</s></p><p type="head"> <s>DEFINITION III.</s></p><p type="main"> <s><emph type="italics"></emph>I call a Matter more Grave<emph.end type="italics"></emph.end> in ſpecie <emph type="italics"></emph>than another, of <lb></lb>which a Maſs, equall to a Maſs of the other, ſhall <lb></lb>weigh more.<emph.end type="italics"></emph.end></s></p> <pb pagenum="406"></pb><p type="main"> <s>And ſo I ſay, that Lead is more grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than Tinn, becauſe <lb></lb>if you take of them two equall Maſſes, that of the Lead weigheth <lb></lb>more.</s></p><p type="head"> <s>DEFINITION IV.</s></p><p type="main"> <s><emph type="italics"></emph>But I call that Body more grave abſolutely than this, if <lb></lb>that weigh more than this, without any reſpect had to <lb></lb>the Maſſes.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And thus a great piece of Wood is ſaid to weigh more than a <lb></lb>little lump of Lead, though the Lead be <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> more heavy than <lb></lb>the Wood. </s><s>And the ſame is to be underſtood of the leſs grave <emph type="italics"></emph>in <lb></lb>ſpecie,<emph.end type="italics"></emph.end> and the leſs grave abſolutely.</s></p><p type="main"> <s>Theſe Termes defined, I take from the Mechanicks two Princi <lb></lb>ples: the firſt is, that</s></p><p type="head"> <s>AXIOME. I.</s></p><p type="main"> <s><emph type="italics"></emph>Weights abſolutely equall, moved with equall Velocity, <lb></lb>are of equall Force and Moment in their operations.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>DEFINITION V.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Moment, amongſt Mechanicians, ſigrifieth that <lb></lb>Vertue, that Force, or that Efficacy, with which <lb></lb>the Mover moves, and the Moveable reſiſts.</s></p><p type="main"> <s><emph type="italics"></emph>Which Vertue dependes not only on the ſimple Gravity, but on the <lb></lb>Velocity of the Motion, and on the diverſe Inclinations of the Spaces <lb></lb>along which the Motion is made: For a deſcending Weight makes a <lb></lb>greater<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in a Space much declining, than in one leſs declining; <lb></lb>and in ſumme, what ever is the occaſion of ſuch Vertue, it ever retaines <lb></lb>the name of<emph.end type="italics"></emph.end> Moment; <emph type="italics"></emph>nor in my Judgement, is this ſence new in our <lb></lb>Idiome, for, if I mistake not, I think we often ſay; This is a weighty <lb></lb>buſineſſe, but the other is of ſmall moment: and we conſider lighter mat <lb></lb>ters and let paſs thoſe of Moment; a Metaphor, I ſuppoſe, taken from <lb></lb>the Mechanicks.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>As for example, two weights equall in abſolute Gravity, being <lb></lb>put into a Ballance of equall Arms, they ſtand in <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> nei <lb></lb>ther one going down, nor the other up: becauſe the equality of the <lb></lb>Diſtances of both, from the Centre on which the Ballance is ſuppor <lb></lb>ted, and about which it moves, cauſeth that thoſe weights, the ſaid <lb></lb>Ballance moving, ſhall in the ſame Time move equall Spaces, that is, <lb></lb>ſhall move with equall Velocity, ſo that there is no reaſon for which <pb pagenum="407"></pb>this Weight ſhould deſcend more than that, or that more than this; <lb></lb>and therefore they make an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> and their Moments continue <lb></lb>of ſemblable and equall Vertue.</s></p><p type="main"> <s>The ſecond Principle is; That</s></p><p type="head"> <s>AXIOME II.</s></p><p type="main"> <s><emph type="italics"></emph>The Moment and Force of the Gravity, is encreaſed by <lb></lb>the Velocity of the Motion.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>So that Weights abſolutely equall, but conjoyned with Velocity <lb></lb>unequall, are of Force, Moment and Vertue unequall: and the <lb></lb>more potent, the more ſwift, according to the proportion of the Ve <lb></lb>locity of the one, to the Velocity of the other. </s><s>Of this we have a <lb></lb>very pertinent example in the Balance or Stiliard of unequall Arms, <lb></lb>at which Weights abſolutely equall being ſuſpended, they do not <lb></lb>weigh down, and gravitate equally, but that which is at a greater <lb></lb>diſtance from the Centre, about which the Beam moves, deſcends, <lb></lb>raiſing the other, and the Motion of this which aſcends is ſlow, and <lb></lb>the other ſwift: and ſuch is the Force and Vertue, which from the <lb></lb>Velocity of the Mover, is conferred on the Moveable, which receives <lb></lb>it, that it can exquiſitely compenſate, as much more Weight added to <lb></lb>the other ſlower Moveable: ſo that if of the Arms of the Balance, <lb></lb>one were ten times as long as the other, whereupon in the Beames <lb></lb>moving about the Centre, the end of that would go ten times as far <lb></lb>as the end of this, a Weight ſuſpended at the greater diſtance, may <lb></lb>ſuſtain and poyſe another ten times more grave abſolutely than it: <lb></lb>and that becauſe the Stiliard moving, the leſſer Weight ſhall move <lb></lb>ten times faſter than the bigger. </s><s>It ought alwayes therefore to be <lb></lb>underſtood, that Motions are according to the ſame Inclinations, <lb></lb>namely, that if one of the Moveables move perpendicularly to the <lb></lb>Horizon, then the other makes its Motion by the like Perpendicular; <lb></lb>and if the Motion of one were to be made Horizontally; that then <lb></lb>the other is made along the ſame Horizontall plain: and in ſumme, <lb></lb>alwayes both in like Inclinations. </s><s>This proportion between the <lb></lb>Gravity and Velocity is found in all Mechanicall Inſtruments: and <lb></lb>is conſidered by <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> as a Principle in his <emph type="italics"></emph>Mechanicall Queſtions<emph.end type="italics"></emph.end>; <lb></lb>whereupon we alſo may take it for a true Aſſumption, That</s></p><p type="head"> <s>AXIOME III.</s></p><p type="main"> <s><emph type="italics"></emph>Weights abſolutely unequall, do alternately counterpoyſe <lb></lb>and become of equall Moments, as oft as their Gravi <lb></lb>ties, with contrary proportion, anſwer to the Velocity of <lb></lb>their Motions.<emph.end type="italics"></emph.end></s></p> <pb pagenum="408"></pb><p type="main"> <s>That is to ſay, that by how much the one is leſs grave than the other, <lb></lb>by ſo much is it in a conſtitution of moving more ſwiftly than that.</s></p><p type="main"> <s>Having prefatically explicated theſe things, we may begin to en <lb></lb>quire, what Bodyes thoſe are which totally ſubmerge in Water, and <lb></lb>go to the Bottom, and which thoſe that by conſtraint float on the <lb></lb>top, ſo that being thruſt by violence under Water, they return to <lb></lb>ſwim, with one part of their Maſs viſible above the Surface of the <lb></lb>Water: and this we will do by conſidering the reſpective operati <lb></lb>on of the ſaid Solids, and of Water: Which operation followes <lb></lb>the Submerſion and ſinking; and this it is, That in the Submerſion <lb></lb><arrow.to.target n="marg1404"></arrow.to.target> <lb></lb>that the Solid maketh, being depreſſed downwards by its proper <lb></lb>Gravity, it comes to drive away the water from the place where it <lb></lb>ſucceſſively ſubenters, and the water repulſed riſeth and aſcends <lb></lb>above its firſt levell, to which Aſcent on the other ſide it, as being a <lb></lb>grave Body of its own nature, reſiſts: And becauſe the deſcending <lb></lb>Solid more and more immerging, greater and greater quantity of <lb></lb>Water aſcends, till the whole Sollid be ſubmerged; its neceſſary to <lb></lb>compare the Moments of the Reſiſtance of the water to Aſcenſion, <lb></lb>with the Moments of the preſſive Gravity of the Solid: And if the <lb></lb>Moments of the Reſiſtance of the water, ſhall equalize the Moments <lb></lb><arrow.to.target n="marg1405"></arrow.to.target> <lb></lb>of the Solid, before its totall Immerſion; in this caſe doubtleſs there <lb></lb>ſhall be made an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> nor ſhall the Body ſink any farther. <lb></lb></s><s>But if the Moment of the Solid, ſhall alwayes exceed the Moments <lb></lb><arrow.to.target n="marg1406"></arrow.to.target> <lb></lb>wherewith the repulſed water ſucceſſively makes Reſiſtance, that <lb></lb>Solid ſhall not only wholly ſubmerge under water, but ſhall deſcend <lb></lb>to the Bottom. </s><s>But if, laſtly, in the inſtant of totall Submerſion, <lb></lb><arrow.to.target n="marg1407"></arrow.to.target> <lb></lb>the equality ſhall be made between the Moments of the prement <lb></lb>Solid, and the reſiſting Water; then ſhall reſt enſue, and the ſaid <lb></lb>Solid ſhall be able to reſt indifferently, in whatſoever part of the <lb></lb>water. </s><s>By this time is manifeſt the neceſſity of comparing the <lb></lb><arrow.to.target n="marg1408"></arrow.to.target> <lb></lb>Gravity of the water, and of the Solid; and this compariſon might <lb></lb>at firſt ſight ſeem ſufficient to conclude and determine which are the <lb></lb>Solids that float a-top, and which thoſe that ſink to the Bottom in the <lb></lb>water, aſſerting that thoſe ſhall float which are leſſe grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> <lb></lb>than the water, and thoſe ſubmerge, which are <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> more grave. <lb></lb></s><s>For it ſeems in appearance, that the Sollid in ſinking continually, <lb></lb>raiſeth ſo much Water in Maſs, as anſwers to the parts of its own <lb></lb>Bulk ſubmerged: whereupon it is impoſſible, that a Solid leſs grave <lb></lb><emph type="italics"></emph>in ſpecie,<emph.end type="italics"></emph.end> than water, ſhould wholly ſink, as being unable to raiſe a <lb></lb>weight greater than its own, and ſuch would a Maſs of water equall <lb></lb>to its own Maſs be. </s><s>And likewiſe it ſeems neceſſary, that the graver <lb></lb>Solids do go to the Bottom, as being of a Force more than ſufficient <lb></lb>for the raiſing a Maſſe of water, equall to its own, though inferiour <lb></lb>in weight. </s><s>Nevertheleſs the buſineſs ſucceeds otherwiſe: and <pb pagenum="409"></pb>though the Concluſions are true, yet are the Cauſes thus aſſigned <lb></lb>deficient, nor is it true, that the Solid in ſubmerging, raiſeth and <lb></lb>repulſeth Maſſes of Water, equall to the parts of it ſelf ſubmerged; <lb></lb>but the Water repulſed, is alwayes leſs than the parts of the Solid <lb></lb><arrow.to.target n="marg1409"></arrow.to.target> <lb></lb>ſubmerged: and ſo much the more by how much the Veſſell in <lb></lb>which the Water is contained is narrower: in ſuch manner that it <lb></lb>hinders not, but that a Solid may ſubmerge all under Water, with <lb></lb>out raiſing ſo much Water in Maſs, as would equall the tenth or <lb></lb>twentieth part of its own Bulk: like as on the contrary, a very <lb></lb><arrow.to.target n="marg1410"></arrow.to.target> <lb></lb>ſmall quantity of Water, may raiſe a very great Solid Maſs, though <lb></lb>ſuch Solid ſhould weigh abſolutely a hundred times as much, or <lb></lb>more, than the ſaid Water, if ſo be that the Matter of that ſame <lb></lb>Solid be <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> leſs grave than the Water. </s><s>And thus a great <lb></lb>Beam, as ſuppoſe of a 1000 weight, may be raiſed and born afloat <lb></lb>by Water, which weighs not 50: and this happens when the Mo <lb></lb>ment of the Water is compenſated by the Velocity of its Motion.</s></p><p type="margin"> <s><margin.target id="marg1404"></margin.target>How the ſub <lb></lb>merſion of So <lb></lb>lids in the Wa <lb></lb>ter, is effected.</s></p><p type="margin"> <s><margin.target id="marg1405"></margin.target>What Solids <lb></lb>ſhall float on the <lb></lb>Water.</s></p><p type="margin"> <s><margin.target id="marg1406"></margin.target>What Solids <lb></lb>ſhall ſinke to the <lb></lb>botome.</s></p><p type="margin"> <s><margin.target id="marg1407"></margin.target>What Solids <lb></lb>ſhall reſt in all <lb></lb>places of the Wa <lb></lb>ter.</s></p><p type="margin"> <s><margin.target id="marg1408"></margin.target>The Gravitie of <lb></lb>the Water and <lb></lb><emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid muſt be <lb></lb>compared in all <lb></lb>Problems, of Na <lb></lb>tation of Bodies.</s></p><p type="margin"> <s><margin.target id="marg1409"></margin.target>The water re <lb></lb>pulſed is ever leſs <lb></lb>than the parts of <lb></lb>the Sollid ſub <lb></lb>merged.</s></p><p type="margin"> <s><margin.target id="marg1410"></margin.target><emph type="italics"></emph>A<emph.end type="italics"></emph.end> ſmall quantity <lb></lb>of water, may <lb></lb>float a very <lb></lb>great Solid Maſs.</s></p><p type="main"> <s>But becauſe ſuch things, propounded thus in abſtract, are ſome <lb></lb>what difficult to be comprehended, it would be good to demonſtrate <lb></lb>them by particular examples; and for facility of demonſtration, we <lb></lb>will ſuppoſe the Veſſels in which we are to put the Water, and place <lb></lb>the Solids, to be inviron'd and included with ſides erected perpendi <lb></lb>cular to the Plane of the Horizon, and the Solid that is to be put <lb></lb>into ſuch veſſell to be either a ſtreight Cylinder, or elſe an upright <lb></lb>Priſme</s></p><p type="main"> <s><emph type="italics"></emph>The which propoſed and declared, I proceed to demonstrate the truth <lb></lb>of what hath been hinted, forming the enſuing Theoreme.<emph.end type="italics"></emph.end></s></p><p type="head"> <s><emph type="italics"></emph>THEOREME I.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>The Maſs of the Water whichaſcends in the ſub <lb></lb><arrow.to.target n="marg1411"></arrow.to.target> <lb></lb>merging of a Solid, Priſme or Cylinder, or that <lb></lb>abaſeth in taking it out, is leſs than the Maſs of <lb></lb>the ſaid Solid, ſo depreſſed or advanced: and <lb></lb>hath to it the ſame proportion, that the Surface <lb></lb>of the Water circumfuſing the Solid, hath to the <lb></lb>ſame circumfuſed Surface, together with the Baſe <lb></lb>of the Solid.</s></p><p type="margin"> <s><margin.target id="marg1411"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he Proportion <lb></lb>of the water rai <lb></lb>ſed to the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid <lb></lb>ſubmerged.</s></p><p type="main"> <s><emph type="italics"></emph>Let the Veſſell be A B C D, and in it the Water raiſed up to the <lb></lb>Levell E F G, before the Solid Priſme H I K be therein immerged; <lb></lb>but after that it is depreſſed under Water, let the Water be raiſed as <lb></lb>high as the Levell L M, the Solid H I K ſhall then be all under Water, <lb></lb>and the Maſs of the elevated Water ſhall be L G, which is leſs than the<emph.end type="italics"></emph.end> <pb pagenum="410"></pb><figure id="fig262"></figure> <lb></lb><emph type="italics"></emph>Maſſe of the Solid depreſſed, namely of <lb></lb>H I K, being equall to the only part E I K, <lb></lb>which is contained under the firſt Levell <lb></lb>E F G. </s><s>Which is manifeſt, becauſe if <lb></lb>the Solid H I K be taken out, the Water <lb></lb>I G ſhall return into the place occupied by <lb></lb>the Maſs E I K, where it was continuate be <lb></lb>fore the ſubmerſion of the Priſme. </s><s>And <lb></lb>the Maſs L G being equall to the Maſs <lb></lb>E K: adde thereto the Maſs E N, and it <lb></lb>ſhall be the whole Maſs E M, compoſed of the parts of the Priſme E N, <lb></lb>and of the Water N F, equall to the whole Solid H I K: And, there <lb></lb>fore, the Maſs L G ſhall have the ſame proportion to E M, as to the <lb></lb>Maſs H I K: But the Maſs L G hath the ſame proportion to the Maſs <lb></lb>E M, as the Surface L M hath to the Surface M H: Therefore it is ma <lb></lb>nifeſt, that the Maſs of Water repulſed L G, is in proportion to the Maſs <lb></lb>of the Solid ſubmerged H I K; as the Surface L M, namely, that of the <lb></lb>Water ambient about the Sollid, to the whole Surface H M, compounded <lb></lb>of the ſaid ambient water, and the Baſe of the Priſme H N. </s><s>But if we <lb></lb>ſuppoſe the firſt Levell of the Water the according to the Surface H M, <lb></lb>and the Priſme allready ſubmerged H I K; and after to be taken out and <lb></lb>raiſed to E A O, and the Water to be faln from the firſt Levell H L M as <lb></lb>low as E F G; It is manifeſt, that the Priſme E A O being the ſame with <lb></lb>H I K, its ſuperiour part H O, ſhall be equall to the inferiour E I K: <lb></lb>and remove the common part E N, and, conſequently, the Maſs of the <lb></lb>Water L G is equall to the Maſs H O; and, therefore, leſs than the <lb></lb>Solid, which is without the Water, namely, the whole Priſme E A O, to <lb></lb>which likewiſe, the ſaid Maſs of Water abated L G, hath the ſame propor <lb></lb>tion, that the Surface of the Waters circumfuſed L M hath to the ſame <lb></lb>circumfuſed Surface, together with the Baſe of the Priſme A O: which <lb></lb>hath the ſame demonſtration with the former caſe above.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>And from hence is inferred, that the Maſs of the Water, that riſeth in <lb></lb>the immerſion of the Solid, or that ebbeth in elevating it, is not equall to <lb></lb>all the Maſs of the Solid, which is ſubmerged or elevated, but to that <lb></lb>part only, which in the immerſion is under the firſt Levell of the Water, <lb></lb>and in the elevation remaines above the firſt Levell: Which is that <lb></lb>which was to be demonſtrated. </s><s>We will now purſue the things that <lb></lb>remain.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And firſt we will demonſtrate that,</s></p> <pb pagenum="411"></pb><p type="head"> <s>THEOREME II.</s></p><p type="main"> <s><emph type="italics"></emph>When in one of the above ſaid Veſſels, of what ever<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1412"></arrow.to.target> <lb></lb><emph type="italics"></emph>breadth, whether wide or narrow, there is placed ſuch <lb></lb>a Priſme or Cylinder, inviron'd with Water, if we ele <lb></lb>vate that Solid perpendicularly, the Water circumfu <lb></lb>ſed ſhall abate, and the Abatement of the Water, <lb></lb>ſhall have the ſame proportion to the Elevation of the <lb></lb>Priſme, as one of the Baſes of the Priſme, hath to <lb></lb>the Surface of the Water Circumfuſed.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1412"></margin.target>The proportion <lb></lb>of the water aba <lb></lb>ted, to the Solid <lb></lb>raiſed.</s></p><p type="main"> <s>Imagine in the Veſſell, as is aforeſaid, the <lb></lb><figure id="fig263"></figure> <lb></lb>Priſme A C D B to be placed, and in the <lb></lb>reſt of the Space the Water to be dif <lb></lb>fuſed as far as the Levell E A: and rai <lb></lb>ſing the Solid, let it be transferred to <lb></lb>G M, and let the Water be abaſed from <lb></lb>E A to N O: I ſay, that the deſcent of <lb></lb>the Water, meaſured by the Line A O, <lb></lb>hath the ſame proportion to the riſe of the <lb></lb>Priſme, meaſured by the Line G A, as the Baſe of the Solid G H <lb></lb>hath to the Surface of the Water N O. </s><s>The which is manifeſt: <lb></lb>becauſe the Maſs of the Solid G A B H, raiſed above the firſt Levell <lb></lb>E A B, is equall to the Maſs of Water that is abaſed E N O A. <lb></lb>Therefore, E N O A and G A B H are two equall Priſmes; for of <lb></lb>equall Priſmes, the Baſes anſwer contrarily to their heights: There <lb></lb>fore, as the Altitude A O is to the Altitude A G, ſo is the Superfi <lb></lb>cies or Baſe G H to the Surface of the Water N O. </s><s>If therefore, <lb></lb>for example, a Pillar were erected in a waſte Pond full of Water, <lb></lb>or elſe in a Well, capable of little more then the Maſs of the ſaid <lb></lb>Pillar, in elevating the ſaid Pillar, and taking it out of the Water, <lb></lb>according as it riſeth, the Water that invirons it will gradually abate, <lb></lb>and the abaſement of the Water at the inſtant of lifting out the <lb></lb>Pillar, ſhall have the ſame proportion, that the thickneſs of the Pillar <lb></lb>hath to the exceſs of the breadth of the ſaid Pond or Well, above <lb></lb>the thickneſs of the ſaid Pillar: ſo that if the breadth of the Well <lb></lb>were an eighth part larger than the thickneſs of the Pillar, and the <lb></lb><arrow.to.target n="marg1413"></arrow.to.target> <lb></lb>breadth of the Pond twenty five times as great as the ſaid thickneſs, <lb></lb>in the Pillars aſcending one foot, the water in the Well ſhall deſcend <lb></lb>ſeven foot, and that in the Pond only 1/25 of a foot.</s></p><p type="margin"> <s><margin.target id="marg1413"></margin.target>Why a Solid <lb></lb>leſs grave <emph type="italics"></emph>in ſpe <lb></lb>cie<emph.end type="italics"></emph.end> than water, <lb></lb>ſtayeth not un <lb></lb>der water, in ve <lb></lb>ry ſmall depthst.</s></p><p type="main"> <s>This Demonſtrated, it will not be difficult to ſhew the true <lb></lb>cauſe, how it comes to paſs, that,</s></p> <pb pagenum="412"></pb><p type="head"> <s>THEOREME III.</s></p><p type="main"> <s><emph type="italics"></emph>A Priſme or regular Cylinder, of a ſubſtance ſpecifically <lb></lb>leſs grave than Water, if it ſhould be totally ſubmerged <lb></lb>in Water, ſtayes not underneath, but riſeth, though the <lb></lb>Water circumfuſed be very little, and in abſolute <lb></lb>Gravity, never ſo much inferiour to the Gravity of the <lb></lb>ſaid Priſme.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let then the Priſme A E F B, be put into the Veſſell C D F B, the <lb></lb>ſame being leſs grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than the Water: and let the <lb></lb>Water infuſed riſe to the height of the Priſme: I ſay, that the <lb></lb>Priſme left at liberty, it ſhall riſe, being born up <lb></lb>by the Water circumfuſed C D E A. </s><s>For the <lb></lb><figure id="fig264"></figure> <lb></lb>Water C E being ſpecifically more grave than <lb></lb>the Solid A F, the abſolute weight of the water <lb></lb>C E, ſhall have greater proportion to the abſo <lb></lb>lute weight of the Priſme A F, than the Maſs <lb></lb>C E hath to the Maſs A F (in regard the Maſs <lb></lb>hath the ſame proportion to the Maſs, that the <lb></lb>weight abſolute hath to the weight abſolute, <lb></lb>in caſe the Maſſes are of the ſame Gravity <emph type="italics"></emph>in ſpecie.<emph.end type="italics"></emph.end>) But <lb></lb>the Maſs C E is to the Maſs A F, as the Surface of the water A C, is <lb></lb>to the Superficies, or Baſe of the Priſme A B; which is the ſame pro <lb></lb>portion as the aſcent of the Priſme when it riſeth, hath to the deſcent <lb></lb>of the water circumfuſed C E.</s></p><p type="main"> <s>Therefore, the abſolute Gravity of the water C E, hath greater <lb></lb>proportion to the abſolute Gravity of the Priſme A F; than the <lb></lb>Aſcent of the Priſme A F, hath to the deſcent of the ſaid <lb></lb>water C E. </s><s>The Moment, therefore, compounded of the abſolute <lb></lb>Gravity of the water C E, and of the Velocity of its deſcent, whilſt <lb></lb>it forceably repulſeth and raiſeth the Solid A F, is greater than the <lb></lb>Moment compounded of the abſolute Gravity of the Priſme A F, and <lb></lb>of the Tardity of its aſcent, with which Moment it contraſts and re <lb></lb>fiſts the repulſe and violence done it by the Moment of the water: <lb></lb>Therefore, the Priſme ſhall be raiſed. <lb></lb><arrow.to.target n="marg1414"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1414"></margin.target>The Proportion <lb></lb>according to <lb></lb>which the Sub <lb></lb>merſion & Na <lb></lb>tation of Solids <lb></lb>is made.</s></p><p type="main"> <s>It followes, now, that we proceed forward to demonſtrate more <lb></lb>particularly, how much ſuch Solids ſhall be inferiour in Gravity to <lb></lb>the water elevated; namely, what part of them ſhall reſt ſubmerged, <lb></lb>and what ſhall be viſible above the Surface of the water: but firſt <lb></lb>it is neceſſary to demonſtrate the ſubſequent Lemma.</s></p> <pb pagenum="413"></pb><p type="head"> <s>LEMMA I.</s></p><p type="main"> <s><emph type="italics"></emph>The abſolute Gravities of Solids, have a proportion com-<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1415"></arrow.to.target> <lb></lb><emph type="italics"></emph>pounded of the proportions of their ſpecificall Gravities, <lb></lb>and of their Maſſes.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1415"></margin.target>The abſolute <lb></lb>Gravity of So <lb></lb>lids, are in a pro <lb></lb>portion com <lb></lb>pounded of their <lb></lb>Specifick Gravi <lb></lb>ties, and of their <lb></lb>Maſſes.</s></p><p type="main"> <s>Let A and B be two Solids. </s><s>I ſay, that the Abſolute Gravity <lb></lb>of A, hath to the Abſolute Gravity of B, a proportion com <lb></lb>pounded of the proportions of the ſpecificall Gravity of A, to <lb></lb>the Specificall Gravity of B, and of the Maſs <lb></lb>A to the Maſs B. </s><s>Let the Line D have the <lb></lb><figure id="fig265"></figure> <lb></lb>ſame proportion to E, that the ſpecifick <lb></lb>Gravity of A, hath to the ſpecifick Gravity <lb></lb>of B; and let E be to F, as the Maſs A to the <lb></lb>Maſs B: It is manifeſt, that the proportion <lb></lb>of D to F, is compounded of the proportions <lb></lb>D and E; and E and F. </s><s>It is requiſite, <lb></lb>therefore, to demonſtrate, that as D is to F, ſo the abſolute Gravity <lb></lb>of A, is to the abſolute Gravity of B. </s><s>Take the Solid C, equall in <lb></lb>Maſs to the Solid A, and of the ſame Gravity <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> with the Solid <lb></lb>B. Becauſe, therefore, A and C are equall in Maſs, the abſolute <lb></lb>Gravity of A, ſhall have to the abſolute Gravity of C, the ſame pro <lb></lb>portion, as the ſpecificall Gravity of A, hath to the ſpecificall Gravity <lb></lb>of C, or of B, which is the ſame <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end>; that is, as D is to E. And, be <lb></lb>cauſe, C and B are of the ſame Gravity <emph type="italics"></emph>in ſpecie,<emph.end type="italics"></emph.end> it ſhall be, that as <lb></lb>the abſolute weight of C, is to the abſolute weight of B, ſo the Maſs <lb></lb>C, or the Maſs A, is to the Maſs B; that is, as the Line E to the Line <lb></lb>F. </s><s>As therefore, the abſolute Gravity of A, is to the abſolute <lb></lb>Gravity of C, ſo is the Line D to the Line E: and, as the abſolute <lb></lb>Gravity of C, is to the abſolute Gravity of B, ſo is the Line E to the <lb></lb>Line F: Therefore, by Equality of proportion, the abſolute Gra <lb></lb>vity of A, is to the abſolute Gravity of B, as the Line D to the <lb></lb>Line F: which was to be demonſtrated. </s><s>I proceed now to demon <lb></lb>ſtrate, how that,</s></p> <pb pagenum="414"></pb><p type="head"> <s>THEOREME IV. <lb></lb><arrow.to.target n="marg1416"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1416"></margin.target>The proportion <lb></lb>of water requi <lb></lb>ſite to make a <lb></lb>Solid ſwim.</s></p><p type="main"> <s><emph type="italics"></emph>If a Solid, Cylinder, or Priſme, leſſe grave ſpecifically <lb></lb>than the Water, being put into a Veſſel, as above, of <lb></lb>whatſoever greatneſſe, and the Water, be afterwards <lb></lb>infuſed, the Solid ſhall reſt in the bottom, unraiſed, till <lb></lb>the Water arrive to that part of the Altitude, of the <lb></lb>ſaid Priſme, to which its whole Altitude hath the <lb></lb>ſame proportion, that the Specificall Gravity of the <lb></lb>Water, hath to the Specificall Gravity of the ſaid <lb></lb>Solid: but infuſing more Water, the Solid ſhall aſcend.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Let the Veſſell be M L G N of any bigneſs, and let there be pla <lb></lb>ced in it the Solid Priſme D F G E, leſs grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than the <lb></lb>water; and look what proportion the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>pecificall Gravity of <lb></lb>the water, hath to that of the Priſme, ſuch let the Altitude D F, have <lb></lb>to the Altitude F B. </s><s>I ſay, that infuſing water to the Altitude F B, <lb></lb>the Solid D G ſhall not float, but ſhall ſtand in <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> ſo, that <lb></lb>that every little quantity of water, that is infuſed, ſhall raiſe it. </s><s>Let <lb></lb>the water, therefore, be infuſed to the Levell A B C, and, becauſe <lb></lb>the Specifick Gravity of the Solid D G, is to the Specifick Gravity of <lb></lb>the water, as the altitude B F is to the altitude F D; that is, as the Maſs <lb></lb>B G to the Maſs G D; as the proportion of the Maſs B G is to the <lb></lb>Maſs G D, as the proportion of the Maſs G D is to the Maſs A F, they <lb></lb>compoſe the Proportion of the Maſs B G to the Maſs A F. Therefore, <lb></lb>the Maſs B G is to the Maſs A F, in a proportion compounded of the <lb></lb>proportions of the Specifick Gravity of the Solid G D, to the Speci <lb></lb>fick Gravity of the water, and of the Maſs G D <lb></lb>to the Maſs A F: But the ſame proportions <lb></lb><figure id="fig266"></figure> <lb></lb>of the Specifick Gravity of G D, to the Specifick <lb></lb>Gravity of the water, and of the Maſs G D to <lb></lb>the Maſs A F, do alſo by the precedent <emph type="italics"></emph>Lemma,<emph.end type="italics"></emph.end> <lb></lb>compound the proportion of the abſolute Gra <lb></lb>vity of the Solid D G, to the abſolute Gravity <lb></lb>of the Maſs of the water A F: Therefore, <lb></lb>as the Maſs B G is to the Maſs A F, ſo is the <lb></lb>Abſolute Gravity of the Solid D G, to the Ab <lb></lb>ſolute Gravity of the Maſs of the water A F. </s><s>But as the Maſs B G <lb></lb>is to the Maſs A F; ſo is the Baſe of the Priſme D E, to the Surface <lb></lb>of the water AB; and ſo is the deſcent of the water A B, to the <lb></lb>Elevation of the Priſme D G; Therefore, the deſcent of the <pb pagenum="415"></pb>water is to the elevation of the Priſme, as the abſolute Gravity of <lb></lb>the Priſme, is to the abſolute Gravity of the water: Therefore, the <lb></lb>Moment reſulting from the abſolute Gravity of the water A F, and <lb></lb>the Velocity of the Motion of declination, with which Moment it <lb></lb>forceth the Priſme D G, to riſe and aſcend, is equall to the Moment <lb></lb>that reſults from the abſolute Gravity of the Priſme D G, and from <lb></lb>the Velocity of the Motion, wherewith being raiſed, it would aſcend: <lb></lb>with which Moment it reſiſts its being raiſed: becauſe, therefore, <lb></lb>ſuch Moments are equall, there ſhall be an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> between the <lb></lb>water and the Solid. </s><s>And, it is manifeſt, that putting a little more <lb></lb>water unto the other A F, it will increaſe the Gravity and Moment, <lb></lb>whereupon the Priſme D G, ſhall be overcome, and elevated till that <lb></lb>the only part B F remaines ſubmerged. </s><s>Which is that that was to <lb></lb>be demonſtrated.</s></p><p type="head"> <s>COROLLARY I.</s></p><p type="main"> <s><emph type="italics"></emph>By what hath been demonſtrated, it is manifeſt, that Solids leſs grave<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1417"></arrow.to.target> <lb></lb>in ſpecie <emph type="italics"></emph>than the water, ſubmerge only ſo far, that as much water in <lb></lb>Maſs, as is the part of the Solid ſubmerged, doth weigh abſolutely as <lb></lb>much as the whole Solid.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1417"></margin.target><emph type="italics"></emph>H<emph.end type="italics"></emph.end>ow far Solids <lb></lb>leſs grave <emph type="italics"></emph>in ſpe <lb></lb>cie<emph.end type="italics"></emph.end> than water, <lb></lb>do ſubmerge.</s></p><p type="main"> <s>For, it being ſuppoſed, that the Specificall Gravity of the water, <lb></lb>is to the Specificall Gravity of the Priſme D G, as the Altitude <lb></lb>D F, is to the Altitude F B; that is, as the Solid D G is to the <lb></lb>Solid B G; we might eaſily demonſtrate, that as much water in Maſs <lb></lb>as is equall to the Solid B G, doth weigh abſolutely as much as the <lb></lb>whole Solid D G; For, by the <emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> foregoing, the Abſolute <lb></lb>Gravity of a Maſs of water, equall to the Maſs B G, hath to the Ab <lb></lb>ſolute Gravity of the Priſme D G, a proportion compounded of the <lb></lb>proportions, of the Maſs B G to the Maſs G D, and of the Specifick <lb></lb>Gravit 7 of the water, to the Specifick Gravity of the Priſme: But <lb></lb>the Gravity <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> of the water, to the Gravity <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> of the <lb></lb>Priſme, is ſuppoſed to be as the Maſs G D to the Maſs G B. There <lb></lb>fore, the Abſolute Gravity of a Maſs of water, equall to the Maſs <lb></lb>B G, is to the Abſolute Gravity of the Solid D G, in a proportion <lb></lb>compounded of the proportions, of the Maſs B G to the Maſs G D, <lb></lb>and of the Maſs D G to the Maſs G B; which is a proportion of <lb></lb>equalitie. </s><s>The Abſolute Gravity, therefore, of a Maſs of Water <lb></lb>equall to the part of the Maſs of the Priſme B G, is equall to the Ab <lb></lb>ſolute Gravity of the whole Solid D G.</s></p> <pb pagenum="416"></pb><p type="head"> <s>COROLLARY II. <lb></lb><arrow.to.target n="marg1418"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1418"></margin.target><emph type="italics"></emph>A<emph.end type="italics"></emph.end> Rule to equi <lb></lb>librate <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olids in <lb></lb>the water.</s></p><p type="main"> <s><emph type="italics"></emph>It followes, moreover, that a Solid leſs grave than the water, being put <lb></lb>into a Veſſell of any imaginable greatneſs, and water being circumfuſed <lb></lb>about it to ſuch a height, that as much water in Maſs, as is the part of <lb></lb>the Solid ſubmerged, doth/> weigh abſolutely as much as the whole Solid; <lb></lb>it ſhall by that water be juſtly ſuſtained, be the circumfuſed Water in <lb></lb>quantity greater or leſſer.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>For, if the Cylinder or Priſme M, leſs grave than the water, <emph type="italics"></emph>v. <lb></lb></s><s>gra.<emph.end type="italics"></emph.end> in Subſequiteriall proportion, ſhall be put into the capaci <lb></lb>ous Veſſell A B C D, and the water raiſed about it, to three <lb></lb>quarters of its height, namely, to its Levell A D: it ſhall be ſuſtained <lb></lb>and exactly poyſed in <emph type="italics"></emph>Equi <lb></lb>librium.<emph.end type="italics"></emph.end> The ſame will hap <lb></lb>pen, if the Veſſell E N S F <lb></lb><figure id="fig267"></figure> <lb></lb>were very ſmall, ſo, that be <lb></lb>tween the Veſſell and the So <lb></lb>lid M, there were but a very <lb></lb>narrow ſpace, and only capable of ſo much water, as the hundredth <lb></lb>part of the Maſs M, by which it ſhould be likewiſe raiſed and erected, <lb></lb>as before it had been elevated to three fourths of the height of the <lb></lb>Solid: which to many at the firſt ſight, may ſeem a notable Paradox, <lb></lb>and beget a conceit, that the Demonſtration of theſe effects, were <lb></lb>ſophiſticall and fallacious: but, for thoſe who ſo repute it, the Ex <lb></lb>periment is a means that may fully ſatisfie them. </s><s>But he that ſhall <lb></lb>but comprehend of what Importance Velocity of Motion is, and how <lb></lb>it exactly compenſates the defect and want of Gravity, will ceaſe to <lb></lb>wonder, in conſidering that at the elevation of the Solid M, the great <lb></lb>Maſs of water A B C D abateth very little, but the little Maſs of <lb></lb>water E N S F decreaſeth very much, and in an inſtant, as the Solid <lb></lb>M before did liſe, howbeit for a very ſhort ſpace: Whereupon the <lb></lb>Moment, compounded of the ſmall Abſolute Gravity of the water <lb></lb>E N S F, and of its great Velocity in ebbing, equalizeth the Force and <lb></lb>and Moment, that reſults from the compoſicion of the immenſe Gra <lb></lb>vity of the water A B C D, with its great ſlowneſſe of ebbing; <lb></lb>ſince that in the Elevation of the Sollid M, the abaſement of the leſ</s></p><p type="main"> <s><arrow.to.target n="marg1419"></arrow.to.target> <lb></lb>ſer water E S, is performed juſt ſo much more ſwiftly than the great <lb></lb>Maſs of water A C, as this is more in Maſs than that which we thus <lb></lb>demonſtrate.</s></p><p type="margin"> <s><margin.target id="marg1419"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he proportion <lb></lb>according to <lb></lb>which water ri <lb></lb>ſeth and falls in <lb></lb>different Veſſels <lb></lb>at the Immerſi <lb></lb>on and Elevati <lb></lb>on of <emph type="italics"></emph>s<emph.end type="italics"></emph.end>olids.</s></p><p type="main"> <s>In the riſing of the Solid M, its elevation hath the ſame proportion <lb></lb>to the circumfuſed water E N S F, that the Surface of the ſaid water, <lb></lb>hath to the Superficies or Baſe of the ſaid Solid M; which Baſe hath <lb></lb>the ſame proportion to the Surface of the water A D, that the abaſe <pb pagenum="417"></pb>ment or ebbing of the water A C, hath to the riſe or elevation of <lb></lb>the ſaid Solid M. Therefore, by Perturbation of proportion, in the <lb></lb>aſcent of the ſaid Solid M, the abaſement of the water A B C D, to <lb></lb>the abaſement of the water E N S F, hath the ſame proportion, that the <lb></lb>Surface of the water E F, hath to the Surface of the water A D; <lb></lb>that is, that the whole Maſs of the water E N S F, hath to the whole <lb></lb>Maſs A B C D, being equally high: It is manifeſt, therefore, that <lb></lb>in the expulſion and elevation of the Solid M, the water E N S F <lb></lb>ſhall exceed in Velocity of <emph type="italics"></emph>M<emph.end type="italics"></emph.end>otion the water A B C D, aſmuch as it <lb></lb>on the other ſide is exceeded by that in quantity: whereupon their <lb></lb>Moments in ſuch operations, are mutually equall.</s></p><p type="main"> <s><emph type="italics"></emph>And, for ampler confirmation, and clearer explication of this, let us <lb></lb>conſider the preſent Figure, (which if I be not deceived, may ſerve to <lb></lb>detect the errors of ſome Practick Mechanitians, who upon a falſe founda <lb></lb>tion ſome times attempt impoſſible enterprizes,) in which, unto the large <lb></lb>Veſſell E I D F, the narrow Funnell or Pipe I C A B is continued, and ſup <lb></lb>poſe water infuſed into them, unto the Levell L G H, which water ſhall <lb></lb>reſt in this poſition, not without admiration in ſome, who cannot conceive<emph.end type="italics"></emph.end> <lb></lb><figure id="fig268"></figure> <lb></lb><emph type="italics"></emph>how it can be, that the heavie charge of the great <lb></lb>Maſs of water G D, preſſing downwards, ſhould <lb></lb>not elevate and repulſe the little quantity of the <lb></lb>other, contained in the Funnell or Pipe C L, by <lb></lb>which the deſcent of it is reſisted and hindered: <lb></lb>But ſuch wonder ſhall ceaſe, if we begin to ſuppoſe <lb></lb>the water G D to be abaſed only to Q D, and <lb></lb>ſhall afterwards conſider, what the water C L <lb></lb>hath done, which to give place to the other, which <lb></lb>is deſcended from the Levell G H, to the Levell <lb></lb>Q O, ſhall of neceſſity have aſcended in the ſame <lb></lb>time, from the Levell Lunto A B. </s><s>And the <lb></lb>aſcent L B, ſhall be ſo much greater than the de <lb></lb>ſcent G Q, by how much the breadth of the Veſſell <lb></lb>G D, is greater than that of the Funnell I C; <lb></lb>which, in ſumme, is as much as the water G D, <lb></lb>is more than the water L C: but in regard that the Moment of the Velocity <lb></lb>of the Motion, in one Moveable, compenſates that of the Gravity of ano <lb></lb>ther, what wonder is it, if the ſwift aſcent of the leſſer Water C L, ſhall <lb></lb>reſiſt the ſlow deſcent of the greater G D<emph.end type="italics"></emph.end>?</s></p><p type="main"> <s>The ſame, therefore, happens in this operation, as in the Stilliard, <lb></lb>in which a weight of two pounds counterpoyſeth an other of 200, <lb></lb>asoften as that ſhall move in the ſame time, a ſpace 100 times great <lb></lb>er than this: which falleth out when one Arme of the Beam is an <pb pagenum="418"></pb>hundred times as long as the other. </s><s>Let the erroneous opinion o <lb></lb><arrow.to.target n="marg1420"></arrow.to.target> <lb></lb>thoſe therefore ceaſe, who hold that a Ship is better, and eaſter born <lb></lb>up in a great abundance of water, then in a leſſer quantity, (<emph type="italics"></emph>this was <lb></lb>believed by<emph.end type="italics"></emph.end> Ariſtotle <emph type="italics"></emph>in his Problems, Sect. </s><s>23, Probl.<emph.end type="italics"></emph.end> 2.) it being or <lb></lb>the contrary true, that its poſſible, that a Ship may as well float in <lb></lb>ten Tun of water, as in an Ocean. <lb></lb><arrow.to.target n="marg1421"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1420"></margin.target>A ſhip flotes as <lb></lb>well in ten Tun <lb></lb>of water as in an <lb></lb>Ocean.</s></p><p type="margin"> <s><margin.target id="marg1421"></margin.target>A Solid ſpeci <lb></lb>fiaclly graver <lb></lb>than the water, <lb></lb>cannot be born <lb></lb>up by any quan <lb></lb>tity of it.</s></p><p type="main"> <s>But following our matter, I ſay, that by what hath been hitherto <lb></lb>demonſtrated, we may underſtand how, that</s></p><p type="head"> <s>COROLLARY III.</s></p><p type="main"> <s><emph type="italics"></emph>One of the above named Solids, when more grave<emph.end type="italics"></emph.end> in ſpecie <emph type="italics"></emph>than the water, <lb></lb>can never be ſuſtained, by any whatever quantity of it.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>For having ſeen how that the Moment wherewith ſuch a Solid <lb></lb>as grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> as the water, contraſts with the Moment of any Maſs <lb></lb>of water whatſoever, is able to retain it, even to its totall Submerſion: <lb></lb>without its ever aſcending; it remaineth, manifeſt, that the water is <lb></lb>far leſs able to raiſe it up, when it exceeds the ſame <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end>: ſo, <lb></lb>that though you infuſe water till its totall Submerſion, it ſhall ſtill <lb></lb>ſtay at the Bottome, and with ſuch Gravity, and Reſiſtance to Eleva <lb></lb>tion, as is the exceſs of its Abſolute Gravity, above the Abſolute Gra <lb></lb>vity of a Maſs equall to it, made of water, or of a Matter <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> <lb></lb>equally grave with the water: and, though you ſhould moreover <lb></lb>adde never ſo much water above the Levell of that which equalizeth <lb></lb>the Altitude of the Solid, it ſhall not, for all that, encreaſe the Preſſion <lb></lb>or Gravitation, of the parts circumfuſed about the ſaid Solid, by <lb></lb>which greater preſſion, it might come to be repulſed, becauſe, the <lb></lb>Reſiſtance is not made, but only by thoſe parts of the water, which <lb></lb>at the Motion of the ſaid Solid do alſo move, and theſe are thoſe <lb></lb>only, which are comprehended by the two Superficies equidiſtant to <lb></lb>the Horizon, and their parallels, that comprehend the Altitude of the <lb></lb>Solid immerged in the water.</s></p><p type="main"> <s>I conceive, I have by this time ſufficiently declared and opened <lb></lb>the way to the contemplation of the true, intrinſecall and proper <lb></lb>Cauſes of diverſe Motions, and of the Reſt of many Solid Bodies in <lb></lb>diverſe <emph type="italics"></emph>Mediums,<emph.end type="italics"></emph.end> and particularly in the water, ſhewing how all ii <lb></lb>effect, depend on the mutuall exceſſes of the Gravity of the Movea <lb></lb>bles and of the <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end>: and, that which did highly import, re <lb></lb>moving the Objection, which peradventure would have begotter <lb></lb>much doubting, and ſcruple in ſome, about the verity of my Con <lb></lb>cluſion, namely, how that notwithſtanding, that the exceſs of the <lb></lb>Gravity of the water, above the Gravity of the Solid, demitted into <lb></lb>it, be the cauſe of its floating and riſing from the Bottom to the Sur <lb></lb>face, yet a quantity of water, that weighs not ten pounds, can raiſe <pb pagenum="419"></pb>Solid that weighs above 100 pounds: in that we have demonſtra <lb></lb>ted, That it ſufficeth, that ſuch difference be found between the <lb></lb>Specificall Gravities of the <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end> and Moveables, let the particular <lb></lb>and abſolute Gravities be what they will: inſomuch, that a Solid, <lb></lb>provided that it be Specifically leſs grave than the water, although <lb></lb>its abſolute weight were 1000 pounds, yet may it be born up and <lb></lb>elevated by ten pounds of water, and leſs: and on the contrary, a <lb></lb>nother Solid, ſo that it be Specifically more grave than the water, <lb></lb>though in abſolute Gravity it were not above a pound, yet all the <lb></lb>water in the Sea, cannot raiſe it from the Bottom, or float it. </s><s>This <lb></lb>ſufficeth me, for my preſent occaſion, to have, by the above declared <lb></lb>Examples, diſcovered and demonſtrated, without extending ſuch <lb></lb>matters farther, and, as I might have done, into a long Treatiſe: <lb></lb>yea, but that there was a neceſſity of reſolving the above propoſed <lb></lb>doubt, I ſhould have contented my ſelf with that only, which is <lb></lb>demonſtrated by <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> in his firſt Book <emph type="italics"></emph>De Inſidentibus hu <lb></lb>mido<emph.end type="italics"></emph.end>: where in generall termes he infers and confirms the ſame </s></p><p type="main"> <s><arrow.to.target n="marg1422"></arrow.to.target> <lb></lb><arrow.to.target n="marg1423"></arrow.to.target> <lb></lb>Concluſions, namely, that Solids (<emph type="italics"></emph>a<emph.end type="italics"></emph.end>) leſs grave than water, ſwim or <lb></lb><arrow.to.target n="marg1424"></arrow.to.target> <lb></lb>float upon it, the (<emph type="italics"></emph>b<emph.end type="italics"></emph.end>) more grave go to the Bottom, and the (<emph type="italics"></emph>c<emph.end type="italics"></emph.end>) e <lb></lb><arrow.to.target n="marg1425"></arrow.to.target> <lb></lb>qually grave reſt indifferently in all places, yea, though they ſhould <lb></lb>be wholly under water.</s></p><p type="margin"> <s><margin.target id="marg1422"></margin.target><emph type="italics"></emph>Of Natation<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1423"></margin.target>(a) <emph type="italics"></emph>Lib. 1. Prop.<emph.end type="italics"></emph.end> 4.</s></p><p type="margin"> <s><margin.target id="marg1424"></margin.target>(b) <emph type="italics"></emph>Id. </s><s>Lib. </s><s>1. <lb></lb>Prop.<emph.end type="italics"></emph.end> 3.</s></p><p type="margin"> <s><margin.target id="marg1425"></margin.target>(c) <emph type="italics"></emph>Id. </s><s>Lib. 1. <lb></lb>Prop.<emph.end type="italics"></emph.end> 3.</s></p><p type="main"> <s>But, becauſe that this Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> peruſed, tranſcri <lb></lb><arrow.to.target n="marg1426"></arrow.to.target> <lb></lb>bed and examined by <emph type="italics"></emph>Signor Franceſco Buonamico,<emph.end type="italics"></emph.end> in his <emph type="italics"></emph>fifth Book <lb></lb>of Motion, Chap.<emph.end type="italics"></emph.end> 29, and afterwards by him confuted, might by the <lb></lb>Authority of ſo renowned, and famous a Philoſopher, be rendered <lb></lb>dubious, and ſuſpected of falſity; I have judged it neceſſary to de <lb></lb>fend it, if I am able ſo to do, and to clear <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> from thoſe <lb></lb>cenſures, with which he appeareth to be charged. <emph type="italics"></emph>Buonamico<emph.end type="italics"></emph.end> re <lb></lb><arrow.to.target n="marg1427"></arrow.to.target> <lb></lb>jecteth the Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> firſt, as not conſentaneous with <lb></lb>the Opinion of <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> adding, that it was a ſtrange thing to him, <lb></lb><arrow.to.target n="marg1428"></arrow.to.target> <lb></lb>that the Water ſhould exceed the Earth in Gravity, ſeeing on the <lb></lb>contrary, that the Gravity of water, increaſeth, by means of the parti <lb></lb><arrow.to.target n="marg1429"></arrow.to.target> <lb></lb>cipation of Earth. </s><s>And he ſubjoyns preſently after, that he was <lb></lb>not ſatisfied with the Reaſons of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> as not being able with <lb></lb>that Doctrine, to aſſign the cauſe whence it comes, that a Boat and <lb></lb>a Veſſell, which otherwiſe, floats above the water, doth ſink to the <lb></lb>Bottom, if once it be filled with water; that by reaſon of the e <lb></lb>quality of Gravity, between the water within it, and the other water <lb></lb>without, it ſhould ſtay a top; but yet, nevertheleſs, we ſee it to go to <lb></lb>the Bottom. <lb></lb><arrow.to.target n="marg1430"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1426"></margin.target>The <emph type="italics"></emph>Authors<emph.end type="italics"></emph.end> <lb></lb>defence of <emph type="italics"></emph>Ar <lb></lb>chimedes<emph.end type="italics"></emph.end> his Do <lb></lb>ctrine, againſt <lb></lb>the oppoſitions <lb></lb>of <emph type="italics"></emph>Buonamico.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1427"></margin.target>His firſt Objecti <lb></lb>on againſt the <lb></lb>Doctrine of <emph type="italics"></emph>Ar <lb></lb>chimedes.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1428"></margin.target>His Second Ob <lb></lb>jection.</s></p><p type="margin"> <s><margin.target id="marg1429"></margin.target>His third Obje <lb></lb>ction.</s></p><p type="margin"> <s><margin.target id="marg1430"></margin.target>His ſourth Ob <lb></lb>jection.</s></p><p type="main"> <s>He farther addes, that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> had clearly confuted the Ancients, <lb></lb>who ſaid, that light Bodies moved upwards, driven by the impulſe </s></p><p type="main"> <s><arrow.to.target n="marg1431"></arrow.to.target> <lb></lb>of the more grave Ambient: which if it were ſo, it ſhould ſeem of <lb></lb>neceſſity to follow, that all naturall Bodies are by nature heavy, <pb pagenum="420"></pb>and none light: For that the ſame would befall the Fire and Air, <lb></lb>if put in the Bottom of the water. </s><s>And, howbeit, <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> grants <lb></lb>a Pulſion in the Elements, by which the Earth is reduced into a Sphe <lb></lb>ricall Figure, yet nevertheleſs, in his judgement, it is not ſuch that it <lb></lb>can remove grave Bodies from their naturall places, but rather, that <lb></lb>it ſend them toward the Centre, to which (as he ſomewhat obſcurely <lb></lb>continues to ſay,) the water principally moves, if it in the interim <lb></lb>meet not with ſomething that reſiſts it, and, by its Gravity, thruſts <lb></lb>it out of its place: in which caſe, if it cannot directly, yet at leaſt <lb></lb>as well as it can, it tends to the Centre: but it happens, that light <lb></lb>Bodies by ſuch Impulſion, do all aſcend upward: but this properly <lb></lb>they have by nature, as alſo, that other of ſwimming. </s><s>He concludes, <lb></lb><arrow.to.target n="marg1432"></arrow.to.target> <lb></lb>laſtly, that he concurs with <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> in his Concluſions; but not <lb></lb>in the Cauſes, which he would referre to the facile and difficult Sepa <lb></lb>ration of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> and to the predominance of the Elements, ſo <lb></lb>that when the Moveable ſuperates the power of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>; as for <lb></lb>example, Lead doth the Continuity of water, it ſhall move thorow it, <lb></lb>elſe not.</s></p><p type="margin"> <s><margin.target id="marg1431"></margin.target>The <emph type="italics"></emph>Ancients<emph.end type="italics"></emph.end> <lb></lb>denved <emph type="italics"></emph>Aoſolute<emph.end type="italics"></emph.end> <lb></lb>Levity.</s></p><p type="margin"> <s><margin.target id="marg1432"></margin.target>The cauſes of <lb></lb>Natation & Sub <lb></lb>merſion, accord <lb></lb>ing to the Peri <lb></lb>pateticks.</s></p><p type="main"> <s>This is all that I have been able to collect, as produced againſt <lb></lb><emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> by <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end>: who hath not well obſerved the <lb></lb>Principles and Suppoſitions of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end>; which yet muſt be <lb></lb>falſe, if the Doctrine be falſe, which depends upon them; but is <lb></lb>contented to alledge therein ſome Inconveniences, and ſome Repug <lb></lb>nances to the Doctrine and Opinion of <emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end> In anſwer to which <lb></lb>Objections, I ſay, firſt, That the being of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> Doctrine, ſim <lb></lb><arrow.to.target n="marg1433"></arrow.to.target> <lb></lb>ply different from the Doctrine of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> ought not to move any <lb></lb>to ſuſpect it, there being no cauſe, why the Authority of this ſhould <lb></lb>be preferred to the Authority of the other: but, becauſe, where the <lb></lb>decrees of Nature are indifferently expoſed to the intellectuall eyes of <lb></lb>each, the Authority of the one and the other, loſeth all anthentical <lb></lb>neſs of Perſwaſion, the abſolute power reſiding in Reaſon; therefore <lb></lb>I paſs to that which he alledgeth in the ſecond place, as an abſurd con <lb></lb><arrow.to.target n="marg1434"></arrow.to.target> <lb></lb>ſequent of the Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> namely, That water ſhould <lb></lb>be more grave than Earth. </s><s>But I really find not, that ever <emph type="italics"></emph>Archi <lb></lb>medes<emph.end type="italics"></emph.end> ſaid ſuch a thing, or that it can be rationally deduced from his <lb></lb>Concluſions: and if that were manifeſt unto me, I verily believe, I <lb></lb>ſhould renounce his Doctrine, as moſt erroneous. </s><s>Perhapsthis Dedu <lb></lb>ction of <emph type="italics"></emph>Buonamico,<emph.end type="italics"></emph.end> is founded upon that which he citeth of the Ve <lb></lb>ſſel, which ſwims as long as its voyd of water, but once full it ſinks to <lb></lb>the Bottom, and underſtanding it of a Veſſel of Earth, he infers againſt <lb></lb><emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> thus: Thou ſayſt that the Solids which ſwim, are leſs grave <lb></lb>than water: this Veſſell ſwimmeth: therefore, this Veſſell is leſſe grave <lb></lb>than water. </s><s>If this be the Illation. </s><s>I eaſily anſwer, granting that this <lb></lb>Veſſell is leſſe grave than water, and denying the other conſequence, <pb pagenum="421"></pb>namely, that Earth is leſs Grave than Water. </s><s>The Veſſel that ſwims <lb></lb>occupieth in the water, not only a place equall to the Maſs of the <lb></lb>Earth, of which it is formed; but equall to the Earth and to the Air <lb></lb>together, contained in its concavity. </s><s>And, if ſuch a Maſs compoun <lb></lb>ded of Earth and Air, ſhall be leſs grave than ſuch another quantity <lb></lb>of water, it ſhall ſwim, and ſhall accord with the Doctrine of <emph type="italics"></emph>Archi <lb></lb>medes<emph.end type="italics"></emph.end>; but if, again, removing the Air, the Veſſell ſhall be filled <lb></lb>with water, ſo that the Solid put in the water, be nothing but <lb></lb>Earth, nor occupieth other place, than that which is only poſſeſt by <lb></lb>Earth, it ſhall then go to the Bottom, by reaſon that the Earth is <lb></lb>heavier than the water: and this correſponds well with the meaning <lb></lb>of <emph type="italics"></emph>Archimedes.<emph.end type="italics"></emph.end> See the ſame effect illuſtrated, with ſuch another <lb></lb>Experiment, In preſſing a Viall Glaſs to the Bottom of the water, <lb></lb>when it is full of Air, it will meet with great reſiſtance, becauſe it is <lb></lb>not the Glaſs alone, that is preſſed under water, but together with <lb></lb>the Glaſs a great Maſs of Air, and ſuch, that if you ſhould take as <lb></lb>much water, as the Maſs of the Glaſs, and of the Air contained in it, <lb></lb>you would have a weight much greater than that of the Viall, and of <lb></lb>its Air: and, therefore, it will not ſubmerge without great violence: <lb></lb>but if we demit only the Glaſs into the water, which ſhall be when <lb></lb>you ſhall fill the Glaſs with water, then ſhall the Glaſs deſcend to <lb></lb>the Bottom; as ſuperiour in Gravity to the water.</s></p><p type="margin"> <s><margin.target id="marg1433"></margin.target>The Authors an <lb></lb>ſwer to the firſt <lb></lb>Objection.</s></p><p type="margin"> <s><margin.target id="marg1434"></margin.target>The Authors an <lb></lb>ſwer to the ſe <lb></lb>cond Objection.</s></p><p type="main"> <s>Returning, therefore, to our firſt purpoſe; I ſay, that Earth is <lb></lb>more grave than water, and that therefore, a Solid of Earth goeth to <lb></lb>the bottom of it; but one may poſſibly make a compoſition of Earth <lb></lb>and Air, which ſhall be leſs grave than a like Maſs of Water; and <lb></lb>this ſhall ſwim: and yet both this and the other experiment ſhall <lb></lb>very well accord with the Doctrine of <emph type="italics"></emph>Archimedes.<emph.end type="italics"></emph.end> But becauſe that <lb></lb>in my judgment it hath nothing of difficulty in it, I will not poſitive <lb></lb>ly affirme that <emph type="italics"></emph>Signor Buonamico,<emph.end type="italics"></emph.end> would by ſuch a diſcourſe object <lb></lb>unto <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> the abſurdity of inferring by his doctrine, that Earth <lb></lb>was leſs grave than Water, though I know not how to conceive what <lb></lb>other accident he could have induced thence.</s></p><p type="main"> <s>Perhaps ſuch a Probleme (in my judgement falſe) was read by <lb></lb><emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> in ſome other Author, by whom peradventure it <lb></lb>was attributed as a ſingular propertie, of ſome particular Water, and <lb></lb>ſo comes now to be uſed with a double errour in confutation of <emph type="italics"></emph>Ar <lb></lb>chimedes,<emph.end type="italics"></emph.end> ſince he ſaith no ſuch thing, nor by him that did ſay it was it <lb></lb>meant of the common Element of Water.</s></p><p type="main"> <s>The third difficulty in the doctrine of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> was, that he <lb></lb><arrow.to.target n="marg1435"></arrow.to.target> <lb></lb>could not render a reaſon whence it aroſe, that a piece of Wood, <lb></lb>and a Veſſell of Wood, which otherwiſe floats, goeth to the bottom, <lb></lb>if filled with Water. <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> hath ſuppoſed that a Verſſell <lb></lb>of Wood, and of Wood that by nature ſwims, as before is ſaid, <pb pagenum="422"></pb>goes to the bottom, if it be filled with water; of which he in the fol <lb></lb>lowing Chapter, which is the 30 of the fifth Book copiouſly diſcourſ <lb></lb>eth: but I (ſpeaking alwayes without diminution of his ſingular <lb></lb>Learning) dare in defence of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> deny this experiment, being <lb></lb>certain that a piece of Wood which by its nature ſinks not in Water, <lb></lb>ſhall not ſinke though it be turned and converted into the forme of a <lb></lb>ny Veſſell whatſoever, and then filled with Water: and he that would <lb></lb>readily ſee the Experiment in ſome other tractable Matter, and that is <lb></lb>eaſily reduced into ſeveral Figures, may take pure Wax, and ma <lb></lb>king it firſt into a Ball or other ſolid Figure, let him adde to it ſo <lb></lb>much Lead as ſhall juſt carry it to the bottome, ſo that being a graine <lb></lb>leſs it could not be able to ſinke it, and making it afterwards into <lb></lb>the forme of a Diſh, and filling it with Water, he ſhall finde that with <lb></lb>out the ſaid Lead it ſhall not ſinke, and that with the Lead it ſhall de <lb></lb>ſcend with much ſlowneſs: & in ſhort he ſhall ſatisfie himſelf, that the <lb></lb>Water included makes no alteration. </s><s>I ſay not all this while, but that <lb></lb>its poſſible of Wood to make Barkes, which being filled with water, <lb></lb>ſinke; but that proceeds not through its Gravity, encreaſed by the <lb></lb>Water, but rather from the Nailes and other Iron Workes, ſo that <lb></lb>it no longer hath a Body leſs grave than Water, but one mixt of Iron <lb></lb>and Wood, more grave than a like Maſſe of Water. </s><s>Therefore let <lb></lb><emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> deſiſt from deſiring a reaſon of an effect, that is <lb></lb>not in nature: yea if the ſinking of the Woodden Veſſell when its full <lb></lb>of Water, may call in queſtion the Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> which <lb></lb>he would not have you to follow, is on the contrary conſonant and a <lb></lb>greeable to the Doctrine of the Peripateticks, ſince it aptly aſſignes a <lb></lb>reaſon why ſuch a Veſſell muſt, when its full of Water, deſcend to the <lb></lb>bottom; converting the Argument the other way, we may with <lb></lb>ſafety ſay that the Doctrine of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> is true, ſince it aptly agre <lb></lb>eth with true experiments, and queſtion the other, whoſe Deducti <lb></lb>ons are faſtened upon etroneouſs Concluſions. </s><s>As for the other point <lb></lb>hinted in this ſame Inſtance, where it ſeemes that <emph type="italics"></emph>Benonamico<emph.end type="italics"></emph.end> under <lb></lb>ſtands the ſame not only of a piece of wood, ſhaped in the forme of a <lb></lb>Veſſell, but alſo of maſſie Wood, which filled, <emph type="italics"></emph>ſcilicet,<emph.end type="italics"></emph.end> as I believe, he <lb></lb>would ſay, ſoaked and ſteeped in Water, goes finally to the bottom <lb></lb>that happens in ſome poroſe Woods, which, while their Poroſity is re <lb></lb>pleniſhed with Air, or other Matter leſs grave than Water, are Maſ <lb></lb>ſes ſpecificially leſs grave than the ſaid Water, like as is that Viall of <lb></lb>Glaſs whileſt it is full of Air: but when, ſuch light Matter depart <lb></lb>ing, there ſucceedeth Water into the ſame Poroſities and Cavities, <lb></lb>there reſults a compound of Water and Glaſs more grave than a like <lb></lb>Maſs of Water: but the exceſs of its Gravity conſiſts in the Matter <lb></lb>of the Glaſs, and not in the Water, which cannot be graver than it <lb></lb>ſelf: ſo that which remaines of the Wood, the Air of its Cavi <pb pagenum="423"></pb>ties departing, if it ſhall be more grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than Water, fil but its <lb></lb>Poroſities with Water, and you ſhal have a Compoſt of Water and <lb></lb>of Wood more grave than Water, but not by vertue of the Water re <lb></lb>ceived into and imbibed by the Poroſities, but of that Matter of the <lb></lb>Wood which remains when the Air is departed: and being ſuch it <lb></lb>ſhall, according to the Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> goe to the bottom, <lb></lb>like as before, according to the ſame Doctrine it did ſwim.</s></p><p type="margin"> <s><margin.target id="marg1435"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he Authors an <lb></lb>ſwer to the third <lb></lb>Objection.</s></p><p type="main"> <s>As to that finally which preſents it ſelf in the fourth place, namely, <lb></lb><arrow.to.target n="marg1436"></arrow.to.target> <lb></lb>that the <emph type="italics"></emph>Ancients<emph.end type="italics"></emph.end> have been heretofore confuted by <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> who <lb></lb>denying Poſitive and Abſolute Levity, and truely eſteeming all Bo <lb></lb>dies to be grave, ſaid, that that which moved upward was driven by <lb></lb>the circumambient Air, and therefore that alſo the Doctrine of <lb></lb><emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> as an adherent to ſuch an Opinion was con <lb></lb>victed and confuted: I anſwer firſt, that <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> in my <lb></lb>judgement hath impoſed upon <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> and deduced from his <lb></lb>words more than ever he intended by them, or may from his Propo <lb></lb>ſitions be collected, in regard that <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> neither denies, nor ad <lb></lb>mitteth Poſitive Levity, nor doth he ſo much as mention it: ſo that <lb></lb>much leſs ought <emph type="italics"></emph>Buonamico<emph.end type="italics"></emph.end> to inferre, that he hath denyed that it <lb></lb>might be the Cauſe and Principle of the Aſcenſion of Fire, and other <lb></lb>Light Bodies: having but only demonſtrated, that Solid Bodies <lb></lb><arrow.to.target n="marg1437"></arrow.to.target> <lb></lb>more grave than Water deſcend in it, according to the exceſs of their <lb></lb>Gravity above the Gravity of that, he demonſtrates likewiſe, how the <lb></lb><arrow.to.target n="marg1438"></arrow.to.target> <lb></lb>leſs grave aſcend in the ſame Water, accordng to its exceſs of Gra <lb></lb>ty, above the Gravity of them. </s><s>So that the moſt that can be gather <lb></lb>ed from the Dem onſtration of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> is, that like as the exceſs <lb></lb>of the Gravity of the Moveable above the Gravity of the Water, is <lb></lb>the Cauſe that it deſcends therein, ſo the exceſs of the Gravity of <lb></lb>the water above that of the Moveable, is a ſufficient Cauſe why it deſ <lb></lb>cends not, but rather betakes it ſelf to ſwim: not enquiring whe <lb></lb>ther of moving upwards there is, or is not any other Cauſe contrary <lb></lb>to Gravity: nor doth <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> diſcourſe leſs properly than if one <lb></lb>ſhould ſay: If the South Winde ſhall aſſault the Barke with greater <lb></lb><emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> than is the violence with which the Streame of the River car <lb></lb>ries it towards the South, the motion of it ſhall be towards the North: <lb></lb>but if the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Water ſhall overcome that of the Winde, its <lb></lb>motion ſhall be towards the South. </s><s>The diſcourſe is excellent and <lb></lb>would be unworthily contradicted by ſuch as ſhould oppoſe it, ſaying: <lb></lb>Thou miſ-alledgeſt as Cauſe of the motion of the Bark towards the <lb></lb>South, the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Stream of the Water above that of the <lb></lb>South Winde; miſ-alledgeſt I ſay, for it is the Force of the North <lb></lb>Winde oppoſite to the South, that is able to drive the Bark towards <lb></lb>the South. </s><s>Such an Objection would be ſuperfluous, becauſe he which <lb></lb>alledgeth for Cauſe of the Motion the ſtream of the Water, denies not <pb pagenum="424"></pb>but that the Winde oppoſite to the South may do the ſame, but only <lb></lb>affirmeth that the force of the Water prevailing over the South <lb></lb>Wind, the Bark ſhall move towards the South: and ſaith no more <lb></lb>than is true. </s><s>And juſt thus when <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> ſaith, that the Gravity <lb></lb>of the Water prevailing over that by which the moveable deſcends to <lb></lb>the Bottom, ſuch moveable ſhall be raiſed from the Bottom to the Sur <lb></lb>face alledgeth a very true Cauſe of ſuch an Accident, nor doth he af <lb></lb>firm or deny that there is, or is not, a vertue contrary to Gravity, called <lb></lb>by ſome Levity, that hath alſo a power of moving ſome Matters up <lb></lb>wards. </s><s>Let therefore the Weapons of <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> be directed a <lb></lb><arrow.to.target n="marg1439"></arrow.to.target> <lb></lb>gainſt <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end> and other <emph type="italics"></emph>Ancients,<emph.end type="italics"></emph.end> who totally denying <emph type="italics"></emph>Levity,<emph.end type="italics"></emph.end> and taking <lb></lb>all Bodies to be grave, ſay that the Motion upwards is made, not <lb></lb>from an intrinſecal Principle of the Moveable, but only by the Im <lb></lb>pulſe of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>; and let <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> and his Doctrine eſcape <lb></lb>him, ſince he hath given him no Cauſe of quarelling with him <lb></lb>But if this Apologie, produced in defence of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> ſhould ſeen <lb></lb>to ſome inſufficient to free him from the Objections and Arguments <lb></lb>produced by <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> againſt <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end> and the other <emph type="italics"></emph>Ancients,<emph.end type="italics"></emph.end> as if they <lb></lb>did alſo fight againſt <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> alledging the Impulſe of the Water <lb></lb><arrow.to.target n="marg1440"></arrow.to.target> <lb></lb>as the Cauſe of the ſwimming of ſome Bodies leſs grave than it, I would <lb></lb>not queſtion, but that I ſhould be able to maintaine the Doctrine of <lb></lb><emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> and thoſe others to be moſt true, who abſolutely deny Levity, <lb></lb>and affirm no other Intrinſecal Principle of Motion to be in Elemen <lb></lb>tary Bodies ſave only that towards the Centre of the Earth, nor no <lb></lb><arrow.to.target n="marg1441"></arrow.to.target> <lb></lb>other Cauſe of moving upwards, ſpeaking of that which hath the re <lb></lb>ſemblance of natural Motion, but only the repulſe of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> ſluid, <lb></lb>and exceeding the Gravity of the Moveable: and as to the Reaſons <lb></lb>of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> on the contrary, I believe that I could be able fully to <lb></lb><arrow.to.target n="marg1442"></arrow.to.target> <lb></lb>anſwer them, and I would aſſay to do it, if it were abſolutely neceſſa <lb></lb>ry to the preſent Matter, or were it not too long a Digreſſion for this <lb></lb>ſhort Treatiſe. </s><s>I will only ſay, that if there were in ſome of our Elle <lb></lb>mentary Bodies an Intrinſecall Principle and Naturall Inclination <lb></lb>to ſhun the Centre of the Earth, and to move towards the Concave <lb></lb>of the Moon, ſuch Bodies, without doubt, would more ſwiftly aſcend <lb></lb>through thoſe <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end> that leaſt oppoſe the Velocity of the Moveable, <lb></lb>and theſe are the more tenuous and ſubtle; as is, for example, the <lb></lb>Air in compariſon of the Water, we daily proving that we can with <lb></lb><arrow.to.target n="marg1443"></arrow.to.target> <lb></lb>farre more expeditious Velocity move a Hand or a Board to and a <lb></lb>gain in one than in the other: nevertheleſs, we never could finde any <lb></lb>Body, that did not aſcend much more ſwiftly in the water than in the <lb></lb><arrow.to.target n="marg1444"></arrow.to.target> <lb></lb>Air. </s><s>Yea of Bodies which we ſee continually to aſcend in the Water, <lb></lb>there is none that having arrived to the confines of the Air, do not whol <lb></lb>ly loſe their Motion; even the Air it ſelf, which riſing with great Ce <lb></lb>lerity through the Water, being once come to its Region it loſeth all</s></p> <pb pagenum="425"></pb><p type="margin"> <s><margin.target id="marg1436"></margin.target>The Authors <lb></lb>anſwer to the <lb></lb>fourth Object <lb></lb>ion.</s></p><p type="margin"> <s><margin.target id="marg1437"></margin.target>Of Natation, <lb></lb>Lib. 1. Prop. </s><s>7.</s></p><p type="margin"> <s><margin.target id="marg1438"></margin.target>Of Natation, <lb></lb>Lib. </s><s>1. Prop. </s><s>4.</s></p><p type="margin"> <s><margin.target id="marg1439"></margin.target><emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> denyeth <lb></lb>Poſitive Levi <lb></lb>ty.</s></p><p type="margin"> <s><margin.target id="marg1440"></margin.target>The Authors <lb></lb>defence of the <lb></lb>doctrine of <emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> <lb></lb>and the <emph type="italics"></emph>Ancients,<emph.end type="italics"></emph.end> <lb></lb>who abſolutely <lb></lb>deny Levity:</s></p><p type="margin"> <s><margin.target id="marg1441"></margin.target>According to <lb></lb><emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> there is no <lb></lb>Principle of the <lb></lb>Motion of de <lb></lb>ſcent in Naturall <lb></lb>Bodies, ſave that <lb></lb>to the Centre.</s></p><p type="margin"> <s><margin.target id="marg1442"></margin.target>No cauſe of <lb></lb>the motion of <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end> cent, ſave the <lb></lb>Impulſe of the <lb></lb><emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> exceed <lb></lb>ing the Move <lb></lb>able in Gravi <lb></lb>tie.</s></p><p type="margin"> <s><margin.target id="marg1443"></margin.target>Bodies aſcend <lb></lb>much ſwifter in <lb></lb>the Water, than <lb></lb>in the Air.</s></p><p type="margin"> <s><margin.target id="marg1444"></margin.target>All Bodies aſ <lb></lb>cending through <lb></lb>Water, loſe <lb></lb>their Motion, <lb></lb>comming to the <lb></lb>confines of the <lb></lb>Air.</s></p><p type="main"> <s>And, howbeit, Experience ſhewes, that the Bodies, ſucceſſively <lb></lb><arrow.to.target n="marg1445"></arrow.to.target> <lb></lb>leſs grave, do moſt expeditiouſly aſcend in water, it cannot be doubt <lb></lb>ed, but that the Ignean Exhalations do aſcend more ſwiftly <lb></lb><arrow.to.target n="marg1446"></arrow.to.target> <lb></lb>through the water, than doth the Air: which Air is ſeen by Experi <lb></lb>ence to aſcend more ſwiftly through the Water, than the Fiery Exha <lb></lb>lations through the Air: Therefore, we muſt of neceſſity conclude, <lb></lb>that the ſaid Exhalations do much more expeditiouſly aſcend through <lb></lb>the Water, than through the Air; and that, conſequently, they are <lb></lb>moved by the Impulſe of the Ambient <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> and not by an intrin <lb></lb>ſick Principle that is in them, of avoiding the Centre of the Earth; <lb></lb>to which other grave Bodies tend.</s></p><p type="margin"> <s><margin.target id="marg1445"></margin.target>The lighter <lb></lb>Bodies alſend <lb></lb>more ſwiftly <lb></lb>through Water.</s></p><p type="margin"> <s><margin.target id="marg1446"></margin.target>Fiery Exhalati <lb></lb>ons ascend tho <lb></lb>row the Water <lb></lb>more ſwiftly <lb></lb>than doth the <lb></lb>Air; & the Air <lb></lb>aſcends more <lb></lb>ſwiftly thorow <lb></lb>the Water, than <lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end>ire thorow the <lb></lb>Air.</s></p><p type="main"> <s>To that which for a finall concluſion, <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> produceth <lb></lb><arrow.to.target n="marg1447"></arrow.to.target> <lb></lb>of going about to reduce the deſcending or not deſcending, to the <lb></lb>eaſie and uneaſie Diviſion of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> and to the predominancy <lb></lb>of the Elements: I anſwer, as to the firſt part, that that cannot in any <lb></lb>manner be admitted as a Cauſe, being that in none of the Fluid <lb></lb><emph type="italics"></emph>Mediums,<emph.end type="italics"></emph.end> as the Air, the Water, and other Liquids, there is any <lb></lb><arrow.to.target n="marg1448"></arrow.to.target> <lb></lb>Reſiſtance againſt Diviſion, but all by every the leaſt Force, are di <lb></lb>vided and penetrated, as I will anon demonſtrate: ſo, that of ſuch <lb></lb>Reſiſtance of Diviſion there can be no Act, ſince it ſelf is not in be <lb></lb>ing. </s><s>As to the other part, I ſay, that the predominancy of the Ele <lb></lb><arrow.to.target n="marg1449"></arrow.to.target> <lb></lb>ments in Moveables, is to be conſidered, as far as to the exceſſe or <lb></lb>defect of Gravity, in relation to the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>: for in that Action, <lb></lb>the Elements operate not, but only, ſo far as they are grave or light: <lb></lb>therefore, to ſay that the Wood of the Firre ſinks not, becauſe Air <lb></lb>predominateth in it, is no more than to ſay, becauſe it is leſs grave <lb></lb>than the Water. </s><s>Yea, even the immediate Cauſe, is its being leſs <lb></lb>grave than the Water: and it being under the predominancy of the <lb></lb><arrow.to.target n="marg1450"></arrow.to.target> <lb></lb>Air, is the Cauſe of its leſs Gravity: Therefore, he that alledgeth the <lb></lb>predominancy of the Element for a Cauſe, brings the Cauſe of the <lb></lb>Cauſe, and not the neereſt and immediate Cauſe. </s><s>Now, who knows <lb></lb>not that the true Cauſe is the immediate, and not the mediate? <lb></lb><arrow.to.target n="marg1451"></arrow.to.target> <lb></lb>Moreover, he that alledgeth Gravity, brings a Cauſe moſt perſpicuous <lb></lb>to Sence: The cauſe we may very eaſily aſſertain our ſelves; <lb></lb>whether Ebony, for example, and Firre, be more or leſs grave than <lb></lb>water: but whether Earth or Air predominates in them, who ſhall <lb></lb><arrow.to.target n="marg1452"></arrow.to.target> <lb></lb>make that manifeſt? </s><s>Certainly, no Experiment can better do it <lb></lb>than to obſerve whether they ſwim or ſink. </s><s>So, that he who knows, <lb></lb>not whether ſuch a Solid ſwims, unleſs when he knows that Air pre <lb></lb>dominates in it, knows not whether it ſwim, unleſs he ſees it ſwim, <lb></lb>for then he knows that it ſwims, when he knows that it is Air that <lb></lb>predominates, but knows not that Air hath the predominance, unleſs <lb></lb>he ſees it ſwim: therefore, he knows not if it ſwims, till ſuch time <lb></lb>as he hath ſeen it ſwim.</s></p> <pb pagenum="426"></pb><p type="margin"> <s><margin.target id="marg1447"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he Authors <lb></lb>confutation of <lb></lb>the Peripateticks <lb></lb>Cauſes of Nata <lb></lb>tion & Submerſi <lb></lb>on.</s></p><p type="margin"> <s><margin.target id="marg1448"></margin.target>Water & other <lb></lb>fluids void of <lb></lb>Reſiſtance a <lb></lb>gainſt Diviſion.</s></p><p type="margin"> <s><margin.target id="marg1449"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he predomi <lb></lb>nancy of Ele <lb></lb>ments in Move <lb></lb>ables to be con <lb></lb>ſidered only in <lb></lb>relation to their <lb></lb>excefs or defect <lb></lb>of Gravity in <lb></lb>reference to the <lb></lb><emph type="italics"></emph>Medium.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1450"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he immedi <lb></lb>ate Cauſe of Na <lb></lb>tation is that the <lb></lb>Moveable is leſs <lb></lb>grave than the <lb></lb>Water.</s></p><p type="margin"> <s><margin.target id="marg1451"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he <emph type="italics"></emph>P<emph.end type="italics"></emph.end>eripate <lb></lb>ticks alledge for <lb></lb>the reaſon of <lb></lb>Natation the <lb></lb>Cauſe of the <lb></lb>Cauſe.</s></p><p type="margin"> <s><margin.target id="marg1452"></margin.target>Gravity a <lb></lb>Cauſe moſt per <lb></lb>ſpicuous to <lb></lb>ſence:</s></p><p type="main"> <s>Let us not then deſpiſe thoſe Hints, though very dark, which <lb></lb>Reaſon, after ſome contemplation, offereth to our Intelligence, and <lb></lb>lets be content to be taught by <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> that then any Body ſhall <lb></lb><arrow.to.target n="marg1453"></arrow.to.target> <lb></lb>ſubmerge in water, when it ſhall be ſpecifically more grave than it <lb></lb>and that if it ſhall be leſs grave, it ſhall of neceſſity ſwim, and <lb></lb><arrow.to.target n="marg1454"></arrow.to.target> <lb></lb>that it will reſt indifferently in any place under water, if its Gravity <lb></lb>be perfectly like to that of the water. <lb></lb><arrow.to.target n="marg1455"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1453"></margin.target>Lib 1. of Na <lb></lb>tation Prop. </s><s>7.</s></p><p type="margin"> <s><margin.target id="marg1454"></margin.target>Id. </s><s>Lib. 1. <lb></lb>Prop. </s><s>4.</s></p><p type="margin"> <s><margin.target id="marg1455"></margin.target>Id. </s><s>Lib. </s><s>1: <lb></lb>Prop. </s><s>3.</s></p><p type="main"> <s>Theſe things explained and proved, I come to conſider that which <lb></lb>offers it ſelf, touching what the Diverſity of figure given unto the <lb></lb>ſaid Moveable hath to do with theſe Motions and Reſts; and pro <lb></lb>ceed to affirme, that,</s></p><p type="head"> <s>THEOREME V.</s></p><p type="main"> <s><emph type="italics"></emph>The diverſity of Figures given to this or that Solid<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1456"></arrow.to.target> <lb></lb><emph type="italics"></emph>cannot any way be a Cauſe of its abſolute Sinking or <lb></lb>Swimming.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1456"></margin.target>Diverſity of <lb></lb>Figure no Cauſe <lb></lb>of its abſolute <lb></lb>Natation or Sub <lb></lb>merſion.</s></p><p type="main"> <s>So that if a Solid being formed, for example, into a Spherical <lb></lb>Figure, doth ſink or ſwim in the water, I ſay, that being formed <lb></lb>into any other Figure, the ſame figure in the ſame water, ſhall <lb></lb>ſink or ſwim: nor can ſuch its Motion by the Expanſion or by o <lb></lb>ther mutation of Figure, be impeded or taken away. <lb></lb><arrow.to.target n="marg1457"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1457"></margin.target>The Expanſi <lb></lb>on of <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure, re <lb></lb>tards the Veloci <lb></lb>ty of the aſcent <lb></lb>or deſcent of the <lb></lb>Moveable in the <lb></lb>water; but doth <lb></lb>not deprive it of <lb></lb>all Motion.</s></p><p type="main"> <s>The Expanſion of the Figure may indeed retard its Velocity, aſ <lb></lb>well of aſcent as deſcent, and more and more according as the ſaid Fi <lb></lb>gure is reduced to a greater breadth and thinneſs: but that it may bere <lb></lb>duced to ſuch a form as that that ſame matter be wholly hindred from <lb></lb>moving in the ſame water, that I hold to be impoſſible. </s><s>In this I have <lb></lb>met with great contradictors, who producing ſome Experiments, and <lb></lb>in perticular a thin Board of Ebony, and a Ball of the ſame Wood <lb></lb>and ſhewing how the Ball in Water deſcended to the bottom, and <lb></lb>the Board being put lightly upon the Water ſubmerged not, but reſt <lb></lb>ed; have held, and with the Authority of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> confirmed them <lb></lb>ſelves in their Opinions, that the Cauſe of that Reſt was the breadth <lb></lb>of the Figure, u able by its ſmall weight to pierce and penetrate the <lb></lb>Reſiſtance of the Waters Craſſitude, which Reſiſtance is readily o <lb></lb>vercome by the other Sphericall Figure.</s></p><p type="main"> <s>This is the Principal point in the preſent Queſtion, in which I per <lb></lb>ſwade my ſelf to be on the right ſide.</s></p><p type="main"> <s>Therefore, beginning to inveſtigate with the examination of ex <lb></lb>quiſite Experiments that really the Figure doth not a jot alter the deſ <lb></lb>cent or Aſcent of the ſame Solids, and having already demonſtra <lb></lb>ted that the greater or leſs Gravity of the Solid in relation to the Gra <lb></lb>vity of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> is the cauſe of Deſcent or Aſcent: when ever we <pb pagenum="427"></pb>would make proof of that, which about this Effect the diverſity of Fi <lb></lb>gure worketh, its neceſſary to make the Experiment with Matter <lb></lb>wherein variety of Gravities hath no place. </s><s>For making uſe of Mat <lb></lb>ters which may be different in their Specifical Gravities, and meeting <lb></lb>with varieties of effects of Aſcending and Deſcending, we ſhall al <lb></lb>wayes be left unſatisfied whether that diverſity derive it ſelf really <lb></lb>from the ſole Figure, or elſe from the divers Gravity alſo. </s><s>We may <lb></lb>remedy this by takeing one only Matter, that is tractable and eaſily <lb></lb>reduceable into every ſort of Figure. </s><s>Moreover, it wil be an excellent <lb></lb>expedient to take a kinde of Matter, exactly alike in Gravity unto the <lb></lb>Water: for that Matter, as far as pertaines to the Gravity, is in <lb></lb>different either to Aſcend or Deſcend; ſo that we may preſently ob <lb></lb>ſerve any the leaſt difference that derives it ſelf from the diverſity of <lb></lb>Figure.</s></p><p type="main"> <s>Now to do this, Wax is moſt apt, which, beſides its incapacity of </s></p><p type="main"> <s><arrow.to.target n="marg1458"></arrow.to.target> <lb></lb>receiveing any ſenſible alteration from its imbibing of Water, is duct <lb></lb>ile or pliant, and the ſame piece is eaſily reduceable into all Figures: <lb></lb>and being <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> a very inconſiderable matter inferiour in Gravity <lb></lb>to the Water, by mixing therewith a little of the fileings of Lead it is <lb></lb>reduced to a Gravity exactly equall to that of the Water.</s></p><p type="margin"> <s><margin.target id="marg1458"></margin.target>An Experi <lb></lb>ment in Wax, <lb></lb>that proveth Fi <lb></lb>gute to have no <lb></lb>Operation in <lb></lb>Natation & Sub <lb></lb>merſion.</s></p><p type="main"> <s>This Matter prepared, and, for example, a Ball being made there <lb></lb>of as bigge as an Orange or biger, and that made ſo grave as to <lb></lb>ſink to the bottom, but ſo lightly, that takeing thence one only Grain <lb></lb>of Lead, it returnes to the top, and being added, it ſubmergeth to <lb></lb>the bottom, let the ſame Wax afterwards be made into a very broad <lb></lb>and thin Flake or Cake; and then, returning to make the ſame Ex <lb></lb>periment, you ſhall ſee that it being put to the bottom, it ſhall, with the <lb></lb>Grain of Lead reſt below, and that Grain deducted, it ſhall aſcend to <lb></lb>the very Surface, and added again it ſhall dive to the bottom. </s><s>And <lb></lb>this ſame effect ſhall happen alwaies in all ſort of Figures, as wel re <lb></lb>gular as irregular: nor ſhall you ever finde any that will ſwim with <lb></lb>out the removall of the Grain of Lead, or ſinke to the bottom unleſs <lb></lb>it be added: and, in ſhort, about the going or not going to the Bot <lb></lb>tom, you ſhall diſcover no diverſity, although, indeed, you ſhall about <lb></lb>the quick and ſlow deſcent: for the more expatiated and diſtended <lb></lb>Figures move more ſlowly aſwel in the diveing to the bottom as in <lb></lb>the riſing to the top; and the other more contracted and compact Fi <lb></lb>gures, more ſpeedily. </s><s>Now I know not what may be expected from <lb></lb>the diverſity of Figures, if the moſt contrary to one another operate <lb></lb>not ſo much as doth a very ſmall Grain of Lead, added or removed.</s></p><p type="main"> <s>Me thinkes I hear ſome of the Adverſaries to raiſe a doubt upon <lb></lb><arrow.to.target n="marg1459"></arrow.to.target> <lb></lb>my produced Experiment. </s><s>And firſt, that they offer to my conſidera <lb></lb>tion, that the Figure, as a Figure ſimply, and disjunct from the Matter <lb></lb>workes not any effect, but requires to be conjoyned with the Matter <pb pagenum="428"></pb>and, furthermore, not with every Matter, but with thoſe only, <lb></lb>wherewith it may be able ro execute the deſired operation. </s><s>Like <lb></lb>as we ſee it verified by Experience, that the Acute and ſharp Angle is <lb></lb>more apt to cut, than the Obtuſe; yet alwaies provided, that both <lb></lb>the one and the other, be joyned with a Matter apt to cut, as for <lb></lb>example, with Steel. </s><s>Therefore, a Knife with a fine and ſharp <lb></lb>edge, cuts Bread or Wood with much eaſe, which it will not do, if <lb></lb>the edge be blunt and thick: but he that will inſtead of Steel, take <lb></lb>Wax, and mould it into a Knife, undoubtedly ſhall never know the <lb></lb>effects of ſharp and blunt edges: becauſe neither of them will cut, <lb></lb>the Wax being unable by reaſon of its flexibility, to overcome the <lb></lb>hardneſs of the Wood and Bread. </s><s>And, therefore, applying the <lb></lb>like diſcourſe to our purpoſe, they ſay, that the difference of Figure <lb></lb>will ſhew different effects, touching Natation and Submerſion, but <lb></lb>not conjoyned with any kind of Matter, but only with thoſe Matters <lb></lb>which, by their Gravity, are apt to reſiſt the Velocity of the water, <lb></lb>whence he that would elect for the Matter, Cork or other light wood <lb></lb>unable, through its Levity, to ſuperate the Craſſitude of the water, <lb></lb>and of that Matter ſhould forme Solids of divers Figures, woulld in <lb></lb>vain ſeek to find out what operation Figure hath in Natation or Sub <lb></lb>merſion; becauſe all would ſwim, and that not through any property <lb></lb>of this or that Figure, but through the debility of the Matter, want <lb></lb>ing ſo much Gravity, as is requiſite to ſuperate and overcome the <lb></lb>Denſity and Craſſitude of the water.</s></p><p type="margin"> <s><margin.target id="marg1459"></margin.target>An objection a <lb></lb>gainſt the Expe <lb></lb>riment in Wax.</s></p><p type="main"> <s>Its needfull, therefore, if wee would ſee the effect wrought by the <lb></lb>Diverſity of Figure, firſt to make choice of a Matter of its nature <lb></lb>apt to penetrate the Craſſitude of the water. </s><s>And, for this effect, <lb></lb><arrow.to.target n="marg1460"></arrow.to.target> <lb></lb>they have made choice of ſuch a Matter, as fit, that being readily re <lb></lb>duced into Sphericall Figure, goes to the Bottom; and it is Ebony <lb></lb>of which they afterwards making a ſmall Board or Splinter, as thin as <lb></lb>a Lath, have illuſtrated how that this, put upon the Surface of the <lb></lb>water, reſts there without deſcending to the Bottom: and making, on <lb></lb>the otherſide, of the ſame wood a Ball, no leſs than a hazell Nut, <lb></lb>they ſhew, that this ſwims not, but deſcendes. </s><s>From which Experi <lb></lb>ment, they think they may frankly conclude, that the Breadth ofthe <lb></lb>Figure in the flat Lath or Board, is the cauſe of its not deſcendingto <lb></lb>the Bottom, foraſmuch as a Ball of the ſame Matter, not different <lb></lb>from the Board in any thing but in Figure, ſubmergeth in the ſame <lb></lb>water to the Bottom. </s><s>The diſcourſe and the Experiment hath really <lb></lb>ſo much of probability and likely hood of truth in it, that it would be <lb></lb>no wonder, if many perſwaded by a certain curſory obſervation, <lb></lb>ſhould yield credit to it; nevertheleſs, I think I am able to diſcover, <lb></lb>how that it is not free from falacy.</s></p><p type="margin"> <s><margin.target id="marg1460"></margin.target>An Experi <lb></lb>ment in Ebany, <lb></lb>brought to diſ <lb></lb>prove the Expe <lb></lb>timent in Wax.</s></p><p type="main"> <s>Beginning, therefore, to examine one by one, all the particulars that <pb pagenum="429"></pb>have been produced, I ſay, that Figures, as ſimple Figures, not only <lb></lb><arrow.to.target n="marg1461"></arrow.to.target> <lb></lb>operate not in naturall things, but neither are they ever ſeperated <lb></lb>from the Corporeall ſubſtance: nor have I ever alledged them ſtript <lb></lb>of ſenſible Matter, like as alſo I freely admit, that in our endeavour <lb></lb>ing to examine the Diverſity of Accidents, dependant upon the va <lb></lb>riety of Figures, it is neceſſary to apply them to Matters, which ob <lb></lb>ſtruct not the various operations of thoſe various Figures: and I ad <lb></lb>mit and grant, that I ſhould do very ill, if I would experiment the in <lb></lb>fluence of Acuteneſſe of edge with a Knife of Wax, applying it to cut <lb></lb>an Oak, becauſe there is no Acuteneſs in Wax able to cut that <lb></lb>very hard wood. </s><s>But yet ſuch an Experiment of this Knife, would <lb></lb>not be beſides the purpoſe, to cut curded Milk, or other very yielding <lb></lb>Matter: yea, in ſuch like Matters, the Wax is more commodious <lb></lb>than Steel; for finding the diverſity depending upon Angles, more or <lb></lb>leſs Acute, for that Milk is indifferently cut with a Raiſor, and with <lb></lb>a Knife, that hath a blunt edge. </s><s>It needs, therefore, that regard be <lb></lb>had, not only to the hardneſs, ſolidity or Gravity of Bodies, which <lb></lb>under divers figures, are to divide and penetrate ſome Matters, but it <lb></lb>forceth alſo, that regard be had, on the other ſide, to the Reſiſtance <lb></lb>of the Matters, to be divided and penetrated. </s><s>But ſince I have in <lb></lb>making the Experiment concerning our Conteſt, choſen a Matter <lb></lb>which penetrates the Reſiſtance of the water; and in all figures deſ <lb></lb>cendes to the Bottome, the Adverſaries can charge me with no defect; <lb></lb>yea, I have propounded ſo much a more excellent Method than they, <lb></lb>in as much as I have removed all other Cauſes, of deſcending or <lb></lb>not deſcending to the Bottom, and retained the only ſole and pure <lb></lb>variety of Figures, demonſtrating that the ſame Figures all deſcende <lb></lb>with the only alteration of a Grain in weight: which Grain being <lb></lb>removed, they return to float and ſwim; it is not true, therefore, <lb></lb>(reſuming the Example by them introduced) that I have gon about <lb></lb>to experiment the efficacy of Acuteneſs, in cutting with Matters un <lb></lb>able to cut, but with Matters proportioned to our occaſion; ſince <lb></lb>they are ſubjected to no other variety, then that alone which depends <lb></lb>on the Figure more or leſs a cute. <lb></lb><arrow.to.target n="marg1462"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1461"></margin.target>Figure is un <lb></lb>ſeperable from <lb></lb>Corporeall Sub <lb></lb>ſtance.</s></p><p type="margin"> <s><margin.target id="marg1462"></margin.target>The anſwer to <lb></lb>the Objection a <lb></lb>gainſt the Expe <lb></lb>riment of the <lb></lb>Wax.</s></p><p type="main"> <s>But let us proceed a little farther, and obſerve, how that indeed <lb></lb>the Conſideration, which, they ſay, ought to be had about the Election <lb></lb>of the Matter, to the end, that it may be proportionate for the ma <lb></lb>king of our experiment, is needleſly introduced, declaring by the ex <lb></lb>ample of Cutting, that like as Acuteneſs is inſufficient to cut, unleſs <lb></lb>when it is in a Matter hard and apt to ſuperate the Reſiſtance of the <lb></lb>wood or other Matter, which we intend to cut; ſo the aptitude of <lb></lb>deſcending or notdeſcending in water, ought and can only be known <lb></lb>in thoſe Matters, that are able to overcome the Renitence, and ſupe <lb></lb>rate the Craſſitude of the water. </s><s>Unto which, I ſay, that to make <lb></lb>diſtinction and election, more of this than of that Matter, on which to <pb pagenum="430"></pb>impreſs the Figures for cutting or penetrating this or that Body, <lb></lb>as the ſolidity or obdurateneſs of the ſaid Bodies ſhall be greater <lb></lb>or leſs, is very neceſſary: but withall I ſubjoyn, that ſuch diſtinct <lb></lb>ion, election and caution would be ſuperfluous and unprofitable, if <lb></lb>the Body to be cut or penetrated, ſhould have no Reſiſtance, or <lb></lb>ſhould not at all withſtand the Cutting or Penitration: and if the <lb></lb>Knife were to be uſed in cutting a Miſt or Smoak, one of Paper <lb></lb>would be equally ſerviceable with one of <emph type="italics"></emph>Damaſcus<emph.end type="italics"></emph.end> Steel: and ſo <lb></lb>by reaſon the water hath not any Reſiſtance againſt the Penitration <lb></lb>of any Solid Body, all choice of Matter is ſuperfluous and needleſs, <lb></lb>and the Election which I ſaid above to have been well made of a <lb></lb>Matter reciprocall in Gravity to water, was not becauſe it was ne <lb></lb>ceſſary, for the overcoming of the craſſiitude of the water, but its <lb></lb>Gravity, with which only it reſiſts the ſinking of Solid Bodies: and <lb></lb>for what concerneth the Reſiſtance of the craſſitude, if we narrowly <lb></lb>conſider it, we ſhall find that all Solid Bodies, as well thoſe that <lb></lb>ſink, as thoſe that ſwim, are indifferently accomodated and apt to <lb></lb>bring us to the knowledge of the truth in queſtion. </s><s>Nor will I <lb></lb>be frighted out of the belief of theſe Concluſions, by the Experi <lb></lb>ments which may be produced againſt me, of many ſeverall Woods, <lb></lb>Corks, Galls, and, moreover, of ſubtle ſlates and plates of all ſorts <lb></lb>of Stone and Mettall, apt by means of their Naturall Gravity, to <lb></lb>move towards the Centre of the Earth, the which, nevertheleſs, be <lb></lb>ing impotent, either through the Figure (as the Adverſaries thinke) <lb></lb>or through Levity, to break and penetrate the Continuity of the <lb></lb>parts of the water, and to diſtract its union, do continue to ſwimm <lb></lb>without ſubmerging in the leaſt: nor on the other ſide, ſhall the <lb></lb>Authority of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> move me, who in more than one place, aſſir <lb></lb>meth the contrary to this, which Experience ſhews me.</s></p><p type="main"> <s><arrow.to.target n="marg1463"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1463"></margin.target>No Solid of <lb></lb>ſuch Levity, nor <lb></lb>of ſuch Figure, <lb></lb>but that it doth <lb></lb>penetrate the <lb></lb>Craſſitude of <lb></lb>the Water.</s></p><p type="main"> <s>I return, therefore, to aſſert, that there is not any Solid of ſuch <lb></lb>Levity, nor of ſuch Figure, that being put upon the water, doth not <lb></lb>divide and penetrate its Craſſitude: yea if any with a more per <lb></lb>ſpicatious eye, ſhall return to obſerve more exactly the thin Boards <lb></lb>of Wood, he ſhall ſee them to be with part of their thickneſs under </s></p><p type="main"> <s><arrow.to.target n="marg1464"></arrow.to.target> <lb></lb>water, and not only with their inferiour Superficies, to kiſſe the <lb></lb>Superiour of the water, as they of neceſſity muſt have believed, who <lb></lb>have ſaid, that ſuch Boards ſubmerge not, as not being able to di <lb></lb>vide the Tenacity of the parts of the water: and, moreover, he <lb></lb>ſhall ſee, that ſubtle ſhivers of Ebony, Stone or Metall, when they <lb></lb>float, have not only broak the Continuity of the water, but are with <lb></lb>all their thickneſs, under the Surface of it; and more and more, <lb></lb>according as the Matters are more grave: ſo that a thin Plate of <lb></lb>Lead, ſhall be lower than the Surface of the circumfuſed water, by <lb></lb>at leaſt twelve times the thickneſs of the Plate, and Gold ſhall dive <pb pagenum="431"></pb>below the Levell of the water, almoſt twenty times the thickneſs <lb></lb>of the Plate, as I ſhall anon declare.</s></p><p type="margin"> <s><margin.target id="marg1464"></margin.target>Bodies of all <lb></lb>Figures, laid up <lb></lb>on the water, do <lb></lb>penetrate its <lb></lb>Craſſitude, and <lb></lb>in what propor <lb></lb>tion.</s></p><p type="main"> <s>But let us proceed to evince, that the water yields and ſufters it <lb></lb>ſelf to be penetrated by every the lighteſt Body; and therewithall <lb></lb>demonſtrate, how, even by Matters that ſubmerge not, we may <lb></lb>come to know that Figure operates nothing about the going or <lb></lb>not going to the Bottom, ſeeing that the water ſuffers it ſelf to be <lb></lb>penetrated equally by every Figure.</s></p><p type="main"> <s>Make a Cone, or a Piramis of Cypreſs, of Firre, or of other <lb></lb><arrow.to.target n="marg1465"></arrow.to.target> <lb></lb>Wood of like Gravity, or of pure Wax, and let its height be ſome <lb></lb>what great, namely a handfull, or more, and put it into the water <lb></lb>with the Baſe downwards: firſt, you ſhall ſee that it will penetrate <lb></lb>the water, nor ſhall it be at all impeded by the largeneſs of the Baſe, <lb></lb>nor yet ſhall it ſink all under water, but the part towards the point <lb></lb>ſhall lye above it: by which ſhall be manifeſt, firſt, that that Solid <lb></lb>forbeares not to ſink out of an inabillity to divide the Continuity <lb></lb>of the water, having already divided it with its broad part, that in <lb></lb>the opinion of the Adverſaries is the leſs apt to make the diviſion. <lb></lb></s><s>The Piramid being thus fixed, note what part of it ſhall be ſub <lb></lb>merged, and revert it afterwards with the point downwards, and <lb></lb>you ſhall ſee that it ſhall not dive into the water more than before, <lb></lb>but if you obſerve how far it ſhall ſink, every perſon expert in <lb></lb>Geometry, may meaſure, that thoſe parts that remain out of the <lb></lb>water, both in the one and in the other Experiment are equall to <lb></lb>an hair: whence he may manifeſtly conclude, that the acute Figure <lb></lb>which ſeemed moſt apt to part and penetrate the water, doth not <lb></lb>part or penetrate it more than the large and ſpacious.</s></p><p type="margin"> <s><margin.target id="marg1465"></margin.target>The Experi <lb></lb>ment of a Cone, <lb></lb>demitted with <lb></lb>its Baſe, and af <lb></lb>ter with its <lb></lb>Point down <lb></lb>wards.</s></p><p type="main"> <s>And he that would have a more eaſie Experiment, let him take <lb></lb>two Cylinders of the ſame Matter, one long and ſmall, and the o <lb></lb>ther ſhert, but very broad, and let him put them in the water, not <lb></lb>diſtended, but erect and endways: he ſhall ſee, if he diligently <lb></lb>meaſure the parts of the one and of the other, that in each of them <lb></lb>the part ſubmerged, retains exactly the ſame proportion to that <lb></lb>out of the water, and that no greater part is ſubmerged of that <lb></lb>long and ſmall one, than of the other more ſpacious and broad: <lb></lb>howbeit, this reſts upon a very large, and that upon a very little <lb></lb>Superficies of water: therefore the diverſity of Figure, occaſioneth <lb></lb>neither facility, nor difficulty, in parting and penetrating the Con <lb></lb>tinuity of the water; and, conſequently, cannot be the Cauſe of the <lb></lb>Natation or Submerſion. </s><s>He may likewiſe diſcover the non <lb></lb>operating of variety of Figures, in ariſing from the Bottom of the <lb></lb>water, towards the Surface, by taking Wax, and tempering it with <lb></lb>a competent quantity of the filings of Lead, ſo that it may become <lb></lb>a conſiderable matter graver than the water: then let him make <pb pagenum="432"></pb>it into a Ball, and thruſt it unto the Bottom of the water; and <lb></lb>faſten to it as much Cork, or other light matter, as juſt ſerveth to <lb></lb>raiſe it, and draw it towards the Surface: for afterwards changing <lb></lb>the ſame Wax into a thin Cake, or into any other Figure, that <lb></lb>ſame Cork ſhall raiſe it in the ſame manner to a hair.</s></p><p type="main"> <s>This ſilenceth not my Antagoniſts, but they ſay, that all the <lb></lb>diſcourſe hitherto made by me little importeth to them, and that it <lb></lb>ſerves their turn, that they have demonſtrated in one only parti <lb></lb>cular, and in what matter, and under what Figure pleaſeth them, <lb></lb>namely, in a Board and in a Ball of Ebony, that this put in the <lb></lb>water, deſcends to the Bottom, and that ſtays atop to ſwim: <lb></lb>and the Matter being the ſame, and the two Bodies differing in no <lb></lb>thing but in Figure, they affirm, that they have with all perſpicuity <lb></lb>demonſtrated and ſenſibly manifeſted what they undertook; and <lb></lb>laſtly, that they have obtained their intent. </s><s>Nevertheleſs, I believe, <lb></lb>and thinke, I can demonſtrate, that that ſame Experiment proveth <lb></lb>nothing againſt my Concluſion.</s></p><p type="main"> <s>And firſt, it is falſe, that the Ball deſcends, and the Board not: <lb></lb><arrow.to.target n="marg1466"></arrow.to.target> <lb></lb>for the Board ſhall alſo deſcend, if you do to both the Figures, as <lb></lb>the words of our Queſtion requireth; that is, if you put them both <lb></lb>into the water. <lb></lb><arrow.to.target n="marg1467"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1466"></margin.target>In Experi <lb></lb>ments of Nata <lb></lb>tion, the Solid <lb></lb>is to be put into, <lb></lb>not upon the <lb></lb>water.</s></p><p type="margin"> <s><margin.target id="marg1467"></margin.target>The Queſtion <lb></lb>of Natation ſta <lb></lb>ted.</s></p><p type="main"> <s><emph type="italics"></emph>The words were theſe. </s><s>That the Antagoniſts having an opinion, that <lb></lb>the Figure would alter the Solid Bodies, in relation to the deſcending <lb></lb>or not deſcending, aſcending or not aſcending in the ſame<emph.end type="italics"></emph.end> Medium, <emph type="italics"></emph>as<emph.end type="italics"></emph.end> <lb></lb>v. </s><s>gr. <emph type="italics"></emph>in the ſame water, in ſuch ſort, that, for Example, a Solid that <lb></lb>being of a Sphericall Figure, ſhall deſcend to the Bottom, being reduced <lb></lb>into ſome other Figure, ſhall not deſcend: I holding the contrary, do <lb></lb>affirm, that a Corporeall Solid Body, which reduced into a Sphericall Fi <lb></lb>gure, or any other, ſhall go to the Bottom, ſhall do the like under whatſoever <lb></lb>other Figure, &c.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>But to be in the water, implies to be placed in the water, and by </s></p><p type="main"> <s><arrow.to.target n="marg1468"></arrow.to.target> <lb></lb><emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> own Definition of place, to be placed, importeth to be in <lb></lb>vironed by the Superficies of the Ambient Body, therefore, then <lb></lb>ſhall the two Figures be in the water, when the Superficies of the <lb></lb>water, ſhall imbrace and inviron them: but when the Adverſaries <lb></lb>ſhew the Board of Ebony not deſcending to the Bottom, they put it <lb></lb>not into the water, but upon the water, where being by a certain im <lb></lb>pediment (as by and by we will ſhew) retained, it is invironed, part <lb></lb>by water, and part by air, which thing is contrary to our agreement, <lb></lb>that was, that the Bodies ſhould be in the water, and not part in <lb></lb>water, and part in air.</s></p> <pb pagenum="433"></pb><p type="margin"> <s><margin.target id="marg1468"></margin.target>Place defined <lb></lb>according to <lb></lb><emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end></s></p><p type="main"> <s><emph type="italics"></emph>The which is again made manifest, by the queſtions being put as well <lb></lb>about the things which go to the Bottom, as thoſe which ariſe from the <lb></lb>Bottom to ſwimme, and who ſees not that things placed in the Bottom, <lb></lb>muſt have water about them.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>It is now to be noted, that the Board of Ebany and the Ball, put <lb></lb><arrow.to.target n="marg1469"></arrow.to.target> <lb></lb><emph type="italics"></emph>into<emph.end type="italics"></emph.end> the water, both ſink, but the Ball more ſwiftly, and the Board <lb></lb>more ſlowly; and ſlower and ſlower, according as it ſhall be more <lb></lb>broad and thin, and of this Tardity the breadth of the Figure is the <lb></lb>true Cauſe: But theſe broad Boards that ſlowly deſcend, are the <lb></lb>ſame, that being put lightly upon the water, do ſwimm: Therefore, <lb></lb>if that were true which the Adverſaries affirm, the ſame numerical <lb></lb>Figure, would in the ſame numericall water, cauſe one while Reſt, and <lb></lb>another while Tardity of Motion, which is impoſſible: for every per <lb></lb><arrow.to.target n="marg1470"></arrow.to.target> <lb></lb>ticular Figure which deſcends to the Bottom, hath of neceſſity its own <lb></lb>determinate Tardity and ſlowneſs, proper and naturall unto it, accor <lb></lb>ding to which it moveth, ſo that every other Tardity, greater or leſſer <lb></lb>is improper to its nature: if, therefore, a Board, as ſuppoſe of a foot <lb></lb>ſquare, deſcendeth naturally with ſix degrees of Tardity, it is impoſſi <lb></lb>ble, that it ſhould deſcend with ten or twenty, unleſs ſome new impe <lb></lb>diment do arreſt it. </s><s>Much leſs can it, by reaſon of the ſame Figure <lb></lb>reſt, and wholly ceaſe to move; but it is neceſſary, that when ever it <lb></lb>reſteth, there do ſome greater impediment intervene than the breadth <lb></lb>of the Figure. </s><s>Therefore, it muſt be ſomewhat elſe, and not the Fi <lb></lb>gure, that ſtayeth the Board of Ebany above water, of which Eigure <lb></lb>the only Effect is the retardment of the Motion, according to which <lb></lb>it deſcendeth more ſlowly than the Ball. </s><s>Let it be confeſſed, there <lb></lb>fore, rationally diſcourſing, that the true and ſole Cauſe of the Ebanys <lb></lb>going to the Bottom, is the exceſs of its Gravity above the Gravity of <lb></lb>the water: and the Cauſe of the greater or leſs Tardity, the breadth <lb></lb>of this Figure, or the contractedneſs of that: but of its Reſt, it can <lb></lb>by no means be allowed, that the quallity of the Figure, is the Cauſe <lb></lb>thereof: aſwell, becauſe, making the Tardity greater, according as <lb></lb>the Figure more dilateth, there cannot be ſo immenſe a Dilatation, to <lb></lb>which there may not be found a correſpondent immence Tardity. <lb></lb></s><s>without reduſing it to Nullity of Motion; as, becauſe the Figures <lb></lb>produced by the Antagoniſts for effecters of Reſt, are the ſelf ſame <lb></lb>that do alſo go to the Bottom. <lb></lb><arrow.to.target n="marg1471"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1469"></margin.target>The conſutati <lb></lb>on of the Expe <lb></lb>riment in the <lb></lb>Ebany.</s></p><p type="margin"> <s><margin.target id="marg1470"></margin.target>Every perticular <lb></lb>Figure hath its <lb></lb>own peculiat <lb></lb>Tardity.</s></p><p type="margin"> <s><margin.target id="marg1471"></margin.target>* The Figure & <lb></lb>Reſiſtance of <lb></lb>the Medium a <lb></lb>gainſt Diviſion, <lb></lb>have nothing to <lb></lb>do with the Ef <lb></lb>fect of Natation <lb></lb>or Submerſion, <lb></lb>by an Experi <lb></lb>ment in Wall <lb></lb>nut tree,</s></p><p type="main"> <s>I will not omit another reaſon, founded alſo upon Experience, and <lb></lb>if I deceive not my ſelf, manifeſtly concluding, how that the Intro <lb></lb>ducton of the breadth or amplitude of Figure, and the Reſiſtance of <lb></lb>the water againſt penetration, have nothing to do in the Effect of de <lb></lb>ſcending, or aſcending, or reſting in the water. ^{*}Take a piece of wood <lb></lb>or other Matter, of which a Ball aſcends from the Bottom of the water <pb pagenum="434"></pb>to the Surface, more ſlowly than a Ball of Ebony of the ſame bigneſſe, <lb></lb>ſo that it is manifeſt, that the Ball of Ebony more readily divideth the <lb></lb>water in deſcending, than the other in aſcending; as for Example, let <lb></lb>the Wood be Walnut-tree. </s><s>Then take a Board of Walnut-tree, like <lb></lb>and equall to that of Ebony of the Antagoniſts, which ſwims; and if <lb></lb>it be true, that this floats above water, by reaſon of the Figure, unable <lb></lb>through its breadth, to pierce the Craſſitude of the ſame, the other of <lb></lb>Wallnut-tree, without all queſtion, being thruſt unto the Bottom, will <lb></lb>ſtay there, as leſs apt, through the ſame impediment of Figure, to di <lb></lb>vide the ſaid Reſiſtance of the water. </s><s>But if we ſhall find, and by <lb></lb>experience ſee, that not only the thin Board, but every other Figure <lb></lb>of the ſame Wallnut-tree will return to float, as undoubtedly we ſhall, <lb></lb>then I muſt deſier my oppoſers to forbear to attribute the floating of <lb></lb>the Ebony, unto the Figure of the Board, in regard that the Reſiſtance <lb></lb>of the water is the ſame, as well to the aſcent, as to the deſcent, and the <lb></lb>force of the Wallnut-trees aſcenſion, is leſſe than the Ebonys force in <lb></lb>going to the Bottom.</s></p><p type="main"> <s>Nay, I will ſay more, that if we ſhall conſider Gold in compariſon <lb></lb><arrow.to.target n="marg1472"></arrow.to.target> <lb></lb>of water, we ſhall find, that it exceeds it in Gravity almoſt twenty times, <lb></lb>ſo that the Force and Impetus, wherewith a Ball of Gold goes to the <lb></lb>Bottom, is very great. </s><s>On the contrary, there want not matters, as <lb></lb>Virgins Wax, and ſome Woods, which are not above a fiftieth part leſs <lb></lb>grave than water, whereupon their Aſcenſion therein is very ſlow, and <lb></lb>a thouſand times weaker than the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Golds deſcent: yet <lb></lb>notwithſtanding, a plate of Gold ſwims without deſcending to the <lb></lb>Bottom, and, on the contrary, we cannot make a Cake of Wax, or thin <lb></lb>Board of Wood, which put in the Bottom of the Water, ſhall reſt there <lb></lb>without aſcending. </s><s>Now if the Figure can obſtruct the Penetration, <lb></lb>and impede the deſcent of Gold, that hath ſo great an <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> how <lb></lb>can it chooſe but ſuffice to reſiſt the ſame Penetration of the other mat <lb></lb>ter in aſcending, when as it hath ſcarce a thouſandth part of the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> <lb></lb>that the Gold hath in deſcending? </s><s>Its therefore, neceſſary, that that <lb></lb>which ſuſpends the thin Plate of Gold, or Board of Ebony, upon the <lb></lb>water, be ſome thing that is wanting to the other Cakes and Boards of <lb></lb>Matters leſs grave than the water; ſince that being put to the Bottom, <lb></lb>and left at liberty, they riſe up to the Surface, without any obſtruction: <lb></lb>But they want not for flatneſs and breadth of Figure: Therefore, the <lb></lb>ſpaciouſneſſe of the Figure, is not that which makes the Gold and Ebony <lb></lb>to ſwim.</s></p><p type="margin"> <s><margin.target id="marg1472"></margin.target>An Experi <lb></lb>ment in Gold, to <lb></lb>prove the non <lb></lb>operating of Fi <lb></lb>gure in Natation <lb></lb>and Submerſion.</s></p><p type="main"> <s>And, becauſe, that the exceſs of their Gravity above the Gravity of <lb></lb>the water, is queſtionleſs the Cauſe of the ſinking of the flat piece of <lb></lb>Ebony, and the thin Plate of Gold, when they go to the Bottom, there <lb></lb>fore, of neceſſity, when they float, the Cauſe of their ſtaying above <lb></lb>water, proceeds from Levity, which in that caſe, by ſome Accident, <pb pagenum="435"></pb>peradventure not hitherto obſerved, cometh to meet with the ſaid <lb></lb>Board, rendering it no longer as it was before, whilſt it did fink more <lb></lb>ponderous than the water, but leſs.</s></p><p type="main"> <s>Now, let us return to take the thin Plate of Gold, or of Silver, or the <lb></lb>thin Board of Ebony, and let us lay it lightly upon the water, ſo that it <lb></lb>ſtay there without ſinking, and diligently obſerve its effect. </s><s>And <lb></lb>firſt, ſee how falſe the aſſertion of <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> and our oponents is, to wit, <lb></lb>that it ſtayeth above water, through its unability to pierce and pene <lb></lb>trate the Reſiſtance of the waters Craſſitude: for it will manifeſtly <lb></lb>appear, not only that the ſaid Plates have penetrated the water, but <lb></lb>alſo that they are a conſiderable matter lower than the Surface of the <lb></lb>ſame, the which continueth eminent, and maketh as it were a Rampert <lb></lb>on all ſides, round about the ſaid Plates, the profundity of which they <lb></lb>ſtay ſwimming: and, according as the ſaid Plates ſhall be more grave <lb></lb>than the water, two, four, ten or twenty times, it is neceſſary, that <lb></lb>their Superficies do ſtay below the univerſall Surface of the water, ſo <lb></lb>much more, than the thickneſs of thoſe Plates, as we ſhal more diſtinctly <lb></lb>ſhew anon. </s><s>In the mean ſpace, for the more eaſie underſtanding of what <lb></lb>I ſay, obſerve with me a little the preſent <lb></lb><figure id="fig269"></figure> <lb></lb>Scheme: in which let us ſuppoſe the Surface <lb></lb>of the water to be diſtended, according to the <lb></lb>Lines F L D B, upon which if one ſhall put a <lb></lb>board of matter ſpecifically more grave than <lb></lb>water, but ſo lightly that it ſubmetge not, it <lb></lb>ſhall not reſt any thing above, but ſhall enter with its whole thickneſs <lb></lb>into the water: and, moreover, ſhall ſink alſo, as we ſee by the Board <lb></lb>A I, O I, whoſe breadth is wholly ſunk into the water, the little Ram <lb></lb>perts of water L A and D O incompaſſing it, whoſe Superficies is no <lb></lb>tably higher than the Superficies of the Board. </s><s>See now whether it be <lb></lb>true, that the ſaid Board goes not to the Bottom, as being of Figure <lb></lb>unapt to penetrate the Craſſitude of the water.</s></p><p type="main"> <s>But, if it hath already penetrated, and overcome the Continuity of <lb></lb><arrow.to.target n="marg1473"></arrow.to.target> <lb></lb>the water, & is of its own nature more grave than the ſaid water, why <lb></lb>doth it not proceed in its ſinking, but ſtop and ſuſpend its ſelf within <lb></lb>that little dimple or cavitie, which with its ponderoſity it hath made in <lb></lb>the water? </s><s>I anſwer; becauſe that in ſubmerging it ſelf, ſo far as till its <lb></lb>Superficies come to the Levell with that of the water, it loſeth a part <lb></lb>of its Gravity, and loſeth the reſt of it as it ſubmergeth & deſcends be <lb></lb>neath the Surface of the water, which maketh Ramperts and Banks <lb></lb>round about it, and it ſuſtaines this loſs by means of its drawing after it, <lb></lb>and carrying along with it, the Air that is above it, and by Contact ad <lb></lb>herent to it, which Air ſucceeds to fill the Cavity that is invironed by <lb></lb>the Ramperts of water: ſo that that which in this caſe deſcends and is <lb></lb>placed in the water, is not only the Board of Ebony or Plate of Iron, <pb pagenum="436"></pb>but a compoſition of Ebony and Air, from which reſulteth a Solid <lb></lb>no longer ſuperiour in Gravity to the water, as was the ſimple Ebony, <lb></lb>or the ſimple Gold. </s><s>And, if we exactly conſider, what, and how <lb></lb>great the Solid is, that in this Experiment enters into the water, and <lb></lb>contraſts with the Gravity of the ſame, it will be found to be all that <lb></lb>which we find to be beneath the Surface of the water, the which is <lb></lb>an aggregate and Compound of a Board of Ebony, and of almoſt <lb></lb>the like quantity of Air, or a Maſs compounded of a Plate of Lead, <lb></lb>and ten or twelve times as much Air. </s><s>But, Genrlemen, you that <lb></lb>are my Antagoniſts in our Queſtion, we require the Identity of <lb></lb>Matter, and the alteration only of the Figure; therefore, you muſt <lb></lb>remove that Air, which being conjoyned with the Board, makes it <lb></lb>become another Body leſs grave than the Water, and put only the <lb></lb>Ebony into the Water, and you ſhall certainly ſee the Board deſcend <lb></lb>to the Bottom; and, if that do not happen, you have got the day. <lb></lb><arrow.to.target n="marg1474"></arrow.to.target> <lb></lb>And to ſeperate the Air from the Ebony, there needs no more but <lb></lb>only to bath the Superficies of the ſaid Board with the ſame Water: <lb></lb>for the Water being thus interpoſed between the Board and the Air, <lb></lb>the other circumfuſed Water ſhall run together without any impedi <lb></lb>ment, and ſhall receive into it the ſole and bare Ebony, as it was to do.</s></p><p type="margin"> <s><margin.target id="marg1473"></margin.target>Why ſolids <lb></lb>having penitra <lb></lb>ted the Water, <lb></lb>do not proceed <lb></lb>to a totail Sub <lb></lb>merſion.</s></p><p type="margin"> <s><margin.target id="marg1474"></margin.target>How to ſepe <lb></lb>rate the Air from <lb></lb>Solids in demit <lb></lb>ting them into <lb></lb>the water.</s></p><p type="main"> <s>But, me thinks I hear ſome of the Adverſaries cunningly oppoſing <lb></lb>this, and telling me, that they will not yield, by any means, that <lb></lb>their Board be wetted, becauſe the weight added thereto by the <lb></lb>Water, by making it heavier than it was before, draws it to the <lb></lb>Bottom, and that the addition of new weight is contrary to our a <lb></lb>greement, which was, that the Matter be the ſame.</s></p><p type="main"> <s>To this, I anſwer, firſt; that treating of the operation of Figure <lb></lb>in Bodies put into the Water, none can ſuppoſe them to be put into <lb></lb>the Water without being wet; nor do I deſire more to be done to <lb></lb>the Board, then I will give you leave to do to the Ball. </s><s>Moreover, <lb></lb>it is untrue, that the Board ſinks by vertue of the new Weight added <lb></lb>to it by the Water, in the ſingle and ſlight bathing of it: for I will <lb></lb>put ten or twenty drops of Water upon the ſame Board, whilſt it is <lb></lb>ſuſtained upon the water, which drops, becauſe not conjoyned with <lb></lb>the other Water circumfuſed, ſhall not ſo encreaſe the weight of it, as <lb></lb>to make it ſink: but if the Board being taken out, and all the water <lb></lb>wiped off that was added thereto, I ſhould bath all its Superficies <lb></lb>with one only very ſmall drop, and put it again upon the water, with <lb></lb>out doubt it ſhall ſink, the other Water running to cover it, not be <lb></lb>ing retained by the ſuperiour Air; which Air by the interpoſition of <lb></lb>the thin vail of water, that takes away its Contiguity unto the Ebony, <lb></lb>ſhall without Renitence be ſeperated, nor doth it in the leaſt oppoſe <lb></lb>the ſucceſſion of the other Water: but rather, to ſpeak better, it <lb></lb>ſhall deſcend freely; becauſe it ſhall be all invironed and covered <pb pagenum="437"></pb>with water, as ſoon as its ſuperiour Superficies, before vailed with <lb></lb>water, doth arrive to the Levell of the univerſall Surface of the ſaid <lb></lb>water. </s><s>To ſay, in the next place, that water can encreaſe the weight <lb></lb><arrow.to.target n="marg1475"></arrow.to.target> <lb></lb>of things that are demitted into it, is moſt falſe, for water hath no <lb></lb>Gravity in water, ſince it deſcends not: yea, if we would well conſi <lb></lb>der what any immenſe Maſs of water doth put upon a grave Body; <lb></lb><arrow.to.target n="marg1476"></arrow.to.target> <lb></lb>that is placed in it, we ſhall find experimentally, that it, on the con <lb></lb>trary, will rather in a great part deminiſh the weight of it, and that <lb></lb>we may be able to lift an huge Stone from the Bottom of the water, <lb></lb>which the water being removed, we are not able to ſtir. </s><s>Nor let <lb></lb>them tell me by way of reply, that although the ſuperpoſed water <lb></lb>augment not the Gravity of things that are in it, yet it increaſeth the <lb></lb>ponderoſity of thoſe that ſwim, and are part in the water and part <lb></lb><arrow.to.target n="marg1477"></arrow.to.target> <lb></lb>in the Air, as is ſeen, for Example, in a Braſs Ketle, which whilſt it <lb></lb>is empty of water, and repleniſhed only with Air ſhall ſwim, but <lb></lb>pouring of Water therein, it ſhall become ſo grave, that it ſhall ſink <lb></lb>to the Bottom, and that by reaſon of the new weight added thereto. <lb></lb></s><s>To this I will return anſwer, as above, that the Gravity of the <lb></lb>Water, contained in the Veſſel is not that which ſinks it to the Bot <lb></lb>tom, but the proper Gravity of the Braſs, ſuperiour to the Specificall <lb></lb><arrow.to.target n="marg1478"></arrow.to.target> <lb></lb>Gravity of the Water: for if the Veſſel were leſs grave than <lb></lb>water, the Ocean would not ſuffice to ſubmerge it. </s><s>And, give me <lb></lb>leave to repeat it again, as the fundamentall and principall point in <lb></lb>this Caſe, that the Air contained in this Veſſel before the infuſion of <lb></lb>the Water, was that which kept it a-float, ſince that there was made <lb></lb><arrow.to.target n="marg1479"></arrow.to.target> <lb></lb>of it, and of the Braſs, a Compoſition leſs grave than an equall quanti <lb></lb>ty of Water: and the place that the Veſſel occupyeth in the <lb></lb>Water whilſt it floats, is not equall to the Braſs alone, but to the <lb></lb>Braſs and to the Air together, which filleth that part of the Veſſel <lb></lb>that is below the Levell of the water: Moreover, when the Water <lb></lb>is infuſed, the Air is removed, and there is a compoſition made of <lb></lb>Braſs and of water, more grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than the ſimple water, but <lb></lb>not by vertue of the water infuſed, as having greater Specifick <lb></lb>Gravity than the other water, but through the proper Gravity of <lb></lb>the Braſs, and through the alienation of the Air. </s><s>Now, as he that <lb></lb>ſhould ſay that Braſs, that by its nature goes to the Bottom, being <lb></lb><arrow.to.target n="marg1480"></arrow.to.target> <lb></lb>formed into the Figure of a Ketle, acquireth from that Figure a <lb></lb>vertue of lying in the Water without ſinking, would ſay that which <lb></lb>is falſe; becauſe that Braſs faſhioned into any whatever Figure, <lb></lb>goeth always to the Bottom, provided, that that which is put into the <lb></lb>water be ſimple Braſs; and it is not the Figure of the Veſſel that <lb></lb>makes the Braſs to float, but it is becauſe that that is not purely <lb></lb>Braſs which is put into the water, but an aggregate of Braſs and of <lb></lb>Air: ſo is it neither more nor leſs falſe, that a thin Plate of Braſs <pb pagenum="438"></pb>or of Ebony, ſwims by vertue of its dilated & broad Figure: for the <lb></lb>truth is, that it bares up without ſubmerging, becauſe that that which <lb></lb>is put in the water, is not pure Braſs or ſimple Ebony, but an ag <lb></lb>gregate of Braſs and Air, or of Ebony and Air. </s><s>And, this is not <lb></lb>contrary unto my Concluſion, the which, (having many a time ſeen <lb></lb>Veſſels of Mettall, and thin pieces of diverſe grave Matters float, by <lb></lb>vertue of the Air conjoyned with them) did affirm, That Figure <lb></lb>was not the Cauſe of the Natation or Submerſion of ſuch Solids as <lb></lb>were placed in the water. </s><s>Nay more, I cannot omit, but muſt tell <lb></lb>my Antagoniſts, that this new conceit of denying that the Superfi <lb></lb>cies of the Board ſhould be bathed, may beget in a third perſon an <lb></lb>opinion of a poverty of Arguments of defence on their part, ſince <lb></lb>that ſuch bathing was never inſiſted upon by them in the beginning <lb></lb>of our Diſpute, and was not queſtioned in the leaſt, being that the <lb></lb>Originall of the diſcourſe aroſe upon the ſwiming of Flakes of Ice, <lb></lb>wherein it would be ſimplicity to require that their Superficies might <lb></lb>bedry: beſides, that whether theſe pieces of Ice be wet or dry they <lb></lb>alwayes ſwim, and as the Adverſaries ſay, by reaſon of the Figure. </s></p><p type="margin"> <s><margin.target id="marg1475"></margin.target>Water hath <lb></lb>no Gravity in <lb></lb>Water.</s></p><p type="margin"> <s><margin.target id="marg1476"></margin.target>Water de <lb></lb>miniſheth the <lb></lb>Gravity of So <lb></lb>lids immerged <lb></lb>therein.</s></p><p type="margin"> <s><margin.target id="marg1477"></margin.target>The Experi <lb></lb>ment of a Braſs <lb></lb>Ketle ſwiming <lb></lb>when empty, & <lb></lb>ſinking when <lb></lb>full, alledged to <lb></lb>prove that water <lb></lb>gravitates in <lb></lb>water, anſwered.</s></p><p type="margin"> <s><margin.target id="marg1478"></margin.target>An Ocean ſuf <lb></lb>ficeth not to <lb></lb>ſink a Veſſel ſpe <lb></lb>cifically leſs <lb></lb>grave than wa <lb></lb>ter.</s></p><p type="margin"> <s><margin.target id="marg1479"></margin.target>Air, the Cauſe <lb></lb>of the Natation <lb></lb>of empty Veſſels <lb></lb>of Matters gra <lb></lb>ver <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than <lb></lb>the water.</s></p><p type="margin"> <s><margin.target id="marg1480"></margin.target>Neither Figure, <lb></lb>nor the breadth <lb></lb>of Figure, is the <lb></lb>Cauſe of Nata <lb></lb>tion.</s></p><p type="main"> <s>Some peradventure, by way of defence, may ſay, that wetting the <lb></lb>Board of Ebony, and that in the ſuperiour Superficies, it would, <lb></lb>though of it ſelf unable to pierce and penetrate the water, be born <lb></lb>downwards, if not by the weight of the additionall water, at leaſt <lb></lb>by that deſire and propenſion that the ſuperiour parts of the water <lb></lb>have to re-unite and rejoyn themſelves: by the Motion of which <lb></lb>parts, the ſaid Board cometh in a certain manner, to be depreſſed <lb></lb>downwards. <lb></lb><arrow.to.target n="marg1481"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1481"></margin.target>The Bathed <lb></lb>Solid deſcends <lb></lb>not out of any <lb></lb>affectation of u <lb></lb>nion in the upper <lb></lb>parts of the wa <lb></lb>ter.</s></p><p type="main"> <s>This weak Refuge will be removed, if we do but conſider, that <lb></lb>the repugnancy of the inferiour parts of the water, is as great against <lb></lb>Diſ-union, as the Inclination of its ſuperiour parts is to union: nor can <lb></lb>the uper unite themſelves without depreſſing the board, nor can it <lb></lb>deſcend without diſuniting the parts of the nether Water: ſo that <lb></lb>it doth follow, by neceſſary conſequence, that for thoſe reſpects, it ſhall <lb></lb>not deſcend. </s><s>Moreover, the ſame that may be ſaid of the upper <lb></lb>parts of the water, may with equall reaſon be ſaid of the nethe, <lb></lb>namely, that deſiring to unite, they ſhall force the ſaid Board <lb></lb>upwards.</s></p><p type="main"> <s>Happily, ſome of theſe Gentlemen that diſſent from me, will won <lb></lb>der, that I affirm, that the contiguous ſuperiour Air is able to ſuſtain <lb></lb>that Plate of <emph type="italics"></emph>B<emph.end type="italics"></emph.end>raſs or of Silver, that ſtayeth above water; as if I <lb></lb><arrow.to.target n="marg1482"></arrow.to.target> <lb></lb>would in a certain ſence allow the Air, a kind of Magnetick vertue <lb></lb>of ſuſtaining the grave <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies, with which it is contiguous. </s><s>To ſa <lb></lb>tisſie all I may, to all doubts, I have been conſidering how by ſome <lb></lb>other ſenſible Experiment I might demonſtrate, how truly that little <lb></lb>contiguous and ſuperiour Air ſuſtaines thoſe Solids, which being by <pb pagenum="439"></pb>nature apt to deſcend to the Bottom, being placed lightly on the water <lb></lb>ſubmerge not, unleſs they be firſt thorowly bathed; and have found, <lb></lb>that one of theſe Bodies having deſcended to the Bottom, by conveigh <lb></lb>ing to it (without touching it in the leaſt) a little Air, which conjoyneth <lb></lb>with the top of the ſame; it becometh ſufficient, not only, as before to <lb></lb>ſuſtain it, but alſo to raiſe it, and to carry it back to the top, where it <lb></lb>ſtays and abideth in the ſame manner, till ſuch time, as the aſſiſtance <lb></lb>of the conjoyned Air is taken away. </s><s>And to this effect, I have taken a <lb></lb>Ball of Wax, and made it with a little Lead, ſo grave, that it leaſurely <lb></lb>deſcends to the Bottom, making with all its Superficies very ſmooth and <lb></lb>pollite: and this being put gently into the water, almoſt wholly ſub <lb></lb><arrow.to.target n="marg1483"></arrow.to.target> <lb></lb>mergeth, there remaining viſſible only a little of the very top, the which <lb></lb>solong as it is conjoyned with the Air, ſhall retain the Ball a-top, but <lb></lb>the Contiguity of the Air taken away by wetting it, it ſhall deſcend to <lb></lb>the Bottom and there remain. </s><s>Now to make it by vertue of the Air, that <lb></lb>before ſuſtained it to return again to the top, and ſtay there, thruſt into <lb></lb>the water a Glaſs reverſed with the mouth downwards, the which ſhall <lb></lb>carry with it the Air it contains, and move this towards the Ball, abaſing <lb></lb>it till ſuch time that you ſee, by the tranſparency of the Glaſs, that the <lb></lb><arrow.to.target n="marg1484"></arrow.to.target> <lb></lb>contained Air do arrive to the ſummity of the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all: then gently with <lb></lb>draw the Glaſs upwards, and you ſhall ſee the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>all to riſe, and afterwards <lb></lb><arrow.to.target n="marg1485"></arrow.to.target> <lb></lb>stay on the top of the water, if you carefully part the Glaſs and the water <lb></lb>without overmuch commoving and diſturbing it. </s><s>There is, therefore, a <lb></lb>certain affinity between the Air and other <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies, which holds them uni <lb></lb>ed, ſo, that they ſeperate not without a kind of violence. </s><s>The ſame <lb></lb><arrow.to.target n="marg1486"></arrow.to.target> <lb></lb>likewiſe is ſeen in the water; for if we ſhall wholly ſubmerge ſome <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ody <lb></lb>in it, ſo that it be thorowly bathed, in the drawing of it afterwards gent <lb></lb>ly out again, we ſhall ſee the water follow it, and riſe notably above its <lb></lb>Surface, before it ſeperates from it. </s><s>Solid <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies, alſo, if they be equall <lb></lb><arrow.to.target n="marg1487"></arrow.to.target> <lb></lb>and alike in Superficies, ſo, that they make an exact Contact without <lb></lb>the interpoſition of the leaſt Air, that may part them in the ſeperation <lb></lb>and yield untill that the ambient <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> ſucceeds to repleniſh the place, <lb></lb>do hold very firmly conjoyned, and are not to be ſeperated without great <lb></lb>force but, becauſe, the Air, Water, and other Liquids, very expedi <lb></lb>tiouſly ſhape themſelves to contact with any Solid <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies, ſo that their <lb></lb>Superficies do exquiſitely adopt themſelves to that of the Solids, without <lb></lb>any thing remaining between them, therefore, the effect of this Con <lb></lb>junction and Adherence is more manifeſtly and frequently obſerved in <lb></lb>them, than in hard and inflexible <emph type="italics"></emph>B<emph.end type="italics"></emph.end>odies, whoſe Superficies do very rate <lb></lb>ly conjoyn with exactneſs of Contact. </s><s>This is therefore that Magne <lb></lb><arrow.to.target n="marg1488"></arrow.to.target> <lb></lb>tick vertue, which with firm Connection conjoyneth all Bodies, that do <lb></lb>touch without the interpoſition of flexible fluids; and, who knows, but <lb></lb>that that a Contact, when it is very exact, may be a ſufficient Cauſe of <lb></lb>the Union and Continuity of the parts of a naturall <emph type="italics"></emph>B<emph.end type="italics"></emph.end>ody?</s></p> <pb pagenum="440"></pb><p type="margin"> <s><margin.target id="marg1482"></margin.target><emph type="italics"></emph>A<emph.end type="italics"></emph.end> Magnetiſme in <lb></lb>the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ir, by which <lb></lb>it bears up thoſe <lb></lb>Solids in the wa <lb></lb>ter, that are con <lb></lb>tiguous with it.</s></p><p type="margin"> <s><margin.target id="marg1483"></margin.target>The Effect of <lb></lb>the Airs Conti <lb></lb>guity in the Na <lb></lb>tation of Solids.</s></p><p type="margin"> <s><margin.target id="marg1484"></margin.target>The force of <lb></lb>Contact.</s></p><p type="margin"> <s><margin.target id="marg1485"></margin.target><emph type="italics"></emph>A<emph.end type="italics"></emph.end>n affectati <lb></lb>on of Conjunct <lb></lb>ion betwixt So <lb></lb>lids and the Air <lb></lb>contiguous to <lb></lb>them.</s></p><p type="margin"> <s><margin.target id="marg1486"></margin.target>The like affect <lb></lb>ation of Con <lb></lb>junction be <lb></lb>twixt Solids & <lb></lb>the water.</s></p><p type="margin"> <s><margin.target id="marg1487"></margin.target>Alſo the like <lb></lb>affectation and <lb></lb>Conjunction be <lb></lb>twixt Solids <lb></lb>themſeives.</s></p><p type="margin"> <s><margin.target id="marg1488"></margin.target>Contact may <lb></lb>be the Cauſe of <lb></lb>the Continuity <lb></lb>of Naturall Bo <lb></lb>dies.</s></p><p type="main"> <s>Now, purſuing my purpoſe, I ſay; that it needs not, that we have <lb></lb>recourſe to the Tenacity, that the parts of the water have amongſt them <lb></lb>ſelves, by which they reſiſt and oppoſe Diviſion, Diſtraction, and Seper <lb></lb>ration, becauſe there is no ſuch Coherence and Reſiſtance of Diviſion <lb></lb>for if there were, it would be no leſs in the internall parts than in thoſe <lb></lb>nearer the ſuperiour or externall Surface, ſo that the ſame Board, find <lb></lb>ing alwayes the ſame Reſiſtance and Renitence, would no leſs ſtop in <lb></lb>the middle of the water than about the Surface, which is falſe. More <lb></lb></s><s>over, what Reſiſtance can we place in the Continuity of the water <lb></lb>if we ſee that it is impoſſible to ſind any Body of whatſoever Matter <lb></lb>Figure or Magnitude, which being put into the water, ſhall be obſtructed <lb></lb>and impeded by the Tenacity of the parts of the water to one another <lb></lb>ſo, but that it is moved upwards or downwards, according as the Cauſe <lb></lb>of their Motion tranſports it? </s><s>And, what greater proof of it can we de <lb></lb>ſier, than that which we daily ſee in Muddy waters, which being put into <lb></lb>Veſſels to be drunk, and being, after ſome hours ſetling, ſtill, as we ſay <lb></lb><arrow.to.target n="marg1489"></arrow.to.target> <lb></lb>thick in the end, after four or ſix dayes they are wholly ſetled, and be <lb></lb>come pure and clear? </s><s>Nor can their Reſiſtance of Penetration ſtay thoſe <lb></lb>impalpable and inſenſible Atomes of Sand, which by reaſon of their <lb></lb>exceeding ſmall force, ſpend ſix dayes in deſcending the ſpace of half <lb></lb>a yard.</s></p><p type="margin"> <s><margin.target id="marg1489"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he ſettlement <lb></lb>of <emph type="italics"></emph>M<emph.end type="italics"></emph.end>uddy Wa <lb></lb>ter, proveth that <lb></lb>that Element <lb></lb>hath no averſi <lb></lb>on to Diviſion.</s></p><p type="main"> <s><emph type="italics"></emph>Nor let them ſay, that the ſeeing of ſuch ſmall Bodies, conſume ſix dayes in <lb></lb>deſcending ſo little a way, is a ſufficient Argument of the Waters Reſiſtance <lb></lb>of Diviſion; becauſe that is no reſiſting of Diviſion, but a retarding of<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1490"></arrow.to.target> <lb></lb><emph type="italics"></emph>Motion; and it would be ſimplicity to ſay, that a thing oppoſeth Diviſion <lb></lb>and that in the ſame inſtant, it permits it ſelf to be divided: nor doth the <lb></lb>Retardation of Motion at all favour the Adverſaries cauſe, for that they are <lb></lb>to inſtance in a thing that wholly prohibiteth Motion, and procureth Reſt; <lb></lb>it is neceſſary, therefore, to find out Bodies that ſtay in the water, if one would <lb></lb>ſhew its repugnancy to Diviſion, and not ſuch as move in it, howbeit <lb></lb>ſlowly.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1490"></margin.target>Water cannot <lb></lb>oppoſe diviſion, <lb></lb>and at the ſame <lb></lb>time permit it <lb></lb>ſelf to be divi <lb></lb>ded.</s></p><p type="main"> <s>What then is this Craſſitude of the water, with which it reſiſteth Di <lb></lb>viſion? </s><s>What, I beſeech you, ſhould it be, if we (as we have ſaid above) <lb></lb>with all diligence attempting the reduction of a Matter into ſo like a <lb></lb>Gravity with the water, that forming it into a dilated Plate it reſts ſuſ <lb></lb>pended as we have ſaid, between the two waters, it be impoſſible to <lb></lb>effect it, though we bring them to ſuch an Equiponderance, that as <lb></lb>much Lead as the fourth part of a Grain of Muſterd-ſeed, added to the <lb></lb>ſame expanded Plate, that in Air [<emph type="italics"></emph>i. </s><s>e. </s><s>out of the water<emph.end type="italics"></emph.end>] ſhall weigh four <lb></lb>or fix pounds, ſinketh it to the Bottom, and being ſubſtracted, it aſcends <lb></lb>to the Surface of the water? </s><s>I cannot ſee, (if what I ſay be true, as it is <lb></lb>moſt certain) what minute vertue and force we can poſſibly find or ima <lb></lb>gine, to which the Reſiſtance of the water againſt Diviſion and Penetra <pb pagenum="441"></pb>tion is not inferiour; whereupon, we muſt of neceſſity conclude <lb></lb>that it is nothing: becanſe, if it were of any ſenſible power, ſome <lb></lb>large Plate might be found or compounded of a Matter alike in Gra <lb></lb>vity to the water, which not only would ſtay between the two wa <lb></lb>ters; but, moreover, ſhould not be able to deſcend or aſcend with <lb></lb>out notable force. </s><s>We may likewiſe collect the ſame from an o <lb></lb><arrow.to.target n="marg1491"></arrow.to.target> <lb></lb>ther Experiment, ſhewing that the Water gives way alſo in the ſame <lb></lb>manner to tranſverſall Diviſion; for if in a ſetled and ſtanding water <lb></lb>we ſhould place any great Maſs that goeth not to the bottom, draw <lb></lb>ing it with a ſingle (Womans) Hair, we might carry it from place to <lb></lb>place without any oppoſition, and this whatever Figure it hath, <lb></lb>though that it poſſeſs a great ſpace of water, as for inſtance, a great <lb></lb>Beam would do moved ſide-ways. </s><s>Perhaps ſome might oppoſe me <lb></lb>and ſay, that if the Reſiſtance of water againſt Diviſion, as I affirm, <lb></lb>were nothing; Ships ſhould not need ſuch a force of Oars and Sayles <lb></lb>for the moving of them from place to place in a tranquile Sea, or <lb></lb>ſtanding Lake. </s><s>To him that ſhould make ſuch an objection, I would <lb></lb><arrow.to.target n="marg1492"></arrow.to.target> <lb></lb>reply, that the water contraſteth not againſt, nor ſimply reſiſteth <lb></lb>Diviſion, but a ſudden Diviſion, and with ſo much greater Reni <lb></lb>tence, by how much greater the Velocity is: and the Cauſe of this <lb></lb>Reſiſtance depends not on Craſſitude, or any other thing that abſo <lb></lb>lutely oppoſeth Diviſion, but becauſe that the parts of the water <lb></lb>divided, in giving way to that Solid that is moved in it, are them <lb></lb>ſelves alſo neceſſitated locally to move, ſome to the one ſide, and ſome <lb></lb>to the other, and ſome downwards: and this muſt no leſs be done <lb></lb>by the waves before the Ship, or other Body ſwimming through the <lb></lb>water, than by the poſteriour and ſubſequent; becauſe, the Ship <lb></lb>proceeding forwards, to make it ſelf a way to receive its Bulk, it is <lb></lb>requiſite, that with the Prow it repulſe the adjacent parts of the <lb></lb>water, as well on one hand as on the other, and that it move them <lb></lb>as much tranſverſly, as is the half of the breadth of the Hull: and <lb></lb>the like removall muſt thoſe waves make, that ſucceeding the Poump <lb></lb>do run from the remoter parts of the Ship towards thoſe of the <lb></lb>middle, ſucceſſively to repleniſh the places, which the Ship in ad <lb></lb>vancing forwards, goeth, leaving vacant. </s><s>Now, becauſe, all Moti <lb></lb><arrow.to.target n="marg1493"></arrow.to.target> <lb></lb>tions are made in Time, and the longer in greater time: and it being <lb></lb>moreover true, that thoſe Bodies that in a certain time are moved <lb></lb>by a certain power ſuch a certain ſpace, ſhall not be moved the ſame <lb></lb>ſpace, and in a ſhorter Time, unleſs by a greater Power: therefore, <lb></lb>the broader Ships move ſlower than the narrower, being put on by <lb></lb>an equall Force: and the ſame Veſſel requires ſo much greater <lb></lb>force of Wind, or Oars, the faſter it is to move.</s></p> <pb pagenum="442"></pb><p type="margin"> <s><margin.target id="marg1491"></margin.target>An hair will <lb></lb>draw a great <lb></lb>Maſs thorow the <lb></lb>Water; which <lb></lb>proveth, that it <lb></lb>hath no Reſiſt <lb></lb>ance againſt <lb></lb>tranſverſall Di <lb></lb>viſion.</s></p><p type="margin"> <s><margin.target id="marg1492"></margin.target>How ſhips are <lb></lb>moved in the <lb></lb>water.</s></p><p type="margin"> <s><margin.target id="marg1493"></margin.target>Bodies moved <lb></lb>a certain ſpace in <lb></lb>a certain Time, <lb></lb>by a certain <lb></lb>power, cannot be <lb></lb>moved the <lb></lb>ſame ſpace, and <lb></lb>in a ſhorter time, <lb></lb>but by a greater <lb></lb>power.</s></p><p type="main"> <s><emph type="italics"></emph>But yet for all this, any great Maſs ſwimming in a ſtanding Lake, may <lb></lb>be moved by any petit force; only it is true, that a leſſer force more <lb></lb>ſlowly moves it: but if the waters Reſiſtance of Diviſion, were in any <lb></lb>manner ſenſible, it would follow, that the ſaid Maſs, ſhould, notwith <lb></lb>ſtanding the percuſſion of ſome ſenſible force, continue immoveable, which is<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1494"></arrow.to.target> <lb></lb><emph type="italics"></emph>not ſo. </s><s>Yea, I will ſay farther, that ſhould we retire our ſelves into the <lb></lb>more internall contemplation of the Nature of water and other Fluids, <lb></lb>perhaps we ſhould diſcover the Conſtitution of their parts to be ſuch, that <lb></lb>they not only do not oppoſe Diviſion, but that they have not any thing in <lb></lb>them to be divided: ſo that the Reſiſtance that is obſerved in moving<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1495"></arrow.to.target> <lb></lb><emph type="italics"></emph>through the water, is like to that which we meet with in paſſing through <lb></lb>a great Throng of People, wherein we find impediment, and not by any <lb></lb>difficulty in the Diviſion, for that none of thoſe perſons are divided <lb></lb>whereof the Croud is compoſed, but only in moving of thoſe perſons ſide <lb></lb>ways which were before divided and disjoyned: and thus we find <lb></lb>Reſiſtance in thruſting a Stick into an heap of Sand, not becauſe any part <lb></lb>of the Sand is to be cut in pieces, but only to be moved and raiſed. two <emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1496"></arrow.to.target> <lb></lb><emph type="italics"></emph>manners of Penetration, therefore, offer themſelves to us, one in Bodies, <lb></lb>whoſe parts were continuall, and here Diviſion ſeemeth neceſſary; the <emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1497"></arrow.to.target> <lb></lb><emph type="italics"></emph>other in the aggregates of parts not continuall, but contiguous only, and <lb></lb>here there is no neceſſity of dividing but of moving only. </s><s>Now, I am <lb></lb>not well reſolved, whether water and other Fluids may be eſteemed to <lb></lb>be of parts continuall or contiguous only; yet I find my ſelf indeed incli<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1498"></arrow.to.target> <lb></lb><emph type="italics"></emph>ned to think that they are rather contiguous (if there be in Naturno <lb></lb>other manner of aggregating, than by the union, or by the touching of the <lb></lb>extreams:) and I am induced thereto by the great difference that I ſee > <lb></lb>between the Conjunction of the parts of an hard or Solid Body, and the<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1499"></arrow.to.target> <lb></lb><emph type="italics"></emph>Conjunction of the ſame parts when the ſame Body ſhall be made Liquid <lb></lb>and Fluid: for if, for example, I take a Maſs of Silver or other Solid <lb></lb>and hard Mettall, I ſhall in dividing it into two parts, find not only the <emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1500"></arrow.to.target> <lb></lb><emph type="italics"></emph>reſiſtance that is found in the moving of it only, but an other incomparably <lb></lb>greater, dependent on that vertue, whatever it be, which holds the parts <lb></lb>united: and ſo if we would divide again thoſe two parts into other two <lb></lb>and ſucceſſively into others and others, we ſhould ſtill find a like Reſiſt <lb></lb>ance, but ever leſs by how much ſmaller the parts to be divided ſhall be; <lb></lb>but if, laſtly, employing moſt ſubtile and acute Inſtruments, ſuch as are <lb></lb>the moſt tenuous parts of the Fire, we ſhall reſolve it (perhaps) into its <lb></lb>laſt and leaſt Particles, there ſhall not be left in them any longer either <lb></lb>Reſiſtance of Diviſion, or ſo much as a capacity of being farther divi <lb></lb>ded, eſpecially by Inſtruments more groſſe than the acuities of Fire: and <lb></lb>what Knife or Raſor put into well melted Silver can we finde, that will <lb></lb>divide a thing which ſurpaſſeth the ſeparating power of Fire? </s><s>Certainly <lb></lb>none: becauſe either the whole ſhall be reduced to the moſt minute and <lb></lb>ultimate Diviſions, or if there remain parts capable ſtill of other Suddi<emph.end type="italics"></emph.end> <pb pagenum="443"></pb><emph type="italics"></emph>diviſions, they cannot receive them, but only from acuter Diviſors than <lb></lb>Fire; but a Stick or Rod of Iron, moved in the melted Met all, is not <lb></lb>ſuch a one. </s><s>Of a like Conſtitution and Conſiſtence, I account the parts<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1501"></arrow.to.target> <lb></lb><emph type="italics"></emph>of Water, and other Liquids to be, namely, incapable of Diviſion by <lb></lb>reaſon of their Temtity; or if not abſolutely indiviſible, yet at leaſt <lb></lb>not to be divided by a Board, or other Solid Body, palpable unto the <lb></lb>band, the Sector being alwayes required to be more ſharp than the Solid <lb></lb>to be cut. </s><s>Solid Bodies, therefore, do only move, and not divide the<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1502"></arrow.to.target> <lb></lb><emph type="italics"></emph>Water, when put into it; whoſe parts being before divided to the ex <lb></lb>treameſt minuity, and therefore capable of being moved, either many of <lb></lb>them at once, or few, or very few, they ſoon give place to every ſmall Cor <lb></lb>puſcle, that deſcends in the ſame: for that, it being little and light, de <lb></lb>ſcending in the Air, and arriving to the Surface of the Water, it meets <lb></lb>with Particles of Water more ſmall, and of leſs Reſiſtance againſt <lb></lb>Motion and Extruſion, than is its own prement and extruſive force, <lb></lb>whereupon it ſubmergeth, and moveth ſuch a portion of them, as is pro <lb></lb>portionate to its Power. </s><s>There is not, therefore, any Reſiſtance in <lb></lb>Water againſt Diviſion, nay, there is not in it any diviſible parts. </s><s>I <lb></lb>adde, moreover, that in caſe yet there ſbould be any ſmall Reſiſtance<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1503"></arrow.to.target> <lb></lb><emph type="italics"></emph>found (which is abſolutely falſe) haply in attempting with an Hair to <lb></lb>move a very great natant Machine, or in eſſaying by the addition of one <lb></lb>ſmall Grain of Lead to ſink, or by removall of it to raiſe a very broad <lb></lb>Plate of Matter, equall in Gravity with Water, (which likewiſe will <lb></lb>not happen, in caſe we proceed with dexterity) we may obſerve that that <lb></lb>Reſiſtance is a very different thing from that which the Adverſaries pro <lb></lb>duce for the Cauſe of the Natation of the Plate of Lead or Board of Ebo <lb></lb>ny, for that one may make a Board of Ebony, which being put upon the <lb></lb>Water ſwimmeth, and cannot be ſubmerged, no not by the addition of an <lb></lb>bundred Grains of Lead put upon the ſame, and afterwards being ba <lb></lb>thed, not only ſinks, though the ſaid Lead be taken away, but though <lb></lb>moreover a quantity of Cork, or of ſome other light Body faſtened to it, <lb></lb>ſufficeth not to hinder it from ſinking unto the bottome: ſo that you <lb></lb>ſee, that although it were granted that there is a certain ſmall Reſiſt <lb></lb>ance of Diviſion found in the ſubstance of the Water, yet this hath no <lb></lb>thing to do with that Cauſe which ſupports the Board above the Water, <lb></lb>with a Reſiſtance an hundred times greater than that which men can <lb></lb>find in the parts of the Water: nor let them tell me, that only the Sur-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1504"></arrow.to.target> <lb></lb><emph type="italics"></emph>face of the Water hath ſuch Reſiſtance, and not the internall parts, or <lb></lb>that ſuch Reſiſtance is found greateſt in the beginning of the Submerſion, <lb></lb>as it alſo ſeems that in the beginning, Motion meets with greater oppoſiti <lb></lb>on, than in the continuance of it; becauſe, firſt, I will permit, that the<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1505"></arrow.to.target> <lb></lb><emph type="italics"></emph>Water be ſtirred, and that the ſuperiour parts be mingled with the mid <lb></lb>dle, and inferiour parts, or that thoſe above be wholly removed, and <lb></lb>thoſe in the middle only made uſe off, and yet you ſhall ſee the effect for<emph.end type="italics"></emph.end> <pb pagenum="444"></pb><emph type="italics"></emph>all that, to be still the ſame: Moreover, that Hair which draws a <lb></lb>Beam through the Water, is likewiſe to divide the upperparts, and is <lb></lb>alſo to begin the Motion, and yet it begins it, and yet it divides it: and <lb></lb>finally, let the Board of Ebony be put in the midway, betwixt the bottome <lb></lb>and the top of the Water, and let it there for a while be ſuſpended and <lb></lb>ſetled, and afterwards let it be left at liberty, and it will instantly begin <lb></lb>its Motion, and will continue it unto the bottome. </s><s>Nay, more, the Board <lb></lb>ſo ſoon as it is dimitted upon the Water, hath not only begun to move <lb></lb>and divide it, but is for a good ſpace dimerged into it.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1494"></margin.target>The parts of <lb></lb>Liquids, ſo farte <lb></lb>from reſiſting <lb></lb>Diviſion, that <lb></lb>they contain not <lb></lb>any thing that <lb></lb>may be divided.</s></p><p type="margin"> <s><margin.target id="marg1495"></margin.target>The Reſiſt <lb></lb>ance a Solid <lb></lb>findeth in mo <lb></lb>ving through <lb></lb>the water, like <lb></lb>to that we meet <lb></lb>with in paſſing <lb></lb>through a <lb></lb>throng of peo <lb></lb>ple;</s></p><p type="margin"> <s><margin.target id="marg1496"></margin.target>Or in thruſt <lb></lb>ing a Stick into <lb></lb>an heap of Sand.</s></p><p type="margin"> <s><margin.target id="marg1497"></margin.target>Two kinds of <lb></lb>Penetration, one <lb></lb>in Bodies conti <lb></lb>nuall, the other <lb></lb>in Bodies only <lb></lb>contiguous.</s></p><p type="margin"> <s><margin.target id="marg1498"></margin.target>Water conſiſts <lb></lb>not of continu <lb></lb>all, but only <lb></lb>of contiguous <lb></lb>parts.</s></p><p type="margin"> <s><margin.target id="marg1499"></margin.target><emph type="italics"></emph>Set what ſatis <lb></lb>faction he hath <lb></lb>given, as to this <lb></lb>point, in Lib. de <lb></lb>Motu. </s><s>Dial.<emph.end type="italics"></emph.end> 2.</s></p><p type="margin"> <s><margin.target id="marg1500"></margin.target>Great differ <lb></lb>ence betwixt the <lb></lb>Conjunction of <lb></lb>the parts of a Bo <lb></lb>dy when Solid, <lb></lb>and when fluid.</s></p><p type="margin"> <s><margin.target id="marg1501"></margin.target>Water conſiſts <lb></lb>of parts that ad <lb></lb>mit of no fat <lb></lb>ther diviſion.</s></p><p type="margin"> <s><margin.target id="marg1502"></margin.target>Solids dimit <lb></lb>ted into the wa <lb></lb>ter, do onely <lb></lb>move, and not <lb></lb>divide it.</s></p><p type="margin"> <s><margin.target id="marg1503"></margin.target>If there were <lb></lb>any Reſiſtance <lb></lb>of Diviſion in <lb></lb>water, it muſt <lb></lb>needs be ſmall, <lb></lb>in that it is over <lb></lb>come by an <lb></lb>Hair, a Grain of <lb></lb>Lead, or a ſlight <lb></lb>bathing of the <lb></lb>Solid.</s></p><p type="margin"> <s><margin.target id="marg1504"></margin.target>The uper parts <lb></lb>of the Water, do <lb></lb>no more reſiſt <lb></lb>Diviſion, than <lb></lb>the middle or <lb></lb>loweſt parts.</s></p><p type="margin"> <s><margin.target id="marg1505"></margin.target>Waters Re <lb></lb>ſiſtance of divi <lb></lb>ſion, not greater <lb></lb>in the begin <lb></lb>ning of the Sub <lb></lb>merſion.</s></p><p type="main"> <s>Let us receive it, therefore, for a true and undoubted Concluſi <lb></lb>on, That the Water hath not any Renitence againſt ſimple Diviſi <lb></lb>on, and that it is not poſſible to find any Solid Body, be it of what <lb></lb>Figure it will, which being put into the Water, its Motion upwards <lb></lb>or downwards, according as it exceedeth, or ſhall be exceeded by <lb></lb>the Water in Gravity (although ſuch exceſſe and difference be in <lb></lb>ſenſible) ſhall be prohibited, and taken away, by the Craſſitude of <lb></lb>the ſaid Water. </s><s>When, therefore, we ſee the Board of Ebony, or <lb></lb>of other Matter, more grave than the Water, to ſtay in the Con <lb></lb>fines of the Water and Air, without ſubmerging, we muſt have re <lb></lb>courſe to ſome other Originall, for the inveſting the Cauſe of that <lb></lb>Effect, than to the breadth of the Figure, unable to overcome the <lb></lb>Renitence with which the Water oppoſeth Diviſion, ſince there is <lb></lb>no Reſiſtance; and from that which is not in being, we can expect <lb></lb>no Action. </s><s>It remains moſt true, therefore, as we have ſaid before, that <lb></lb>this ſo ſucceds, for that that which in ſuch manner put upon the wa <lb></lb>ter, not the ſame Body with that which is put <emph type="italics"></emph>into<emph.end type="italics"></emph.end> the Water: becauſe <lb></lb>this which is put <emph type="italics"></emph>into<emph.end type="italics"></emph.end> the Water, is the pure Board of Ebony, which <lb></lb>for that it is more grave than the Water, ſinketh, and that which is <lb></lb>put <emph type="italics"></emph>upon<emph.end type="italics"></emph.end> the Water, is a Compoſition of Ebony, and of ſo much <lb></lb>Air, that both together are ſpecifically leſs grave than the Water, <lb></lb>and therefore they do not deſcend.</s></p><p type="main"> <s>I will farther confirm this which I ſay. </s><s>Gentlemen, my Antago <lb></lb>niſts, we are agreed, that the exceſs or defect of the Gravity of the <lb></lb>Solid, unto the Gravity of the Water, is the true and proper Cauſe <lb></lb>of Natation or Submerſion. <lb></lb><arrow.to.target n="marg1506"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1506"></margin.target>Great Caution <lb></lb>to be had in ex <lb></lb>perimenting the <lb></lb>operation of Fi <lb></lb>gure in Natati <lb></lb>on.</s></p><p type="main"> <s>Now, if you will ſhew that beſides the former Cauſe, there is ano <lb></lb>ther which is ſo powerfull, that it can hinder and remove the Sub <lb></lb>merſion of thoſe very Solids, that by their Gravity ſink, and if you <lb></lb>will ſay, that this is the breadth or ampleneſs of Figure, you are ob <lb></lb>lieged, when ever you would ſhew ſuch an Experiment, firſt to make <lb></lb>the circumſtances certain, that that Solid which you put into the <lb></lb>Water, be not leſs grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than it, for if you ſhould not do ſo <lb></lb>any one might with reaſon ſay, that not the Figure, but the Levity <lb></lb>was the cauſe of that Natation. </s><s>But I ſay, that when you ſhall di <pb pagenum="445"></pb>mit a Board of Ebony into the Water, you do not put therein a Solid <lb></lb>more grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than the Water, but one lighter, for be ſides the <lb></lb>Ebony, there is in the Water a Maſs of Air, united with the Ebony, <lb></lb>and ſuch, and ſo light, that of both there reſults a Compoſition leſs <lb></lb>grave than the Water: See, therefore, that you remove the Air, and <lb></lb>put the Ebony alone into the Water, for ſo you ſhall immerge a So <lb></lb>lid more grave then the Water, and if this ſhall not go to the Bottom, <lb></lb>you have well Philoſophized, and I ill.</s></p><p type="main"> <s>Now, ſince we have found the true Cauſe of the Natation of thoſe <lb></lb>Bodies, which otherwiſe as being graver than the Water, would de <lb></lb>ſcend to the bottom, I think, that for the perfect and diſtinct know <lb></lb>ledge of this buſineſs, it would be good to proceed in a way of diſ <lb></lb>covering demonſtratively thoſe particular Accidents that do attend <lb></lb>theſe effects, and,</s></p><p type="head"> <s>PROBL. I.</s></p><p type="main"> <s><emph type="italics"></emph>To finde what proportion ſeverall Figures of different<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1507"></arrow.to.target> <lb></lb><emph type="italics"></emph>Matters ought to have, unto the Gravity of the <lb></lb>Water, that ſo they may be able by vertue of the <lb></lb>Contigucus Air to ſtay afloat.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1507"></margin.target>To finde the <lb></lb>proportion Fi <lb></lb>gures ought to <lb></lb>have to the wa <lb></lb>ters Gravity, <lb></lb>that by help of <lb></lb>the contiguous <lb></lb>Air, they may <lb></lb>ſwim.</s></p><p type="main"> <s>Let, therefore, for better illuſtration, D F N E be a Veſſell, <lb></lb>wherein the water is contained, and ſuppoſe a Plate or Board, <lb></lb>whoſe thickneſs is comprehended between the Lines I C and <lb></lb>O S, and let it be of Matter exceeding the water in Gravity, ſo that <lb></lb>being put upon the water, it dimergeth and abaſeth below the Levell <lb></lb>of the ſaid water, leaving the little Banks A I and B C, which are at <lb></lb>the greateſt height they can be, ſo that if the Plate I S ſhould but <lb></lb>deſcend any little ſpace farther, the little Banks or Ramparts would <lb></lb>no longer conſiſt, but expulſing the Air A I C B, they would dif <lb></lb>fuſe themſelves over the Superficies I C, and <lb></lb>would ſubmerge the Plate. </s><s>The height AIBC <lb></lb>is therefore the greateſt profundity that the <lb></lb><figure id="fig270"></figure> <lb></lb>little <emph type="italics"></emph>B<emph.end type="italics"></emph.end>anks of water admit of. </s><s>Now I ſay, <lb></lb>that from this, and from the proportion in Gra <lb></lb>vity, that the Matter of the Plate hath to the <lb></lb>water, we may eaſily ſinde of what thickneſs, at moſt, we may make <lb></lb>the ſaid Plates, to the end, they may be able to bear up above water: <lb></lb>for if the Matter of the Plate or <emph type="italics"></emph>B<emph.end type="italics"></emph.end>oard I S were, for Example, as <lb></lb>heavy again as the water, a <emph type="italics"></emph>B<emph.end type="italics"></emph.end>oard of that Matter ſhall be, at the moſt <lb></lb>of a thickneſs equall to the greateſt height of the <emph type="italics"></emph>B<emph.end type="italics"></emph.end>anks, that is, as <lb></lb>thick as A I is high: which we will thus demonſtrate. </s><s>Lot the So <lb></lb>lid I S be donble in Gravity to the water, and let it be a regular <pb pagenum="446"></pb>Priſme, or Cylinder, to wit, that hath its two flat Superficies, ſuperi <lb></lb>our and inferiour, alike and equall, and at Right Angles with the o <lb></lb>ther laterall Superficies, and let its thickneſs I O be equall to the <lb></lb>greateſt Altitude of the Banks of water: I ſay, that if it be put upon <lb></lb>the water, it will not ſubmerge: for the Altitude <lb></lb>A I being equall to the Altitude I O, the Maſs <lb></lb>of the Air A B C I ſhall be equall to the Maſs of <lb></lb><figure id="fig271"></figure> <lb></lb>the Solid C I O S: and the whole Maſs A O S B <lb></lb>double to the Maſs I S; And ſince the Maſs <lb></lb>of the Air A C, neither encreaſeth nor dimi <lb></lb>niſheth the Gravity of the Maſs I S, and the Solid I S was ſuppoſed <lb></lb>double in Gravity to the water; Therefore as much water as the <lb></lb>Maſs ſubmerged A O S B, compounded of the Air A I C B, and of <lb></lb>the Solid I O S C, weighs juſt as much as the ſame ſubmerged Maſs <lb></lb>A O S B: but when ſuch a Maſs of water, as is the ſubmerged part of <lb></lb>the Solid, weighs as much as the ſaid Solid, it deſcends not farther, <lb></lb><arrow.to.target n="marg1508"></arrow.to.target> <lb></lb>but reſteth, as by <emph type="italics"></emph>(a) Archimedes,<emph.end type="italics"></emph.end> and above by us, hath been de> <lb></lb>monſtrated: Therefore, I S ſhall deſcend no farther, but ſhall reſt. <lb></lb>And if the Solid I S ſhall be Seſquialter in Gravity to the water, it <lb></lb>ſhall float, as long as its thickneſs be not above twice as much as the <lb></lb>greateſt Altitude of the Ramparts of water, that is, of A I. </s><s>For I S <lb></lb>being Seſquialter in Gravity to the water, and the Altitude O I <lb></lb>being double to I A, the Solid ſubmerged A O S B, ſhall be alſo <lb></lb>Seſquialter in Maſs to the Solid I S. </s><s>And becauſe the Air A C, <lb></lb>neither increaſeth nor diminiſheth the ponderoſity of the Solid I S: <lb></lb>Therefore, as much water in quantity as the ſubmerged Maſs AOSB, <lb></lb>weighs as much as the ſaid Maſs ſubmerged: And, therefore, that <lb></lb>Maſs ſhall reſt. </s><s>And briefly in generall.</s></p><p type="margin"> <s><margin.target id="marg1508"></margin.target>Of Natation <lb></lb>Lib. 1. Prop. </s><s>3.</s></p><p type="head"> <s>THEOREME. VI.</s></p><p type="main"> <s><emph type="italics"></emph>When ever the exceſs of the Gravity of the Solid above<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1509"></arrow.to.target> <lb></lb><emph type="italics"></emph>the Gravity of the Water, ſhall have the ſame pro <lb></lb>portion to the Gravity of the Water, that the Alti <lb></lb>tude of the Rampart, hath to the thickneſs of the <lb></lb>Solid, that Solid ſhall not ſink, but being never ſo lit <lb></lb>tle thicker it ſhall.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1509"></margin.target>The proporti <lb></lb>on of the great <lb></lb>eſt thickneſs of <lb></lb>Solids, beyond <lb></lb>which encrea <lb></lb>ſed they ſink.</s></p><p type="main"> <s>Let the Solid I S be ſuperior in Gravity to the water, and of ſuch <lb></lb>thickneſs, that the Altitude of the Rampart A I, be in proporti <lb></lb>on to the thickneſs of the Solid I O, as the exceſs of the Gravi <lb></lb>ty of the ſaid Solid I S, above the Gravity of a Maſs of water equall <lb></lb>to the Maſs I S, is to the Gravity of the Maſs of water equall to the <pb pagenum="447"></pb>Maſs I S. </s><s>I ſay, that the Solid I S ſhall not <lb></lb>ſinke, but being never ſo little thicker it ſhall <lb></lb>go to the bottom: For being that as A I is <lb></lb><figure id="fig272"></figure> <lb></lb>to I O, ſo is the Exceſs of the Gravity of the <lb></lb>Solid I S, above the Gravity of a Maſs of water <lb></lb>equall to the Maſs I S, to the Gravity of the <lb></lb>ſaid Maſs of water: Therefore, compounding, as A O is to O I, ſo <lb></lb>ſhall the Gravity of the Solid I S, be to the Gravity of a Maſs of water <lb></lb>equall to the Maſs I S: And, converting, as I O is to O A, ſo ſhall the <lb></lb>Gravity of a Maſs of water equall to the Maſs I S, be to the Gravity <lb></lb>of the Solid I S: But as I O is to O A, ſo is a Maſs of water I S, to a <lb></lb>Maſs of water equall to the Maſs A B S O: and ſo is the Gravity of <lb></lb>a Maſs of water I S, to the Gravity of a Maſs of water A S: Therefore <lb></lb>as the Gravity of a Maſs of water, equall to the Maſs I S, is to the <lb></lb>Gravity of the Solid I S, ſo is the ſame Gravity of a Maſs of water <lb></lb>I S, to the Gravity of a Maſs of Water A S: Therefore the Gra <lb></lb>vity of the Solid I S, is equall to the Gravity of a Maſs of water e <lb></lb>quall to the Maſs A S: But the Gravity of the Solid I S, is the ſame <lb></lb>with the Gravity of the Solid A S, compounded of the Solid I S, <lb></lb>and of the Air A B C I. </s><s>Therefore the whole compounded Solid <lb></lb>A O S B, weighs as much as the water that would be compriſed in the <lb></lb>place of the ſaid Compound A O S B: And, therefore, it ſhall make <lb></lb>an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> and reſt, and that ſame Solid I O S C ſhall ſinke no <lb></lb>farther. </s><s>But if its thickneſs I O ſhould be increaſed, it would be ne <lb></lb>ceſſary alſo to encreaſe the Altitude of the Rampart A I, to main <lb></lb>tain the due proportion: But by what hath been ſuppoſed, the Alti <lb></lb>tude of the Rampart A I, is the greateſt that the Nature of the <lb></lb>Water and Air do admit, without the waters repulſing the Air ad <lb></lb>herent to the Superficies of the Solid I C, and poſſeſſing the ſpace <lb></lb>A I C B: Therefore, a Solid of greater thickneſs than I O, and of the <lb></lb>ſame Matter with the Solid I S, ſhall not reſt without ſubmerging, <lb></lb>but ſhall deſcend to the bottome: which was to be demonſtrated. <lb></lb></s><s>In conſequence of this that hath been demonſtrated, ſundry and va <lb></lb>rious Concluſions may be gathered, by which the truth of my prin <lb></lb>cipall Propoſition comes to be more and more confirmed, and the <lb></lb>imperfection of all former Argumentations touching the preſent <lb></lb>Queſtion cometh to be diſcovered.</s></p><p type="main"> <s><emph type="italics"></emph>And firſt we gather from the things demonstrated, that,<emph.end type="italics"></emph.end></s></p> <pb pagenum="448"></pb><p type="head"> <s>THEOREME VII. <lb></lb><arrow.to.target n="marg1510"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1510"></margin.target>The heavieſt <lb></lb>Bodies may <lb></lb>ſwimme.</s></p><p type="main"> <s><emph type="italics"></emph>All Matters, how heavy ſoever, even to Gold it ſelf, the <lb></lb>heavieſt of all Bodies, known by us, may float upon <lb></lb>the Water.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Becauſe its Gravity being conſidered to be almoſt twenty times <lb></lb>greater than that of the water, and, moreover, the greateſt Alti <lb></lb>tude that the Rampart of water can be extended to, without break <lb></lb>ing the Contiguity of the Air, adherent to the Surface of the Solid, <lb></lb>that is put upon the water being predetermined, if we ſhould make <lb></lb>a Plate of Gold ſo thin, that it exceeds not the nineteenth part ofthe <lb></lb>Altitude of the ſaid Rampart, this put lightly upon the water ſhall <lb></lb>reſt, without going to the bottom: and if Ebony ſhall chance to be <lb></lb>in ſeſquiſeptimall proportion more grave than the water, the greateſt <lb></lb>thickneſs that can be allowed to a Board of Ebony, ſo that it may be <lb></lb>able to ſtay above water without ſinking, would be ſeaven times <lb></lb>more than the height of the Rampart Tinn, <emph type="italics"></emph>v. </s><s>gr.<emph.end type="italics"></emph.end> eight times more <lb></lb>grave than water, ſhall ſwimm as oft as the thickneſs of its Plate,</s></p><p type="main"> <s><arrow.to.target n="marg1511"></arrow.to.target> <lb></lb>exceeds not the 7th part of the Altitude of the Rampart.</s></p><p type="margin"> <s><margin.target id="marg1511"></margin.target><emph type="italics"></emph>He elſewhere <lb></lb>cites this as a <lb></lb>Propoſition, there <lb></lb>fore I make it of <lb></lb>that number.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And here I will not omit to note, as a ſecond Corrollary dependent <lb></lb>upon the things demonſtrated, that,</s></p><p type="head"> <s>THEOREME VIII. <lb></lb><arrow.to.target n="marg1512"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1512"></margin.target>Natation and <lb></lb>Submerſion, col <lb></lb>lected from the <lb></lb>thickneſs, exclu <lb></lb>ding the length <lb></lb>and breadth of <lb></lb>Plates.</s></p><p type="main"> <s><emph type="italics"></emph>The Expanſion of Figure not only is not the Cauſe of the <lb></lb>Natation of thoſe grave Bodies, which otherwiſe <lb></lb>do ſubmerge, but alſo the determining what be thoſe <lb></lb>Boards of Ebony, or Plates of Iron or Gold that will <lb></lb>ſwimme, depends not on it, rather that ſame determina <lb></lb>tion is to be collected from the only thickneſs of thoſe <lb></lb>Figures of Ebony or Gold, wholly excluding the con <lb></lb>ſideration of length and breadth, as having no way <lb></lb>any ſhare in this Effect.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>It hath already been manifeſted, that the only cauſe of the Nata <lb></lb>tion of the ſaid Plates, is the reduction of them to be leſs grave <lb></lb>than the water, by means of the connexion of that Air, which de <lb></lb>ſcendeth together with them, and poſſeſſeth place in the water; <lb></lb>which place ſo occupyed, if before the circumfuſed water diffuſeth <lb></lb>it ſelf to fill it, it be capable of as much water, as ſhall weigh equall <lb></lb>with the Plate, the Plate ſhall remain ſuſpended, and ſinke no <lb></lb>farther.</s></p> <pb pagenum="449"></pb><p type="main"> <s>Now let us ſee on which of theſe three dimenſions of the Solid <lb></lb>depends the terminating, what and how much the Maſs of that ought <lb></lb>to be, that ſo the aſſiſtance of the Air contiguous unto it, may ſuffice <lb></lb>to render it ſpecifically leſs grave than the water, whereupon it may <lb></lb>reſt without Submerſion. </s><s>It ſhall undoubtedly be found, that the <lb></lb>length and breadth have not any thing to do in the ſaid determina <lb></lb>tion, but only the height, or if you will the thickneſs: for, if we take <lb></lb>a Plate or Board, as for Example, of Ebony, whoſe Altitude hath <lb></lb>unto the greateſt poſſible Altitude of the Rampart, the proportion <lb></lb>above declared, for which cauſe it ſwims indeed, but yet not if we <lb></lb>never ſo little increaſe its thickneſs; I ſay, that retaining its thick <lb></lb>neſs, and encreaſing its Superficies to twice, four times, or ten times <lb></lb>its bigneſs, or dminiſning it by dividing it into four, or ſix, or <lb></lb>twenty, or a hundred parts, it ſhall ſtill in the ſame manner continue <lb></lb>to float: but encreaſing its thickneſs only a Hairs breadth, it will <lb></lb>alwaies ſubmerge, although we ſhould multiply the Superficies a <lb></lb>hundred and a hundred times. </s><s>Now foraſmuch as that this is a <lb></lb>Cauſe, which being added, we adde alſo the Effect, and being remo <lb></lb>ved, it is removed; and by augmenting or leſſening the length or <lb></lb>breadth in any manner, the effect of going, or not going to the bot <lb></lb>tom, is not added or removed: I conclude, that the greatneſs and <lb></lb>ſmalneſs of the Superficies hath no influence upon the Natation or <lb></lb>Submerſion. </s><s>And that the proportion of the Altitude of the Ram <lb></lb>parts of Water, to the Altitude of the Solid, being conſtituted in <lb></lb>the manner aforeſaid, the greatneſs or ſmalneſs of the Superficies, <lb></lb>makes not any variation, is manifeſt from that which hath been above <lb></lb>demonſtrated, and from this, that, <emph type="italics"></emph>The Priſms and Cylinders which<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1513"></arrow.to.target> <lb></lb><emph type="italics"></emph>have the ſame Baſe, are in proportion to one another as their heights:<emph.end type="italics"></emph.end> <lb></lb>Whence Cylinders or Prifmes, namely, the Board, be they great or <lb></lb>little, ſo that they be all of equall thickneſs, have the ſame proportion <lb></lb>to their Conterminall Air, which hath for Baſe the ſaid Superficies of <lb></lb>the Board, and for height the Ramparts of water; ſo that alwayes <lb></lb>of that Air, and of the Board, Solids are compounded, that in Gravity <lb></lb>equall a Maſs of water equall to the Maſs of the Solids, compounded <lb></lb>of Air, and of the Board: whereupon all the ſaid Solids do in the <lb></lb>ſame manner continue afloat. </s><s>We will conclude in the third place, <lb></lb>that,</s></p> <pb pagenum="450"></pb><p type="margin"> <s><margin.target id="marg1513"></margin.target>Priſmes and <lb></lb>Cylinders ha <lb></lb>ving the ſame <lb></lb>Baſe, are to one <lb></lb>another as their <lb></lb>heights.</s></p><p type="head"> <s>THEOREME. IX. <lb></lb><arrow.to.target n="marg1514"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1514"></margin.target>All Figures <lb></lb>of all Matters, <lb></lb>float by hep of <lb></lb>the Rampart re <lb></lb>pleniſhed with <lb></lb>Air, and ſome <lb></lb>but only touch <lb></lb>the water.</s></p><p type="main"> <s><emph type="italics"></emph>All ſorts of Figures of whatſoever Matter, albeit more <lb></lb>grave than the Water, do by Benefit of the ſaid Ram <lb></lb>part, not only float, but ſome Figures, though of the <lb></lb>graveſt Matter, do ſtay wholly above Water, wetting <lb></lb>only the inferiour Surface that toucheth the Water.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And theſe ſhall be all Figures, which from the inferiour Baſe up <lb></lb>wards, grow leſſer and leſſer; the which we ſhall exemplifie for <lb></lb>this time in Piramides or Cones, of which Figures the paſſions sre <lb></lb>common. </s><s>We will demonſtrate therefore, that,</s></p><p type="main"> <s><emph type="italics"></emph>It is poſſible to form a Piramide, of any whatſoever Matter propoſed, <lb></lb>which being put with its Baſe upon the Water, reſts not only without <lb></lb>ſubmerging, but without wetting it more then its Baſe.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>For the explication of which it is requiſite, that we firſt demonſtrate <lb></lb>the ſubſequent Lemma, namely, that,</s></p><p type="head"> <s>LEMMA II.</s></p><p type="main"> <s><emph type="italics"></emph>Solids whoſe Maſſes anſwer in proportion contrarily to<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1515"></arrow.to.target> <lb></lb><emph type="italics"></emph>their Specificall Gravities, are equall in Abſolute <lb></lb>Gravities.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1515"></margin.target>Solids whoſe <lb></lb>Maſſes are in <lb></lb>contrary pro <lb></lb>portion to their <lb></lb>Specifick Gra <lb></lb>vities, are equall <lb></lb>in abſolute Gra <lb></lb>vity.</s></p><p type="main"> <s>Let A C and B be two Solids, and let the Maſs A C be to the <lb></lb>Maſs B, as the Specificall Gravity of the Solid B, is to the Speci <lb></lb>ficall Gravity of the Solid A C: I ſay, the Solids A C and B are <lb></lb>equall in abſolute weight, that is, equally grave. For <lb></lb><figure id="fig273"></figure> <lb></lb>if the Maſs A C be equall to the Maſs B, then, by the <lb></lb>Aſſumption, the Specificall Gravity of B, ſhall be e <lb></lb>quall to the Specificall Gravity of A C, and being e <lb></lb>quall in Maſs, and of the ſame Specificall Gravity they <lb></lb>ſhall abſolutely weigh one as much as another. </s><s>But <lb></lb>if their Maſſes ſhall be unequall, let the Maſs A C be greater, and in it <lb></lb>take the part C, equall to the Maſs B. And, becauſe the Maſſes B <lb></lb>and C are equall; the Abſolute weight of B, ſhall have the ſame pro <lb></lb>portion to the Abſolute weight of C, that the Specificall Gravity of <lb></lb>B, hath to the Specificall Gravity of C; or of C A, which is the <lb></lb>ſame <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end>: But look what proportion the Specificall Gravity of <lb></lb>B, hath to the Specificall Gravity of C A, the like proportion, by the <lb></lb>Aſſumption, hath the Maſs C A, to the Maſs B; that is, to the Maſs C: <pb pagenum="451"></pb>Therefore, the abſolute weight of B, to the abſolute weight of C, is <lb></lb>as the Maſs A C to the Maſs <emph type="italics"></emph>C<emph.end type="italics"></emph.end>: But as the Maſs AC, is to the Maſs C, <lb></lb>ſo is the abſolute weight of A C, to the abſolute weight of C: There <lb></lb>fore the abſolute weight of B, hath the ſame proportion to the abſo <lb></lb>lute weight of C, that the abſolute weight of A C, hath to the ab <lb></lb>ſolute weight of C: Therefore, the two Solids A C and B are equall <lb></lb>in abſolute Gravity: which was to be demonſtrated. </s><s>Having de <lb></lb>monſtrated this, I ſay,</s></p><p type="head"> <s>THEOREME X.</s></p><p type="main"> <s><emph type="italics"></emph>That it is poſſible of any aſſigned Matter, to form a Pi-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1516"></arrow.to.target> <lb></lb><emph type="italics"></emph>ramide or Cone upon any Baſe, which being put upon <lb></lb>the Water ſhall not ſubmerge, nor wet any more than <lb></lb>its Baſe.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1516"></margin.target>There may be <lb></lb>Cones and Pira <lb></lb>mides of any <lb></lb><emph type="italics"></emph>M<emph.end type="italics"></emph.end>atter, which <lb></lb>demittedinto the <lb></lb>water, reſt only <lb></lb>their Baſes.</s></p><p type="main"> <s>Let the greateſt poſſible Altitude of the Rampart be the Line D B, <lb></lb>and the Diameter of the Baſe of the Cone to be made of any Mat <lb></lb>ter aſſigned B C, at right angles to D B: And as the Specificall Gravity <lb></lb>of the Matter of the Piramide or Cone to be made, is to the Specificall <lb></lb>Gravity of the water, ſo let the Altitude of the <lb></lb><figure id="fig274"></figure> <lb></lb>Rampart D B, be to the third part of the Piramide <lb></lb>or Cone A B C, deſcribed upon the Baſe, whoſe <lb></lb>Diameter is B C: I ſay, that the ſaid Cone A B C, <lb></lb>and any other Cone, lower then the ſame, ſhall reſt <lb></lb>upon the Surface of the water B C without ſinking. <lb></lb></s><s>Draw D F parallel to B C, and ſuppoſe the Priſme <lb></lb>or Cylinder E C, which ſhall be tripple to the Cone <lb></lb>A B C. And, becauſe the Cylinder D C hath the ſame proportion <lb></lb>to the Cylinder C E, that the Altitude D B, hath to the Altitude B E: <lb></lb>But the Cylinder C E, is to the Cone A B C, as the Altitude E B is to <lb></lb>the third part of the Altitude of the Cone: Therefore, by Equality of <lb></lb>proportion, the Cylinder D C is to the Cone A B C, as D B is to the <lb></lb>third part of the Altitude B E: But as D B is to the third part of B E, <lb></lb>ſo is the Specificall Gravity of the Cone A B C, to the Specificall Gra <lb></lb>vity of the water: Therefore, as the Maſs of the Solid D C, is to the <lb></lb>Maſs of the Cone A <emph type="italics"></emph>B<emph.end type="italics"></emph.end> C, ſo is the Specificall Gravity of the ſaid Cone, <lb></lb>to the Specificall Gravity of the water: Therefore, by the precedent <lb></lb>Lemma, the Cone A B C weighs in abſolute Gravity as much as a <lb></lb>Maſs of Water equall to the Maſs D C: But the water which by the <lb></lb>impoſition of the Cone A B C, is driven out of its place, is as much <lb></lb>as would preciſely lie in the place D C, and is equall in weight to the <lb></lb>Cone that diſplaceth it: Therefore, there ſhall be an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> <lb></lb>and the Cone ſhall reſt without farther ſubmerging. </s><s>And its ma <lb></lb>nifeſt,</s></p> <pb pagenum="452"></pb><p type="head"> <s>COROLARY I. <lb></lb><arrow.to.target n="marg1517"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1517"></margin.target>Amongſt Cones <lb></lb>of the ſame Baſe, <lb></lb>thoſe of leaſt Al <lb></lb>titude ſhall ſink <lb></lb>the leaſt.</s></p><p type="main"> <s><emph type="italics"></emph>That making upon the ſame Baſis, a Cone of a leſs Altitude, it ſhall be <lb></lb>alſo leſs grave, and ſhall ſo much the more reſt without Submerſion.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>COROLARY II.</s></p><p type="main"> <s><emph type="italics"></emph>It is manifeſt, alſo, that one may make Cones and Piramids of any Matter <emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1518"></arrow.to.target> <lb></lb><emph type="italics"></emph>whatſoever, more grave than the water, which being put into the <lb></lb>water, with the Apix or Point downwards, reſt without Submerſion. <emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1518"></margin.target>There may be <lb></lb>Cones and Pira <lb></lb>mides of any <lb></lb>Matter, which <lb></lb>demitted with <lb></lb>the Point down <lb></lb>wards do float a <lb></lb>top.</s></p><p type="main"> <s>Becauſe if we reaſſume what hath been above demonſtrated, of <lb></lb>Priſms and Cylinders, and that on Baſes equall to thoſe of the <lb></lb>ſaid Cylinders, we make Cones of the ſame Matter, and thrree <lb></lb>times as high as the Cylinders, they ſhall reſt afloat, for that in Maſs <lb></lb>and Gravity they ſhall be equall to thoſe Cylinders, and by having <lb></lb>their Baſes equall to thoſe of the Cylinders, they ſhall leave equall <lb></lb>Maſſes of Air included within the Ramparts. </s><s>This, which for Exam <lb></lb>ple ſake hath been demonſtrated, in Priſms, Cylinders, Cones and <lb></lb>Piramids, might be proved in all other Solid Figures, but it would <lb></lb>require a whole Volume (ſuch is the multitude and variety of their <lb></lb>Symptoms and Accidents) to comprehend the particuler demonſtration <lb></lb>of them all, and of their ſeverall Segments: but I will to avoid prolixity <lb></lb>in the preſent Diſcourſe, content my ſelf, that by what I have declared <lb></lb>every one of ordinary Capacity may comprehend, that there is not <lb></lb>any Matter ſo grave, no not Gold it ſelf, of which one may not form <lb></lb>all ſorts of Figures, which by vertue of the ſuperiour Air adherent to <lb></lb>them, and not by the Waters Reſiſtance of Penetration, do remain <lb></lb>afloat, ſo that they ſink not. </s><s>Nay, farther, I will ſhew, for removing <lb></lb>that Error, that,</s></p><p type="head"> <s>THEOREME XI. <lb></lb><arrow.to.target n="marg1519"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1519"></margin.target>A Piramide or <lb></lb>Cone, demitted <lb></lb>with the Point <lb></lb>downwards ſhal <lb></lb>ſwim, with its <lb></lb>Baſe downward <lb></lb>ſhall ſink.</s></p><p type="main"> <s><emph type="italics"></emph>A Piramide or Cone put into the Water, with the Point <lb></lb>downward ſhall ſwimme, and the ſame put with the <lb></lb>Baſe downwards ſhall ſinke, and it ſhall be impoſſible <lb></lb>to make it float.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Now the quite contrary would happen, if the difficulty of Pene <lb></lb>trating the water, were that which had hindred the deſcent, for <lb></lb>that the ſaid Cone is far apter to pierce and penetrate with its ſharp <lb></lb>Point, than with its broad and ſpacious Baſe.</s></p><p type="main"> <s>And, to demonſtrate this, let the Cone be <emph type="italics"></emph>A B C,<emph.end type="italics"></emph.end> twice as grave <lb></lb>as the water, and let its height be tripple to the height of the Rampart <lb></lb><emph type="italics"></emph>D A E C<emph.end type="italics"></emph.end>: I ſay, firſt, that being put lightly into the water with the <pb pagenum="453"></pb>Point downwards, it ſhall not deſcend to the bot <lb></lb>tom: for the Aeriall Cylinder contained betwixt <lb></lb><figure id="fig275"></figure> <lb></lb>the Ramparts <emph type="italics"></emph>D A C E,<emph.end type="italics"></emph.end> is equall in Maſs to the <lb></lb>Cone <emph type="italics"></emph>A B C<emph.end type="italics"></emph.end>; ſo that the whole Maſs of the Solid <lb></lb>compounded of the Air <emph type="italics"></emph>D A C E,<emph.end type="italics"></emph.end> and of the Cone <lb></lb><emph type="italics"></emph>A B C,<emph.end type="italics"></emph.end> ſhall be double to the Cone <emph type="italics"></emph>A C B:<emph.end type="italics"></emph.end> And, <lb></lb>becauſe the Cone <emph type="italics"></emph>A B C<emph.end type="italics"></emph.end> is ſuppoſed to be of Matter double in Gra <lb></lb>vity to the water, therefore as much water as the whole Maſſe <lb></lb><emph type="italics"></emph>D A B C E,<emph.end type="italics"></emph.end> placed beneath the Levell of the water, weighs as much <lb></lb>as the Cone <emph type="italics"></emph>A B C<emph.end type="italics"></emph.end>: and, therefore, there ſhall be an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> <lb></lb>and the Cone <emph type="italics"></emph>A B C<emph.end type="italics"></emph.end> ſhall deſcend no lower. </s><s>Now, I ſay farther, <lb></lb>that the ſame Cone placed with the Baſe downwards, ſhall ſink to <lb></lb>the bottom, without any poſſibility of returning again, by any means <lb></lb>to ſwimme.</s></p><p type="main"> <s>Let, therefore, the Cone be <emph type="italics"></emph>A B D,<emph.end type="italics"></emph.end> double in Gravity to the <lb></lb>water, and let its height be tripple the height <lb></lb><figure id="fig276"></figure> <lb></lb>of the Rampart of water L B: It is already <lb></lb>manifeſt, that it ſhall not ſtay wholly out of <lb></lb>the water, becauſe the Cylinder being com <lb></lb>prehended betwixt the Ramparts <emph type="italics"></emph>L B D P,<emph.end type="italics"></emph.end> <lb></lb>equall to the Cone <emph type="italics"></emph>A B D,<emph.end type="italics"></emph.end> and the Matter of <lb></lb>the Cone, beig double in Gravity to the <lb></lb>water, it is evident that the weight of the ſaid <lb></lb>Cone ſhall be double to the weight of the Maſs of water equall to the <lb></lb>Cylinder <emph type="italics"></emph>L B D P<emph.end type="italics"></emph.end>: Therefore it ſhall not reſt in this ſtate, but <lb></lb>ſhall deſcend.</s></p><p type="head"> <s>COROLARY I.</s></p><p type="main"> <s><emph type="italics"></emph>I ſay farther; that much leſſe ſhall the ſaid Cone stay afloat, if one<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1520"></arrow.to.target> <lb></lb><emph type="italics"></emph>immerge a part thereof.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1520"></margin.target>Much leſs ſhall <lb></lb>the ſaid Cone <lb></lb>ſwim, if one im <lb></lb>merge a part <lb></lb>thereof.</s></p><p type="main"> <s>Which you may ſee, comparing with the water as well the part <lb></lb>that ſhall immerge as the other above water. </s><s>Let us therefore <lb></lb>of the Cone A B D, ſubmergeth part N T O S, and advance the <lb></lb>Point N S F above water. </s><s>The Altitude of the Cone F N S, ſhall <lb></lb>either be more than half the whole Altitude of the Cone F T O, or <lb></lb>it ſhall not be more: if it ſhall be more than half, the Cone F N S <lb></lb>ſhall be more than half of the Cylinder E N S C: for the Altitude <lb></lb>of the Cone F N S, ſhall be more than Seſquialter of the Altitude <lb></lb>of the Cylinder E N S C: And, becauſe the Matter of the Cone is <lb></lb>ſuppoſed to be double in Specificall Gravity to the water, the water <lb></lb>which would be contained within the Rampart E N S C, would be <lb></lb>leſs grave abſolutely than the Cone F N S; ſo that the whole Cone <lb></lb>F N S cannot be ſuſtained by the Rampart: But the part immerged <lb></lb>N T O S, by being double in Specificall Gravity to the water, ſhall <pb pagenum="454"></pb>tend to the bottom: Therefore, the whole <emph type="italics"></emph>C<emph.end type="italics"></emph.end>one F T O, as well in <lb></lb>reſpect of the part ſubmerged, as the part above water ſhall de <lb></lb>ſcend to the bottom. </s><s>But if the Altitude of the Point F N S, ſhall <lb></lb>be half the Altitude of the whole Cone F T O, the ſame Altitude of <lb></lb>the ſaid <emph type="italics"></emph>C<emph.end type="italics"></emph.end>one F N S ſhall be Seſquialter to the Altitude E N: and, <lb></lb>therefore, E N S C ſhall be double to the Cone F N S; and as much <lb></lb>water in Maſs as the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>ylinder E N S C, would weigh as much as the <lb></lb>part of the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>one F N S. But, becauſe the other immerged part <lb></lb>N T O S, is double in Gravity to the water, a Maſs of water equall <lb></lb>to that compounded of the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>ylinder E N S C, and of the Solid N T O S, <lb></lb>ſhall weigh leſs than the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>one F T O, by as much as the weight of <lb></lb>a Maſs of water equall to the Solid N T O S: Therefore, the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>one <lb></lb>ſha l alſo deſcend. </s><s>Again, becauſe the Solid N T O S, is ſeptuple <lb></lb>to the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>one F N S, to which the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>ylinder E S is double, the propor <lb></lb>tion of the Solid N T O S, ſhall be to the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>ylinder E N S C, as ſeaven <lb></lb>to two: Therefore, the whole Solid compounded of the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>ylinder <lb></lb>E N S C, and of the Solid N T O S, is much leſs than double the <lb></lb>Solid N T O S: Therefore, the ſingle Solid N T O S, is much graver <lb></lb>than a Maſs of water equall to the Maſs, compounded of the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>y <lb></lb>linder E N S C, and of N T O S.</s></p><p type="head"> <s>COROLARY II. <lb></lb><arrow.to.target n="marg1521"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1521"></margin.target>Part of the <lb></lb>Cones towards <lb></lb>the Cuſpis remo <lb></lb>ved, it ſhall ſtill <lb></lb>ſink.</s></p><p type="main"> <s><emph type="italics"></emph>From whence it followeth, that though one ſhould remove and take a <lb></lb>way the part of the Cone F N S, the ſole remainder N T O S would <lb></lb>go to the bottom.<emph.end type="italics"></emph.end></s></p><p type="head"> <s>COROLARY III.</s></p><p type="main"> <s><emph type="italics"></emph>And if we ſhould more depreſs the Cone F T O, it would be ſo much the<emph.end type="italics"></emph.end></s></p><p type="main"> <s><arrow.to.target n="marg1522"></arrow.to.target> <lb></lb><emph type="italics"></emph>more impoſſible that it ſhould ſuſtain it ſelf afloat, the part ſubmerged <lb></lb>N T O S ſtill encreaſing, and the Maſs of Air contained in the Rampart <lb></lb>diminiſhing, which ever grows leſs, the more the Cone ſubmergeth.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1522"></margin.target>The more the <lb></lb>Cone is immer <lb></lb>ged, the more <lb></lb>impoſſible is its <lb></lb>floating.</s></p><p type="main"> <s>That Cone, therefore, that with its Baſe upwards, and its <lb></lb><emph type="italics"></emph>Cuſpis<emph.end type="italics"></emph.end> downwards doth ſwimme, being dimitted with its Baſe <lb></lb>downward muſt of neceſſity ſinke. </s><s>They have argued farre <lb></lb>from the truth, therefore, who have aſcribed the cauſe of Natation <lb></lb>to waters reſiſtance of Diviſion, as to a paſſive principle, and to the <lb></lb>breadth of the Figure, with which the diviſion is to be made, as the <lb></lb>Efficient.</s></p><p type="main"> <s>I come in the fourth place, to collect and conclude the reaſon of <lb></lb>that which I have propoſed to the Adverſaries, namely,</s></p> <pb pagenum="455"></pb><p type="head"> <s>THE OREME XII.</s></p><p type="main"> <s><emph type="italics"></emph>That it is poſſible to fo m Solid Bodies, of what Figure<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1523"></arrow.to.target> <lb></lb><emph type="italics"></emph>and greatneſs ſoever, that of their own Nature goe <lb></lb>to the Bottome; But by the help of the Air con <lb></lb>tained in the Rampart, reſt without ſubmerging.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1523"></margin.target>Solids of any <lb></lb>Figure & great <lb></lb>neſſe, that natu <lb></lb>rally ſink, may <lb></lb>by help of the <lb></lb>Air in the Ram <lb></lb>part ſwimme.</s></p><p type="main"> <s>The truth of this Propoſition is ſufficiently manifeſt in all thoſe <lb></lb>Solid Figures, that determine in their uppermoſt part in a plane <lb></lb>Superficies: for making ſuch Figures of ſome Matter ſpecifi <lb></lb>cally as grave as the water, putting them into the water, ſo that the <lb></lb>whole Maſs be covered, it is manifeſt, that they ſhall reſt in all <lb></lb>places, provided, that ſuch a Matter equall in weight to the water, <lb></lb>may be exactly adjuſted: and they ſhall by conſequence, reſt or <lb></lb>lie even with the Levell of the water, without making any Rampart. <lb></lb></s><s>If, therefore, in reſpect of the Matter, ſuch Figures are apt to reſt <lb></lb>without ſubmerging, though deprived of the help of the Rampart, <lb></lb>it is manifeſt, that they may admit ſo much encreaſe of Gravity, <lb></lb>(without encreaſing their Maſſes) as is the weight of as much water <lb></lb>as would be contained within the Rampart, that is made about their <lb></lb>upper plane Surface: by the help of which being ſuſtained, they <lb></lb>ſhall reſt afloat, but being bathed, they ſhall deſcend, having been <lb></lb>made graver than the water. </s><s>In Figures, therefore, that determine <lb></lb>above in a plane, we may cleerly comprehend, that the Rampart <lb></lb>added or removed, may prohibit or permit the deſcent: but in thoſe <lb></lb>Figures that go leſſening upwards towards the top, ſome Perſons <lb></lb>may, and that not without much ſeeming Reaſon, doubt whether <lb></lb>the ſame may be done, and eſpecially by thoſe which terminate in a <lb></lb>very acute Point, ſuch as are your Cones and ſmall Piramids. </s><s>Touch <lb></lb>ing theſe, therefore, as more dubious than the reſt, I will endeavour <lb></lb>to demonſtrate, that they alſo lie under the ſame Accident of going, <lb></lb>or not going to the Bottom, be they of any whatever bigneſs. </s><s>Let <lb></lb>therefore the Cone be A B D, made of a matter <lb></lb>ſpecifically as grave as the water; it is manifeſt <lb></lb><figure id="fig277"></figure> <lb></lb>that being put all under water, it ſhall reſt in <lb></lb>all places (alwayes provided, that it ſhall weigh <lb></lb>exactly as much as the water, which is almoſt <lb></lb>impoſſible to effect) and that any ſmall weight <lb></lb>being added to it, it ſhall ſink to the bottom: <lb></lb>but if it ſhall deſcend downwards gently, I ſay, <lb></lb>that it ſhall make the Rampart E S T O, and <lb></lb>that there ſhall ſtay out of the water the point A S T, tripple in <lb></lb>height to the Rampart E S: which is manifeſt, for the Matter of the <pb pagenum="456"></pb>Cone weighing equally with the water, the part ſubmerged S B D T, <lb></lb>becomes indifferent to move downwards or upwards; and the Cone <lb></lb><emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> being equall in Maſs to the water that would be contained in <lb></lb>the concave of the Rampart <emph type="italics"></emph>E S T O,<emph.end type="italics"></emph.end> ſhall be alſo equall unto it in <lb></lb>Gravity: and, therefore, there ſhall be a perfect <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> and, <lb></lb>conſequently, a Reſt. </s><s>Now here ariſeth a doubt, whether the <lb></lb>Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> may be made heavier, in ſuch ſort, that when it is put <lb></lb>wholly under water, it goes to the bottom, but yet not in ſuch ſort, <lb></lb>as to take from the Rampart the vertue of ſuſtaining it that it ſink not, <lb></lb>and, the reaſon of the doubt is this: that although at ſuch time as <lb></lb>the Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> is ſpecifically as grave as the water, the Rampart <lb></lb><emph type="italics"></emph>E S T O<emph.end type="italics"></emph.end> ſuſtaines it, not only when the point <emph type="italics"></emph>A S T<emph.end type="italics"></emph.end> is tripple in <lb></lb>height to the Altitude of the Rampart <emph type="italics"></emph>E S,<emph.end type="italics"></emph.end> but alſo when a leſſer <lb></lb>part is above water; [for although in the Deſcent of the Cone the <lb></lb>Point <emph type="italics"></emph>A S T<emph.end type="italics"></emph.end> by little and little diminiſheth, and ſo likewiſe the <lb></lb>Rampart <emph type="italics"></emph>E S T O,<emph.end type="italics"></emph.end> yet the Point diminiſheth in <lb></lb><figure id="fig278"></figure> <lb></lb>greater proportion than the Rampart, in that <lb></lb>it diminiſheth according to all the three Di <lb></lb>menſions, but the Rampart according to two <lb></lb>only, the Altitude ſtill remaining the ſame; <lb></lb>or, if you will, becauſe the Cone <emph type="italics"></emph>S T<emph.end type="italics"></emph.end> goes di <lb></lb>miniſhing, according to the proportion of the <lb></lb>cubes of the Lines that do ſucceſſively become <lb></lb>the Diameters of the Baſes of emergent Cones, <lb></lb>and the Ramparts diminiſh according to the proportion of the <lb></lb>Squares of the ſame Lines; whereupon the proportions of the Points <lb></lb>are alwayes Seſquialter of the proportions of the Cylinders, con <lb></lb>tained within the Rampart; ſo that if, for Example, the height of <lb></lb>the emergent Point were double, or equall to the height of the <lb></lb>Rampart, in theſe caſes, the Cylinder contained within the Ram <lb></lb>part, would be much greater than the ſaid Point, becauſe it would be <lb></lb>either ſeſquialter or tripple, by reaſon of which it would perhaps <lb></lb>ſerve over and above to fuſtain the whole Cone, ſince the part ſub <lb></lb>merged would no longer weigh any thing;] yet, nevertheleſs, when <lb></lb>any Gravity is added to the whole Maſs of the Cone, ſo that alſo the <lb></lb>part ſubmerged is not without ſome exceſſe of Gravity above the <lb></lb>Gravity of the water, it is not manifeſt, whether the Cylinder con <lb></lb>tained within the Rampart, in the deſcent that the Cone ſhall make, <lb></lb>can be reduced to ſuch a proportion unto the emergent Point, and to <lb></lb>ſuch an exceſſe of Maſs above the Maſs of it, as to compenſate the <lb></lb>exceſſe of the Cones Specificall Gravity above the Gravity of the wa <lb></lb>ter: and the Scruple ariſeth, becauſe that howbeit in the deſcent <lb></lb>made by the Cone, the emergent Point <emph type="italics"></emph>A S T<emph.end type="italics"></emph.end> diminiſheth, whereby <lb></lb>there is alſo a diminution of the exceſs of the Cones Gravity above <pb pagenum="459"></pb>the Gravity of the water, yet the caſe ſtands ſo, that the Rampart <lb></lb>doth alſo contract it ſelf, and the Cylinder contained in it doth de <lb></lb>miniſh. </s><s>Nevertheleſs it ſhall be demonſtrated, how that the Cone <lb></lb><emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> being of any ſuppoſed bigneſſe, and made at the firſt of a <lb></lb>Matter exactly equall in Gravity to the Water, if there may <lb></lb>be affixed to it ſome Weight, by means of which it may deſcend to <lb></lb>the bottom, when ſubmerged under water, it may alſo by vertue of <lb></lb>the Rampart ſtay above without ſinking.</s></p><p type="main"> <s>Let, therefore, the Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> be of any ſuppoſed greatneſſe, <lb></lb>and alike in ſpecificall Gravity to the water. </s><s>It is manifeſt, that <lb></lb>being put lightly into the water, it ſhall reſt without deſcending; <lb></lb>and it ſhall advance above water, the Point <lb></lb><figure id="fig279"></figure> <lb></lb><emph type="italics"></emph>AS T,<emph.end type="italics"></emph.end> tripple in height to the height of the <lb></lb>Rampart <emph type="italics"></emph>E S<emph.end type="italics"></emph.end>: Now, ſuppoſe the Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> <lb></lb>more depreſſed, ſo that it advance above wa <lb></lb>ter, only the Point <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> higher by half than <lb></lb>the Point <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> with the Rampart about it <lb></lb><emph type="italics"></emph>C I R N.<emph.end type="italics"></emph.end> And, becauſe, the Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> is <lb></lb>to the Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> as the cube of the Line <emph type="italics"></emph>S T<emph.end type="italics"></emph.end> <lb></lb>is to the cube of the Line <emph type="italics"></emph>I R,<emph.end type="italics"></emph.end> but the Cylin <lb></lb>der <emph type="italics"></emph>E S T O,<emph.end type="italics"></emph.end> is to the Cylinder <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> as the Square of <emph type="italics"></emph>S T<emph.end type="italics"></emph.end> to <lb></lb>the Square of <emph type="italics"></emph>I R,<emph.end type="italics"></emph.end> the Cone <emph type="italics"></emph>A S T<emph.end type="italics"></emph.end> ſhall be Octuple to the Cone <lb></lb><emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> and the Cylinder <emph type="italics"></emph>E S T O,<emph.end type="italics"></emph.end> quadruple to the Cylinder <emph type="italics"></emph>C I R N<emph.end type="italics"></emph.end>: <lb></lb>But the Cone <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> is equall to the Cylinder E <emph type="italics"></emph>S T O<emph.end type="italics"></emph.end>: Therefore, <lb></lb>the Cylinder <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> ſhall be double to the Cone <emph type="italics"></emph>A I R:<emph.end type="italics"></emph.end> and the <lb></lb>water which might be contained in the Rampart <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> would be <lb></lb>double in Maſs and in Weight to the Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> and, therefore, <lb></lb>would be able to ſuſtain the double of the Weight of the Cone <emph type="italics"></emph>AIR<emph.end type="italics"></emph.end>: <lb></lb>Therefore, if to the whole Cone <emph type="italics"></emph>A B D,<emph.end type="italics"></emph.end> there be added as much <lb></lb>Weight as the Gravity of the Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> that is to ſay, the eighth <lb></lb>part of the weight of the Cone <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> it alſo ſhall be ſuſtained by <lb></lb>the Rampart <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> but without that it ſhall go to the bottome: <lb></lb>the Cone <emph type="italics"></emph>A B D,<emph.end type="italics"></emph.end> being, by the addition of the eighth part of the <lb></lb>weight of the Cone <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> made ſpecifically more grave than the <lb></lb>water. </s><s>But if the Altitude of the Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> were two thirds <lb></lb>of the Altitude of the Cone <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> the Cone <emph type="italics"></emph>A S T<emph.end type="italics"></emph.end> would be to the <lb></lb>Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> as twenty ſeven to eight; and the Cylinder <emph type="italics"></emph>E S T O,<emph.end type="italics"></emph.end> to <lb></lb>the Cylinder <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> as nine to four, that is, as twenty ſeven to <lb></lb>twelve; and, therefore, the Cylinder <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> to the Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> <lb></lb>as twelve to eight; and the exceſs of the Cylinder <emph type="italics"></emph>C I R N,<emph.end type="italics"></emph.end> above <lb></lb>the Cone <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> to the Cone <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> as four to twenty ſeven: there <lb></lb>fore if to the Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> be added ſo much weight as is the four <lb></lb>twenty ſevenths of the weight of the Cone <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> which is a little <lb></lb>more then its ſeventh part, it alſo ſhall continue to ſwimme, and <pb pagenum="460"></pb>the height of the emergent Point ſhall be double to the height of the <lb></lb>Rampart. </s><s>This that hath been demonſtrated in Cones, exactly holds <lb></lb>in Piramides, although the one or the other ſhould be very ſharp in <lb></lb><arrow.to.target n="marg1524"></arrow.to.target> <lb></lb>their Point or Cuſpis: From whence we conclude, that the ſame <lb></lb>Accident ſhall ſo much the more eaſily happen in all other Figures, <lb></lb>by how much the leſs ſharp the Tops ſhall be, in which they deter <lb></lb>mine, being aſſiſted by more ſpacious Ramparts.</s></p><p type="margin"> <s><margin.target id="marg1524"></margin.target>Natatiou eaſi <lb></lb>eſt effected in <lb></lb>Figures broad <lb></lb>toward the top.</s></p><p type="head"> <s>THEOREME XIII. <lb></lb><arrow.to.target n="marg1525"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1525"></margin.target>All Figures ſink <lb></lb>or ſwim, upon <lb></lb>bathing or not <lb></lb>bathing of their <lb></lb>tops.</s></p><p type="main"> <s><emph type="italics"></emph>All Figures, therefore, of whatever greatneſſe, may <lb></lb>go, and not go, to the Bottom, according as their Sumi <lb></lb>ties or Tops ſhall be bathed or not bathed.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And this Accident being common to all ſorts of Figures, without <lb></lb>exception of ſo much as one. </s><s>Figure hath, therefore, no part <lb></lb>in the production of this Effect, of ſometimes ſinking, and ſome <lb></lb>times again not ſinking, but only the being ſometimes conjoyned <lb></lb>to, and ſometimes ſeperated from, the ſupereminent Air: which <lb></lb>cauſe, in fine, who ſo ſhall rightly, and, as we ſay, with both his <lb></lb>Eyes, conſider this buſineſs, will find that it is reduced to, yea, that <lb></lb>it really is the ſame with, the true, Naturall and primary cauſe of <lb></lb>Natation or Submerſion; to wit, the exceſs or deficiency of the <lb></lb>Gravity of the water, in relation to the Gravity of that Solid Mag <lb></lb>nitude, that is demitted into the water. </s><s>For like as a Plate of Lead, <lb></lb>as thick as the back of a Knife, which being put into the water by it <lb></lb>ſelf alone goes to the bottom, if upon it you faſten a piece of Cork <lb></lb>four fingers thick, doth continue afloat, for that now the Solid that <lb></lb>is demitted in the water, is not, as before, more grave than the water, <lb></lb>but leſs, ſo the Board of Ebony, of its own nature more grave than <lb></lb>water; and, therefore, deſcending to the bottom, when it is demit <lb></lb>ted by it ſelf alone into the water, if it ſhall be put upon the water, <lb></lb>conjoyned with an Expanded vail of Air, that together with the <lb></lb>Ebony doth deſcend, and that it be ſuch, as that it doth make with <lb></lb>it a compound leſs grave than ſo much water in Maſs, as equalleth <lb></lb>the Maſs already ſubmerged and depreſſed beneath the Levell of the <lb></lb>waters Surface, it ſhall not deſcend any farther, but ſhall reſt, for <lb></lb>no other than the univerſall and moſt common cauſe, which is that <lb></lb>Solid Magnitudes, leſs grave <emph type="italics"></emph>inſpecie<emph.end type="italics"></emph.end> than the water, go not to the <lb></lb>bottom.</s></p><p type="main"> <s>So that if one ſhould take a Plate of Lead, as for Example, a finger <lb></lb>thick, and an handfull broad every way, and ſhould attempt to make <lb></lb>it ſwimme, with putting it lightly on the water, he would loſe his <lb></lb>Labour, becauſe that if it ſhould be depreſſed an Hairs breadth be <pb pagenum="461"></pb>yond the poſſible Altitude of the Ramparts of water, it would dive <lb></lb>and ſink; but if whilſt it is going downwards, one ſhould make <lb></lb>certain Banks or Ramparts about it, that ſhould hinder the do fuſion <lb></lb>of the water upon the ſaid Plate, the which Banks ſhould riſe ſo <lb></lb>high, as that they might be able to contain as much water, as ſhould <lb></lb>weigh equally with the ſaid Plate, it would, without all Queſtion, <lb></lb>deſcend no lower, but would reſt, as being ſuſtained by vertue of <lb></lb>the Air contained within the aforeſaid Ramparts: and, in ſhort, <lb></lb>there would be a Veſſell by this means formed with the bottom of <lb></lb>Lead. </s><s>But if the thinneſs of the Lead ſhall be ſuch, that a very <lb></lb>ſmall height of Rampart would ſuffice to contain ſo much Air, as might <lb></lb>keep it afloat, it ſhall alſo reſt without the Artificiall Banks or Ram <lb></lb>parts, but yet not without the Air, becauſe the Air by it ſelf makes <lb></lb>Banks ſufficient for a ſmall height, to reſiſt the Superfuſion of the <lb></lb>water: ſo that that which in this caſe ſwimmes, is as it were a <lb></lb>Veſſell filled with Air, by vertue of which it continueth afloat.</s></p><p type="main"> <s>I will, in the laſt place, with an other Experimeut, attempt to <lb></lb>remove all difficulties, if ſo be there ſhould yet be any doubt leſt in <lb></lb>any one, touching the opperation of this ^{*}Continuity of the Air, with </s></p><p type="main"> <s><arrow.to.target n="marg1526"></arrow.to.target> <lb></lb>the thin Plate which ſwims, and afterwards put an end to this part of <lb></lb>my diſcourſe.</s></p><p type="margin"> <s><margin.target id="marg1526"></margin.target>*Or rather Cor <lb></lb>tiguity,</s></p><p type="main"> <s>I ſuppoſe my ſelf to be queſtioning with ſome of my Oponents.</s></p><p type="main"> <s>Whether Figure have any influence upon the encreaſe or diminu <lb></lb><arrow.to.target n="marg1527"></arrow.to.target> <lb></lb>tion of the Reſiſtance in any Weight againſt its being raiſed in the <lb></lb>Air, and I ſuppoſe, that I am to maintain the Affirmative, aſſert <lb></lb>ing that a Maſs of Lead, reduced to the Figure of a Ball, ſhall be <lb></lb>raiſed with leſs force, then if the ſame had been made into a thinne <lb></lb>and broad Plate, becauſe that it in this ſpacious Figure, hath a great <lb></lb>quantity of Air to penetrate, and in that other, more compacted and <lb></lb>contracted very little: and to demonſtrate the truth of ſuch my O <lb></lb>pinion, I will hang in a ſmall thred firſt the Ball or Bullet, and put <lb></lb>that into the water, tying the thred that upholds it to one end of <lb></lb>the Ballance that I hold in the Air, and to the other end I by degrees <lb></lb>adde ſo much Weight, till that at laſt it brings up the Ball of Lead <lb></lb>out of the water: to do which, ſuppoſe a Gravity of thirty Ounces <lb></lb>ſufficeth; I afcerwards reduce the ſaid Lead into a flat and thinne <lb></lb>Plate, the which I likewiſe put into the water, ſuſpended by three <lb></lb>threds, which hold it parallel to the Surface of the water, and put <lb></lb>ting in the ſame manner, Weights to the other end, till ſuch time as <lb></lb>the Place comes to be raiſed and drawn out of the water: I finde <lb></lb>that thirty ſix ounces will not ſuffice to ſeperate it from the water, <lb></lb>and raiſe it thorow the Air: and arguing from this Experiment, I af <lb></lb>firm, that I have fully demonſtrated the truth of my Propoſition. <lb></lb></s><s>He re my Oponents deſires me to look down, ſhewing me a thing <pb pagenum="462"></pb>which I had not before obſerved, to wit, that in the Aſcent of the <lb></lb>Plate out of the water, it draws after it another Plate <emph type="italics"></emph>(if I may ſo <lb></lb>call it)<emph.end type="italics"></emph.end> of water, which before it divides and parts from the inferiour <lb></lb>Surface of the Plate of Lead, is raiſed above the Levell of the other <lb></lb>water, more than the thickneſs of the back of a Knife: Then he <lb></lb>goeth to repeat the Experiment with the Ball, and makes me ſee, <lb></lb>that it is but a very ſmall quantity of water, which cleaves to its <lb></lb>compacted and contracted Figure: and then he ſubjoynes, that its <lb></lb>no wonder, if in ſeperating the thinne and broad Plate from the <lb></lb>water, we meet with much greater Reſiſtance, than in ſeperating the <lb></lb>Ball, ſince together with the Plate, we are to raiſe a great quantity of <lb></lb>water, which occurreth not in the Ball: He telleth me moreover, <lb></lb>how that our Queſtion is, whether the Reſiſtance of Elevation be <lb></lb>greater in a dilated Plate of Lead, than in a Ball, and not whether <lb></lb>more reſiſteth a Plate of Lead with a great quantity of water, or a <lb></lb>Ball with a very little water: He ſheweth me in the cloſe, that the <lb></lb>putting the Plate and the Ball firſt into the water, to make proofe <lb></lb>thereby of their Reſiſtance in the Air, is beſides our caſe, which <lb></lb>treats of Elivating in the Air, and of things placed in the Air, and <lb></lb>not of the Reſiſtance that is made in the Confines of the Air and <lb></lb>water, and by things which are part in Air and part in water: and <lb></lb>laſtly, they make me feel with my hand, that when the thinne Plate <lb></lb>is in the Air, and free from the weight of the water, it is raiſed with <lb></lb>the very ſame Force that raiſeth the Ball. </s><s>Seeing, and underſtand <lb></lb>ing theſe things, I know not what to do, unleſs to grant my ſelf con <lb></lb>vinced, and to thank ſuch a Friend, for having made me to ſee that <lb></lb>which I never till then obſerved: and, being advertiſed by this ſame <lb></lb>Accident, to tell my Adverſaries, that our Queſtion is, whether a <lb></lb>Board and a Ball of Ebony, equally go to the bottom in water, and <lb></lb>not a Ball of Ebony and a Board of Ebony, joyned with another <lb></lb>flat Body of Air: and, farthermore, that we ſpeak of ſinking, and <lb></lb>not ſinking to the bottom, in water, and not of that which happeneth <lb></lb>in the Confines of the water and Air to Bodies that be part in the <lb></lb>Air, and part in the water; nor much leſs do we treat of the greater <lb></lb>or leſſer Force requiſite in ſeperating this or that Body from the Air; <lb></lb>not omitting to tell them, in the laſt place, that the Air doth reſiſt, <lb></lb>and gravitate downwards in the water, juſt ſo much as the water (if <lb></lb>I may ſo ſpeak) gravitates and reſiſts upwards in the Air, and that the <lb></lb>ſame force is required to ſinke a Bladder under water, that is full of <lb></lb>Air, as to raiſe it in the Air, being full of water, removing the con <lb></lb>ſideration of the weight of that Filme or Skinne, and confidering the <lb></lb>water and the Air only. </s><s>And it is likewiſe true, that the ſame Force <lb></lb>is required to ſink a Cup or ſuch like Veſſell under water, whilſt it is <lb></lb>full of Air, as to raiſe it above the Superficies of the water, keeping <pb pagenum="463"></pb>it with the mouth downwards; whilſt it is full of water, which is <lb></lb>conſtrained in the ſame manner to follow the Cup which contains it, <lb></lb>and to riſe above the other water into the Region of the Air, as the <lb></lb>Air is forced to follow the ſame Veſſell under the Surface of the wa <lb></lb>ter, till that in this caſe the water, ſurmounting the brimme of the <lb></lb>Cup, breaks in, driving thence the Air, and in that caſe, the ſaid <lb></lb>brimme coming out of the water, and arriving to the Confines of the <lb></lb>Air, the water falls down, and the Air ſub-enters to fill the cavity of <lb></lb>the Cup: upon which enſues, that he no leſs tranſgreſſes the Arti <lb></lb>cles of the <emph type="italics"></emph>Convention,<emph.end type="italics"></emph.end> who produceth a Plate conjoyned with much <lb></lb>Air, to ſee if it de ſeend to the bottom in water, then he that makes <lb></lb>proof of the Reſiſtance againſt Elevation in Air with a Plate of Lead, <lb></lb>joyned with a like quantity of water.</s></p><p type="margin"> <s><margin.target id="marg1527"></margin.target>An Experi <lb></lb>ment of the op <lb></lb>peration of Fi <lb></lb>gures, in en <lb></lb>creaſing or leſ <lb></lb>ſening of the <lb></lb>Airs Reſiſtance <lb></lb>of Diviſion.</s></p><p type="main"> <s>I have ſaid all that I could at preſent think of, to maintain the <lb></lb><arrow.to.target n="marg1528"></arrow.to.target> <lb></lb>Aſſertion I have undertook. </s><s>It remains, that I examine that which <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath writ of this matter towards the end of his Book <emph type="italics"></emph>De Cælo<emph.end type="italics"></emph.end>; <lb></lb>wherein I ſhall note two things: the one that it being true as hath <lb></lb><arrow.to.target n="marg1529"></arrow.to.target> <lb></lb>been demonſtrated, that Figure hath nothing to do about the moving <lb></lb>or not moving it ſelf upwards or downwards, it ſeemes that <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> <lb></lb>at his firſt falling upon this Sp. </s><s>culation, was of the ſame opinion, as <lb></lb>in my opinion may be collected from the examination of his words. <lb></lb></s><s>Tis true, indeed, that in eſſaying afterwards to render a reaſon of <lb></lb>ſuch effect, as not having in my conceit hit upon the right, (which <lb></lb>in the ſecond place I will examine) it ſeems that he is brought to <lb></lb>admit the largeneſſe of Figure, to be intereſſed in this operation. <lb></lb></s><s>As to the firſt particuler, hear the preciſe words of <emph type="italics"></emph>Aristotle.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1528"></margin.target><emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> opi <lb></lb>nion touching <lb></lb>the Operation <lb></lb>of Figure ex <lb></lb>amined.</s></p><p type="margin"> <s><margin.target id="marg1529"></margin.target><emph type="italics"></emph>Ariſtot de Cælo,<emph.end type="italics"></emph.end> <lb></lb>Lib. 4. Cap. 66.</s></p><p type="main"> <s><emph type="italics"></emph>Figures are not the Cauſes of moving ſimply upwards or downwards,<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1530"></arrow.to.target> <lb></lb><emph type="italics"></emph>but of moving more ſlowly or ſwiftly, and by what means this comes to <lb></lb>paſs, it is not difficult to ſee.<emph.end type="italics"></emph.end></s></p><p type="margin"> <s><margin.target id="marg1530"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> makes <lb></lb>not Figure the <lb></lb>cauſe of Motion <lb></lb>abſolutely, but <lb></lb>of ſwiſt or ſlow <lb></lb>motion,</s></p><p type="main"> <s>Here firſt I note, that the terms being four, which fall under the <lb></lb>preſent conſideration, namely, Motion, Reſt, Slowly and Swiftly: <lb></lb><arrow.to.target n="marg1531"></arrow.to.target> <lb></lb>And <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> naming Figures as Cauſes of Tardity and Velocity, ex <lb></lb>cluding them from being the Cauſe of abſolute and ſimple Motion, <lb></lb>it ſeems neceſſary, that he exclude them on the other ſide, from being <lb></lb>the Cauſe of Reſt, ſo that his meaning is this. </s><s>Figures are not the <lb></lb>Cauſes of moving or not moving abſolutely, but of moving quickly <lb></lb>or ſlowly: and, here, if any ſhould ſay the mind of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> is to <lb></lb>exclude Figures from being Cauſes of Motion, but yet not from <lb></lb>being Cauſes of Reſt, ſo that the ſence would be to remove from <lb></lb>Figures, there being the Cauſes of moving ſimply, but yet not there <lb></lb>being Cauſes of Reſt, I would demand, whether we ought with <lb></lb><emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> to underſtand, that all Figures univerſally, are, in ſome <lb></lb>manner, the cauſes of Reſt in thoſe Bodies, which otherwiſe would <lb></lb>move, or elſe ſome particular Figures only, as for Example, broad <pb pagenum="464"></pb>and thinne Figures: If all indifferently, then every Body ſhall reſt: <lb></lb>becauſe every Body hath ſome Figure, which is falſe: but if ſome <lb></lb>particular Figures only may be in ſome manner a Cauſe of Reſt, as, <lb></lb>for Example, the broad, then the others would be in ſome manner <lb></lb>the Cauſes of Motion: for if from ſeeing ſome Bodies of a contracted <lb></lb>Figure move, which after dilated into Plates reſt, may be inferred, <lb></lb>that the Amplitude of Figure hath a part in the Cauſe of that Reſt; <lb></lb>ſo from ſeeing ſuch like Figures reſt, which afterwards contracted <lb></lb>move, it may with the ſame reaſon be affirmed, that the united and <lb></lb>contracted Figure, hath a part in cauſing Motion, as the remover of <lb></lb>that which impeded it: The which again is directly oppoſite to what <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſaith, namely, that Figures are not the Cauſes of Motion. <lb></lb></s><s>Beſides, if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> had admitted and not excluded Figures from be <lb></lb>ing Cauſes of not moving in ſome Bodies, which moulded into ano <lb></lb>ther Figure would move, he would have impertinently propounded <lb></lb>in a dubitative manner, in the words immediately following, whence <lb></lb>it is, that the large and thinne Plates of Lead or Iron, reſt upon the <lb></lb>water, ſince the Cauſe was apparent, namely, the Amplitude of <lb></lb>Figure. </s><s>Let us conclude, therefore, that the meaning of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>in this place is to affirm, that Figures are not the Cauſes of abſolutely <lb></lb>moving or not moving, but only of moving ſwiftly or ſlowly: which <lb></lb>we ought the rather to believe, in regard it is indeed a meſt true con <lb></lb>ceipt and opinion. </s><s>Now the mird of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> being ſuch, and ap <lb></lb>pearing by conſequence, rather contrary at the firſt ſight, then fa <lb></lb>vourable to the aſſertion of the Oponents, it is neceſſary, that their <lb></lb>Interpretation be not exactly the ſame with that, but ſuch, as being <lb></lb>in part underſtood by ſome of them, and in part by others, was ſet <lb></lb>down: and it may eaſily be indeed ſo, being an Interpretation <lb></lb>conſonent to the ſence of the more famous Interpretors, which is, <lb></lb>that the Adverbe <emph type="italics"></emph>Simply<emph.end type="italics"></emph.end> or <emph type="italics"></emph>Abſolutely,<emph.end type="italics"></emph.end> put in the Text, orght not to <lb></lb>be joyned to the Verbe to <emph type="italics"></emph>Move,<emph.end type="italics"></emph.end> but with the Noun <emph type="italics"></emph>Cauſes<emph.end type="italics"></emph.end>: ſo that <lb></lb>the purport of <emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> words, is to affirm, That Figures are not the <lb></lb>Cauſes abſolutely of moving or not moving, but yet are Cauſes <emph type="italics"></emph>Se <lb></lb>cundum quid, viz<emph.end type="italics"></emph.end> in ſome ſort; by which means, they are called <lb></lb>Auxiliary and Concomitant Cauſes: and this Propoſition is received <lb></lb>and aſſerted as true by <emph type="italics"></emph>Signor Buonamico Lib.<emph.end type="italics"></emph.end> 5. <emph type="italics"></emph>Cap.<emph.end type="italics"></emph.end> 28. where he <lb></lb>thus writes. <emph type="italics"></emph>There are other Cauſes concomitant, by which ſome <lb></lb>things float, and others ſink, among which the Figures of Bodies hath <lb></lb>the firſt place,<emph.end type="italics"></emph.end> &c.</s></p><p type="margin"> <s><margin.target id="marg1531"></margin.target>Lib. 4. Cap. 61 <lb></lb>Text. </s><s>42.</s></p><p type="main"> <s>Concerning this Propoſition, I meet with many doubts and diffi <lb></lb>culties, for which me thinks the words of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> are not capable of <lb></lb>ſuch a conſtruction and ſence, and the difficulties are theſe.</s></p><p type="main"> <s>Firſt in the order and diſpoſure of the words of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> the par <lb></lb>ticle <emph type="italics"></emph>Simpliciter,<emph.end type="italics"></emph.end> or if you will <emph type="italics"></emph>abſoluté,<emph.end type="italics"></emph.end> is conjoyned with the Verb <pb pagenum="465"></pb><emph type="italics"></emph>to move,<emph.end type="italics"></emph.end> and ſeperated from the Noun <emph type="italics"></emph>Cauſes,<emph.end type="italics"></emph.end> the which is a great <lb></lb>preſumption in my favour, ſeeing that the writing and the Text <lb></lb>ſaith, Figures are not the Cauſe of moving ſimply upwards or <lb></lb>downwards, but of quicker or ſlower Motion: and, ſaith not, <lb></lb>Figures are not ſimply the Cauſes of moving upwards or down <lb></lb>wards, and when the words of a Text receive, tranſpoſed, a ſence <lb></lb>different from that which they found, taken in the order wherein <lb></lb>the Author diſpoſeth them, it is not convenient to inverte them. <lb></lb></s><s>And who will affirm that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> deſiring to write a Propoſition, <lb></lb>would diſpoſe the words in ſuch ſort, that they ſhould import a <lb></lb>different, nay, a contrary ſence? </s><s>contrary, I ſay, becauſe under <lb></lb>ſtood as they are written; they ſay, that Figures are not the <lb></lb>Cauſes of Motion, but inverted, they ſay, that Figures are the <lb></lb>Cauſes of Motion, &c.</s></p><p type="main"> <s>Moreover, if the intent of <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> had been to ſay, that Figures <lb></lb>are not ſimply the Cauſes of moving upwards or downwards, but <lb></lb>only Cauſes <emph type="italics"></emph>Secundum quid,<emph.end type="italics"></emph.end> he would not have adjoyned thoſe <lb></lb>words, <emph type="italics"></emph>but they are Cauſes of the more ſwift or ſlow Motion<emph.end type="italics"></emph.end>; yea, the <lb></lb>ſubjoining this would have been not only ſuperfluous but falſe, for <lb></lb>that the whole tenour of the Propoſition would import thus much. <lb></lb></s><s>Figures are not the abſolute Cauſes of moving upwards or down <lb></lb>wards, but are the abſolute Cauſe of the ſwift or ſlow Motion; <lb></lb>which is not true: becauſe the primary Cauſes of greater or leſſer <lb></lb>Velocity, are by <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in the 4th of his <emph type="italics"></emph>Phyſicks, Text.<emph.end type="italics"></emph.end> 71. attri <lb></lb>buted to the greater or leſſer Gravity of Moveables, compared a <lb></lb>mong themſelves, and to the greater or leſſer Reſiſtance of the <lb></lb><emph type="italics"></emph>Medium's,<emph.end type="italics"></emph.end> depending on their greater or leſs Craſſitude: and theſe <lb></lb>are inſerted by <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> as the primary Cauſes; and theſe two only <lb></lb>are in that place nominated: and Figure comes afterwards to be <lb></lb>conſidered, <emph type="italics"></emph>Text.<emph.end type="italics"></emph.end> 74. rather as an Inſtrumentall Cauſe of the force <lb></lb>of the Gravity, the which divides either with the Figure, or with <lb></lb>the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end>; and, indeed, Figure by it ſelf without the force of <lb></lb>Gravity or Levity, would opperate nothing.</s></p><p type="main"> <s>Iadde, that if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> had an opinion that Figure had been in <lb></lb>ſome ſort the Cauſe of moving or not moving, the inquiſition <lb></lb>which he makes immediately in a doubtfull manner, whence it <lb></lb>comes, that a Plate of Lead flotes, would have been impertinent; <lb></lb>for if but juſt before he had ſaid, that Figure was in a certain ſort <lb></lb>the Cauſe of moving or not moving, he needed not to call in <lb></lb>Queſtion, by what Cauſe the Plate of Lead ſwims, and then aſcri <lb></lb>bing the Cauſe to its Figure; and framing a diſcourſe in this manner. <lb></lb></s><s>Figure is a Cauſe <emph type="italics"></emph>Secundum quid<emph.end type="italics"></emph.end> of not ſinking: but, now, if it be <lb></lb>doubted, for what Cauſe a thin Plate of Lead goes not to the bottom; <lb></lb>it ſhall be anſwered, that that proceeds from its Figure: a diſcourſe <pb pagenum="466"></pb>which would be indecent in a Child, much more in <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>; For <lb></lb>where is the occaſion of doubting? </s><s>And who ſees not, that if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>had held, that Figure was in ſome ſort a Cauſe of Natation, he <lb></lb>would without the leaſt Heſitation have writ; That Figure is in a <lb></lb>certain ſort the Cauſe of Natation, and therefore the Plate of Lead <lb></lb>in reſpect of its large and expatiated Figure ſwims; but if we take <lb></lb>the propoſition of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> as I ſay, and as it is writte n, and as in <lb></lb>deed it is true, the enſuing words come in very oppoſitely, as well in <lb></lb>the introduction of ſwift and ſlow, as in the queſtion, which very <lb></lb>pertinently offers it ſelf, and would ſay thus much.</s></p><p type="main"> <s>Figures are not the Cauſe of moving or not moving ſimply up <lb></lb>wards or downwards, but of moving more quickly or ſlowly: But if <lb></lb>it be ſo, the Cauſe is doubtfull, whence it proceeds, that a Plate of <lb></lb>Lead or of Iron broad and thin doth ſwim, &c. </s><s>And the occaſion of <lb></lb>the doubt is obvious, becauſe it ſeems at the firſt glance, that the <lb></lb>Figure is the Cauſe of this Natation, ſince the ſame Lead, or a leſs <lb></lb>quantity, but in another Figure, goes to the bottom, and we have <lb></lb>already affirmed, that the Figure hath no ſhare in this effect.</s></p><p type="main"> <s>Laſtly, if the intent of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in this place had been to ſay, <lb></lb>that Figures, although not abſolutely, are at leaſt in ſome meaſure <lb></lb>the Cauſe of moving or not moving: I would have it conſidered, <lb></lb>that he names no leſs the Motion upwards, than the other down <lb></lb>wards: and becauſe in exemplifying it afterwards, he produceth <lb></lb>no other Experiments than of a Plate of Lead, and Board of Ebony, <lb></lb>Matters that of their own Nature go to the bottom, but by vertue <lb></lb>(as our Adverſaries ſay) of their Figure, reſt afloat; it is ſit that <lb></lb>they ſhould produce ſome other Experiment of thoſe Matters, which <lb></lb>by their Nature ſwims, but retained by their Figure reſt at the <lb></lb>bottom. </s><s>But ſince this is impoſſible to be done, we conclude, that <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in this place, hath not attributed any action to the Figure <lb></lb>of ſimply moving or not moving.</s></p><p type="main"> <s>But though he hath exquiſitely Philoſophiz'd, in inveſtigating <lb></lb>the ſolution of the doubts he propoſeth, yet will I not undertake <lb></lb>to maintain, rather various difficulties, that preſent themſelves <lb></lb>unto me, give me occaſion of ſuſpecting that he hath not entirely <lb></lb>diſplaid unto us, the true Cauſe of the preſent Concluſion: which <lb></lb>difficulties I will propound one by one, ready to change opinion, <lb></lb>when ever I am ſhewed, that the Truth is different from what I ſay; <lb></lb>to the confeſſion whereof I am much more inclinable than to contra <lb></lb>diction. <lb></lb><arrow.to.target n="marg1532"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1532"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> erred <lb></lb>in affirming a <lb></lb>Needle dimitted <lb></lb>long wayes to <lb></lb>ſink.</s></p><p type="main"> <s><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> having propounded the Queſtion, whence it proceeds, <lb></lb>that broad Plates of Iron or Lead, float or ſwim; he addeth (as <lb></lb>it were ſtrengthening the occaſion of doubting) foraſmuch as other <lb></lb>things, leſs, and leſs grave, be they round or long, as for inſtance a <pb pagenum="467"></pb>Needle go to the bottom. </s><s>Now I here doubt, or rather am certain, <lb></lb>that a Needle put lightly upon the water, reſts afloat, no leſs than the <lb></lb>thin Plates of Iron or Lead. </s><s>I cannot believe, albeit it hath been <lb></lb>told me, that ſome to defend <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſhould ſay, that he intends a <lb></lb>Needle demitted not longwayes but endwayes, and with the Point <lb></lb>downwards; nevertheleſs, not to leave them ſo much as this, though <lb></lb>very weak refuge, and which in my judgement <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf <lb></lb>would refuſe, I ſay it ought to be underſtood, that the Needle muſt <lb></lb>be demitted, according to the Dimenſion named by <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> which <lb></lb>is the length: becauſe, if any other Dimenſion than that which is <lb></lb>named, might or ought to be taken, I would ſay, that even the Plates <lb></lb>of Iron and Lead, ſink to the bottom, if they be put into the water <lb></lb>edgewayes and not flatwayes. </s><s>But becauſe <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſaith, broad <lb></lb>Figures go not to the bottom, it is to be underſtood, being demitted <lb></lb>broadwayes: and, therefore, when he ſaith, long Figures as a <lb></lb>Needle, albeit light, reſt not afloat, it ought to be underſtood of <lb></lb>them when demitted longwayes.</s></p><p type="main"> <s><emph type="italics"></emph>Morcover, to ſay that<emph.end type="italics"></emph.end> Ariſtotle <emph type="italics"></emph>is to be underſtood of the Needle de <lb></lb>mitted with the Point downwards, is to father upon him a great imper <lb></lb>tinency; for in this place he ſaith, that little Particles of Lead or Iron, <lb></lb>if they be round or long as a Needle, do ſink to the bottome; ſo that by <lb></lb>his Opinion, a Particle or ſmall Grain of Iron cannot ſwim: and if he <lb></lb>thus believed, what a great folly would it be to ſubjoyn, that neither <lb></lb>would a Needle demitted endwayes ſwim? </s><s>And what other is ſuch a <lb></lb>Needle, but many ſuch like Graines accumulated one upon another? </s><s>It <lb></lb>was too unworthy of ſuch a man to ſay, that one ſingle Grain of Iron could <lb></lb>not ſwim, and that neither can it ſwim, though you put a hundred more <lb></lb>upon it.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Laſtly, either <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> believed, that a Needle demitted long <lb></lb>wayes upon the water, would ſwim, or he believed that it would <lb></lb>not ſwim: If he believed it would not ſwim, he might well ſpeak <lb></lb>as indeed he did; but if he believed and knew that it would ſloat, <lb></lb>why, together with the dubious Problem of the Natation of broad <lb></lb>Figure, though of ponderous Matter, hath he not alſo introduced <lb></lb>the Queſtion; whence it proceeds, that even long and ſlender Fi <lb></lb>gures, howbeit of Iron or Lead do ſwim? </s><s>And the rather, for that <lb></lb>the occaſion of doubting ſeems greater in long and narrow Figures, <lb></lb>than in broad and thin, as from <emph type="italics"></emph>Aristotles<emph.end type="italics"></emph.end> not having doubted of it, <lb></lb>is manifeſted.</s></p><p type="main"> <s>No leſſer an inconvenience would they faſten upon <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> who <lb></lb>in his defence ſhould ſay, that he means a Needle pretty thick, and <lb></lb>not a ſmall one; for take it for granted to be intended of a ſmall one <pb pagenum="468"></pb>and it ſhall ſuffice to reply, that he believed that it would ſwim; <lb></lb>and I will again charge him with having avoided a more wonderfull <lb></lb>and intricate Probleme, and introduced the more facile and leſs <lb></lb>wonderfull.</s></p><p type="main"> <s>We ſay freely therefore; that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> did hold, that only the <lb></lb>broad Figure did ſwim, but the long and ſlender, ſuch as a Needle, <lb></lb>not. </s><s>The which nevertheleſs is falſe, as it is alſo falſe in round <lb></lb>Bodies: becauſe, as from what hath been predemonſtrated, may be ga <lb></lb>thered, little Balls of Lead and Iron, do in like manner ſwim.</s></p><p type="main"> <s>He propoſeth likewiſe another Concluſion, which likewiſe ſeems </s></p><p type="main"> <s><arrow.to.target n="marg1533"></arrow.to.target> <lb></lb>different from the truth, and it is, That ſome things, by reaſon of <lb></lb>their littleneſs fly in the Air, as the ſmall duſt of the Earth, and the <lb></lb>thin leaves of beaten Gold: but in my Opinion, Experience ſhews <lb></lb>us, that that happens not only in the Air, but alſo in the water, in <lb></lb>which do deſcend, even thoſe Particles or Atomes of Earth, that <lb></lb>diſtur be it, whoſe minuity is ſuch, that they are not deſervable, ſave <lb></lb>only when they are many hundreds together. </s><s>Therefore, the duſt <lb></lb>of the Earth, and beaten Gold, do not any way ſuſtain themſelves <lb></lb>in the Air, but deſcend downwards, and only fly to and again in <lb></lb>the ſame, when ſtrong Windes raiſe them, or other agitations of the <lb></lb>Air commove them: and this alſo happens in the commotion of the <lb></lb>water, which raiſeth its Sand from the bottom, and makes it muddy. <lb></lb></s><s>But <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> cannot mean this impediment of the commotion, of <lb></lb>which he makes no mention, nor names other than the lightneſs of <lb></lb>ſuch Minutiæ or Atomes, and the Reſiſtance of the Craſſitudes of the <lb></lb>Water and Air, by which we ſee, that he ſpeakes of a calme, and <lb></lb>not diſturbed and agitated Air: but in that caſe, neither Gold nor <lb></lb>Earth, be they never ſo ſmall, are ſuſtained, but ſpeedily deſcend. <lb></lb><arrow.to.target n="marg1534"></arrow.to.target></s></p><p type="margin"> <s><margin.target id="marg1533"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> af <lb></lb>fir meth ſome <lb></lb>Bodies volatile <lb></lb>for their Minu <lb></lb>ity, Text. </s><s>42.</s></p><p type="margin"> <s><margin.target id="marg1534"></margin.target><emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> pla <lb></lb>ced the Cauſe of <lb></lb>Natation in <lb></lb>certain ſiery A <lb></lb>tomes.</s></p><p type="main"> <s>He paſſeth next to confute <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> which, by his Teſtimony <lb></lb>would have it, that ſome Fiery Atomes, which continually aſcend <lb></lb>through the water, do ſpring upwards, and ſuſtain thoſe grave Bodies, <lb></lb>which are very broad, and that the narrow deſcend to the bottom, </s></p><p type="main"> <s><arrow.to.target n="marg1535"></arrow.to.target> <lb></lb>for that but a ſmall quantity of thoſe Atomes, encounter and reſiſt <lb></lb>them.</s></p><p type="margin"> <s><margin.target id="marg1535"></margin.target><emph type="italics"></emph>Ariſtot. </s><s>De Cœlo<emph.end type="italics"></emph.end> <lb></lb>lib. 4. cap. 6. <lb></lb>text. </s><s>43.</s></p><p type="main"> <s>I ſay, <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> confutes this poſition, ſaying, that that ſhould <lb></lb><arrow.to.target n="marg1536"></arrow.to.target> <lb></lb>much more occurre in the Air, as the ſame <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> inſtances a <lb></lb>gainſt himſelf, but after he had moved the objection, he ſlightly re <lb></lb>ſolves it, with ſaying, that thoſe Corpuſcles which aſcend in the Air, <lb></lb>make not their <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> conjunctly. </s><s>Here I will not ſay, that the <lb></lb><arrow.to.target n="marg1537"></arrow.to.target> <lb></lb>reaſon alledged by <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> is true, but I will only ſay, it ſeems <lb></lb>in my judgement, that it is not wholly confuted by <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> whilſt he <lb></lb>ſaith, that were it true, that the calid aſcending Atomes, ſhould <lb></lb>ſuſtain Bodies grave, but very broad, it would much more be done <lb></lb>in the Air, than in Water, for that haply in the Opinion of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> <pb pagenum="469"></pb>the ſaid calid Atomes aſcend with much greater Force and Velocity <lb></lb>through the Air, than through the water. </s><s>And if this be ſo, as I veri <lb></lb>ly believe it is, the Objection of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in my judgement ſeems to <lb></lb>give occaſion of ſuſpecting, that he may poſſibly be deceived in more <lb></lb>than one particular: Firſt, becauſe thoſe calid Atomes, (whether <lb></lb>they be Fiery Corpuſcles, or whether they be Exhalations, or in <lb></lb>ſhort, whatever other matter they be, that aſcends upwards through <lb></lb>the Air) cannot be believed to mount faſter through Air, than <lb></lb>through water: but rather on the contrary, they peradventure move <lb></lb>more impetuouſly through the water, than through the Air, as hath <lb></lb>been in part demonſtrated above. </s><s>And here I cannot finde the rea <lb></lb>ſon, why <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſeeing, that the deſeending Motion of the ſame <lb></lb>Moveable, is more ſwift in Air, than in water, hath not advertiſed <lb></lb>us, that from the contrary Motion, the contrary ſhould neceſſarily <lb></lb>follow; to wit, that it is more ſwift in the water, than in the Air: for <lb></lb>ſince that the Moveable which deſcendeth, moves ſwifter through <lb></lb>the Air, than through the water, if we ſhould ſuppoſe its Gravity <lb></lb>gradually to diminiſh, it would firſt become ſuch, that deſcending <lb></lb>ſwiftly through the Air, it would deſcend but ſlowly through the <lb></lb>water: and then again, it might be ſuch, that deſcending in the <lb></lb>Air, it ſhould aſcend in the water: and being made yet leſs grave, <lb></lb>it ſhall aſcend ſwiftly through the water, and yet deſcend likewiſe <lb></lb>through the Air: and in ſhort, before it can begin to aſcend, though <lb></lb>but ſlowly through the Air, it ſhall aſcend ſwiftly through the water: <lb></lb>how then is it true, that aſcending Moveables move ſwifter through <lb></lb>the Air, than through the water?</s></p><p type="margin"> <s><margin.target id="marg1536"></margin.target><emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> con <lb></lb>futed by <emph type="italics"></emph>Ari <lb></lb>ſtotle,<emph.end type="italics"></emph.end> text 43.</s></p><p type="margin"> <s><margin.target id="marg1537"></margin.target><emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> con <lb></lb>futation of <emph type="italics"></emph>De <lb></lb>mocritus<emph.end type="italics"></emph.end> refuted <lb></lb>by the Author.</s></p><p type="main"> <s>That which hath made <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> believe, the Motion of Aſcent to be <lb></lb>ſwifter in Air, than in water, was firſt, the having referred the <lb></lb>Cauſes of ſlow and quick, as well in the Motion of Aſcent, as of <lb></lb>Deſcent, only to the diverſity of the Figures of the Moveable, and to <lb></lb>the more or leſs Reſiſtance of the greater or leſſer Craſſitude, or Ra <lb></lb>rity of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>; not regarding the compariſon of the Exceſſes <lb></lb>of the Gravities of the Moveables, and of the <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end>: the which <lb></lb>notwithſtanding, is the moſt principal point in this affair: for if the <lb></lb>augmentation and diminution of the Tardity or Velocity, ſhould <lb></lb>have only reſpect to the Denſity or Rarity of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> every Body <lb></lb>that deſcends in Air, would deſcend in water: becauſe whatever <lb></lb>difference is found between the Craſſitude of the water, and that of <lb></lb>the Air, may well be found between the Velocity of the ſame Move <lb></lb>able in the Air, and ſome other Velocity: and this ſhould be its <lb></lb>proper Velocity in the water, which is abſolutely falſe. </s><s>The other <lb></lb>occaſion is, that he did believe, that like as there is a poſitive and in <lb></lb>trinſecall Quality, whereby Elementary Bodies have a propenſion <lb></lb>of moving towards the Centre of the Earth, ſo there is another like <pb pagenum="470"></pb>wiſe intrinſecall, whereby ſome of thoſe Bodies have an <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of <lb></lb><arrow.to.target n="marg1538"></arrow.to.target> <lb></lb>flying the Centre, and moving upwards: by Vertue of which in <lb></lb>trinſe call Principle, called by him Levity, the Moveables which have <lb></lb>that ſame Motion more eaſily penetrate the more ſubtle <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> <lb></lb>than the more denſe: but ſuch a Propoſition appears likewiſe un <lb></lb>certain, as I have above hinted in part, and as with Reaſons and <lb></lb>Experiments, I could demonſtrate, did not the preſent Argument im <lb></lb>portune me, or could I diſpatch it in few words.</s></p><p type="margin"> <s><margin.target id="marg1538"></margin.target>Lib. 4. Cap. 5.</s></p><p type="main"> <s>The Objection therefore of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> againſt <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> whilſt <lb></lb>he ſaith, that if the Fiery aſcending Atomes ſhould ſuſtain Bodies <lb></lb>grave, but of a diſtended Figure, it would be more obſervable in <lb></lb>the Air than in the water, becauſe ſuch Corpuſcles move ſwifter in <lb></lb>that, than in this, is not good; yea the contrary would evene, for <lb></lb>that they aſcend more ſlowly through the Air: and, beſides their <lb></lb>moving ſlowly, they aſcend, not united together, as in the water, <lb></lb>but diſcontinue, and, as we ſay, ſcatter: And, therefore, as <lb></lb><emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> well replyes, reſolving the inſtance they make not their <lb></lb>puſh or <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> conjunctly.</s></p><p type="main"> <s><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> in the ſecond place, deceives himſelf, whilſt he will <lb></lb>have the ſaid grave Bodies to be more eaſily ſuſtained by the ſaid <lb></lb>Fiery aſcending Atomes in the Air than in the Water: not obſerv <lb></lb>ing, that the ſaid Bodies are much more grave in that, than in this, <lb></lb>and that ſuch a Body weighs ten pounds in the Air, which will not <lb></lb>in the water weigh 1/2 an ounce; how can it then be more eaſily <lb></lb>ſuſtained in the Air, than in the Water?</s></p><p type="main"> <s>Let us conclude, therefore, that <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> hath in this particular <lb></lb>better Philoſophated than <emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end> But yet will not I affirm, that <emph type="italics"></emph>De-<emph.end type="italics"></emph.end> <lb></lb><arrow.to.target n="marg1539"></arrow.to.target> <lb></lb><emph type="italics"></emph>mocritus<emph.end type="italics"></emph.end> hath reaſon'd rightly, but I rather ſay, that there is a ma <lb></lb>nifeſt Experiment that overthrows his Reaſon, and this it is, That <lb></lb>if it were true, that calid aſcending Atomes ſhould uphold a Body, <lb></lb>that if they did not hinder, would go to the bottom, it would follow, <lb></lb>that we may find a Matter very little ſuperiour in Gravity to the <lb></lb>water, the which being reduced into a Ball, or other contracted <lb></lb>Figure, ſhould go to the bottom, as encountring but few Fiery A <lb></lb>tomes; and which being diſtended afterwards into a dilated and <lb></lb>thin Plate, ſhould come to be thruſt upwards by the impulſion of a <lb></lb>great Multitude of thoſe Corpuſcles, and at laſt carried to the very <lb></lb>Surface of the water: which wee ſee not to happen; Experience <lb></lb>ſhewing us, that a Body <emph type="italics"></emph>v. </s><s>gra.<emph.end type="italics"></emph.end> of a Sphericall Figure, which very <lb></lb>hardly, and with very great leaſure goeth to the bottom, will reſt <lb></lb>there, and will alſo deſcend thither, being reduced into whatſoever <lb></lb>other diſtended Figure. </s><s>We muſt needs ſay then, either that in the <lb></lb>water, there are no ſuch aſcending Fiery Atoms, or if that ſuch there <lb></lb>be, that they are not able to raiſe and lift up any Plate of a Matter, <pb pagenum="471"></pb>that without them would go to the bottom: Of which two Pofitions, <lb></lb>I eſteem the ſecond to be true, underſtanding it of water, conſtituted <lb></lb>in its naturall Coldneſs. </s><s>But if we take a Veſſel of Glaſs, or Braſs, <lb></lb>or any other hard matter, full of cold water, within which is put a <lb></lb>Solid of a flat or concave Figure, but that in Gravity exceeds the <lb></lb>water ſo little, that it goes ſlowly to the bottom; I ſay, that putting <lb></lb>ſome burning Coals under the ſaid Veſſel, as ſoon as the new Fiery <lb></lb>Atomes ſhall have penetrated the ſubſtance of the Veſſel, they ſhall <lb></lb>without doubt, aſcend through that of the water, and thruſting a <lb></lb>gainſt the foreſaid Solid, they ſhall drive it to the Superficies, and <lb></lb>there detain it, as long as the incurſions of the ſaid Corpuſcles ſhall <lb></lb>laſt, which ceaſing after the removall of the Fire, the Solid being a <lb></lb>bandoned by its ſupporters, ſhall return to the bottom.</s></p><p type="margin"> <s><margin.target id="marg1539"></margin.target><emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> con <lb></lb>futed by the <lb></lb>Authour.</s></p><p type="main"> <s>But <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> notes, that this Caufe only takes place when we <lb></lb>treat of raiſing and ſuſtaining of Plates of Matters, but very little <lb></lb>heavier than the water, or extreamly thin: but in Matters very <lb></lb>grave, and of ſome thickneſs, as Plates of Lead or other Mettal, that <lb></lb>ſame Effect wholly ceaſeth: In Teſtimony of which, let's obſerve <lb></lb>that ſuch Plates, being raiſed by the Fiery Atomes, aſcend through <lb></lb>all the depth of the water, and ſtop at the Confines of the Air, ſtill <lb></lb>ſtaying under water: but the Plates of the Opponents ſtay not, but <lb></lb>only when they have their upper Superficies dry, nor is there any <lb></lb>means to be uſed, that when they are within the water, they may <lb></lb>not ſink to the bottom. </s><s>The cauſe, therefore, of the Supernatation <lb></lb>of the things of which <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> ſpeaks is one, and that of the Super <lb></lb>natation of the things of which we ſpeak is another. </s><s>But, returning <lb></lb><arrow.to.target n="marg1540"></arrow.to.target> <lb></lb>to <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> methinks that he hath more weakly confuted <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> <lb></lb>than <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> himſelf hath done: For <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> having propounded <lb></lb>the Objection which he maketh againſt him, and oppoſed him with <lb></lb>ſaying, that if the calid aſcendent Corpuſcles were thoſe that raiſed <lb></lb>the thin Plate, much more then would ſuch a Solid be raiſed and <lb></lb>born upwards through the Air, it ſheweth that the deſire in <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>to detect <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> was predominate over the exquiſiteneſs of Solid <lb></lb>Philoſophizing: which deſire of his he hath diſcovered in other oc <lb></lb>caſions, and that we may not digreſs too far from this place, in the <lb></lb>Text precedent to this Chapter which we have in hand; where he <lb></lb><arrow.to.target n="marg1541"></arrow.to.target> <lb></lb>attempts to confute the ſame <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> for that he, not content <lb></lb>ing himſelf with names only, had eſſayed more particularly to de <lb></lb>clare what things Gravity and Levity were; that is, the Cauſes of <lb></lb>deſcending and aſcending, (and had introduced Repletion and Va <lb></lb>cuity) aſcribing this to Fire, by which it moves upwards, and that to <lb></lb>the Earth, by which it deſcends; afterwards attributing to the <lb></lb>Air more of Fire, and to the water more of Earth. </s><s>But <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> <lb></lb>deſiring a poſitive Cauſe, even of aſcending Motion, and not as <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end> <pb pagenum="472"></pb>or theſe others, a ſimple negation, or privation, ſuch as Vacuity <lb></lb><arrow.to.target n="marg1542"></arrow.to.target> <lb></lb>would be in reference to Repletion, argueth againſt <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> and <lb></lb>ſaith: If it be true, as you ſuppoſe, then there ſhall be a great Maſs <lb></lb>of water, which ſhall have more of Fire, than a ſmall Maſs of Air, <lb></lb>and a great Maſs of Air, which ſhall have more of Earth than a lit <lb></lb>tle Maſs of water, whereby it would enſue, that a great Maſs of Air, <lb></lb>ſhould come more ſwiftly downwards, than a little quantity of <lb></lb>water: But that is never in any caſe ſoever: Therefore <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> <lb></lb>diſcourſeth erroneouſly.</s></p><p type="margin"> <s><margin.target id="marg1540"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſhews <lb></lb>his deſire of <lb></lb>finding <emph type="italics"></emph>Demo <lb></lb>critus<emph.end type="italics"></emph.end> in an Er <lb></lb>ror, to exceed <lb></lb>that of diſco <lb></lb>veting Truth.</s></p><p type="margin"> <s><margin.target id="marg1541"></margin.target>Cap. 5. Text 41.</s></p><p type="margin"> <s><margin.target id="marg1542"></margin.target>Id. </s><s>ibid.</s></p><p type="main"> <s>But in my opinion, the Doctrine of <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> is not by this alle <lb></lb>gation overthrown, but if I erre not, the manner of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> deduction <lb></lb>either concludes not, or if it do conclude any thing, it may with e <lb></lb>quall force be reſtored againſt himſelf. <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> will grant to <lb></lb><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> that there may be a great Maſs of Air taken, which con <lb></lb>tains more Earth, than a ſmall quantity of water, but yet will deny, <lb></lb>that ſuch a Maſs of Air, ſhall go faſter downwards than a little water, <lb></lb>and that for many reaſons. </s><s>Firſt, becauſe if the greater quantity <lb></lb>of Earth, contained in the great Maſs of Air, ought to cauſe a greater <lb></lb>Velocity than a leſs quantity of Earth, contained in a little quantity <lb></lb>of water, it would be neceſſary, firſt, that it were true, that a <lb></lb>greater Maſs of pure Earth, ſhould move more ſwiftly than a leſs: <lb></lb>But this is falſe, though <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in many places affirms it to be true: <lb></lb>becauſe not the greater abſolute, but the greater ſpecificall Gravity, <lb></lb><arrow.to.target n="marg1543"></arrow.to.target> <lb></lb>is the cauſe of greater Velocity: nor doth a Ball of Wood, weigh <lb></lb>ing ten pounds, deſcend more ſwiftly than one weighing ten Ounces, <lb></lb>and that is of the ſame Matter: but indeed a Bullet of Lead of four <lb></lb>Ounces, deſcendeth more ſwiftly than a Ball of Wood of twenty <lb></lb>Pounds: becauſe the Lead is more grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than the Wood. <lb></lb></s><s>Therefore, its not neceſſary, that a great Maſs of Air, by reaſon of <lb></lb>the much Earth contained in it, do deſcend more ſwiftly than a little <lb></lb><arrow.to.target n="marg1544"></arrow.to.target> <lb></lb>Maſs of water, but on the contrary, any whatſoever Maſs of water, <lb></lb>ſhall move more ſwiftly than any other of Air, by reaſon the partici <lb></lb>pation of the terrene parts <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> is greater in the water, than in the <lb></lb>Air. </s><s>Let us note, in the ſecond place, how that in multiplying the <lb></lb>Maſs of the Air, we not only multiply that which is therein of terrene, <lb></lb>but its Fire alſo: whence the Cauſe of aſcending, no leſs encreaſeth, <lb></lb>by vertue of the Fire, than that of deſcending on the account of its <lb></lb>multiplied Earth. </s><s>It was requiſite in increaſing the greatneſs of the <lb></lb>Air, to multiply that which it hath of terrene only, leaving its Fire <lb></lb>in its firſt ſtate, for then the terrene parts of the augmented Air, <lb></lb>overcoming the terrene parts of the ſmall quantity of water, it might <lb></lb>with more probability have been pretended, that the great quanti <lb></lb>ty of Air, ought to deſcend with a greater <emph type="italics"></emph>Impetus,<emph.end type="italics"></emph.end> than the little <lb></lb>quantity of water.</s></p> <pb pagenum="467"></pb><p type="margin"> <s><margin.target id="marg1543"></margin.target>The greater <lb></lb>Specificall, not <lb></lb>the greater ab <lb></lb>ſolute Gravity, <lb></lb>is the Cauſe of <lb></lb>Velocity.</s></p><p type="margin"> <s><margin.target id="marg1544"></margin.target>Any Maſs of <lb></lb>water ſhal move <lb></lb>more ſwiftly, <lb></lb>than any of Air, <lb></lb>and why.</s></p><p type="main"> <s>Therefore, the Fallacy lyes more in the Diſcourſe of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> than <lb></lb>in that of <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> who with ſeverall other Reaſons might oppoſe <lb></lb><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> and alledge; If it be true, that the extreame Elements be <lb></lb>one ſimply grave, and the other ſimply light, and that the mean <lb></lb>Elements participate of the one, and of the other Nature; but the <lb></lb>Air more of Levity, and the water more of Gravity, then there ſhall <lb></lb>be a great Maſs of Air, whoſe Gravity ſhall exceed the Gravity of a <lb></lb>little quantity of water; and therefore ſuch a Maſs of Air ſhall de <lb></lb>ſcend more ſwiftly than that little water: But that is never ſeen to <lb></lb>occurr: Therefore its not true, that the mean Elements do partici <lb></lb>pate of the one, and the other quality. </s><s>This argument is fallacious, <lb></lb>no leſs than the other againſt <emph type="italics"></emph>Democritus.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>Laſtly, <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> having ſaid, that if the Poſition of <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> <lb></lb>were true, it would follow, that a great Maſs of Air ſhould move <lb></lb>more ſwiftly than a ſmall Maſs of water, and afterwards ſubjoyned, <lb></lb>that that is never ſeen in any Caſe: methinks others may become de <lb></lb>ſirous to know of him in what place this ſhould evene, which he de <lb></lb>duceth againſt <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> and what Experiment teacheth us, that <lb></lb>it never falls out ſo. </s><s>To ſuppoſe to ſee it in the Element of water, <lb></lb>or in that of the Air is vain, becauſe neither doth water through <lb></lb>water, nor Air through Air move, nor would they ever by any <lb></lb>whatever participation others aſſign them, of Earth or of Fire: the <lb></lb>Earth, in that it is not a Body fluid, and yielding to the mobility of <lb></lb>other Bodies, is a moſt improper place and <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> for ſuch an Ex <lb></lb>periment: <emph type="italics"></emph>Vacuum,<emph.end type="italics"></emph.end> according to the ſame <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf, there <lb></lb>is none, and were there, nothing would move in it: there remaine <lb></lb>the Region of Fire, but being ſo far diſtant from us, what Experi <lb></lb>ment can aſſure us, or hath aſſertained <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in ſuch ſort, that he <lb></lb>ſhould as of a thing moſt obvious to ſence, affirm what he produ <lb></lb>ceth in confutation of <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> to wit, that a great Maſs of Air, <lb></lb>is moved no ſwifter than a little one of water? </s><s>But I will dwell no <lb></lb>longer upon this matter, whereon I have ſpoke ſufficiently: but <lb></lb>leaving <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> I return to the Text of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> wherein he <lb></lb>goes about to render the true reaſon, how it comes to paſs, that the <lb></lb>thin Plates of Iron or Lead do ſwim on the water; and, moreover, <lb></lb>that Gold it ſelf being beaten into thin Leaves, not only ſwims in <lb></lb>water, but flyeth too and again in the Air. </s><s>He ſuppoſeth that of <lb></lb><arrow.to.target n="marg1545"></arrow.to.target> <lb></lb>Continualls, ſome are eaſily diviſible, others not: and that of the <lb></lb>eaſily diviſible, ſome are more ſo, and ſome leſs: and theſe he <lb></lb>affirms we ſhould eſteem the Cauſes. </s><s>He addes that that is eaſily <lb></lb>diviſible, which is well terminated, and the more the more diviſible, <lb></lb>and that the Air is more ſo, than the water, and the water than the <lb></lb>Earth. </s><s>And, laſtly, he ſuppoſeth that in each kind, the leſſe quan <lb></lb>tity is eaſlyer divided and broken than the greater.</s></p> <pb pagenum="474"></pb><p type="margin"> <s><margin.target id="marg1545"></margin.target><emph type="italics"></emph>De Cœlo<emph.end type="italics"></emph.end> l. </s><s>4. c. <lb></lb></s><s>6. t. </s><s>44.</s></p><p type="main"> <s>Here I note, that the Concluſions of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in generall are all <lb></lb>true, but methinks, that he applyeth them to particulars, in which <lb></lb>they have no place, as indeed they have in others, as for Example, <lb></lb>Wax is more eaſily diviſible than Lead, and Lead than Silver, in <lb></lb>aſmuch as Wax receives all the terms more eaſiler than Lead, and <lb></lb>Lead than Silver. </s><s>Its true, moreover, that a little quantity of Sil <lb></lb>ver is eaſlier divided than a great Maſs: and all theſe Propoſitions <lb></lb>are true, becauſe true it is, that in Silver, Lead and Wax, there <lb></lb>is ſimply a Reſiſtance againſt Diviſion, and where there is the abſo <lb></lb>lute, there is alſo the reſpective. </s><s>But if as well in water as in Air, <lb></lb>there be no Renitence againſt ſimple Diviſion, how can we ſay, that <lb></lb>the water is eaſlier divided than the Air? </s><s>We know not how to ex <lb></lb>tricate our ſelves from the Equivocation: whereupon I return to <lb></lb>anſwer, that Reſiſtance of abſolute Diviſion is one thing, and Re <lb></lb>ſiſtance of Diviſion made with ſuch and ſuch Velocity is another. <lb></lb></s><s>But to produce Reſt, and to abate the Motion, the Reſiſtance of <lb></lb>abſolute Diviſion is neceſſary; and the Reſiſtance of ſpeedy Di <lb></lb>viſion, cauſeth not Reſt, but ſlowneſs of Motion. </s><s>But that as well <lb></lb>in the Air, as in water, there is no Reſiſtance of ſimple Diviſion, is <lb></lb>manifeſt, for that there is not found any Solid Body which divides <lb></lb>not the Air, and alſo the water: and that beaten Gold, or ſmall <lb></lb>duſt, are not able to ſuperate the Reſiſtance of the Air, is contrary <lb></lb>to that which Experience ſhews us, for we ſee Gold and Duſt to go <lb></lb>waving to and again in the Air, and at laſt to deſcend down <lb></lb>wards, and to do the ſame in the water, if it be put therein, and ſe <lb></lb>parated from the Air. </s><s>And, becauſe, as I ſay, neither the water, <lb></lb>nor the Air do reſiſt ſimple Diviſion, it cannot be ſaid, that the water <lb></lb>reſiſts more than the Air. </s><s>Nor let any object unto me, the Exam <lb></lb>ple of moſt light Bodies, as a Feather, or a little of the pith of El <lb></lb>der, or water-reed that divides the Air and not the water, and from <lb></lb>this infer, that the Ait is eaſlier diviſible than the water; for I ſay <lb></lb>unto them, that if they do well obſerve, they ſhall ſee the ſame <lb></lb><arrow.to.target n="marg1546"></arrow.to.target> <lb></lb>Body likewiſe divide the Continuity of the water, and ſubmerge in <lb></lb>part, and in ſuch a part, as that ſo much water in Maſs would weigh <lb></lb>as much as the whole Solid. </s><s>And if they ſhal yet perſiſt in their doubt, <lb></lb>that ſuch a Solid ſinks not through inability to divide the water, I will <lb></lb>return them this reply, that if they put it under water, and then let it <lb></lb>go, they ſhall ſee it divide the water, and preſently aſcend with no leſs <lb></lb>celerity, than that with which it divided the Air in deſcending: ſo that <lb></lb>to ſay that this Solid aſcends in the Air, but that coming to the water, <lb></lb>it ceaſeth its Motion, and therefore the water is more difficult to be <lb></lb>divided, concludes nothing: for I, on the contrary, will propoſe them <lb></lb>a piece of Wood, or of Wax, which riſeth from the bottom of the <lb></lb>water, and eaſily divides its Reſiſtance, which afterwards being arri <pb pagenum="475"></pb>ved at the Air, ſtayeth there, and hardly toucheth it; whence I may <lb></lb>aswell ſay, that the water is more eaſier divided than the Air</s></p><p type="margin"> <s><margin.target id="marg1546"></margin.target><emph type="italics"></emph>Archimed. </s><s>De <lb></lb>Inſident, humi<emph.end type="italics"></emph.end> lib. <lb></lb></s><s>2. prop. 1.</s></p><p type="main"> <s>I will not on this occaſion forbear to give warning of another fal <lb></lb>lacy of theſe perſons, who attribute the reaſon of ſinking or ſwimming <lb></lb>to the greater or leſſe Reſiſtance of the Craſſitude of the water againſt <lb></lb>Diviſion, making uſe of the example of an Egg, which in ſweet water <lb></lb>goeth to the bottom, but in ſalt water ſwims; and alledging for the <lb></lb>cauſe thereof, the faint Reſiſtance of freſh water againſt Diviſion, and <lb></lb>the ſtrong Reſiſtance of ſalt water But if I miſtake not, from the ſame <lb></lb>Experiment, we may aswell deduce the quite contrary; namely, that <lb></lb>the freſh water is more denſe, and the ſalt more tenuous and ſubtle, <lb></lb>ſince an Egg from the bottom of ſalt water ſpeedily aſcends to the <lb></lb>top, and divides its Reſiſtance, which it cannot do in the freſh, in whoſe <lb></lb>bottom it ſtays, being unable to riſe upwards. </s><s>Into ſuch like perplex <lb></lb>ities, do falſe Principles Lead men: but he that rightly Philoſophating, <lb></lb>ſhall acknowledge the exceſſes of the Gravities of the Moveables and <lb></lb>of the Mediums, to be the Cauſes of thoſe effects, will ſay, that the <lb></lb>Egg ſinks to the bottom in freſh water, for that it is more grave than <lb></lb>it, and ſwimeth in the ſalt, for that its leſs grave than it: and ſhall <lb></lb>without any abſurdity, very ſolidly eſtabliſh his Concluſions.</s></p><p type="main"> <s>Therefore the reaſon totally ceaſeth, that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſubjoyns in the <lb></lb><arrow.to.target n="marg1547"></arrow.to.target> <lb></lb>Text ſaying; The things, therefore, which have great breadth remain <lb></lb>above, becauſe they comprehend much, and that which is greater, <lb></lb>is not eaſily divided. </s><s>Such diſcourſing ceaſeth, I ſay, becauſe its not <lb></lb>true, that there is in water or in Air any Reſiſtance of Diviſion; be <lb></lb>ſides that the Plate of Lead when it ſtays, hath already divided and <lb></lb>penetrated the Craſſitude of the water, and profounded it ſelf ten or <lb></lb>twelve times more than its own thickneſs: beſides that ſuch Reſiſtance <lb></lb>of Diviſion, were it ſuppoſed to be in the water, could not rationally <lb></lb>be affirmed to be more in its ſuperiour parts than in the middle, and <lb></lb>lower: but if there were any difference, the inferiour ſhould be the <lb></lb>more denſe, ſo that the Plate would be no leſs unable to penetrate <lb></lb>the lower, than the ſuperiour parts of the water; nevertheleſs we ſee <lb></lb>that no ſooner do we wet the ſuperious Superficies of the Board or <lb></lb>thin Piece of Wood, but it precipitatly, and without any retenſion, <lb></lb>deſcends to the bottom.</s></p><p type="margin"> <s><margin.target id="marg1547"></margin.target>Text 45.</s></p><p type="main"> <s>I believe not after all this, that any (thinking perhaps thereby to <lb></lb>defend <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end>) will ſay, that it being true, that the much water re <lb></lb>ſiſts more than the little, the ſaid Board being put lower deſcendeth, <lb></lb>becauſe there remaineth a leſs Maſs of water to be divided by it: be <lb></lb>cauſe if after the having ſeen the ſame Board ſwim in four Inches of <lb></lb>water, and alſo after that in the ſame to ſink, he ſhall try the ſame <lb></lb>Experiment upon a profundity of ten or twenty fathom water, he <lb></lb>ſhall ſee the very ſelf ſame effect. </s><s>And here I will take occaſion to <pb pagenum="476"></pb>remember, for the removall of an Error that is too common; That <lb></lb>that Ship or other whatſoever Body, that on the depth of an hundred <lb></lb>or a thouſand fathom, ſwims with ſubmerging only ſix fathom of its <lb></lb>own height, [<emph type="italics"></emph>or in the Sea dialect, that draws ſix fathom water<emph.end type="italics"></emph.end>] ſhall <lb></lb>ſwim in the ſame manner in water, that hath but ſix fathom and half <lb></lb><arrow.to.target n="marg1548"></arrow.to.target> <lb></lb>an Inch of depth. </s><s>Nor do I on the other ſide, think that it can be <lb></lb>ſaid, that the ſuperiour parts of the water are the more denſe, al <lb></lb>though a moſt grave Authour hath eſteemed the ſuperiour water in <lb></lb>the Sea to be ſo, grounding his opinion upon its being more ſalt, than <lb></lb>that at the bottom: but I doubt the Experiment, whether hitherto <lb></lb>in taking the water from the bottom, the Obſervatour did not light <lb></lb>upon ſome ſpring of freſh water there ſpouting up: but we plainly <lb></lb>ſee on the contrary, the freſh Waters of Rivers to dilate themſelves <lb></lb>for ſome miles beyond their place of meeting with the ſalt water of <lb></lb>the Sea, without deſcending in it, or mixing with it, unleſs by the <lb></lb>intervention of ſome commotion or turbulency of the Windes.</s></p><p type="margin"> <s><margin.target id="marg1548"></margin.target>A Ship that <lb></lb>in 100 Fathome <lb></lb>water draweth <lb></lb>6 Fathome, ſhall <lb></lb>float in 6 Fa <lb></lb>thome and 1/2 an <lb></lb>Inch of depth.</s></p><p type="main"> <s>But returning to <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> I ſay, that the breadth of Figure hath <lb></lb>nothing to do in this buſineſs more or leſs, becauſe the ſaid Plate of <lb></lb><arrow.to.target n="marg1549"></arrow.to.target> <lb></lb>Lead, or other Matter, cut into long Slices, ſwim neither more nor <lb></lb>leſs; and the ſame ſhall the Slices do, being cut anew into little <lb></lb>pieces, becauſe its not the breadth but the thickneſs that operates in <lb></lb>this buſineſs. </s><s>I ſay farther, that in caſe it were really true, that the <lb></lb><arrow.to.target n="marg1550"></arrow.to.target> <lb></lb>Renitence to Diviſion were the proper Cauſe of ſwimming, the Fi <lb></lb>gures more narrow and ſhort, would much better ſwim than the more <lb></lb>ſpacious and broad, ſo that augmenting the breadth of the Figure, <lb></lb>the facility of ſupernatation will be deminiſhed, and decreaſing, that <lb></lb>this will encreaſe.</s></p><p type="margin"> <s><margin.target id="marg1549"></margin.target>Thickneſs not <lb></lb>breadth of Fi <lb></lb>gure to be re <lb></lb>ſpected in Na <lb></lb>tation.</s></p><p type="margin"> <s><margin.target id="marg1550"></margin.target>Were Reni <lb></lb>tence the cauſe <lb></lb>of Natation, <lb></lb>breadth of Fi <lb></lb>gure would <lb></lb>hinder the <lb></lb>ſwiming of Bo <lb></lb>dies.</s></p><p type="main"> <s>And for declaration of what I ſay, conſider that when a thin Plate <lb></lb>of Lead deſcends, dividing the water, the Diviſion and diſcontinu <lb></lb>ation is made between the parts of the water, invironing the perime <lb></lb>ter or Circumference of the ſaid Plate, and according to the big <lb></lb>neſs greater or leſſer of that circuit, it hath to divide a greater or <lb></lb>leſſer quantity of water, ſo that if the circuit, ſuppoſe of a Board, <lb></lb>be ten Feet in ſinking it flatways, it is to make the ſeperation and <lb></lb>diviſion, and to ſo ſpeak, an inciſſion upon ten Feet of water; and <lb></lb>likewiſe a leſſer Board that is four Feet in Perimeter, muſt make an <lb></lb>inceſſion of four Feet. </s><s>This granted, he that hath any knowledge <lb></lb>in Geometry, will comprehend, not only that a Board ſawed in many <lb></lb>long thin pieces, will much better float than when it was entire, but <lb></lb>that all Figures, the more ſhort and narrow they be, ſhall ſo much the <lb></lb>better ſwim. </s><s>Let the Board ABCD be, for Example, eight <lb></lb>Palmes long, and five broad, its circuit ſhall be twenty ſix Palmes; <lb></lb>and ſo many muſt the inceſſion be, which it ſhall make in the water to <lb></lb>deſcend therein: but if we do ſaw ir, as ſuppoſe into eight little <pb pagenum="469"></pb>pieces, according to the Lines E F, G H, <emph type="italics"></emph>&c.<emph.end type="italics"></emph.end> making ſeven Segments, <lb></lb>we muſt adde to the twenty ſix Palmes of the circuit of the whole <lb></lb>Board, ſeventy others; whereupon the eight little pieces ſo cut and <lb></lb>ſeperated, have to cut ninty ſix Palmes of water. </s><s>And, if moreover, <lb></lb>we cur each of the ſaid pieces into five parts, re <lb></lb><figure id="fig280"></figure> <lb></lb>ducing them into Squares, to the circuit of ninty <lb></lb>ſix Palmes, with four cuts of eight Palmes apiece; <lb></lb>we ſhall adde alſo ſixty four Palmes, whereupon <lb></lb>the ſaid Squares to deſcend in the water, muſt <lb></lb>divide one hundred and ſixty Palmes of water, <lb></lb>but the Reſiſtance is much greater than that of <lb></lb>twenty ſix; therefore to the leſſer Superficies, <lb></lb>we ſhall reduce them, ſo much the more eaſily <lb></lb>will they float: and the ſame will happen in all <lb></lb>other Figures, whoſe Superficies are ſimular amongſt themſelves, but <lb></lb>different in bigneſs: becauſe the ſaid Superficies, being either demini <lb></lb>ſhed or encreaſed, always diminiſh or encreaſe their Perimeters in <lb></lb>ſubduple proportion; to wit, the Reſiſtance that they find in pene <lb></lb>trating the water; therefore the little pieces gradually ſwim, with more <lb></lb>and more facility as their breadth is leſſened.</s></p><p type="main"> <s><emph type="italics"></emph>This is manifeſt; for keeping ſtill the ſame height of the Solid, with <lb></lb>the ſame proportion as the Baſe encreaſeth or deminiſheth, doth the ſaid <lb></lb>Solid alſo encreaſe or diminiſh; whereupon the Solid more diminiſhing <lb></lb>than the Circuit, the Cauſe of Submerſion more diminiſheth than the Cauſe <lb></lb>of Natation: And on the contrary, the Solid more encreaſing than the <lb></lb>Circuit, the Cauſe of Submerſion encreaſeth more, that of Natation <lb></lb>leſs.<emph.end type="italics"></emph.end></s></p><p type="main"> <s>And this may all be dedueed out of the Doctrine of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> a <lb></lb>gainſt his own Doctrine.</s></p><p type="main"> <s>Laſtly, to that which we read in the latter part of the Text, that <lb></lb><arrow.to.target n="marg1551"></arrow.to.target> <lb></lb>is to ſay, that we muſt compare the Gravity of the Moveable with <lb></lb>the Reſiſtance of the Medium againſt Diviſion, becauſe if the force of <lb></lb>the Gravity exceed the Reſiſtance of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> the Moveable will <lb></lb>deſcend, if not it will float. </s><s>I need not make any other anſwer, <lb></lb>but that which hath been already delivered; namely, that its not <lb></lb>the Reſiſtance of abſolute Diviſion, (which neither is in Water nor <lb></lb>Air) but the Gravity of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> that muſt be compared with the <lb></lb>Gravity of the Moveables; and if that of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> be greater, the <lb></lb>Moveable ſhall not deſcend, nor ſo much as make a totall Submerſion, <lb></lb>but a partiall only: becauſe in the place which it would occupy in <lb></lb>the water, there muſt not remain a Body that weighs leſs than a like <lb></lb>quantity of water: but if the Moveable be more grave, it ſhall deſ <lb></lb>cend to the bottom, and poſſeſs a place where it is more conformable <pb></pb> for it to remain, than another Body that is leſs grave. </s><s>And this <lb></lb>is the only true proper and abſolute Cauſe of Natation and Sub <lb></lb>merſion, ſo that nothing elſe hath part therein: and the Board of the <lb></lb>Adverſaries ſwimmeth, when it is conjoyned with as much Air, <lb></lb>as, together with it, doth form a Body leſs grave than ſo much water <lb></lb>as would fill the place that the ſaid Compound occupyes in the <lb></lb>water; but when they ſhall demit the ſimple Ebony into <lb></lb>the water, according to the Tenour of our Que <lb></lb>ſtion, it ſhall alwayes go to the bottom, <lb></lb>though it were as thin as a <lb></lb>Paper.</s></p><p type="margin"> <s><margin.target id="marg1551"></margin.target>Lib. 4. c. </s><s>6. <lb></lb>Text 45.</s></p><p type="head"> <s><emph type="italics"></emph>FINIS.<emph.end type="italics"></emph.end></s></p> </chap> </body> <back></back> </text></archimedes>