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DE Specs Version 2.1.1 Autumn 2011
author Klaus Thoden <kthoden@mpiwg-berlin.mpg.de>
date Thu, 02 May 2013 11:29:00 +0200
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1 <?xml version="1.0"?>
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2 <archimedes xmlns:xlink="http://www.w3.org/1999/xlink" > <info>
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3 <author>Galilei, Galileo</author>
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4 <title>Discourse concerning the natation of bodies</title>
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5 <date>1663</date>
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6 <place>London</place>
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7 <translator>Thomas Salusbury</translator>
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8 <lang>en</lang>
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9 <cvs_file>galil_natat_074_en_1663.xml</cvs_file>
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10 <cvs_version></cvs_version>
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11 <locator>074.xml</locator>
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12 </info> <text> <front> <section>
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14 <pb></pb>
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16 <p type="head">
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18 <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">
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20 <s>By GALILEUS GALILEI: Philoſopher and <lb></lb>Mathematician, unto His moſt Serene Highneſſe.</s></p><p type="head">
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22 <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">
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24 <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>
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27 <pb pagenum="401"></pb><p type="head">
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29 <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">
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31 <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">
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33 <s><margin.target id="marg1393"></margin.target>His Nuncio Sl­<lb></lb>derio.</s></p><p type="main">
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35 <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
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36 <lb></lb>Moon, together with the Conſequents depending thereupon, have
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37 <lb></lb>not ſo much occaſioned the demur, as the inveſtigation of the times
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38 <lb></lb>of the Converſions of each of the Four Medicean Planets about <emph type="italics"></emph>Ju­
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39 <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
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40 <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
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41 <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> &amp; 29 <emph type="italics"></emph>m.<emph.end type="italics"></emph.end> of its Sphere in an houre, make­
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42 <lb></lb>ing its whole revolution in one naturall day, and 18 hours, and almoſt
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43 <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,
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44 <lb></lb>in an hour, and its compleat converſion is conſummate in 3 dayes, 13
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45 <lb></lb>hours, and one third, or thereabouts. </s><s>The third paſſeth in an hour,
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46 <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
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47 <lb></lb>dayes, 4 hours, or very neer. </s><s>The fourth, and more remote than the
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48 <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,
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49 <lb></lb>and finiſheth it all in 16 dayes, and very neer 18 hours. </s><s>But be­
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50 <lb></lb>cauſe the exceſſive velocity of their returns or reſtitutions, requires a
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51 <lb></lb>moſt ſcrupulous preciſeneſſe to calculate their places, in times paſt
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54 <pb pagenum="402"></pb>and future, eſpecially if the time be for many Moneths or Years; I
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55 <lb></lb>am therefore forced, with other Obſervations, and more exact than
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56 <lb></lb>the former, and in times more remote from one another, to correct
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57 <lb></lb>the Tables of ſuch Motions, and limit them even to the ſhorteſt mo­
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58 <lb></lb>ment: for ſuch exactneſſe my firſt Obſervations ſuffice not; not only
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59 <lb></lb>in regard of the ſhort intervals of Time, but becauſe I had not as then
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60 <lb></lb>found out a way to meaſure the diſtances between the ſaid Planets
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61 <lb></lb>by any Inſtrument: I Obſerved ſuch Intervals with ſimple relation
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62 <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
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63 <lb></lb>the eye, the which, though they admit not errors of above a Minute,
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64 <lb></lb>yet they ſuffice not for the determination of the exact greatneſs of the
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65 <lb></lb>Spheres of thoſe Stars. </s><s>But now that I have hit upon a way of ta­
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66 <lb></lb>king ſuch meaſures without failing, ſcarce in a very few Seconds, I will
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67 <lb></lb>continue the obſervation to the very occultation of <emph type="italics"></emph>JVPITER,<emph.end type="italics"></emph.end>
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68 <lb></lb>which ſhall ſerve to bring us to the perfect knowledge of the Moti­
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69 <lb></lb>ons, and Magnitudes of the Orbes of the ſaid Planets, together
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70 <lb></lb><arrow.to.target n="marg1394"></arrow.to.target>
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71 <lb></lb>alſo with ſome other conſequences thence ariſing. </s><s>I adde to theſe
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72 <lb></lb>things the obſervation of ſome obſcure Spots, which are diſcover­
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73 <lb></lb>ed in the Solar Body, which changing, poſition in that, propounds
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74 <lb></lb>to our conſideration a great argument either that the Sun revolves in
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75 <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
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76 <lb></lb><emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> revolve about it, inviſible in other times, by reaſon of their
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77 <lb></lb>ſmall digreſſions, leſſe than that of <emph type="italics"></emph>Mercury,<emph.end type="italics"></emph.end> and only viſible when
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78 <lb></lb>they interpoſe between the Sun and our eye, or elſe hint the truth
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79 <lb></lb>of both this and that; the certainty of which things ought not to be
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80 <lb></lb>contemned, nor omitted.</s></p><p type="margin">
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81
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82 <s><margin.target id="marg1394"></margin.target>The Authors
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83 <lb></lb>Obſervations of
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84 <lb></lb>the Solar Spots.</s></p><p type="main">
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85
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86 <s><emph type="italics"></emph>Continuall obſervation hath at laſt aſſured me that theſe Spots are
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87 <lb></lb>matters contiguous to the Body of the Sun, there continually produced
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88 <lb></lb>in great number, and afterwards diſſolved, ſome in a ſhorter, ſome in a
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89 <lb></lb>longer time, and to be by the Converſion or Revolution of the Sun in it
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90 <lb></lb>ſelfe, which in a Lunar Moneth, or thereabouts, finiſheth its Period,
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91 <lb></lb>caried about in a Circle, an accident great of it ſelfe, and greater for
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92 <lb></lb>its Conſequences.<emph.end type="italics"></emph.end>
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93 <lb></lb><arrow.to.target n="marg1395"></arrow.to.target></s></p><p type="margin">
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94
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95 <s><margin.target id="marg1395"></margin.target>The occaſion in­
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96 <lb></lb>ducing the Au­
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97 <lb></lb>thor to write
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98 <lb></lb>this Treatiſe.</s></p><p type="main">
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99
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100 <s>As to the other particular in the next place. ^{*} Many cauſes have
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101 <lb></lb>moved me to write the preſent Tract, the ſubject whereof, is the
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102 <lb></lb>Diſpute which I held ſome dayes ſince, with ſome learned men of
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103 <lb></lb>this City, about which, as your Highneſſe knows, have followed
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104 <lb></lb>many Diſcourſes: The principall of which Cauſes hath been the
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105 <lb></lb>Intimation of your Highneſſe, having commended to me Writing,
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106 <lb></lb>as a ſingular means to make true known from falſe, reall from appa­
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107 <lb></lb>rent Reaſons, farr better than by Diſputing vocally, where the
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108 <lb></lb>one or the other, or very often both the Diſputants, through too
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109
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110
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111 <pb pagenum="403"></pb>greate heate, or exalting of the voyce, either are not underſtood,
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112 <lb></lb>or elſe being tranſported by oſtentation of not yeilding to one ano­
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113 <lb></lb>ther, farr from the firſt Propoſition, with the novelty, of the
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114 <lb></lb>various Propoſals, confound both themſelves and their Auditors.</s></p><p type="main">
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115
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116 <s>Moreover, it ſeemed to me convenient to informe your High­
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117 <lb></lb>neſſe of all the ſequell, concerning the Controverſie of which I
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118 <lb></lb>treat, as it hath been advertiſed often already by others: and becauſe
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119 <lb></lb>the Doctrine which I follow, in the diſcuſſion of the point in hand,
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120 <lb></lb>is different from that of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>; and interferes with his Principles,
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121 <lb></lb>I have conſidered that againſt the Authority of that moſt famous
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122 <lb></lb>Man, which amongſt many makes all ſuſpected that comes not from
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123 <lb></lb>the Schooles of the Peripateticks, its farr better to give ones Reaſons
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124 <lb></lb>by the Pen than by word of mouth and therfore I reſolved to write the
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125 <lb></lb>preſent diſcourſe: in which yet I hope to demonſtrate that it was not
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126 <lb></lb>out of capritiouſneſſe, or for that I had not read or underſtood
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127 <lb></lb><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> that I ſometimes ſwerve from his opinion, but becauſe
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128 <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">
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129
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130 <s><arrow.to.target n="marg1396"></arrow.to.target>
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131 <lb></lb>tought me to fix my judgment on that which is grounded upon
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132 <lb></lb>Reaſon, and not on the bare Authority of the Maſter; and it is
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133 <lb></lb>moſt certaine according to the ſentence of <emph type="italics"></emph>Alcinoos,<emph.end type="italics"></emph.end> that philoſopha­
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134 <lb></lb><arrow.to.target n="marg1397"></arrow.to.target>
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135 <lb></lb>ting ſhould be free. </s><s>Nor is the reſolution of our Queſtion in my
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136 <lb></lb>judgment without ſome benefit to the Univerſall, foraſmuch as
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137 <lb></lb>treating whether the figure of Solids operates, or not, in their going,
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138 <lb></lb>or not going to the bottome in Water, in occurrences of building
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139 <lb></lb>Bridges or other Fabricks on the Water, which happen commonly
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140 <lb></lb>in affairs of grand import, it may be of great availe to know the
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141 <lb></lb>truth.</s></p><p type="margin">
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142
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143 <s><margin.target id="marg1396"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> prefers
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144 <lb></lb>Reaſon to the
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145 <lb></lb>Authority ofan
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146 <lb></lb>Author.</s></p><p type="margin">
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147
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148 <s><margin.target id="marg1397"></margin.target>The benefit of
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149 <lb></lb>this Argument.</s></p><p type="main">
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150
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151 <s>I ſay therfore, that being the laſt Summer in company with certain
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152 <lb></lb><arrow.to.target n="marg1398"></arrow.to.target>
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153 <lb></lb>Learned men, it was ſaid in the argumentation; That Condenſation
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154 <lb></lb>was the propriety of Cold, and there was alledged for inſtance, the
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155 <lb></lb>example of Ice: now I at that time ſaid, that, in my judgment,
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156 <lb></lb>the Ice ſhould be rather Water rarified than condenſed, and my
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157 <lb></lb><arrow.to.target n="marg1399"></arrow.to.target>
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158 <lb></lb>reaſon was, becauſe Condenſation begets diminution of Maſs, and
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159 <lb></lb>augmentation of gravity, and Rarifaction cauſeth greater Lightneſs,
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160 <lb></lb>and augmentarion of Maſſe: and Water in freezing, encreaſeth in
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161 <lb></lb>Maſſe, and the Ice made thereby is lighter than the Water on which
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162 <lb></lb>it ſwimmeth.</s></p><p type="margin">
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163
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164 <s><margin.target id="marg1398"></margin.target>Condenſation
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165 <lb></lb>the Propriety of
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166 <lb></lb>Cold, according
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167 <lb></lb>to the Peripate­
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168 <lb></lb>ticks.</s></p><p type="margin">
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169
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170 <s><margin.target id="marg1399"></margin.target>Ice rather water
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171 <lb></lb>rarified, than
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172 <lb></lb>condenſed, and
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173 <lb></lb>why:</s></p><p type="main">
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174
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175 <s><emph type="italics"></emph>What I ſay, is manifeſt, becauſe, the medium ſubtracting from the
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176 <lb></lb>whole Gravity of Sollids the weight of ſuch another Maſſe of the ſaid<emph.end type="italics"></emph.end>
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177 <lb></lb><arrow.to.target n="marg1400"></arrow.to.target>
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178 <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
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179 <lb></lb>Humido; <emph type="italics"></emph>when ever the Maſſe of the ſaid Solid encreaſeth by Diſtraction,
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180 <lb></lb>the more ſhall the<emph.end type="italics"></emph.end> Medium <emph type="italics"></emph>detract from its entire Gravity; and leſſe,
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181 <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">
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182
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183
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184 <pb pagenum="404"></pb>
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185
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186 <s><margin.target id="marg1400"></margin.target>In lib: 1. of Na­
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187 <lb></lb>tation of Bodies
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188 <lb></lb>Prop. </s><s>7.</s></p><p type="margin">
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189
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190 <s><margin.target id="marg1401"></margin.target>Figure operates
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191 <lb></lb>not in the Nata­
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192 <lb></lb>tion of Sollids.</s></p><p type="main">
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193
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194 <s>It was anſwered me, that that proceeded not from the greater Levity;
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195 <lb></lb><arrow.to.target n="marg1401"></arrow.to.target>
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196 <lb></lb>but from the Figure, large and flat, which not being able to pene­
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197 <lb></lb>trate the Reſiſtance of the Water, is the cauſe that it ſubmergeth not.
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198 <lb></lb></s><s>I replied, that any piece of Ice, of whatſoever Figure, ſwims upon
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199 <lb></lb>the Water, a manifeſt ſigne, that its being never ſo flat and broad,
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200 <lb></lb>hath not any part in its floating: and added, that it was a manifeſt
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201 <lb></lb>proofe hereof to ſee a piece of Ice of very broad Figure being thruſt
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202 <lb></lb>to the botome of the Water, ſuddenly return to flote atoppe, which
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203 <lb></lb>had it been more grave, and had its ſwimming proceeded from its
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204 <lb></lb>Forme, unable to penetrate the Reſiſtance of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> that
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205 <lb></lb>would be altogether impoſſible; I concluded therefore, that the Figure
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206 <lb></lb>was in ſort a Cauſe of the Natation or Submerſion of Bodies,
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207 <lb></lb>but the greater or leſſe Gravity in reſpect of the Water: and there­
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208 <lb></lb>fore all Bodyes heavier than it of what Figure ſoever they be, indiffe­
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209 <lb></lb>rently go to the bottome, and the lighter, though of any figure, float
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210 <lb></lb>indifferently on the top: and I ſuppoſe that thoſe which hold other­
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211 <lb></lb>wiſe, were induced to that beliefe, by ſeeing how that diverſity
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212 <lb></lb>of Formes or Figures, greatly altereth the Veloſity, and Tardity
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213 <lb></lb>of Motion; ſo that Bodies of Figure broad and thin, deſcend
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214 <lb></lb>far more leaſurely into the Water, than thoſe of a more compacted
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215 <lb></lb>Figure, though both made of the ſame Matter: by which ſome
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216 <lb></lb>might be induced to believe that the Dilatation of the Figure might
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217 <lb></lb>reduce it to ſuch ampleneſſe that it ſhould not only retard but wholly
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218 <lb></lb>impede and take away the Motion, which I hold to be falſe. </s><s>Upon
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219 <lb></lb>this Concluſion, in many dayes diſcourſe, was ſpoken much, and
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220 <lb></lb>many things, and divers Experiments produced, of which your
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221 <lb></lb>Highneſſe heard, and ſaw ſome, and in this diſcourſe ſhall have
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222 <lb></lb>all that which hath been produced againſt my Aſſertion, and what
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223 <lb></lb>hath been ſuggeſted to my thoughts on this matter, and for con­
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224 <lb></lb>firmation of my Concluſion: which if it ſhall ſuffice to remove that
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225 <lb></lb>(as I eſteem hitherto falſe) Opinion, I ſhall thinke I have not
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226 <lb></lb>unprofitably ſpent my paynes and time. </s><s>and although that come
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227 <lb></lb>not to paſſe, yet ought I to promiſe another benefit to my ſelfe,
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228 <lb></lb>namely, of attaining the knowledge of the truth, by hearing my
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229 <lb></lb>Fallacyes confuted, and true demonſtrations produced by thoſe
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230 <lb></lb>of the contrary opinion.</s></p><p type="main">
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231
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232 <s>And to proceed with the greateſt plainneſs and perſpicuity that
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233 <lb></lb>I can poſſible, it is, I conceive, neceſſary, firſt of all to declare
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234 <lb></lb>what is the true, intrinſecall, and totall Cauſe, of the aſcending of
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235 <lb></lb>ſome Sollid Bodyes in the Water, and therein floating; or on the
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236 <lb></lb>contrary, of their ſinking. </s><s>and ſo much the rather in aſmuch as I
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237 <lb></lb>cannot ſatisfie my ſelfe in that which <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> hath left written on
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238 <lb></lb>this Subject.</s></p><p type="margin">
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239 <s><margin.target id="marg1402"></margin.target>The cauſe of the
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240 <lb></lb>Natation &amp; ſub­</s></p> <p type="main">
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241
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242 <s>I ſay then the Cauſe why ſome Sollid Bodyes deſcend to the
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243 <lb></lb><arrow.to.target n="marg1402"></arrow.to.target>
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244
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245
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246 <pb pagenum="405"></pb>Bottom of Water, is the exceſſe of their Gravity, above the
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247 <lb></lb><arrow.to.target n="marg1403"></arrow.to.target>
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248 <lb></lb>Gravity of the Water; and on the contrary, the exceſs of the
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249 <lb></lb>Waters Gravity above the Gravity of thoſe, is the Cauſe that others
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250 <lb></lb>do not deſcend, rather that they riſe from the Bottom, and aſcend
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251 <lb></lb>to the Surface. </s><s>This was ſubtilly demonſtrated by <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> in
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252 <lb></lb>his Book Of the NATATION of BODIES: Conferred afterwards
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253 <lb></lb>by a very grave Author, but, if I erre not inviſibly, as below for
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254 <lb></lb>defence of him, I ſhall endeavour to prove.</s></p><p type="margin">
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255
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256 <s><margin.target id="marg1403"></margin.target>merſion of Sol­
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257 <lb></lb>ids in the Wa­
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258 <lb></lb>ter.</s></p><p type="main">
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259
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260 <s>I, with a different Method, and by other meanes, will endeavour
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261 <lb></lb>to demonſtrate the ſame, reducing the Cauſes of ſuch Effects to
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262 <lb></lb>more intrinſecall and immediate Principles, in which alſo are diſco­
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263 <lb></lb>vered the Cauſes of ſome admirable and almoſt incredible Acci­
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264 <lb></lb>dents, as that would be, that a very little quantity of Water, ſhould
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265 <lb></lb>be able, with its ſmall weight, to raiſe and ſuſtain a Solid Body, an
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266 <lb></lb>hundred or a thouſand times heavier than it.</s></p><p type="main">
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267
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268 <s>And becauſe demonſtrative Order ſo requires, I ſhall define cer­
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269 <lb></lb>tain Termes, and afterwards explain ſome Propoſitions, of which,
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270 <lb></lb>as of things true and obvious, I may make uſe of to my preſent pur­
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271 <lb></lb>poſe.</s></p><p type="head">
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272
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273 <s>DEFINITION I.</s></p><p type="main">
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274
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275 <s><emph type="italics"></emph>I then call equally Grave<emph.end type="italics"></emph.end> in ſpecie, <emph type="italics"></emph>thoſe Matters
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276 <lb></lb>of which equall Maſſes weigh equally.<emph.end type="italics"></emph.end></s></p><p type="main">
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277
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278 <s>As if for example, two Balls, one of Wax, and the other of ſome
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279 <lb></lb>Wood of equall Maſſe, were alſo equall in Weight, we ſay, that
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280 <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">
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281
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282 <s>DEFINITION II.</s></p><p type="main">
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283
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284 <s><emph type="italics"></emph>But equally grave in Abſolute Gravity, we call two
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285 <lb></lb>Sollids, weighing equally, though of Maſs they be
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286 <lb></lb>unequall.<emph.end type="italics"></emph.end></s></p><p type="main">
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287
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288 <s>As for example, a Maſs of Lead, and another of Wood, that
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289 <lb></lb>weigh each ten pounds, I call equall in Abſolute Gravity, though
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290 <lb></lb>the Maſs of the Wood be much greater then that of the Lead.</s></p><p type="main">
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291
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292 <s><emph type="italics"></emph>And, conſequently, leſs Grave<emph.end type="italics"></emph.end> in ſpecie.</s></p><p type="head">
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293
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294 <s>DEFINITION III.</s></p><p type="main">
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295
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296 <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
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297 <lb></lb>which a Maſs, equall to a Maſs of the other, ſhall
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298 <lb></lb>weigh more.<emph.end type="italics"></emph.end></s></p>
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299
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300
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301 <pb pagenum="406"></pb><p type="main">
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302
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303 <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
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304 <lb></lb>if you take of them two equall Maſſes, that of the Lead weigheth
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305 <lb></lb>more.</s></p><p type="head">
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306
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307 <s>DEFINITION IV.</s></p><p type="main">
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308
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309 <s><emph type="italics"></emph>But I call that Body more grave abſolutely than this, if
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310 <lb></lb>that weigh more than this, without any reſpect had to
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311 <lb></lb>the Maſſes.<emph.end type="italics"></emph.end></s></p><p type="main">
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312
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313 <s>And thus a great piece of Wood is ſaid to weigh more than a
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314 <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
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315 <lb></lb>the Wood. </s><s>And the ſame is to be underſtood of the leſs grave <emph type="italics"></emph>in
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316 <lb></lb>ſpecie,<emph.end type="italics"></emph.end> and the leſs grave abſolutely.</s></p><p type="main">
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317
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318 <s>Theſe Termes defined, I take from the Mechanicks two Princi­
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319 <lb></lb>ples: the firſt is, that</s></p><p type="head">
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320
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321 <s>AXIOME. I.</s></p><p type="main">
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322
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323 <s><emph type="italics"></emph>Weights abſolutely equall, moved with equall Velocity,
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324 <lb></lb>are of equall Force and Moment in their operations.<emph.end type="italics"></emph.end></s></p><p type="head">
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325
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326 <s><emph type="italics"></emph>DEFINITION V.<emph.end type="italics"></emph.end></s></p><p type="main">
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327
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328 <s>Moment, amongſt Mechanicians, ſigrifieth that
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329 <lb></lb>Vertue, that Force, or that Efficacy, with which
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330 <lb></lb>the Mover moves, and the Moveable reſiſts.</s></p><p type="main">
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331
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332 <s><emph type="italics"></emph>Which Vertue dependes not only on the ſimple Gravity, but on the
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333 <lb></lb>Velocity of the Motion, and on the diverſe Inclinations of the Spaces
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334 <lb></lb>along which the Motion is made: For a deſcending Weight makes a
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335 <lb></lb>greater<emph.end type="italics"></emph.end> Impetus <emph type="italics"></emph>in a Space much declining, than in one leſs declining;
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336 <lb></lb>and in ſumme, what ever is the occaſion of ſuch Vertue, it ever retaines
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337 <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
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338 <lb></lb>Idiome, for, if I mistake not, I think we often ſay; This is a weighty
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339 <lb></lb>buſineſſe, but the other is of ſmall moment: and we conſider lighter mat­
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340 <lb></lb>ters and let paſs thoſe of Moment; a Metaphor, I ſuppoſe, taken from
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341 <lb></lb>the Mechanicks.<emph.end type="italics"></emph.end></s></p><p type="main">
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342
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343 <s>As for example, two weights equall in abſolute Gravity, being
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344 <lb></lb>put into a Ballance of equall Arms, they ſtand in <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> nei­
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345 <lb></lb>ther one going down, nor the other up: becauſe the equality of the
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346 <lb></lb>Diſtances of both, from the Centre on which the Ballance is ſuppor­
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347 <lb></lb>ted, and about which it moves, cauſeth that thoſe weights, the ſaid
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348 <lb></lb>Ballance moving, ſhall in the ſame Time move equall Spaces, that is,
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349 <lb></lb>ſhall move with equall Velocity, ſo that there is no reaſon for which
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350
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351
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352 <pb pagenum="407"></pb>this Weight ſhould deſcend more than that, or that more than this;
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353 <lb></lb>and therefore they make an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> and their Moments continue
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354 <lb></lb>of ſemblable and equall Vertue.</s></p><p type="main">
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355
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356 <s>The ſecond Principle is; That</s></p><p type="head">
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357
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358 <s>AXIOME II.</s></p><p type="main">
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359
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360 <s><emph type="italics"></emph>The Moment and Force of the Gravity, is encreaſed by
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361 <lb></lb>the Velocity of the Motion.<emph.end type="italics"></emph.end></s></p><p type="main">
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362
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363 <s>So that Weights abſolutely equall, but conjoyned with Velocity
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364 <lb></lb>unequall, are of Force, Moment and Vertue unequall: and the
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365 <lb></lb>more potent, the more ſwift, according to the proportion of the Ve­
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366 <lb></lb>locity of the one, to the Velocity of the other. </s><s>Of this we have a
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367 <lb></lb>very pertinent example in the Balance or Stiliard of unequall Arms,
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368 <lb></lb>at which Weights abſolutely equall being ſuſpended, they do not
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369 <lb></lb>weigh down, and gravitate equally, but that which is at a greater
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370 <lb></lb>diſtance from the Centre, about which the Beam moves, deſcends,
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371 <lb></lb>raiſing the other, and the Motion of this which aſcends is ſlow, and
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372 <lb></lb>the other ſwift: and ſuch is the Force and Vertue, which from the
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373 <lb></lb>Velocity of the Mover, is conferred on the Moveable, which receives
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374 <lb></lb>it, that it can exquiſitely compenſate, as much more Weight added to
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375 <lb></lb>the other ſlower Moveable: ſo that if of the Arms of the Balance,
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376 <lb></lb>one were ten times as long as the other, whereupon in the Beames
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377 <lb></lb>moving about the Centre, the end of that would go ten times as far
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378 <lb></lb>as the end of this, a Weight ſuſpended at the greater diſtance, may
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379 <lb></lb>ſuſtain and poyſe another ten times more grave abſolutely than it:
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380 <lb></lb>and that becauſe the Stiliard moving, the leſſer Weight ſhall move
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381 <lb></lb>ten times faſter than the bigger. </s><s>It ought alwayes therefore to be
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382 <lb></lb>underſtood, that Motions are according to the ſame Inclinations,
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383 <lb></lb>namely, that if one of the Moveables move perpendicularly to the
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384 <lb></lb>Horizon, then the other makes its Motion by the like Perpendicular;
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385 <lb></lb>and if the Motion of one were to be made Horizontally; that then
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386 <lb></lb>the other is made along the ſame Horizontall plain: and in ſumme,
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387 <lb></lb>alwayes both in like Inclinations. </s><s>This proportion between the
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388 <lb></lb>Gravity and Velocity is found in all Mechanicall Inſtruments: and
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389 <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>;
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390 <lb></lb>whereupon we alſo may take it for a true Aſſumption, That</s></p><p type="head">
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391
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392 <s>AXIOME III.</s></p><p type="main">
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393
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394 <s><emph type="italics"></emph>Weights abſolutely unequall, do alternately counterpoyſe
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395 <lb></lb>and become of equall Moments, as oft as their Gravi­
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396 <lb></lb>ties, with contrary proportion, anſwer to the Velocity of
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397 <lb></lb>their Motions.<emph.end type="italics"></emph.end></s></p>
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398
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399
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400 <pb pagenum="408"></pb><p type="main">
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401
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402 <s>That is to ſay, that by how much the one is leſs grave than the other,
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403 <lb></lb>by ſo much is it in a conſtitution of moving more ſwiftly than that.</s></p><p type="main">
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404
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405 <s>Having prefatically explicated theſe things, we may begin to en­
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406 <lb></lb>quire, what Bodyes thoſe are which totally ſubmerge in Water, and
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407 <lb></lb>go to the Bottom, and which thoſe that by conſtraint float on the
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408 <lb></lb>top, ſo that being thruſt by violence under Water, they return to
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409 <lb></lb>ſwim, with one part of their Maſs viſible above the Surface of the
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410 <lb></lb>Water: and this we will do by conſidering the reſpective operati­
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411 <lb></lb>on of the ſaid Solids, and of Water: Which operation followes
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412 <lb></lb>the Submerſion and ſinking; and this it is, That in the Submerſion
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413 <lb></lb><arrow.to.target n="marg1404"></arrow.to.target>
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414 <lb></lb>that the Solid maketh, being depreſſed downwards by its proper
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415 <lb></lb>Gravity, it comes to drive away the water from the place where it
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416 <lb></lb>ſucceſſively ſubenters, and the water repulſed riſeth and aſcends
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417 <lb></lb>above its firſt levell, to which Aſcent on the other ſide it, as being a
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418 <lb></lb>grave Body of its own nature, reſiſts: And becauſe the deſcending
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419 <lb></lb>Solid more and more immerging, greater and greater quantity of
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420 <lb></lb>Water aſcends, till the whole Sollid be ſubmerged; its neceſſary to
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421 <lb></lb>compare the Moments of the Reſiſtance of the water to Aſcenſion,
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422 <lb></lb>with the Moments of the preſſive Gravity of the Solid: And if the
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423 <lb></lb>Moments of the Reſiſtance of the water, ſhall equalize the Moments
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424 <lb></lb><arrow.to.target n="marg1405"></arrow.to.target>
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425 <lb></lb>of the Solid, before its totall Immerſion; in this caſe doubtleſs there
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426 <lb></lb>ſhall be made an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> nor ſhall the Body ſink any farther.
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427 <lb></lb></s><s>But if the Moment of the Solid, ſhall alwayes exceed the Moments
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428 <lb></lb><arrow.to.target n="marg1406"></arrow.to.target>
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429 <lb></lb>wherewith the repulſed water ſucceſſively makes Reſiſtance, that
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430 <lb></lb>Solid ſhall not only wholly ſubmerge under water, but ſhall deſcend
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431 <lb></lb>to the Bottom. </s><s>But if, laſtly, in the inſtant of totall Submerſion,
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432 <lb></lb><arrow.to.target n="marg1407"></arrow.to.target>
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433 <lb></lb>the equality ſhall be made between the Moments of the prement
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434 <lb></lb>Solid, and the reſiſting Water; then ſhall reſt enſue, and the ſaid
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435 <lb></lb>Solid ſhall be able to reſt indifferently, in whatſoever part of the
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436 <lb></lb>water. </s><s>By this time is manifeſt the neceſſity of comparing the
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437 <lb></lb><arrow.to.target n="marg1408"></arrow.to.target>
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438 <lb></lb>Gravity of the water, and of the Solid; and this compariſon might
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439 <lb></lb>at firſt ſight ſeem ſufficient to conclude and determine which are the
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440 <lb></lb>Solids that float a-top, and which thoſe that ſink to the Bottom in the
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441 <lb></lb>water, aſſerting that thoſe ſhall float which are leſſe grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end>
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442 <lb></lb>than the water, and thoſe ſubmerge, which are <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> more grave.
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443 <lb></lb></s><s>For it ſeems in appearance, that the Sollid in ſinking continually,
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444 <lb></lb>raiſeth ſo much Water in Maſs, as anſwers to the parts of its own
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445 <lb></lb>Bulk ſubmerged: whereupon it is impoſſible, that a Solid leſs grave
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446 <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
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447 <lb></lb>weight greater than its own, and ſuch would a Maſs of water equall
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448 <lb></lb>to its own Maſs be. </s><s>And likewiſe it ſeems neceſſary, that the graver
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449 <lb></lb>Solids do go to the Bottom, as being of a Force more than ſufficient
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450 <lb></lb>for the raiſing a Maſſe of water, equall to its own, though inferiour
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451 <lb></lb>in weight. </s><s>Nevertheleſs the buſineſs ſucceeds otherwiſe: and
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452
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453
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454 <pb pagenum="409"></pb>though the Concluſions are true, yet are the Cauſes thus aſſigned
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455 <lb></lb>deficient, nor is it true, that the Solid in ſubmerging, raiſeth and
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456 <lb></lb>repulſeth Maſſes of Water, equall to the parts of it ſelf ſubmerged;
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457 <lb></lb>but the Water repulſed, is alwayes leſs than the parts of the Solid
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458 <lb></lb><arrow.to.target n="marg1409"></arrow.to.target>
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459 <lb></lb>ſubmerged: and ſo much the more by how much the Veſſell in
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460 <lb></lb>which the Water is contained is narrower: in ſuch manner that it
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461 <lb></lb>hinders not, but that a Solid may ſubmerge all under Water, with­
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462 <lb></lb>out raiſing ſo much Water in Maſs, as would equall the tenth or
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463 <lb></lb>twentieth part of its own Bulk: like as on the contrary, a very
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464 <lb></lb><arrow.to.target n="marg1410"></arrow.to.target>
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465 <lb></lb>ſmall quantity of Water, may raiſe a very great Solid Maſs, though
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466 <lb></lb>ſuch Solid ſhould weigh abſolutely a hundred times as much, or
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467 <lb></lb>more, than the ſaid Water, if ſo be that the Matter of that ſame
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468 <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
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469 <lb></lb>Beam, as ſuppoſe of a 1000 weight, may be raiſed and born afloat
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470 <lb></lb>by Water, which weighs not 50: and this happens when the Mo­
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471 <lb></lb>ment of the Water is compenſated by the Velocity of its Motion.</s></p><p type="margin">
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472
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473 <s><margin.target id="marg1404"></margin.target>How the ſub­
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474 <lb></lb>merſion of So­
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475 <lb></lb>lids in the Wa­
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476 <lb></lb>ter, is effected.</s></p><p type="margin">
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477
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478 <s><margin.target id="marg1405"></margin.target>What Solids
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479 <lb></lb>ſhall float on the
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480 <lb></lb>Water.</s></p><p type="margin">
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481
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482 <s><margin.target id="marg1406"></margin.target>What Solids
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483 <lb></lb>ſhall ſinke to the
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484 <lb></lb>botome.</s></p><p type="margin">
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485
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486 <s><margin.target id="marg1407"></margin.target>What Solids
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487 <lb></lb>ſhall reſt in all
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488 <lb></lb>places of the Wa­
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489 <lb></lb>ter.</s></p><p type="margin">
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490
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491 <s><margin.target id="marg1408"></margin.target>The Gravitie of
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492 <lb></lb>the Water and
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493 <lb></lb><emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid muſt be
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494 <lb></lb>compared in all
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495 <lb></lb>Problems, of Na­
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496 <lb></lb>tation of Bodies.</s></p><p type="margin">
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497
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498 <s><margin.target id="marg1409"></margin.target>The water re­
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499 <lb></lb>pulſed is ever leſs
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500 <lb></lb>than the parts of
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501 <lb></lb>the Sollid ſub­
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502 <lb></lb>merged.</s></p><p type="margin">
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503
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504 <s><margin.target id="marg1410"></margin.target><emph type="italics"></emph>A<emph.end type="italics"></emph.end> ſmall quantity
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505 <lb></lb>of water, may
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506 <lb></lb>float a very
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507 <lb></lb>great Solid Maſs.</s></p><p type="main">
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508
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509 <s>But becauſe ſuch things, propounded thus in abſtract, are ſome­
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510 <lb></lb>what difficult to be comprehended, it would be good to demonſtrate
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511 <lb></lb>them by particular examples; and for facility of demonſtration, we
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512 <lb></lb>will ſuppoſe the Veſſels in which we are to put the Water, and place
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513 <lb></lb>the Solids, to be inviron&#039;d and included with ſides erected perpendi­
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514 <lb></lb>cular to the Plane of the Horizon, and the Solid that is to be put
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515 <lb></lb>into ſuch veſſell to be either a ſtreight Cylinder, or elſe an upright
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516 <lb></lb>Priſme</s></p><p type="main">
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517
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518 <s><emph type="italics"></emph>The which propoſed and declared, I proceed to demonstrate the truth
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519 <lb></lb>of what hath been hinted, forming the enſuing Theoreme.<emph.end type="italics"></emph.end></s></p><p type="head">
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520
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521 <s><emph type="italics"></emph>THEOREME I.<emph.end type="italics"></emph.end></s></p><p type="main">
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522
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523 <s>The Maſs of the Water whichaſcends in the ſub­
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524 <lb></lb><arrow.to.target n="marg1411"></arrow.to.target>
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525 <lb></lb>merging of a Solid, Priſme or Cylinder, or that
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526 <lb></lb>abaſeth in taking it out, is leſs than the Maſs of
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527 <lb></lb>the ſaid Solid, ſo depreſſed or advanced: and
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528 <lb></lb>hath to it the ſame proportion, that the Surface
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529 <lb></lb>of the Water circumfuſing the Solid, hath to the
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530 <lb></lb>ſame circumfuſed Surface, together with the Baſe
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531 <lb></lb>of the Solid.</s></p><p type="margin">
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532
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533 <s><margin.target id="marg1411"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he Proportion
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534 <lb></lb>of the water rai­
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535 <lb></lb>ſed to the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olid
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536 <lb></lb>ſubmerged.</s></p><p type="main">
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537
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538 <s><emph type="italics"></emph>Let the Veſſell be A B C D, and in it the Water raiſed up to the
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539 <lb></lb>Levell E F G, before the Solid Priſme H I K be therein immerged;
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540 <lb></lb>but after that it is depreſſed under Water, let the Water be raiſed as
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541 <lb></lb>high as the Levell L M, the Solid H I K ſhall then be all under Water,
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542 <lb></lb>and the Maſs of the elevated Water ſhall be L G, which is leſs than the<emph.end type="italics"></emph.end>
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543
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544
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545 <pb pagenum="410"></pb><figure id="fig262"></figure>
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546 <lb></lb><emph type="italics"></emph>Maſſe of the Solid depreſſed, namely of
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547 <lb></lb>H I K, being equall to the only part E I K,
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548 <lb></lb>which is contained under the firſt Levell
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549 <lb></lb>E F G. </s><s>Which is manifeſt, becauſe if
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550 <lb></lb>the Solid H I K be taken out, the Water
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551 <lb></lb>I G ſhall return into the place occupied by
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552 <lb></lb>the Maſs E I K, where it was continuate be­
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553 <lb></lb>fore the ſubmerſion of the Priſme. </s><s>And
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554 <lb></lb>the Maſs L G being equall to the Maſs
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555 <lb></lb>E K: adde thereto the Maſs E N, and it
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556 <lb></lb>ſhall be the whole Maſs E M, compoſed of the parts of the Priſme E N,
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557 <lb></lb>and of the Water N F, equall to the whole Solid H I K: And, there­
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558 <lb></lb>fore, the Maſs L G ſhall have the ſame proportion to E M, as to the
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559 <lb></lb>Maſs H I K: But the Maſs L G hath the ſame proportion to the Maſs
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560 <lb></lb>E M, as the Surface L M hath to the Surface M H: Therefore it is ma­
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561 <lb></lb>nifeſt, that the Maſs of Water repulſed L G, is in proportion to the Maſs
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562 <lb></lb>of the Solid ſubmerged H I K; as the Surface L M, namely, that of the
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563 <lb></lb>Water ambient about the Sollid, to the whole Surface H M, compounded
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564 <lb></lb>of the ſaid ambient water, and the Baſe of the Priſme H N. </s><s>But if we
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565 <lb></lb>ſuppoſe the firſt Levell of the Water the according to the Surface H M,
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566 <lb></lb>and the Priſme allready ſubmerged H I K; and after to be taken out and
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567 <lb></lb>raiſed to E A O, and the Water to be faln from the firſt Levell H L M as
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568 <lb></lb>low as E F G; It is manifeſt, that the Priſme E A O being the ſame with
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569 <lb></lb>H I K, its ſuperiour part H O, ſhall be equall to the inferiour E I K:
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570 <lb></lb>and remove the common part E N, and, conſequently, the Maſs of the
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571 <lb></lb>Water L G is equall to the Maſs H O; and, therefore, leſs than the
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572 <lb></lb>Solid, which is without the Water, namely, the whole Priſme E A O, to
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573 <lb></lb>which likewiſe, the ſaid Maſs of Water abated L G, hath the ſame propor­
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574 <lb></lb>tion, that the Surface of the Waters circumfuſed L M hath to the ſame
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575 <lb></lb>circumfuſed Surface, together with the Baſe of the Priſme A O: which
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576 <lb></lb>hath the ſame demonſtration with the former caſe above.<emph.end type="italics"></emph.end></s></p><p type="main">
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577
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578 <s><emph type="italics"></emph>And from hence is inferred, that the Maſs of the Water, that riſeth in
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579 <lb></lb>the immerſion of the Solid, or that ebbeth in elevating it, is not equall to
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580 <lb></lb>all the Maſs of the Solid, which is ſubmerged or elevated, but to that
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581 <lb></lb>part only, which in the immerſion is under the firſt Levell of the Water,
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582 <lb></lb>and in the elevation remaines above the firſt Levell: Which is that
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583 <lb></lb>which was to be demonſtrated. </s><s>We will now purſue the things that
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584 <lb></lb>remain.<emph.end type="italics"></emph.end></s></p><p type="main">
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585
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586 <s>And firſt we will demonſtrate that,</s></p>
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587
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588
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589 <pb pagenum="411"></pb><p type="head">
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590
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591 <s>THEOREME II.</s></p><p type="main">
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592
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593 <s><emph type="italics"></emph>When in one of the above ſaid Veſſels, of what ever<emph.end type="italics"></emph.end>
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594 <lb></lb><arrow.to.target n="marg1412"></arrow.to.target>
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595 <lb></lb><emph type="italics"></emph>breadth, whether wide or narrow, there is placed ſuch
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596 <lb></lb>a Priſme or Cylinder, inviron&#039;d with Water, if we ele­
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597 <lb></lb>vate that Solid perpendicularly, the Water circumfu­
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598 <lb></lb>ſed ſhall abate, and the Abatement of the Water,
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599 <lb></lb>ſhall have the ſame proportion to the Elevation of the
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600 <lb></lb>Priſme, as one of the Baſes of the Priſme, hath to
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601 <lb></lb>the Surface of the Water Circumfuſed.<emph.end type="italics"></emph.end></s></p><p type="margin">
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602
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603 <s><margin.target id="marg1412"></margin.target>The proportion
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604 <lb></lb>of the water aba­
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605 <lb></lb>ted, to the Solid
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606 <lb></lb>raiſed.</s></p><p type="main">
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607
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608 <s>Imagine in the Veſſell, as is aforeſaid, the
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609 <lb></lb><figure id="fig263"></figure>
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610 <lb></lb>Priſme A C D B to be placed, and in the
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611 <lb></lb>reſt of the Space the Water to be dif­
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612 <lb></lb>fuſed as far as the Levell E A: and rai­
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613 <lb></lb>ſing the Solid, let it be transferred to
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614 <lb></lb>G M, and let the Water be abaſed from
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615 <lb></lb>E A to N O: I ſay, that the deſcent of
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616 <lb></lb>the Water, meaſured by the Line A O,
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617 <lb></lb>hath the ſame proportion to the riſe of the
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618 <lb></lb>Priſme, meaſured by the Line G A, as the Baſe of the Solid G H
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619 <lb></lb>hath to the Surface of the Water N O. </s><s>The which is manifeſt:
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620 <lb></lb>becauſe the Maſs of the Solid G A B H, raiſed above the firſt Levell
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621 <lb></lb>E A B, is equall to the Maſs of Water that is abaſed E N O A.
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622 <lb></lb>Therefore, E N O A and G A B H are two equall Priſmes; for of
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623 <lb></lb>equall Priſmes, the Baſes anſwer contrarily to their heights: There­
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624 <lb></lb>fore, as the Altitude A O is to the Altitude A G, ſo is the Superfi­
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625 <lb></lb>cies or Baſe G H to the Surface of the Water N O. </s><s>If therefore,
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626 <lb></lb>for example, a Pillar were erected in a waſte Pond full of Water,
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627 <lb></lb>or elſe in a Well, capable of little more then the Maſs of the ſaid
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628 <lb></lb>Pillar, in elevating the ſaid Pillar, and taking it out of the Water,
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629 <lb></lb>according as it riſeth, the Water that invirons it will gradually abate,
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630 <lb></lb>and the abaſement of the Water at the inſtant of lifting out the
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631 <lb></lb>Pillar, ſhall have the ſame proportion, that the thickneſs of the Pillar
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632 <lb></lb>hath to the exceſs of the breadth of the ſaid Pond or Well, above
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633 <lb></lb>the thickneſs of the ſaid Pillar: ſo that if the breadth of the Well
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634 <lb></lb>were an eighth part larger than the thickneſs of the Pillar, and the
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635 <lb></lb><arrow.to.target n="marg1413"></arrow.to.target>
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636 <lb></lb>breadth of the Pond twenty five times as great as the ſaid thickneſs,
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637 <lb></lb>in the Pillars aſcending one foot, the water in the Well ſhall deſcend
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638 <lb></lb>ſeven foot, and that in the Pond only 1/25 of a foot.</s></p><p type="margin">
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639
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640 <s><margin.target id="marg1413"></margin.target>Why a Solid
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641 <lb></lb>leſs grave <emph type="italics"></emph>in ſpe­
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642 <lb></lb>cie<emph.end type="italics"></emph.end> than water,
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643 <lb></lb>ſtayeth not un­
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644 <lb></lb>der water, in ve­
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645 <lb></lb>ry ſmall depthst.</s></p><p type="main">
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646
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647 <s>This Demonſtrated, it will not be difficult to ſhew the true
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648 <lb></lb>cauſe, how it comes to paſs, that,</s></p>
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649
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650
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651 <pb pagenum="412"></pb><p type="head">
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652
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653 <s>THEOREME III.</s></p><p type="main">
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654
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655 <s><emph type="italics"></emph>A Priſme or regular Cylinder, of a ſubſtance ſpecifically
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656 <lb></lb>leſs grave than Water, if it ſhould be totally ſubmerged
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657 <lb></lb>in Water, ſtayes not underneath, but riſeth, though the
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658 <lb></lb>Water circumfuſed be very little, and in abſolute
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659 <lb></lb>Gravity, never ſo much inferiour to the Gravity of the
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660 <lb></lb>ſaid Priſme.<emph.end type="italics"></emph.end></s></p><p type="main">
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661
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662 <s>Let then the Priſme A E F B, be put into the Veſſell C D F B, the
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663 <lb></lb>ſame being leſs grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than the Water: and let the
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664 <lb></lb>Water infuſed riſe to the height of the Priſme: I ſay, that the
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665 <lb></lb>Priſme left at liberty, it ſhall riſe, being born up
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666 <lb></lb>by the Water circumfuſed C D E A. </s><s>For the
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667 <lb></lb><figure id="fig264"></figure>
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668 <lb></lb>Water C E being ſpecifically more grave than
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669 <lb></lb>the Solid A F, the abſolute weight of the water
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670 <lb></lb>C E, ſhall have greater proportion to the abſo­
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671 <lb></lb>lute weight of the Priſme A F, than the Maſs
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672 <lb></lb>C E hath to the Maſs A F (in regard the Maſs
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673 <lb></lb>hath the ſame proportion to the Maſs, that the
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674 <lb></lb>weight abſolute hath to the weight abſolute,
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675 <lb></lb>in caſe the Maſſes are of the ſame Gravity <emph type="italics"></emph>in ſpecie.<emph.end type="italics"></emph.end>) But
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676 <lb></lb>the Maſs C E is to the Maſs A F, as the Surface of the water A C, is
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677 <lb></lb>to the Superficies, or Baſe of the Priſme A B; which is the ſame pro­
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678 <lb></lb>portion as the aſcent of the Priſme when it riſeth, hath to the deſcent
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679 <lb></lb>of the water circumfuſed C E.</s></p><p type="main">
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680
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681 <s>Therefore, the abſolute Gravity of the water C E, hath greater
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682 <lb></lb>proportion to the abſolute Gravity of the Priſme A F; than the
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683 <lb></lb>Aſcent of the Priſme A F, hath to the deſcent of the ſaid
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684 <lb></lb>water C E. </s><s>The Moment, therefore, compounded of the abſolute
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685 <lb></lb>Gravity of the water C E, and of the Velocity of its deſcent, whilſt
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686 <lb></lb>it forceably repulſeth and raiſeth the Solid A F, is greater than the
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687 <lb></lb>Moment compounded of the abſolute Gravity of the Priſme A F, and
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688 <lb></lb>of the Tardity of its aſcent, with which Moment it contraſts and re­
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689 <lb></lb>fiſts the repulſe and violence done it by the Moment of the water:
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690 <lb></lb>Therefore, the Priſme ſhall be raiſed.
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691 <lb></lb><arrow.to.target n="marg1414"></arrow.to.target></s></p><p type="margin">
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692
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693 <s><margin.target id="marg1414"></margin.target>The Proportion
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694 <lb></lb>according to
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695 <lb></lb>which the Sub­
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696 <lb></lb>merſion &amp; Na
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697 <lb></lb>tation of Solids
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698 <lb></lb>is made.</s></p><p type="main">
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699
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700 <s>It followes, now, that we proceed forward to demonſtrate more
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701 <lb></lb>particularly, how much ſuch Solids ſhall be inferiour in Gravity to
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702 <lb></lb>the water elevated; namely, what part of them ſhall reſt ſubmerged,
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703 <lb></lb>and what ſhall be viſible above the Surface of the water: but firſt
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704 <lb></lb>it is neceſſary to demonſtrate the ſubſequent Lemma.</s></p>
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705
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706
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707 <pb pagenum="413"></pb><p type="head">
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708
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709 <s>LEMMA I.</s></p><p type="main">
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710
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711 <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">
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712
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713 <s><arrow.to.target n="marg1415"></arrow.to.target>
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714 <lb></lb><emph type="italics"></emph>pounded of the proportions of their ſpecificall Gravities,
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715 <lb></lb>and of their Maſſes.<emph.end type="italics"></emph.end></s></p><p type="margin">
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716
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717 <s><margin.target id="marg1415"></margin.target>The abſolute
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718 <lb></lb>Gravity of So­
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719 <lb></lb>lids, are in a pro­
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720 <lb></lb>portion com­
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721 <lb></lb>pounded of their
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722 <lb></lb>Specifick Gravi­
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723 <lb></lb>ties, and of their
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724 <lb></lb>Maſſes.</s></p><p type="main">
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725
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726 <s>Let A and B be two Solids. </s><s>I ſay, that the Abſolute Gravity
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727 <lb></lb>of A, hath to the Abſolute Gravity of B, a proportion com­
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728 <lb></lb>pounded of the proportions of the ſpecificall Gravity of A, to
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729 <lb></lb>the Specificall Gravity of B, and of the Maſs
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730 <lb></lb>A to the Maſs B. </s><s>Let the Line D have the
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731 <lb></lb><figure id="fig265"></figure>
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732 <lb></lb>ſame proportion to E, that the ſpecifick
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733 <lb></lb>Gravity of A, hath to the ſpecifick Gravity
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734 <lb></lb>of B; and let E be to F, as the Maſs A to the
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735 <lb></lb>Maſs B: It is manifeſt, that the proportion
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736 <lb></lb>of D to F, is compounded of the proportions
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737 <lb></lb>D and E; and E and F. </s><s>It is requiſite,
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738 <lb></lb>therefore, to demonſtrate, that as D is to F, ſo the abſolute Gravity
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739 <lb></lb>of A, is to the abſolute Gravity of B. </s><s>Take the Solid C, equall in
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740 <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
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741 <lb></lb>B. Becauſe, therefore, A and C are equall in Maſs, the abſolute
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742 <lb></lb>Gravity of A, ſhall have to the abſolute Gravity of C, the ſame pro­
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743 <lb></lb>portion, as the ſpecificall Gravity of A, hath to the ſpecificall Gravity
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744 <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
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745 <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
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746 <lb></lb>the abſolute weight of C, is to the abſolute weight of B, ſo the Maſs
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747 <lb></lb>C, or the Maſs A, is to the Maſs B; that is, as the Line E to the Line
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748 <lb></lb>F. </s><s>As therefore, the abſolute Gravity of A, is to the abſolute
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749 <lb></lb>Gravity of C, ſo is the Line D to the Line E: and, as the abſolute
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750 <lb></lb>Gravity of C, is to the abſolute Gravity of B, ſo is the Line E to the
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751 <lb></lb>Line F: Therefore, by Equality of proportion, the abſolute Gra­
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752 <lb></lb>vity of A, is to the abſolute Gravity of B, as the Line D to the
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753 <lb></lb>Line F: which was to be demonſtrated. </s><s>I proceed now to demon­
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754 <lb></lb>ſtrate, how that,</s></p>
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755
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756
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757 <pb pagenum="414"></pb><p type="head">
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758
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759 <s>THEOREME IV.
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760 <lb></lb><arrow.to.target n="marg1416"></arrow.to.target></s></p><p type="margin">
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761
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762 <s><margin.target id="marg1416"></margin.target>The proportion
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763 <lb></lb>of water requi­
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764 <lb></lb>ſite to make a
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765 <lb></lb>Solid ſwim.</s></p><p type="main">
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766
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767 <s><emph type="italics"></emph>If a Solid, Cylinder, or Priſme, leſſe grave ſpecifically
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768 <lb></lb>than the Water, being put into a Veſſel, as above, of
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769 <lb></lb>whatſoever greatneſſe, and the Water, be afterwards
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770 <lb></lb>infuſed, the Solid ſhall reſt in the bottom, unraiſed, till
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771 <lb></lb>the Water arrive to that part of the Altitude, of the
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772 <lb></lb>ſaid Priſme, to which its whole Altitude hath the
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773 <lb></lb>ſame proportion, that the Specificall Gravity of the
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774 <lb></lb>Water, hath to the Specificall Gravity of the ſaid
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775 <lb></lb>Solid: but infuſing more Water, the Solid ſhall aſcend.<emph.end type="italics"></emph.end></s></p><p type="main">
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776
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777 <s>Let the Veſſell be M L G N of any bigneſs, and let there be pla­
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778 <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
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779 <lb></lb>water; and look what proportion the <emph type="italics"></emph>S<emph.end type="italics"></emph.end>pecificall Gravity of
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780 <lb></lb>the water, hath to that of the Priſme, ſuch let the Altitude D F, have
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781 <lb></lb>to the Altitude F B. </s><s>I ſay, that infuſing water to the Altitude F B,
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782 <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
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783 <lb></lb>that every little quantity of water, that is infuſed, ſhall raiſe it. </s><s>Let
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784 <lb></lb>the water, therefore, be infuſed to the Levell A B C, and, becauſe
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785 <lb></lb>the Specifick Gravity of the Solid D G, is to the Specifick Gravity of
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786 <lb></lb>the water, as the altitude B F is to the altitude F D; that is, as the Maſs
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787 <lb></lb>B G to the Maſs G D; as the proportion of the Maſs B G is to the
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788 <lb></lb>Maſs G D, as the proportion of the Maſs G D is to the Maſs A F, they
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789 <lb></lb>compoſe the Proportion of the Maſs B G to the Maſs A F. Therefore,
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790 <lb></lb>the Maſs B G is to the Maſs A F, in a proportion compounded of the
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791 <lb></lb>proportions of the Specifick Gravity of the Solid G D, to the Speci­
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792 <lb></lb>fick Gravity of the water, and of the Maſs G D
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793 <lb></lb>to the Maſs A F: But the ſame proportions
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794 <lb></lb><figure id="fig266"></figure>
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795 <lb></lb>of the Specifick Gravity of G D, to the Specifick
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796 <lb></lb>Gravity of the water, and of the Maſs G D to
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797 <lb></lb>the Maſs A F, do alſo by the precedent <emph type="italics"></emph>Lemma,<emph.end type="italics"></emph.end>
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798 <lb></lb>compound the proportion of the abſolute Gra­
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799 <lb></lb>vity of the Solid D G, to the abſolute Gravity
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800 <lb></lb>of the Maſs of the water A F: Therefore,
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801 <lb></lb>as the Maſs B G is to the Maſs A F, ſo is the
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802 <lb></lb>Abſolute Gravity of the Solid D G, to the Ab­
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803 <lb></lb>ſolute Gravity of the Maſs of the water A F. </s><s>But as the Maſs B G
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804 <lb></lb>is to the Maſs A F; ſo is the Baſe of the Priſme D E, to the Surface
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805 <lb></lb>of the water AB; and ſo is the deſcent of the water A B, to the
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806 <lb></lb>Elevation of the Priſme D G; Therefore, the deſcent of the
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807
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808
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809 <pb pagenum="415"></pb>water is to the elevation of the Priſme, as the abſolute Gravity of
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810 <lb></lb>the Priſme, is to the abſolute Gravity of the water: Therefore, the
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811 <lb></lb>Moment reſulting from the abſolute Gravity of the water A F, and
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812 <lb></lb>the Velocity of the Motion of declination, with which Moment it
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813 <lb></lb>forceth the Priſme D G, to riſe and aſcend, is equall to the Moment
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814 <lb></lb>that reſults from the abſolute Gravity of the Priſme D G, and from
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815 <lb></lb>the Velocity of the Motion, wherewith being raiſed, it would aſcend:
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816 <lb></lb>with which Moment it reſiſts its being raiſed: becauſe, therefore,
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817 <lb></lb>ſuch Moments are equall, there ſhall be an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> between the
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818 <lb></lb>water and the Solid. </s><s>And, it is manifeſt, that putting a little more
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819 <lb></lb>water unto the other A F, it will increaſe the Gravity and Moment,
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820 <lb></lb>whereupon the Priſme D G, ſhall be overcome, and elevated till that
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821 <lb></lb>the only part B F remaines ſubmerged. </s><s>Which is that that was to
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822 <lb></lb>be demonſtrated.</s></p><p type="head">
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823
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824 <s>COROLLARY I.</s></p><p type="main">
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825
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826 <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">
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827
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828 <s><arrow.to.target n="marg1417"></arrow.to.target>
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829 <lb></lb>in ſpecie <emph type="italics"></emph>than the water, ſubmerge only ſo far, that as much water in
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830 <lb></lb>Maſs, as is the part of the Solid ſubmerged, doth weigh abſolutely as
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831 <lb></lb>much as the whole Solid.<emph.end type="italics"></emph.end></s></p><p type="margin">
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832
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833 <s><margin.target id="marg1417"></margin.target><emph type="italics"></emph>H<emph.end type="italics"></emph.end>ow far Solids
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834 <lb></lb>leſs grave <emph type="italics"></emph>in ſpe­
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835 <lb></lb>cie<emph.end type="italics"></emph.end> than water,
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836 <lb></lb>do ſubmerge.</s></p><p type="main">
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837
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838 <s>For, it being ſuppoſed, that the Specificall Gravity of the water,
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839 <lb></lb>is to the Specificall Gravity of the Priſme D G, as the Altitude
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840 <lb></lb>D F, is to the Altitude F B; that is, as the Solid D G is to the
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841 <lb></lb>Solid B G; we might eaſily demonſtrate, that as much water in Maſs
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842 <lb></lb>as is equall to the Solid B G, doth weigh abſolutely as much as the
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843 <lb></lb>whole Solid D G; For, by the <emph type="italics"></emph>Lemma<emph.end type="italics"></emph.end> foregoing, the Abſolute
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844 <lb></lb>Gravity of a Maſs of water, equall to the Maſs B G, hath to the Ab­
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845 <lb></lb>ſolute Gravity of the Priſme D G, a proportion compounded of the
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846 <lb></lb>proportions, of the Maſs B G to the Maſs G D, and of the Specifick
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847 <lb></lb>Gravit 7 of the water, to the Specifick Gravity of the Priſme: But
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848 <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
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849 <lb></lb>Priſme, is ſuppoſed to be as the Maſs G D to the Maſs G B. There­
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850 <lb></lb>fore, the Abſolute Gravity of a Maſs of water, equall to the Maſs
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851 <lb></lb>B G, is to the Abſolute Gravity of the Solid D G, in a proportion
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852 <lb></lb>compounded of the proportions, of the Maſs B G to the Maſs G D,
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853 <lb></lb>and of the Maſs D G to the Maſs G B; which is a proportion of
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854 <lb></lb>equalitie. </s><s>The Abſolute Gravity, therefore, of a Maſs of Water
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855 <lb></lb>equall to the part of the Maſs of the Priſme B G, is equall to the Ab­
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856 <lb></lb>ſolute Gravity of the whole Solid D G.</s></p>
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857
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858
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859 <pb pagenum="416"></pb><p type="head">
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860
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861 <s>COROLLARY II.
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862 <lb></lb><arrow.to.target n="marg1418"></arrow.to.target></s></p><p type="margin">
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863
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864 <s><margin.target id="marg1418"></margin.target><emph type="italics"></emph>A<emph.end type="italics"></emph.end> Rule to equi­
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865 <lb></lb>librate <emph type="italics"></emph>S<emph.end type="italics"></emph.end>olids in
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866 <lb></lb>the water.</s></p><p type="main">
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867
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868 <s><emph type="italics"></emph>It followes, moreover, that a Solid leſs grave than the water, being put
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869 <lb></lb>into a Veſſell of any imaginable greatneſs, and water being circumfuſed
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870 <lb></lb>about it to ſuch a height, that as much water in Maſs, as is the part of
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871 <lb></lb>the Solid ſubmerged, doth/&gt; weigh abſolutely as much as the whole Solid;
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872 <lb></lb>it ſhall by that water be juſtly ſuſtained, be the circumfuſed Water in
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873 <lb></lb>quantity greater or leſſer.<emph.end type="italics"></emph.end></s></p><p type="main">
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874
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875 <s>For, if the Cylinder or Priſme M, leſs grave than the water, <emph type="italics"></emph>v.
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876 <lb></lb></s><s>gra.<emph.end type="italics"></emph.end> in Subſequiteriall proportion, ſhall be put into the capaci­
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877 <lb></lb>ous Veſſell A B C D, and the water raiſed about it, to three
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878 <lb></lb>quarters of its height, namely, to its Levell A D: it ſhall be ſuſtained
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879 <lb></lb>and exactly poyſed in <emph type="italics"></emph>Equi­
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880 <lb></lb>librium.<emph.end type="italics"></emph.end> The ſame will hap­
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881 <lb></lb>pen, if the Veſſell E N S F
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882 <lb></lb><figure id="fig267"></figure>
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883 <lb></lb>were very ſmall, ſo, that be­
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884 <lb></lb>tween the Veſſell and the So­
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885 <lb></lb>lid M, there were but a very
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886 <lb></lb>narrow ſpace, and only capable of ſo much water, as the hundredth
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887 <lb></lb>part of the Maſs M, by which it ſhould be likewiſe raiſed and erected,
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888 <lb></lb>as before it had been elevated to three fourths of the height of the
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889 <lb></lb>Solid: which to many at the firſt ſight, may ſeem a notable Paradox,
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890 <lb></lb>and beget a conceit, that the Demonſtration of theſe effects, were
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891 <lb></lb>ſophiſticall and fallacious: but, for thoſe who ſo repute it, the Ex­
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892 <lb></lb>periment is a means that may fully ſatisfie them. </s><s>But he that ſhall
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893 <lb></lb>but comprehend of what Importance Velocity of Motion is, and how
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894 <lb></lb>it exactly compenſates the defect and want of Gravity, will ceaſe to
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895 <lb></lb>wonder, in conſidering that at the elevation of the Solid M, the great
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896 <lb></lb>Maſs of water A B C D abateth very little, but the little Maſs of
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897 <lb></lb>water E N S F decreaſeth very much, and in an inſtant, as the Solid
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898 <lb></lb>M before did liſe, howbeit for a very ſhort ſpace: Whereupon the
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899 <lb></lb>Moment, compounded of the ſmall Abſolute Gravity of the water
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900 <lb></lb>E N S F, and of its great Velocity in ebbing, equalizeth the Force and
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901 <lb></lb>and Moment, that reſults from the compoſicion of the immenſe Gra­
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902 <lb></lb>vity of the water A B C D, with its great ſlowneſſe of ebbing;
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903 <lb></lb>ſince that in the Elevation of the Sollid M, the abaſement of the leſ­</s></p><p type="main">
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904
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905 <s><arrow.to.target n="marg1419"></arrow.to.target>
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906 <lb></lb>ſer water E S, is performed juſt ſo much more ſwiftly than the great
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907 <lb></lb>Maſs of water A C, as this is more in Maſs than that which we thus
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908 <lb></lb>demonſtrate.</s></p><p type="margin">
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909
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910 <s><margin.target id="marg1419"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he proportion
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911 <lb></lb>according to
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912 <lb></lb>which water ri­
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913 <lb></lb>ſeth and falls in
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914 <lb></lb>different Veſſels
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915 <lb></lb>at the Immerſi­
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916 <lb></lb>on and Elevati­
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917 <lb></lb>on of <emph type="italics"></emph>s<emph.end type="italics"></emph.end>olids.</s></p><p type="main">
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918
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919 <s>In the riſing of the Solid M, its elevation hath the ſame proportion
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920 <lb></lb>to the circumfuſed water E N S F, that the Surface of the ſaid water,
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921 <lb></lb>hath to the Superficies or Baſe of the ſaid Solid M; which Baſe hath
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922 <lb></lb>the ſame proportion to the Surface of the water A D, that the abaſe­
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923
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924
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925 <pb pagenum="417"></pb>ment or ebbing of the water A C, hath to the riſe or elevation of
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926 <lb></lb>the ſaid Solid M. Therefore, by Perturbation of proportion, in the
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927 <lb></lb>aſcent of the ſaid Solid M, the abaſement of the water A B C D, to
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928 <lb></lb>the abaſement of the water E N S F, hath the ſame proportion, that the
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929 <lb></lb>Surface of the water E F, hath to the Surface of the water A D;
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930 <lb></lb>that is, that the whole Maſs of the water E N S F, hath to the whole
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931 <lb></lb>Maſs A B C D, being equally high: It is manifeſt, therefore, that
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932 <lb></lb>in the expulſion and elevation of the Solid M, the water E N S F
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933 <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
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934 <lb></lb>on the other ſide is exceeded by that in quantity: whereupon their
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935 <lb></lb>Moments in ſuch operations, are mutually equall.</s></p><p type="main">
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936
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937 <s><emph type="italics"></emph>And, for ampler confirmation, and clearer explication of this, let us
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938 <lb></lb>conſider the preſent Figure, (which if I be not deceived, may ſerve to
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939 <lb></lb>detect the errors of ſome Practick Mechanitians, who upon a falſe founda­
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940 <lb></lb>tion ſome times attempt impoſſible enterprizes,) in which, unto the large
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941 <lb></lb>Veſſell E I D F, the narrow Funnell or Pipe I C A B is continued, and ſup­
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942 <lb></lb>poſe water infuſed into them, unto the Levell L G H, which water ſhall
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943 <lb></lb>reſt in this poſition, not without admiration in ſome, who cannot conceive<emph.end type="italics"></emph.end>
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944 <lb></lb><figure id="fig268"></figure>
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945 <lb></lb><emph type="italics"></emph>how it can be, that the heavie charge of the great
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946 <lb></lb>Maſs of water G D, preſſing downwards, ſhould
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947 <lb></lb>not elevate and repulſe the little quantity of the
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948 <lb></lb>other, contained in the Funnell or Pipe C L, by
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949 <lb></lb>which the deſcent of it is reſisted and hindered:
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950 <lb></lb>But ſuch wonder ſhall ceaſe, if we begin to ſuppoſe
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951 <lb></lb>the water G D to be abaſed only to Q D, and
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952 <lb></lb>ſhall afterwards conſider, what the water C L
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953 <lb></lb>hath done, which to give place to the other, which
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954 <lb></lb>is deſcended from the Levell G H, to the Levell
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955 <lb></lb>Q O, ſhall of neceſſity have aſcended in the ſame
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956 <lb></lb>time, from the Levell Lunto A B. </s><s>And the
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957 <lb></lb>aſcent L B, ſhall be ſo much greater than the de­
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958 <lb></lb>ſcent G Q, by how much the breadth of the Veſſell
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959 <lb></lb>G D, is greater than that of the Funnell I C;
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960 <lb></lb>which, in ſumme, is as much as the water G D,
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961 <lb></lb>is more than the water L C: but in regard that the Moment of the Velocity
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962 <lb></lb>of the Motion, in one Moveable, compenſates that of the Gravity of ano­
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963 <lb></lb>ther, what wonder is it, if the ſwift aſcent of the leſſer Water C L, ſhall
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964 <lb></lb>reſiſt the ſlow deſcent of the greater G D<emph.end type="italics"></emph.end>?</s></p><p type="main">
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965
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966 <s>The ſame, therefore, happens in this operation, as in the Stilliard,
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967 <lb></lb>in which a weight of two pounds counterpoyſeth an other of 200,
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968 <lb></lb>asoften as that ſhall move in the ſame time, a ſpace 100 times great­
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969 <lb></lb>er than this: which falleth out when one Arme of the Beam is an
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970
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971
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972 <pb pagenum="418"></pb>hundred times as long as the other. </s><s>Let the erroneous opinion o
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973 <lb></lb><arrow.to.target n="marg1420"></arrow.to.target>
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974 <lb></lb>thoſe therefore ceaſe, who hold that a Ship is better, and eaſter born
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975 <lb></lb>up in a great abundance of water, then in a leſſer quantity, (<emph type="italics"></emph>this was
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976 <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
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977 <lb></lb>the contrary true, that its poſſible, that a Ship may as well float in
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978 <lb></lb>ten Tun of water, as in an Ocean.
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979 <lb></lb><arrow.to.target n="marg1421"></arrow.to.target></s></p><p type="margin">
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980
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981 <s><margin.target id="marg1420"></margin.target>A ſhip flotes as
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982 <lb></lb>well in ten Tun
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983 <lb></lb>of water as in an
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984 <lb></lb>Ocean.</s></p><p type="margin">
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985
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986 <s><margin.target id="marg1421"></margin.target>A Solid ſpeci­
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987 <lb></lb>fiaclly graver
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988 <lb></lb>than the water,
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989 <lb></lb>cannot be born
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990 <lb></lb>up by any quan­
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991 <lb></lb>tity of it.</s></p><p type="main">
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992
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993 <s>But following our matter, I ſay, that by what hath been hitherto
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994 <lb></lb>demonſtrated, we may underſtand how, that</s></p><p type="head">
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995
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996 <s>COROLLARY III.</s></p><p type="main">
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997
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998 <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,
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999 <lb></lb>can never be ſuſtained, by any whatever quantity of it.<emph.end type="italics"></emph.end></s></p><p type="main">
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1000
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1001 <s>For having ſeen how that the Moment wherewith ſuch a Solid
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1002 <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
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1003 <lb></lb>of water whatſoever, is able to retain it, even to its totall Submerſion:
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1004 <lb></lb>without its ever aſcending; it remaineth, manifeſt, that the water is
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1005 <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,
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1006 <lb></lb>that though you infuſe water till its totall Submerſion, it ſhall ſtill
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1007 <lb></lb>ſtay at the Bottome, and with ſuch Gravity, and Reſiſtance to Eleva­
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1008 <lb></lb>tion, as is the exceſs of its Abſolute Gravity, above the Abſolute Gra­
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1009 <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>
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1010 <lb></lb>equally grave with the water: and, though you ſhould moreover
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1011 <lb></lb>adde never ſo much water above the Levell of that which equalizeth
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1012 <lb></lb>the Altitude of the Solid, it ſhall not, for all that, encreaſe the Preſſion
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1013 <lb></lb>or Gravitation, of the parts circumfuſed about the ſaid Solid, by
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1014 <lb></lb>which greater preſſion, it might come to be repulſed, becauſe, the
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1015 <lb></lb>Reſiſtance is not made, but only by thoſe parts of the water, which
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1016 <lb></lb>at the Motion of the ſaid Solid do alſo move, and theſe are thoſe
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1017 <lb></lb>only, which are comprehended by the two Superficies equidiſtant to
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1018 <lb></lb>the Horizon, and their parallels, that comprehend the Altitude of the
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1019 <lb></lb>Solid immerged in the water.</s></p><p type="main">
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1020
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1021 <s>I conceive, I have by this time ſufficiently declared and opened
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1022 <lb></lb>the way to the contemplation of the true, intrinſecall and proper
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1023 <lb></lb>Cauſes of diverſe Motions, and of the Reſt of many Solid Bodies in
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1024 <lb></lb>diverſe <emph type="italics"></emph>Mediums,<emph.end type="italics"></emph.end> and particularly in the water, ſhewing how all ii
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1025 <lb></lb>effect, depend on the mutuall exceſſes of the Gravity of the Movea­
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1026 <lb></lb>bles and of the <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end>: and, that which did highly import, re­
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1027 <lb></lb>moving the Objection, which peradventure would have begotter
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1028 <lb></lb>much doubting, and ſcruple in ſome, about the verity of my Con­
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1029 <lb></lb>cluſion, namely, how that notwithſtanding, that the exceſs of the
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1030 <lb></lb>Gravity of the water, above the Gravity of the Solid, demitted into
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1031 <lb></lb>it, be the cauſe of its floating and riſing from the Bottom to the Sur­
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1032 <lb></lb>face, yet a quantity of water, that weighs not ten pounds, can raiſe
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1033
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1034
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1035 <pb pagenum="419"></pb>Solid that weighs above 100 pounds: in that we have demonſtra­
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1036 <lb></lb>ted, That it ſufficeth, that ſuch difference be found between the
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1037 <lb></lb>Specificall Gravities of the <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end> and Moveables, let the particular
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1038 <lb></lb>and abſolute Gravities be what they will: inſomuch, that a Solid,
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1039 <lb></lb>provided that it be Specifically leſs grave than the water, although
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1040 <lb></lb>its abſolute weight were 1000 pounds, yet may it be born up and
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1041 <lb></lb>elevated by ten pounds of water, and leſs: and on the contrary, a­
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1042 <lb></lb>nother Solid, ſo that it be Specifically more grave than the water,
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1043 <lb></lb>though in abſolute Gravity it were not above a pound, yet all the
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1044 <lb></lb>water in the Sea, cannot raiſe it from the Bottom, or float it. </s><s>This
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1045 <lb></lb>ſufficeth me, for my preſent occaſion, to have, by the above declared
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1046 <lb></lb>Examples, diſcovered and demonſtrated, without extending ſuch
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1047 <lb></lb>matters farther, and, as I might have done, into a long Treatiſe:
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1048 <lb></lb>yea, but that there was a neceſſity of reſolving the above propoſed
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1049 <lb></lb>doubt, I ſhould have contented my ſelf with that only, which is
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1050 <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
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1051 <lb></lb>mido<emph.end type="italics"></emph.end>: where in generall termes he infers and confirms the ſame </s></p><p type="main">
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1052
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1053 <s><arrow.to.target n="marg1422"></arrow.to.target>
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1054 <lb></lb><arrow.to.target n="marg1423"></arrow.to.target>
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1055 <lb></lb>Concluſions, namely, that Solids (<emph type="italics"></emph>a<emph.end type="italics"></emph.end>) leſs grave than water, ſwim or
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1056 <lb></lb><arrow.to.target n="marg1424"></arrow.to.target>
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1057 <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
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1058 <lb></lb><arrow.to.target n="marg1425"></arrow.to.target>
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1059 <lb></lb>qually grave reſt indifferently in all places, yea, though they ſhould
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1060 <lb></lb>be wholly under water.</s></p><p type="margin">
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1061
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1062 <s><margin.target id="marg1422"></margin.target><emph type="italics"></emph>Of Natation<emph.end type="italics"></emph.end></s></p><p type="margin">
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1063
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1064 <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">
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1065
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1066 <s><margin.target id="marg1424"></margin.target>(b) <emph type="italics"></emph>Id. </s><s>Lib. </s><s>1.
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1067 <lb></lb>Prop.<emph.end type="italics"></emph.end> 3.</s></p><p type="margin">
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1068
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1069 <s><margin.target id="marg1425"></margin.target>(c) <emph type="italics"></emph>Id. </s><s>Lib. 1.
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1070 <lb></lb>Prop.<emph.end type="italics"></emph.end> 3.</s></p><p type="main">
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1071
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1072 <s>But, becauſe that this Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> peruſed, tranſcri­
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1073 <lb></lb><arrow.to.target n="marg1426"></arrow.to.target>
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1074 <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
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1075 <lb></lb>of Motion, Chap.<emph.end type="italics"></emph.end> 29, and afterwards by him confuted, might by the
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1076 <lb></lb>Authority of ſo renowned, and famous a Philoſopher, be rendered
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1077 <lb></lb>dubious, and ſuſpected of falſity; I have judged it neceſſary to de­
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1078 <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
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1079 <lb></lb>cenſures, with which he appeareth to be charged. <emph type="italics"></emph>Buonamico<emph.end type="italics"></emph.end> re­
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1080 <lb></lb><arrow.to.target n="marg1427"></arrow.to.target>
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1081 <lb></lb>jecteth the Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> firſt, as not conſentaneous with
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1082 <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,
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1083 <lb></lb><arrow.to.target n="marg1428"></arrow.to.target>
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1084 <lb></lb>that the Water ſhould exceed the Earth in Gravity, ſeeing on the
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1085 <lb></lb>contrary, that the Gravity of water, increaſeth, by means of the parti­
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1086 <lb></lb><arrow.to.target n="marg1429"></arrow.to.target>
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1087 <lb></lb>cipation of Earth. </s><s>And he ſubjoyns preſently after, that he was
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1088 <lb></lb>not ſatisfied with the Reaſons of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> as not being able with
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1089 <lb></lb>that Doctrine, to aſſign the cauſe whence it comes, that a Boat and
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1090 <lb></lb>a Veſſell, which otherwiſe, floats above the water, doth ſink to the
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1091 <lb></lb>Bottom, if once it be filled with water; that by reaſon of the e­
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1092 <lb></lb>quality of Gravity, between the water within it, and the other water
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1093 <lb></lb>without, it ſhould ſtay a top; but yet, nevertheleſs, we ſee it to go to
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1094 <lb></lb>the Bottom.
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1095 <lb></lb><arrow.to.target n="marg1430"></arrow.to.target></s></p><p type="margin">
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1096
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1097 <s><margin.target id="marg1426"></margin.target>The <emph type="italics"></emph>Authors<emph.end type="italics"></emph.end>
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1098 <lb></lb>defence of <emph type="italics"></emph>Ar­
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1099 <lb></lb>chimedes<emph.end type="italics"></emph.end> his Do­
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1100 <lb></lb>ctrine, againſt
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1101 <lb></lb>the oppoſitions
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1102 <lb></lb>of <emph type="italics"></emph>Buonamico.<emph.end type="italics"></emph.end></s></p><p type="margin">
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1103
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1104 <s><margin.target id="marg1427"></margin.target>His firſt Objecti­
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1105 <lb></lb>on againſt the
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1106 <lb></lb>Doctrine of <emph type="italics"></emph>Ar­
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1107 <lb></lb>chimedes.<emph.end type="italics"></emph.end></s></p><p type="margin">
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1108
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1109 <s><margin.target id="marg1428"></margin.target>His Second Ob­
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1110 <lb></lb>jection.</s></p><p type="margin">
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1111
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1112 <s><margin.target id="marg1429"></margin.target>His third Obje­
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1113 <lb></lb>ction.</s></p><p type="margin">
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1114
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1115 <s><margin.target id="marg1430"></margin.target>His ſourth Ob­
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1116 <lb></lb>jection.</s></p><p type="main">
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1117
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1118 <s>He farther addes, that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> had clearly confuted the Ancients,
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1119 <lb></lb>who ſaid, that light Bodies moved upwards, driven by the impulſe </s></p><p type="main">
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1120
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1121 <s><arrow.to.target n="marg1431"></arrow.to.target>
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1122 <lb></lb>of the more grave Ambient: which if it were ſo, it ſhould ſeem of
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1123 <lb></lb>neceſſity to follow, that all naturall Bodies are by nature heavy,
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1124
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1125
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1126 <pb pagenum="420"></pb>and none light: For that the ſame would befall the Fire and Air,
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1127 <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
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1128 <lb></lb>a Pulſion in the Elements, by which the Earth is reduced into a Sphe­
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1129 <lb></lb>ricall Figure, yet nevertheleſs, in his judgement, it is not ſuch that it
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1130 <lb></lb>can remove grave Bodies from their naturall places, but rather, that
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1131 <lb></lb>it ſend them toward the Centre, to which (as he ſomewhat obſcurely
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1132 <lb></lb>continues to ſay,) the water principally moves, if it in the interim
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1133 <lb></lb>meet not with ſomething that reſiſts it, and, by its Gravity, thruſts
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1134 <lb></lb>it out of its place: in which caſe, if it cannot directly, yet at leaſt
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1135 <lb></lb>as well as it can, it tends to the Centre: but it happens, that light
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1136 <lb></lb>Bodies by ſuch Impulſion, do all aſcend upward: but this properly
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1137 <lb></lb>they have by nature, as alſo, that other of ſwimming. </s><s>He concludes,
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1138 <lb></lb><arrow.to.target n="marg1432"></arrow.to.target>
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1139 <lb></lb>laſtly, that he concurs with <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> in his Concluſions; but not
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1140 <lb></lb>in the Cauſes, which he would referre to the facile and difficult Sepa­
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1141 <lb></lb>ration of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> and to the predominance of the Elements, ſo
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1142 <lb></lb>that when the Moveable ſuperates the power of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>; as for
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1143 <lb></lb>example, Lead doth the Continuity of water, it ſhall move thorow it,
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1144 <lb></lb>elſe not.</s></p><p type="margin">
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1145
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1146 <s><margin.target id="marg1431"></margin.target>The <emph type="italics"></emph>Ancients<emph.end type="italics"></emph.end>
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1147 <lb></lb>denved <emph type="italics"></emph>Aoſolute<emph.end type="italics"></emph.end>
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1148 <lb></lb>Levity.</s></p><p type="margin">
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1149
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1150 <s><margin.target id="marg1432"></margin.target>The cauſes of
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1151 <lb></lb>Natation &amp; Sub­
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1152 <lb></lb>merſion, accord­
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1153 <lb></lb>ing to the Peri­
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1154 <lb></lb>pateticks.</s></p><p type="main">
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1155
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1156 <s>This is all that I have been able to collect, as produced againſt
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1157 <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
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1158 <lb></lb>Principles and Suppoſitions of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end>; which yet muſt be
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1159 <lb></lb>falſe, if the Doctrine be falſe, which depends upon them; but is
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1160 <lb></lb>contented to alledge therein ſome Inconveniences, and ſome Repug­
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1161 <lb></lb>nances to the Doctrine and Opinion of <emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end> In anſwer to which
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1162 <lb></lb>Objections, I ſay, firſt, That the being of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> Doctrine, ſim­
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1163 <lb></lb><arrow.to.target n="marg1433"></arrow.to.target>
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1164 <lb></lb>ply different from the Doctrine of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> ought not to move any
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1165 <lb></lb>to ſuſpect it, there being no cauſe, why the Authority of this ſhould
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1166 <lb></lb>be preferred to the Authority of the other: but, becauſe, where the
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1167 <lb></lb>decrees of Nature are indifferently expoſed to the intellectuall eyes of
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1168 <lb></lb>each, the Authority of the one and the other, loſeth all anthentical­
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1169 <lb></lb>neſs of Perſwaſion, the abſolute power reſiding in Reaſon; therefore
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1170 <lb></lb>I paſs to that which he alledgeth in the ſecond place, as an abſurd con­
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1171 <lb></lb><arrow.to.target n="marg1434"></arrow.to.target>
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1172 <lb></lb>ſequent of the Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> namely, That water ſhould
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1173 <lb></lb>be more grave than Earth. </s><s>But I really find not, that ever <emph type="italics"></emph>Archi­
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1174 <lb></lb>medes<emph.end type="italics"></emph.end> ſaid ſuch a thing, or that it can be rationally deduced from his
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1175 <lb></lb>Concluſions: and if that were manifeſt unto me, I verily believe, I
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1176 <lb></lb>ſhould renounce his Doctrine, as moſt erroneous. </s><s>Perhapsthis Dedu­
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1177 <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
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1178 <lb></lb>ſſel, which ſwims as long as its voyd of water, but once full it ſinks to
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1179 <lb></lb>the Bottom, and underſtanding it of a Veſſel of Earth, he infers againſt
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1180 <lb></lb><emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> thus: Thou ſayſt that the Solids which ſwim, are leſs grave
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1181 <lb></lb>than water: this Veſſell ſwimmeth: therefore, this Veſſell is leſſe grave
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1182 <lb></lb>than water. </s><s>If this be the Illation. </s><s>I eaſily anſwer, granting that this
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1183 <lb></lb>Veſſell is leſſe grave than water, and denying the other conſequence,
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1184
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1185
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1186 <pb pagenum="421"></pb>namely, that Earth is leſs Grave than Water. </s><s>The Veſſel that ſwims
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1187 <lb></lb>occupieth in the water, not only a place equall to the Maſs of the
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1188 <lb></lb>Earth, of which it is formed; but equall to the Earth and to the Air
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1189 <lb></lb>together, contained in its concavity. </s><s>And, if ſuch a Maſs compoun­
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1190 <lb></lb>ded of Earth and Air, ſhall be leſs grave than ſuch another quantity
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1191 <lb></lb>of water, it ſhall ſwim, and ſhall accord with the Doctrine of <emph type="italics"></emph>Archi­
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1192 <lb></lb>medes<emph.end type="italics"></emph.end>; but if, again, removing the Air, the Veſſell ſhall be filled
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1193 <lb></lb>with water, ſo that the Solid put in the water, be nothing but
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1194 <lb></lb>Earth, nor occupieth other place, than that which is only poſſeſt by
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1195 <lb></lb>Earth, it ſhall then go to the Bottom, by reaſon that the Earth is
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1196 <lb></lb>heavier than the water: and this correſponds well with the meaning
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1197 <lb></lb>of <emph type="italics"></emph>Archimedes.<emph.end type="italics"></emph.end> See the ſame effect illuſtrated, with ſuch another
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1198 <lb></lb>Experiment, In preſſing a Viall Glaſs to the Bottom of the water,
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1199 <lb></lb>when it is full of Air, it will meet with great reſiſtance, becauſe it is
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1200 <lb></lb>not the Glaſs alone, that is preſſed under water, but together with
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1201 <lb></lb>the Glaſs a great Maſs of Air, and ſuch, that if you ſhould take as
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1202 <lb></lb>much water, as the Maſs of the Glaſs, and of the Air contained in it,
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1203 <lb></lb>you would have a weight much greater than that of the Viall, and of
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1204 <lb></lb>its Air: and, therefore, it will not ſubmerge without great violence:
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1205 <lb></lb>but if we demit only the Glaſs into the water, which ſhall be when
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1206 <lb></lb>you ſhall fill the Glaſs with water, then ſhall the Glaſs deſcend to
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1207 <lb></lb>the Bottom; as ſuperiour in Gravity to the water.</s></p><p type="margin">
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1208
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1209 <s><margin.target id="marg1433"></margin.target>The Authors an­
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1210 <lb></lb>ſwer to the firſt
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1211 <lb></lb>Objection.</s></p><p type="margin">
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1212
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1213 <s><margin.target id="marg1434"></margin.target>The Authors an­
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1214 <lb></lb>ſwer to the ſe­
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1215 <lb></lb>cond Objection.</s></p><p type="main">
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1216
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1217 <s>Returning, therefore, to our firſt purpoſe; I ſay, that Earth is
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1218 <lb></lb>more grave than water, and that therefore, a Solid of Earth goeth to
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1219 <lb></lb>the bottom of it; but one may poſſibly make a compoſition of Earth
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1220 <lb></lb>and Air, which ſhall be leſs grave than a like Maſs of Water; and
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1221 <lb></lb>this ſhall ſwim: and yet both this and the other experiment ſhall
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1222 <lb></lb>very well accord with the Doctrine of <emph type="italics"></emph>Archimedes.<emph.end type="italics"></emph.end> But becauſe that
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1223 <lb></lb>in my judgment it hath nothing of difficulty in it, I will not poſitive­
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1224 <lb></lb>ly affirme that <emph type="italics"></emph>Signor Buonamico,<emph.end type="italics"></emph.end> would by ſuch a diſcourſe object
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1225 <lb></lb>unto <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> the abſurdity of inferring by his doctrine, that Earth
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1226 <lb></lb>was leſs grave than Water, though I know not how to conceive what
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1227 <lb></lb>other accident he could have induced thence.</s></p><p type="main">
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1228
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1229 <s>Perhaps ſuch a Probleme (in my judgement falſe) was read by
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1230 <lb></lb><emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> in ſome other Author, by whom peradventure it
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1231 <lb></lb>was attributed as a ſingular propertie, of ſome particular Water, and
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1232 <lb></lb>ſo comes now to be uſed with a double errour in confutation of <emph type="italics"></emph>Ar­
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1233 <lb></lb>chimedes,<emph.end type="italics"></emph.end> ſince he ſaith no ſuch thing, nor by him that did ſay it was it
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1234 <lb></lb>meant of the common Element of Water.</s></p><p type="main">
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1235
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1236 <s>The third difficulty in the doctrine of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> was, that he
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1237 <lb></lb><arrow.to.target n="marg1435"></arrow.to.target>
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1238 <lb></lb>could not render a reaſon whence it aroſe, that a piece of Wood,
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1239 <lb></lb>and a Veſſell of Wood, which otherwiſe floats, goeth to the bottom,
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1240 <lb></lb>if filled with Water. <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> hath ſuppoſed that a Verſſell
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1241 <lb></lb>of Wood, and of Wood that by nature ſwims, as before is ſaid,
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1242
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1243
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1244 <pb pagenum="422"></pb>goes to the bottom, if it be filled with water; of which he in the fol­
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1245 <lb></lb>lowing Chapter, which is the 30 of the fifth Book copiouſly diſcourſ­
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1246 <lb></lb>eth: but I (ſpeaking alwayes without diminution of his ſingular
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1247 <lb></lb>Learning) dare in defence of <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> deny this experiment, being
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1248 <lb></lb>certain that a piece of Wood which by its nature ſinks not in Water,
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1249 <lb></lb>ſhall not ſinke though it be turned and converted into the forme of a­
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1250 <lb></lb>ny Veſſell whatſoever, and then filled with Water: and he that would
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1251 <lb></lb>readily ſee the Experiment in ſome other tractable Matter, and that is
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1252 <lb></lb>eaſily reduced into ſeveral Figures, may take pure Wax, and ma­
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1253 <lb></lb>king it firſt into a Ball or other ſolid Figure, let him adde to it ſo
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1254 <lb></lb>much Lead as ſhall juſt carry it to the bottome, ſo that being a graine
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1255 <lb></lb>leſs it could not be able to ſinke it, and making it afterwards into
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1256 <lb></lb>the forme of a Diſh, and filling it with Water, he ſhall finde that with­
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1257 <lb></lb>out the ſaid Lead it ſhall not ſinke, and that with the Lead it ſhall de­
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1258 <lb></lb>ſcend with much ſlowneſs: &amp; in ſhort he ſhall ſatisfie himſelf, that the
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1259 <lb></lb>Water included makes no alteration. </s><s>I ſay not all this while, but that
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1260 <lb></lb>its poſſible of Wood to make Barkes, which being filled with water,
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1261 <lb></lb>ſinke; but that proceeds not through its Gravity, encreaſed by the
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1262 <lb></lb>Water, but rather from the Nailes and other Iron Workes, ſo that
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1263 <lb></lb>it no longer hath a Body leſs grave than Water, but one mixt of Iron
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1264 <lb></lb>and Wood, more grave than a like Maſſe of Water. </s><s>Therefore let
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1265 <lb></lb><emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> deſiſt from deſiring a reaſon of an effect, that is
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1266 <lb></lb>not in nature: yea if the ſinking of the Woodden Veſſell when its full
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1267 <lb></lb>of Water, may call in queſtion the Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> which
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1268 <lb></lb>he would not have you to follow, is on the contrary conſonant and a­
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1269 <lb></lb>greeable to the Doctrine of the Peripateticks, ſince it aptly aſſignes a
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1270 <lb></lb>reaſon why ſuch a Veſſell muſt, when its full of Water, deſcend to the
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1271 <lb></lb>bottom; converting the Argument the other way, we may with
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1272 <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
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1273 <lb></lb>eth with true experiments, and queſtion the other, whoſe Deducti­
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1274 <lb></lb>ons are faſtened upon etroneouſs Concluſions. </s><s>As for the other point
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1275 <lb></lb>hinted in this ſame Inſtance, where it ſeemes that <emph type="italics"></emph>Benonamico<emph.end type="italics"></emph.end> under­
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1276 <lb></lb>ſtands the ſame not only of a piece of wood, ſhaped in the forme of a
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1277 <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
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1278 <lb></lb>would ſay, ſoaked and ſteeped in Water, goes finally to the bottom
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1279 <lb></lb>that happens in ſome poroſe Woods, which, while their Poroſity is re­
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1280 <lb></lb>pleniſhed with Air, or other Matter leſs grave than Water, are Maſ­
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1281 <lb></lb>ſes ſpecificially leſs grave than the ſaid Water, like as is that Viall of
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1282 <lb></lb>Glaſs whileſt it is full of Air: but when, ſuch light Matter depart­
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1283 <lb></lb>ing, there ſucceedeth Water into the ſame Poroſities and Cavities,
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1284 <lb></lb>there reſults a compound of Water and Glaſs more grave than a like
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1285 <lb></lb>Maſs of Water: but the exceſs of its Gravity conſiſts in the Matter
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1286 <lb></lb>of the Glaſs, and not in the Water, which cannot be graver than it
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1287 <lb></lb>ſelf: ſo that which remaines of the Wood, the Air of its Cavi­
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1288
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1289
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1290 <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
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1291 <lb></lb>Poroſities with Water, and you ſhal have a Compoſt of Water and
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1292 <lb></lb>of Wood more grave than Water, but not by vertue of the Water re­
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1293 <lb></lb>ceived into and imbibed by the Poroſities, but of that Matter of the
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1294 <lb></lb>Wood which remains when the Air is departed: and being ſuch it
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1295 <lb></lb>ſhall, according to the Doctrine of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> goe to the bottom,
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1296 <lb></lb>like as before, according to the ſame Doctrine it did ſwim.</s></p><p type="margin">
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1297
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1298 <s><margin.target id="marg1435"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he Authors an­
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1299 <lb></lb>ſwer to the third
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1300 <lb></lb>Objection.</s></p><p type="main">
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1301
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1302 <s>As to that finally which preſents it ſelf in the fourth place, namely,
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1303 <lb></lb><arrow.to.target n="marg1436"></arrow.to.target>
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1304 <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
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1305 <lb></lb>denying Poſitive and Abſolute Levity, and truely eſteeming all Bo­
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1306 <lb></lb>dies to be grave, ſaid, that that which moved upward was driven by
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1307 <lb></lb>the circumambient Air, and therefore that alſo the Doctrine of
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1308 <lb></lb><emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> as an adherent to ſuch an Opinion was con­
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1309 <lb></lb>victed and confuted: I anſwer firſt, that <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> in my
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1310 <lb></lb>judgement hath impoſed upon <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> and deduced from his
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1311 <lb></lb>words more than ever he intended by them, or may from his Propo­
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1312 <lb></lb>ſitions be collected, in regard that <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> neither denies, nor ad­
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1313 <lb></lb>mitteth Poſitive Levity, nor doth he ſo much as mention it: ſo that
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1314 <lb></lb>much leſs ought <emph type="italics"></emph>Buonamico<emph.end type="italics"></emph.end> to inferre, that he hath denyed that it
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1315 <lb></lb>might be the Cauſe and Principle of the Aſcenſion of Fire, and other
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1316 <lb></lb>Light Bodies: having but only demonſtrated, that Solid Bodies
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1317 <lb></lb><arrow.to.target n="marg1437"></arrow.to.target>
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1318 <lb></lb>more grave than Water deſcend in it, according to the exceſs of their
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1319 <lb></lb>Gravity above the Gravity of that, he demonſtrates likewiſe, how the
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1320 <lb></lb><arrow.to.target n="marg1438"></arrow.to.target>
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1321 <lb></lb>leſs grave aſcend in the ſame Water, accordng to its exceſs of Gra­
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1322 <lb></lb>ty, above the Gravity of them. </s><s>So that the moſt that can be gather­
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1323 <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
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1324 <lb></lb>of the Gravity of the Moveable above the Gravity of the Water, is
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1325 <lb></lb>the Cauſe that it deſcends therein, ſo the exceſs of the Gravity of
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1326 <lb></lb>the water above that of the Moveable, is a ſufficient Cauſe why it deſ­
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1327 <lb></lb>cends not, but rather betakes it ſelf to ſwim: not enquiring whe­
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1328 <lb></lb>ther of moving upwards there is, or is not any other Cauſe contrary
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1329 <lb></lb>to Gravity: nor doth <emph type="italics"></emph>Archimedes<emph.end type="italics"></emph.end> diſcourſe leſs properly than if one
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1330 <lb></lb>ſhould ſay: If the South Winde ſhall aſſault the Barke with greater
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1331 <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
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1332 <lb></lb>ries it towards the South, the motion of it ſhall be towards the North:
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1333 <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
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1334 <lb></lb>motion ſhall be towards the South. </s><s>The diſcourſe is excellent and
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1335 <lb></lb>would be unworthily contradicted by ſuch as ſhould oppoſe it, ſaying:
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1336 <lb></lb>Thou miſ-alledgeſt as Cauſe of the motion of the Bark towards the
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1337 <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
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1338 <lb></lb>South Winde; miſ-alledgeſt I ſay, for it is the Force of the North
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1339 <lb></lb>Winde oppoſite to the South, that is able to drive the Bark towards
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1340 <lb></lb>the South. </s><s>Such an Objection would be ſuperfluous, becauſe he which
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1341 <lb></lb>alledgeth for Cauſe of the Motion the ſtream of the Water, denies not
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1342
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1343
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1344 <pb pagenum="424"></pb>but that the Winde oppoſite to the South may do the ſame, but only
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1345 <lb></lb>affirmeth that the force of the Water prevailing over the South
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1346 <lb></lb>Wind, the Bark ſhall move towards the South: and ſaith no more
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1347 <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
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1348 <lb></lb>of the Water prevailing over that by which the moveable deſcends to
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1349 <lb></lb>the Bottom, ſuch moveable ſhall be raiſed from the Bottom to the Sur­
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1350 <lb></lb>face alledgeth a very true Cauſe of ſuch an Accident, nor doth he af­
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1351 <lb></lb>firm or deny that there is, or is not, a vertue contrary to Gravity, called
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1352 <lb></lb>by ſome Levity, that hath alſo a power of moving ſome Matters up
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1353 <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
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1354 <lb></lb><arrow.to.target n="marg1439"></arrow.to.target>
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1355 <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
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1356 <lb></lb>all Bodies to be grave, ſay that the Motion upwards is made, not
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1357 <lb></lb>from an intrinſecal Principle of the Moveable, but only by the Im­
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1358 <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
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1359 <lb></lb>him, ſince he hath given him no Cauſe of quarelling with him
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1360 <lb></lb>But if this Apologie, produced in defence of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> ſhould ſeen
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1361 <lb></lb>to ſome inſufficient to free him from the Objections and Arguments
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1362 <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
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1363 <lb></lb>did alſo fight againſt <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> alledging the Impulſe of the Water
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1364 <lb></lb><arrow.to.target n="marg1440"></arrow.to.target>
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1365 <lb></lb>as the Cauſe of the ſwimming of ſome Bodies leſs grave than it, I would
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1366 <lb></lb>not queſtion, but that I ſhould be able to maintaine the Doctrine of
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1367 <lb></lb><emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> and thoſe others to be moſt true, who abſolutely deny Levity,
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1368 <lb></lb>and affirm no other Intrinſecal Principle of Motion to be in Elemen­
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1369 <lb></lb>tary Bodies ſave only that towards the Centre of the Earth, nor no
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1370 <lb></lb><arrow.to.target n="marg1441"></arrow.to.target>
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1371 <lb></lb>other Cauſe of moving upwards, ſpeaking of that which hath the re­
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1372 <lb></lb>ſemblance of natural Motion, but only the repulſe of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> ſluid,
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1373 <lb></lb>and exceeding the Gravity of the Moveable: and as to the Reaſons
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1374 <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
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1375 <lb></lb><arrow.to.target n="marg1442"></arrow.to.target>
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1376 <lb></lb>anſwer them, and I would aſſay to do it, if it were abſolutely neceſſa­
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1377 <lb></lb>ry to the preſent Matter, or were it not too long a Digreſſion for this
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1378 <lb></lb>ſhort Treatiſe. </s><s>I will only ſay, that if there were in ſome of our Elle­
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1379 <lb></lb>mentary Bodies an Intrinſecall Principle and Naturall Inclination
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1380 <lb></lb>to ſhun the Centre of the Earth, and to move towards the Concave
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1381 <lb></lb>of the Moon, ſuch Bodies, without doubt, would more ſwiftly aſcend
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1382 <lb></lb>through thoſe <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end> that leaſt oppoſe the Velocity of the Moveable,
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1383 <lb></lb>and theſe are the more tenuous and ſubtle; as is, for example, the
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1384 <lb></lb>Air in compariſon of the Water, we daily proving that we can with
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1385 <lb></lb><arrow.to.target n="marg1443"></arrow.to.target>
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1386 <lb></lb>farre more expeditious Velocity move a Hand or a Board to and a­
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1387 <lb></lb>gain in one than in the other: nevertheleſs, we never could finde any
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1388 <lb></lb>Body, that did not aſcend much more ſwiftly in the water than in the
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1389 <lb></lb><arrow.to.target n="marg1444"></arrow.to.target>
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1390 <lb></lb>Air. </s><s>Yea of Bodies which we ſee continually to aſcend in the Water,
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1391 <lb></lb>there is none that having arrived to the confines of the Air, do not whol­
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1392 <lb></lb>ly loſe their Motion; even the Air it ſelf, which riſing with great Ce­
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1393 <lb></lb>lerity through the Water, being once come to its Region it loſeth all</s></p>
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1394
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1395
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1396 <pb pagenum="425"></pb><p type="margin">
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1397
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1398 <s><margin.target id="marg1436"></margin.target>The Authors
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1399 <lb></lb>anſwer to the
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1400 <lb></lb>fourth Object­
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1401 <lb></lb>ion.</s></p><p type="margin">
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1402
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1403 <s><margin.target id="marg1437"></margin.target>Of Natation,
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1404 <lb></lb>Lib. 1. Prop. </s><s>7.</s></p><p type="margin">
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1405
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1406 <s><margin.target id="marg1438"></margin.target>Of Natation,
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1407 <lb></lb>Lib. </s><s>1. Prop. </s><s>4.</s></p><p type="margin">
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1408
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1409 <s><margin.target id="marg1439"></margin.target><emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> denyeth
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1410 <lb></lb>Poſitive Levi­
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1411 <lb></lb>ty.</s></p><p type="margin">
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1412
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1413 <s><margin.target id="marg1440"></margin.target>The Authors
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1414 <lb></lb>defence of the
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1415 <lb></lb>doctrine of <emph type="italics"></emph>Plato<emph.end type="italics"></emph.end>
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1416 <lb></lb>and the <emph type="italics"></emph>Ancients,<emph.end type="italics"></emph.end>
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1417 <lb></lb>who abſolutely
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1418 <lb></lb>deny Levity:</s></p><p type="margin">
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1419
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1420 <s><margin.target id="marg1441"></margin.target>According to
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1421 <lb></lb><emph type="italics"></emph>Plato<emph.end type="italics"></emph.end> there is no
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1422 <lb></lb>Principle of the
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1423 <lb></lb>Motion of de­
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1424 <lb></lb>ſcent in Naturall
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1425 <lb></lb>Bodies, ſave that
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1426 <lb></lb>to the Centre.</s></p><p type="margin">
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1427
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1428 <s><margin.target id="marg1442"></margin.target>No cauſe of
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1429 <lb></lb>the motion of
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1430 <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end> cent, ſave the
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1431 <lb></lb>Impulſe of the
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1432 <lb></lb><emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> exceed­
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1433 <lb></lb>ing the Move­
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1434 <lb></lb>able in Gravi­
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1435 <lb></lb>tie.</s></p><p type="margin">
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1436
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1437 <s><margin.target id="marg1443"></margin.target>Bodies aſcend
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1438 <lb></lb>much ſwifter in
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1439 <lb></lb>the Water, than
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1440 <lb></lb>in the Air.</s></p><p type="margin">
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1441
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1442 <s><margin.target id="marg1444"></margin.target>All Bodies aſ­
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1443 <lb></lb>cending through
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1444 <lb></lb>Water, loſe
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1445 <lb></lb>their Motion,
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1446 <lb></lb>comming to the
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1447 <lb></lb>confines of the
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1448 <lb></lb>Air.</s></p><p type="main">
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1449
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1450 <s>And, howbeit, Experience ſhewes, that the Bodies, ſucceſſively
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1451 <lb></lb><arrow.to.target n="marg1445"></arrow.to.target>
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1452 <lb></lb>leſs grave, do moſt expeditiouſly aſcend in water, it cannot be doubt­
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1453 <lb></lb>ed, but that the Ignean Exhalations do aſcend more ſwiftly
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1454 <lb></lb><arrow.to.target n="marg1446"></arrow.to.target>
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1455 <lb></lb>through the water, than doth the Air: which Air is ſeen by Experi­
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1456 <lb></lb>ence to aſcend more ſwiftly through the Water, than the Fiery Exha­
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1457 <lb></lb>lations through the Air: Therefore, we muſt of neceſſity conclude,
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1458 <lb></lb>that the ſaid Exhalations do much more expeditiouſly aſcend through
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1459 <lb></lb>the Water, than through the Air; and that, conſequently, they are
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1460 <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
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1461 <lb></lb>ſick Principle that is in them, of avoiding the Centre of the Earth;
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1462 <lb></lb>to which other grave Bodies tend.</s></p><p type="margin">
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1463
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1464 <s><margin.target id="marg1445"></margin.target>The lighter
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1465 <lb></lb>Bodies alſend
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1466 <lb></lb>more ſwiftly
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1467 <lb></lb>through Water.</s></p><p type="margin">
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1468
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1469 <s><margin.target id="marg1446"></margin.target>Fiery Exhalati­
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1470 <lb></lb>ons ascend tho­
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1471 <lb></lb>row the Water
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1472 <lb></lb>more ſwiftly
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1473 <lb></lb>than doth the
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1474 <lb></lb>Air; &amp; the Air
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1475 <lb></lb>aſcends more
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1476 <lb></lb>ſwiftly thorow
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1477 <lb></lb>the Water, than
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1478 <lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end>ire thorow the
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1479 <lb></lb>Air.</s></p><p type="main">
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1480
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1481 <s>To that which for a finall concluſion, <emph type="italics"></emph>Signor Buonamico<emph.end type="italics"></emph.end> produceth
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1482 <lb></lb><arrow.to.target n="marg1447"></arrow.to.target>
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1483 <lb></lb>of going about to reduce the deſcending or not deſcending, to the
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1484 <lb></lb>eaſie and uneaſie Diviſion of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> and to the predominancy
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1485 <lb></lb>of the Elements: I anſwer, as to the firſt part, that that cannot in any
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1486 <lb></lb>manner be admitted as a Cauſe, being that in none of the Fluid
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1487 <lb></lb><emph type="italics"></emph>Mediums,<emph.end type="italics"></emph.end> as the Air, the Water, and other Liquids, there is any
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1488 <lb></lb><arrow.to.target n="marg1448"></arrow.to.target>
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1489 <lb></lb>Reſiſtance againſt Diviſion, but all by every the leaſt Force, are di­
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1490 <lb></lb>vided and penetrated, as I will anon demonſtrate: ſo, that of ſuch
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1491 <lb></lb>Reſiſtance of Diviſion there can be no Act, ſince it ſelf is not in be­
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1492 <lb></lb>ing. </s><s>As to the other part, I ſay, that the predominancy of the Ele­
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1493 <lb></lb><arrow.to.target n="marg1449"></arrow.to.target>
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1494 <lb></lb>ments in Moveables, is to be conſidered, as far as to the exceſſe or
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1495 <lb></lb>defect of Gravity, in relation to the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>: for in that Action,
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1496 <lb></lb>the Elements operate not, but only, ſo far as they are grave or light:
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1497 <lb></lb>therefore, to ſay that the Wood of the Firre ſinks not, becauſe Air
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1498 <lb></lb>predominateth in it, is no more than to ſay, becauſe it is leſs grave
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1499 <lb></lb>than the Water. </s><s>Yea, even the immediate Cauſe, is its being leſs
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1500 <lb></lb>grave than the Water: and it being under the predominancy of the
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1501 <lb></lb><arrow.to.target n="marg1450"></arrow.to.target>
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1502 <lb></lb>Air, is the Cauſe of its leſs Gravity: Therefore, he that alledgeth the
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1503 <lb></lb>predominancy of the Element for a Cauſe, brings the Cauſe of the
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1504 <lb></lb>Cauſe, and not the neereſt and immediate Cauſe. </s><s>Now, who knows
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1505 <lb></lb>not that the true Cauſe is the immediate, and not the mediate?
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1506 <lb></lb><arrow.to.target n="marg1451"></arrow.to.target>
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1507 <lb></lb>Moreover, he that alledgeth Gravity, brings a Cauſe moſt perſpicuous
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1508 <lb></lb>to Sence: The cauſe we may very eaſily aſſertain our ſelves;
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1509 <lb></lb>whether Ebony, for example, and Firre, be more or leſs grave than
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1510 <lb></lb>water: but whether Earth or Air predominates in them, who ſhall
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1511 <lb></lb><arrow.to.target n="marg1452"></arrow.to.target>
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1512 <lb></lb>make that manifeſt? </s><s>Certainly, no Experiment can better do it
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1513 <lb></lb>than to obſerve whether they ſwim or ſink. </s><s>So, that he who knows,
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1514 <lb></lb>not whether ſuch a Solid ſwims, unleſs when he knows that Air pre­
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1515 <lb></lb>dominates in it, knows not whether it ſwim, unleſs he ſees it ſwim,
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1516 <lb></lb>for then he knows that it ſwims, when he knows that it is Air that
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1517 <lb></lb>predominates, but knows not that Air hath the predominance, unleſs
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1518 <lb></lb>he ſees it ſwim: therefore, he knows not if it ſwims, till ſuch time
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1519 <lb></lb>as he hath ſeen it ſwim.</s></p>
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1520
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1521
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1522 <pb pagenum="426"></pb><p type="margin">
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1523
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1524 <s><margin.target id="marg1447"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he Authors
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1525 <lb></lb>confutation of
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1526 <lb></lb>the Peripateticks
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1527 <lb></lb>Cauſes of Nata­
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1528 <lb></lb>tion &amp; Submerſi­
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1529 <lb></lb>on.</s></p><p type="margin">
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1530
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1531 <s><margin.target id="marg1448"></margin.target>Water &amp; other
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1532 <lb></lb>fluids void of
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1533 <lb></lb>Reſiſtance a­
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1534 <lb></lb>gainſt Diviſion.</s></p><p type="margin">
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1535
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1536 <s><margin.target id="marg1449"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he predomi­
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1537 <lb></lb>nancy of Ele­
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1538 <lb></lb>ments in Move­
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1539 <lb></lb>ables to be con­
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1540 <lb></lb>ſidered only in
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1541 <lb></lb>relation to their
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1542 <lb></lb>excefs or defect
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1543 <lb></lb>of Gravity in
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1544 <lb></lb>reference to the
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1545 <lb></lb><emph type="italics"></emph>Medium.<emph.end type="italics"></emph.end></s></p><p type="margin">
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1546
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1547 <s><margin.target id="marg1450"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he immedi­
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1548 <lb></lb>ate Cauſe of Na­
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1549 <lb></lb>tation is that the
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1550 <lb></lb>Moveable is leſs
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1551 <lb></lb>grave than the
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1552 <lb></lb>Water.</s></p><p type="margin">
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1553
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1554 <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
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1555 <lb></lb>ticks alledge for
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1556 <lb></lb>the reaſon of
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1557 <lb></lb>Natation the
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1558 <lb></lb>Cauſe of the
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1559 <lb></lb>Cauſe.</s></p><p type="margin">
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1560
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1561 <s><margin.target id="marg1452"></margin.target>Gravity a
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1562 <lb></lb>Cauſe moſt per­
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1563 <lb></lb>ſpicuous to
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1564 <lb></lb>ſence:</s></p><p type="main">
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1565
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1566 <s>Let us not then deſpiſe thoſe Hints, though very dark, which
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1567 <lb></lb>Reaſon, after ſome contemplation, offereth to our Intelligence, and
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1568 <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
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1569 <lb></lb><arrow.to.target n="marg1453"></arrow.to.target>
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1570 <lb></lb>ſubmerge in water, when it ſhall be ſpecifically more grave than it
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1571 <lb></lb>and that if it ſhall be leſs grave, it ſhall of neceſſity ſwim, and
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1572 <lb></lb><arrow.to.target n="marg1454"></arrow.to.target>
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1573 <lb></lb>that it will reſt indifferently in any place under water, if its Gravity
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1574 <lb></lb>be perfectly like to that of the water.
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1575 <lb></lb><arrow.to.target n="marg1455"></arrow.to.target></s></p><p type="margin">
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1576
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1577 <s><margin.target id="marg1453"></margin.target>Lib 1. of Na­
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1578 <lb></lb>tation Prop. </s><s>7.</s></p><p type="margin">
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1579
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1580 <s><margin.target id="marg1454"></margin.target>Id. </s><s>Lib. 1.
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1581 <lb></lb>Prop. </s><s>4.</s></p><p type="margin">
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1582
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1583 <s><margin.target id="marg1455"></margin.target>Id. </s><s>Lib. </s><s>1:
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1584 <lb></lb>Prop. </s><s>3.</s></p><p type="main">
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1585
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1586 <s>Theſe things explained and proved, I come to conſider that which
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1587 <lb></lb>offers it ſelf, touching what the Diverſity of figure given unto the
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1588 <lb></lb>ſaid Moveable hath to do with theſe Motions and Reſts; and pro­
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1589 <lb></lb>ceed to affirme, that,</s></p><p type="head">
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1590
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1591 <s>THEOREME V.</s></p><p type="main">
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1592
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1593 <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">
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1594
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1595 <s><arrow.to.target n="marg1456"></arrow.to.target>
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1596 <lb></lb><emph type="italics"></emph>cannot any way be a Cauſe of its abſolute Sinking or
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1597 <lb></lb>Swimming.<emph.end type="italics"></emph.end></s></p><p type="margin">
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1598
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1599 <s><margin.target id="marg1456"></margin.target>Diverſity of
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1600 <lb></lb>Figure no Cauſe
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1601 <lb></lb>of its abſolute
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1602 <lb></lb>Natation or Sub­
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1603 <lb></lb>merſion.</s></p><p type="main">
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1604
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1605 <s>So that if a Solid being formed, for example, into a Spherical
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1606 <lb></lb>Figure, doth ſink or ſwim in the water, I ſay, that being formed
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1607 <lb></lb>into any other Figure, the ſame figure in the ſame water, ſhall
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1608 <lb></lb>ſink or ſwim: nor can ſuch its Motion by the Expanſion or by o­
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1609 <lb></lb>ther mutation of Figure, be impeded or taken away.
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1610 <lb></lb><arrow.to.target n="marg1457"></arrow.to.target></s></p><p type="margin">
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1611
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1612 <s><margin.target id="marg1457"></margin.target>The Expanſi­
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1613 <lb></lb>on of <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure, re­
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1614 <lb></lb>tards the Veloci­
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1615 <lb></lb>ty of the aſcent
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1616 <lb></lb>or deſcent of the
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1617 <lb></lb>Moveable in the
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1618 <lb></lb>water; but doth
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1619 <lb></lb>not deprive it of
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1620 <lb></lb>all Motion.</s></p><p type="main">
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1621
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1622 <s>The Expanſion of the Figure may indeed retard its Velocity, aſ
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1623 <lb></lb>well of aſcent as deſcent, and more and more according as the ſaid Fi­
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1624 <lb></lb>gure is reduced to a greater breadth and thinneſs: but that it may bere
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1625 <lb></lb>duced to ſuch a form as that that ſame matter be wholly hindred from
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1626 <lb></lb>moving in the ſame water, that I hold to be impoſſible. </s><s>In this I have
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1627 <lb></lb>met with great contradictors, who producing ſome Experiments, and
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1628 <lb></lb>in perticular a thin Board of Ebony, and a Ball of the ſame Wood
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1629 <lb></lb>and ſhewing how the Ball in Water deſcended to the bottom, and
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1630 <lb></lb>the Board being put lightly upon the Water ſubmerged not, but reſt­
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1631 <lb></lb>ed; have held, and with the Authority of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> confirmed them
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1632 <lb></lb>ſelves in their Opinions, that the Cauſe of that Reſt was the breadth
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1633 <lb></lb>of the Figure, u able by its ſmall weight to pierce and penetrate the
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1634 <lb></lb>Reſiſtance of the Waters Craſſitude, which Reſiſtance is readily o­
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1635 <lb></lb>vercome by the other Sphericall Figure.</s></p><p type="main">
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1636
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1637 <s>This is the Principal point in the preſent Queſtion, in which I per­
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1638 <lb></lb>ſwade my ſelf to be on the right ſide.</s></p><p type="main">
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1639
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1640 <s>Therefore, beginning to inveſtigate with the examination of ex­
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1641 <lb></lb>quiſite Experiments that really the Figure doth not a jot alter the deſ­
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1642 <lb></lb>cent or Aſcent of the ſame Solids, and having already demonſtra­
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1643 <lb></lb>ted that the greater or leſs Gravity of the Solid in relation to the Gra­
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1644 <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
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1645
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1646
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1647 <pb pagenum="427"></pb>would make proof of that, which about this Effect the diverſity of Fi­
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1648 <lb></lb>gure worketh, its neceſſary to make the Experiment with Matter
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1649 <lb></lb>wherein variety of Gravities hath no place. </s><s>For making uſe of Mat­
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1650 <lb></lb>ters which may be different in their Specifical Gravities, and meeting
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1651 <lb></lb>with varieties of effects of Aſcending and Deſcending, we ſhall al­
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1652 <lb></lb>wayes be left unſatisfied whether that diverſity derive it ſelf really
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1653 <lb></lb>from the ſole Figure, or elſe from the divers Gravity alſo. </s><s>We may
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1654 <lb></lb>remedy this by takeing one only Matter, that is tractable and eaſily
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1655 <lb></lb>reduceable into every ſort of Figure. </s><s>Moreover, it wil be an excellent
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1656 <lb></lb>expedient to take a kinde of Matter, exactly alike in Gravity unto the
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1657 <lb></lb>Water: for that Matter, as far as pertaines to the Gravity, is in­
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1658 <lb></lb>different either to Aſcend or Deſcend; ſo that we may preſently ob­
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1659 <lb></lb>ſerve any the leaſt difference that derives it ſelf from the diverſity of
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1660 <lb></lb>Figure.</s></p><p type="main">
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1661
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1662 <s>Now to do this, Wax is moſt apt, which, beſides its incapacity of </s></p><p type="main">
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1663
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1664 <s><arrow.to.target n="marg1458"></arrow.to.target>
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1665 <lb></lb>receiveing any ſenſible alteration from its imbibing of Water, is duct­
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1666 <lb></lb>ile or pliant, and the ſame piece is eaſily reduceable into all Figures:
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1667 <lb></lb>and being <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> a very inconſiderable matter inferiour in Gravity
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1668 <lb></lb>to the Water, by mixing therewith a little of the fileings of Lead it is
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1669 <lb></lb>reduced to a Gravity exactly equall to that of the Water.</s></p><p type="margin">
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1670
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1671 <s><margin.target id="marg1458"></margin.target>An Experi­
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1672 <lb></lb>ment in Wax,
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1673 <lb></lb>that proveth Fi­
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1674 <lb></lb>gute to have no
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1675 <lb></lb>Operation in
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1676 <lb></lb>Natation &amp; Sub­
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1677 <lb></lb>merſion.</s></p><p type="main">
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1678
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1679 <s>This Matter prepared, and, for example, a Ball being made there­
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1680 <lb></lb>of as bigge as an Orange or biger, and that made ſo grave as to
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1681 <lb></lb>ſink to the bottom, but ſo lightly, that takeing thence one only Grain
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1682 <lb></lb>of Lead, it returnes to the top, and being added, it ſubmergeth to
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1683 <lb></lb>the bottom, let the ſame Wax afterwards be made into a very broad
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1684 <lb></lb>and thin Flake or Cake; and then, returning to make the ſame Ex­
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1685 <lb></lb>periment, you ſhall ſee that it being put to the bottom, it ſhall, with the
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1686 <lb></lb>Grain of Lead reſt below, and that Grain deducted, it ſhall aſcend to
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1687 <lb></lb>the very Surface, and added again it ſhall dive to the bottom. </s><s>And
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1688 <lb></lb>this ſame effect ſhall happen alwaies in all ſort of Figures, as wel re­
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1689 <lb></lb>gular as irregular: nor ſhall you ever finde any that will ſwim with­
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1690 <lb></lb>out the removall of the Grain of Lead, or ſinke to the bottom unleſs
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1691 <lb></lb>it be added: and, in ſhort, about the going or not going to the Bot­
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1692 <lb></lb>tom, you ſhall diſcover no diverſity, although, indeed, you ſhall about
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1693 <lb></lb>the quick and ſlow deſcent: for the more expatiated and diſtended
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1694 <lb></lb>Figures move more ſlowly aſwel in the diveing to the bottom as in
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1695 <lb></lb>the riſing to the top; and the other more contracted and compact Fi­
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1696 <lb></lb>gures, more ſpeedily. </s><s>Now I know not what may be expected from
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1697 <lb></lb>the diverſity of Figures, if the moſt contrary to one another operate
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1698 <lb></lb>not ſo much as doth a very ſmall Grain of Lead, added or removed.</s></p><p type="main">
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1699
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1700 <s>Me thinkes I hear ſome of the Adverſaries to raiſe a doubt upon
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1701 <lb></lb><arrow.to.target n="marg1459"></arrow.to.target>
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1702 <lb></lb>my produced Experiment. </s><s>And firſt, that they offer to my conſidera­
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1703 <lb></lb>tion, that the Figure, as a Figure ſimply, and disjunct from the Matter
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1704 <lb></lb>workes not any effect, but requires to be conjoyned with the Matter­
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1705
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1706
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1707 <pb pagenum="428"></pb>and, furthermore, not with every Matter, but with thoſe only,
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1708 <lb></lb>wherewith it may be able ro execute the deſired operation. </s><s>Like
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1709 <lb></lb>as we ſee it verified by Experience, that the Acute and ſharp Angle is
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1710 <lb></lb>more apt to cut, than the Obtuſe; yet alwaies provided, that both
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1711 <lb></lb>the one and the other, be joyned with a Matter apt to cut, as for
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1712 <lb></lb>example, with Steel. </s><s>Therefore, a Knife with a fine and ſharp
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1713 <lb></lb>edge, cuts Bread or Wood with much eaſe, which it will not do, if
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1714 <lb></lb>the edge be blunt and thick: but he that will inſtead of Steel, take
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1715 <lb></lb>Wax, and mould it into a Knife, undoubtedly ſhall never know the
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1716 <lb></lb>effects of ſharp and blunt edges: becauſe neither of them will cut,
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1717 <lb></lb>the Wax being unable by reaſon of its flexibility, to overcome the
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1718 <lb></lb>hardneſs of the Wood and Bread. </s><s>And, therefore, applying the
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1719 <lb></lb>like diſcourſe to our purpoſe, they ſay, that the difference of Figure
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1720 <lb></lb>will ſhew different effects, touching Natation and Submerſion, but
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1721 <lb></lb>not conjoyned with any kind of Matter, but only with thoſe Matters
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1722 <lb></lb>which, by their Gravity, are apt to reſiſt the Velocity of the water,
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1723 <lb></lb>whence he that would elect for the Matter, Cork or other light wood
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1724 <lb></lb>unable, through its Levity, to ſuperate the Craſſitude of the water,
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1725 <lb></lb>and of that Matter ſhould forme Solids of divers Figures, woulld in
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1726 <lb></lb>vain ſeek to find out what operation Figure hath in Natation or Sub­
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1727 <lb></lb>merſion; becauſe all would ſwim, and that not through any property
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1728 <lb></lb>of this or that Figure, but through the debility of the Matter, want­
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1729 <lb></lb>ing ſo much Gravity, as is requiſite to ſuperate and overcome the
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1730 <lb></lb>Denſity and Craſſitude of the water.</s></p><p type="margin">
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1731
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1732 <s><margin.target id="marg1459"></margin.target>An objection a­
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1733 <lb></lb>gainſt the Expe­
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1734 <lb></lb>riment in Wax.</s></p><p type="main">
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1735
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1736 <s>Its needfull, therefore, if wee would ſee the effect wrought by the
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1737 <lb></lb>Diverſity of Figure, firſt to make choice of a Matter of its nature
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1738 <lb></lb>apt to penetrate the Craſſitude of the water. </s><s>And, for this effect,
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1739 <lb></lb><arrow.to.target n="marg1460"></arrow.to.target>
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1740 <lb></lb>they have made choice of ſuch a Matter, as fit, that being readily re­
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1741 <lb></lb>duced into Sphericall Figure, goes to the Bottom; and it is Ebony
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1742 <lb></lb>of which they afterwards making a ſmall Board or Splinter, as thin as
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1743 <lb></lb>a Lath, have illuſtrated how that this, put upon the Surface of the
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1744 <lb></lb>water, reſts there without deſcending to the Bottom: and making, on
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1745 <lb></lb>the otherſide, of the ſame wood a Ball, no leſs than a hazell Nut,
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1746 <lb></lb>they ſhew, that this ſwims not, but deſcendes. </s><s>From which Experi­
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1747 <lb></lb>ment, they think they may frankly conclude, that the Breadth ofthe
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1748 <lb></lb>Figure in the flat Lath or Board, is the cauſe of its not deſcendingto
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1749 <lb></lb>the Bottom, foraſmuch as a Ball of the ſame Matter, not different
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1750 <lb></lb>from the Board in any thing but in Figure, ſubmergeth in the ſame
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1751 <lb></lb>water to the Bottom. </s><s>The diſcourſe and the Experiment hath really
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1752 <lb></lb>ſo much of probability and likely hood of truth in it, that it would be
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1753 <lb></lb>no wonder, if many perſwaded by a certain curſory obſervation,
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1754 <lb></lb>ſhould yield credit to it; nevertheleſs, I think I am able to diſcover,
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1755 <lb></lb>how that it is not free from falacy.</s></p><p type="margin">
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1756
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1757 <s><margin.target id="marg1460"></margin.target>An Experi­
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1758 <lb></lb>ment in Ebany,
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1759 <lb></lb>brought to diſ­
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1760 <lb></lb>prove the Expe­
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1761 <lb></lb>timent in Wax.</s></p><p type="main">
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1762
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1763 <s>Beginning, therefore, to examine one by one, all the particulars that
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1764
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1765
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1766 <pb pagenum="429"></pb>have been produced, I ſay, that Figures, as ſimple Figures, not only
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1767 <lb></lb><arrow.to.target n="marg1461"></arrow.to.target>
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1768 <lb></lb>operate not in naturall things, but neither are they ever ſeperated
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1769 <lb></lb>from the Corporeall ſubſtance: nor have I ever alledged them ſtript
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1770 <lb></lb>of ſenſible Matter, like as alſo I freely admit, that in our endeavour­
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1771 <lb></lb>ing to examine the Diverſity of Accidents, dependant upon the va­
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1772 <lb></lb>riety of Figures, it is neceſſary to apply them to Matters, which ob­
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1773 <lb></lb>ſtruct not the various operations of thoſe various Figures: and I ad­
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1774 <lb></lb>mit and grant, that I ſhould do very ill, if I would experiment the in­
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1775 <lb></lb>fluence of Acuteneſſe of edge with a Knife of Wax, applying it to cut
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1776 <lb></lb>an Oak, becauſe there is no Acuteneſs in Wax able to cut that
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1777 <lb></lb>very hard wood. </s><s>But yet ſuch an Experiment of this Knife, would
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1778 <lb></lb>not be beſides the purpoſe, to cut curded Milk, or other very yielding
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1779 <lb></lb>Matter: yea, in ſuch like Matters, the Wax is more commodious
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1780 <lb></lb>than Steel; for finding the diverſity depending upon Angles, more or
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1781 <lb></lb>leſs Acute, for that Milk is indifferently cut with a Raiſor, and with
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1782 <lb></lb>a Knife, that hath a blunt edge. </s><s>It needs, therefore, that regard be
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1783 <lb></lb>had, not only to the hardneſs, ſolidity or Gravity of Bodies, which
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1784 <lb></lb>under divers figures, are to divide and penetrate ſome Matters, but it
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1785 <lb></lb>forceth alſo, that regard be had, on the other ſide, to the Reſiſtance
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1786 <lb></lb>of the Matters, to be divided and penetrated. </s><s>But ſince I have in
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1787 <lb></lb>making the Experiment concerning our Conteſt, choſen a Matter
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1788 <lb></lb>which penetrates the Reſiſtance of the water; and in all figures deſ­
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1789 <lb></lb>cendes to the Bottome, the Adverſaries can charge me with no defect;
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1790 <lb></lb>yea, I have propounded ſo much a more excellent Method than they,
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1791 <lb></lb>in as much as I have removed all other Cauſes, of deſcending or
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1792 <lb></lb>not deſcending to the Bottom, and retained the only ſole and pure
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1793 <lb></lb>variety of Figures, demonſtrating that the ſame Figures all deſcende
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1794 <lb></lb>with the only alteration of a Grain in weight: which Grain being
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1795 <lb></lb>removed, they return to float and ſwim; it is not true, therefore,
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1796 <lb></lb>(reſuming the Example by them introduced) that I have gon about
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1797 <lb></lb>to experiment the efficacy of Acuteneſs, in cutting with Matters un­
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1798 <lb></lb>able to cut, but with Matters proportioned to our occaſion; ſince
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1799 <lb></lb>they are ſubjected to no other variety, then that alone which depends
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1800 <lb></lb>on the Figure more or leſs a cute.
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1801 <lb></lb><arrow.to.target n="marg1462"></arrow.to.target></s></p><p type="margin">
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1802
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1803 <s><margin.target id="marg1461"></margin.target>Figure is un­
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1804 <lb></lb>ſeperable from
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1805 <lb></lb>Corporeall Sub­
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1806 <lb></lb>ſtance.</s></p><p type="margin">
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1807
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1808 <s><margin.target id="marg1462"></margin.target>The anſwer to
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1809 <lb></lb>the Objection a­
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1810 <lb></lb>gainſt the Expe­
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1811 <lb></lb>riment of the
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1812 <lb></lb>Wax.</s></p><p type="main">
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1813
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1814 <s>But let us proceed a little farther, and obſerve, how that indeed
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1815 <lb></lb>the Conſideration, which, they ſay, ought to be had about the Election
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1816 <lb></lb>of the Matter, to the end, that it may be proportionate for the ma­
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1817 <lb></lb>king of our experiment, is needleſly introduced, declaring by the ex­
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1818 <lb></lb>ample of Cutting, that like as Acuteneſs is inſufficient to cut, unleſs
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1819 <lb></lb>when it is in a Matter hard and apt to ſuperate the Reſiſtance of the
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1820 <lb></lb>wood or other Matter, which we intend to cut; ſo the aptitude of
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1821 <lb></lb>deſcending or notdeſcending in water, ought and can only be known
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1822 <lb></lb>in thoſe Matters, that are able to overcome the Renitence, and ſupe­
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1823 <lb></lb>rate the Craſſitude of the water. </s><s>Unto which, I ſay, that to make
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1824 <lb></lb>diſtinction and election, more of this than of that Matter, on which to
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1825
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1826
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1827 <pb pagenum="430"></pb>impreſs the Figures for cutting or penetrating this or that Body,
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1828 <lb></lb>as the ſolidity or obdurateneſs of the ſaid Bodies ſhall be greater
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1829 <lb></lb>or leſs, is very neceſſary: but withall I ſubjoyn, that ſuch diſtinct­
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1830 <lb></lb>ion, election and caution would be ſuperfluous and unprofitable, if
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1831 <lb></lb>the Body to be cut or penetrated, ſhould have no Reſiſtance, or
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1832 <lb></lb>ſhould not at all withſtand the Cutting or Penitration: and if the
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1833 <lb></lb>Knife were to be uſed in cutting a Miſt or Smoak, one of Paper
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1834 <lb></lb>would be equally ſerviceable with one of <emph type="italics"></emph>Damaſcus<emph.end type="italics"></emph.end> Steel: and ſo
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1835 <lb></lb>by reaſon the water hath not any Reſiſtance againſt the Penitration
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1836 <lb></lb>of any Solid Body, all choice of Matter is ſuperfluous and needleſs,
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1837 <lb></lb>and the Election which I ſaid above to have been well made of a
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1838 <lb></lb>Matter reciprocall in Gravity to water, was not becauſe it was ne­
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1839 <lb></lb>ceſſary, for the overcoming of the craſſiitude of the water, but its
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1840 <lb></lb>Gravity, with which only it reſiſts the ſinking of Solid Bodies: and
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1841 <lb></lb>for what concerneth the Reſiſtance of the craſſitude, if we narrowly
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1842 <lb></lb>conſider it, we ſhall find that all Solid Bodies, as well thoſe that
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1843 <lb></lb>ſink, as thoſe that ſwim, are indifferently accomodated and apt to
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1844 <lb></lb>bring us to the knowledge of the truth in queſtion. </s><s>Nor will I
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1845 <lb></lb>be frighted out of the belief of theſe Concluſions, by the Experi­
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1846 <lb></lb>ments which may be produced againſt me, of many ſeverall Woods,
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1847 <lb></lb>Corks, Galls, and, moreover, of ſubtle ſlates and plates of all ſorts
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1848 <lb></lb>of Stone and Mettall, apt by means of their Naturall Gravity, to
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1849 <lb></lb>move towards the Centre of the Earth, the which, nevertheleſs, be­
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1850 <lb></lb>ing impotent, either through the Figure (as the Adverſaries thinke)
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1851 <lb></lb>or through Levity, to break and penetrate the Continuity of the
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1852 <lb></lb>parts of the water, and to diſtract its union, do continue to ſwimm
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1853 <lb></lb>without ſubmerging in the leaſt: nor on the other ſide, ſhall the
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1854 <lb></lb>Authority of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> move me, who in more than one place, aſſir­
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1855 <lb></lb>meth the contrary to this, which Experience ſhews me.</s></p><p type="main">
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1856
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1857 <s><arrow.to.target n="marg1463"></arrow.to.target></s></p><p type="margin">
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1858
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1859 <s><margin.target id="marg1463"></margin.target>No Solid of
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1860 <lb></lb>ſuch Levity, nor
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1861 <lb></lb>of ſuch Figure,
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1862 <lb></lb>but that it doth
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1863 <lb></lb>penetrate the
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1864 <lb></lb>Craſſitude of
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1865 <lb></lb>the Water.</s></p><p type="main">
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1866
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1867 <s>I return, therefore, to aſſert, that there is not any Solid of ſuch
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1868 <lb></lb>Levity, nor of ſuch Figure, that being put upon the water, doth not
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1869 <lb></lb>divide and penetrate its Craſſitude: yea if any with a more per­
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1870 <lb></lb>ſpicatious eye, ſhall return to obſerve more exactly the thin Boards
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1871 <lb></lb>of Wood, he ſhall ſee them to be with part of their thickneſs under </s></p><p type="main">
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1872
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1873 <s><arrow.to.target n="marg1464"></arrow.to.target>
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1874 <lb></lb>water, and not only with their inferiour Superficies, to kiſſe the
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1875 <lb></lb>Superiour of the water, as they of neceſſity muſt have believed, who
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1876 <lb></lb>have ſaid, that ſuch Boards ſubmerge not, as not being able to di­
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1877 <lb></lb>vide the Tenacity of the parts of the water: and, moreover, he
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1878 <lb></lb>ſhall ſee, that ſubtle ſhivers of Ebony, Stone or Metall, when they
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1879 <lb></lb>float, have not only broak the Continuity of the water, but are with
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1880 <lb></lb>all their thickneſs, under the Surface of it; and more and more,
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1881 <lb></lb>according as the Matters are more grave: ſo that a thin Plate of
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1882 <lb></lb>Lead, ſhall be lower than the Surface of the circumfuſed water, by
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1883 <lb></lb>at leaſt twelve times the thickneſs of the Plate, and Gold ſhall dive
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1884
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1885
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1886 <pb pagenum="431"></pb>below the Levell of the water, almoſt twenty times the thickneſs
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1887 <lb></lb>of the Plate, as I ſhall anon declare.</s></p><p type="margin">
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1888
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1889 <s><margin.target id="marg1464"></margin.target>Bodies of all
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1890 <lb></lb>Figures, laid up­
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1891 <lb></lb>on the water, do
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1892 <lb></lb>penetrate its
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1893 <lb></lb>Craſſitude, and
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1894 <lb></lb>in what propor­
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1895 <lb></lb>tion.</s></p><p type="main">
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1896
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1897 <s>But let us proceed to evince, that the water yields and ſufters it
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1898 <lb></lb>ſelf to be penetrated by every the lighteſt Body; and therewithall
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1899 <lb></lb>demonſtrate, how, even by Matters that ſubmerge not, we may
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1900 <lb></lb>come to know that Figure operates nothing about the going or
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1901 <lb></lb>not going to the Bottom, ſeeing that the water ſuffers it ſelf to be
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1902 <lb></lb>penetrated equally by every Figure.</s></p><p type="main">
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1903
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1904 <s>Make a Cone, or a Piramis of Cypreſs, of Firre, or of other
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1905 <lb></lb><arrow.to.target n="marg1465"></arrow.to.target>
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1906 <lb></lb>Wood of like Gravity, or of pure Wax, and let its height be ſome­
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1907 <lb></lb>what great, namely a handfull, or more, and put it into the water
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1908 <lb></lb>with the Baſe downwards: firſt, you ſhall ſee that it will penetrate
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1909 <lb></lb>the water, nor ſhall it be at all impeded by the largeneſs of the Baſe,
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1910 <lb></lb>nor yet ſhall it ſink all under water, but the part towards the point
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1911 <lb></lb>ſhall lye above it: by which ſhall be manifeſt, firſt, that that Solid
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1912 <lb></lb>forbeares not to ſink out of an inabillity to divide the Continuity
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1913 <lb></lb>of the water, having already divided it with its broad part, that in
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1914 <lb></lb>the opinion of the Adverſaries is the leſs apt to make the diviſion.
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1915 <lb></lb></s><s>The Piramid being thus fixed, note what part of it ſhall be ſub­
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1916 <lb></lb>merged, and revert it afterwards with the point downwards, and
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1917 <lb></lb>you ſhall ſee that it ſhall not dive into the water more than before,
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1918 <lb></lb>but if you obſerve how far it ſhall ſink, every perſon expert in
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1919 <lb></lb>Geometry, may meaſure, that thoſe parts that remain out of the
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1920 <lb></lb>water, both in the one and in the other Experiment are equall to
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1921 <lb></lb>an hair: whence he may manifeſtly conclude, that the acute Figure
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1922 <lb></lb>which ſeemed moſt apt to part and penetrate the water, doth not
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1923 <lb></lb>part or penetrate it more than the large and ſpacious.</s></p><p type="margin">
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1924
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1925 <s><margin.target id="marg1465"></margin.target>The Experi­
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1926 <lb></lb>ment of a Cone,
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1927 <lb></lb>demitted with
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1928 <lb></lb>its Baſe, and af­
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1929 <lb></lb>ter with its
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1930 <lb></lb>Point down­
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1931 <lb></lb>wards.</s></p><p type="main">
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1932
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1933 <s>And he that would have a more eaſie Experiment, let him take
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1934 <lb></lb>two Cylinders of the ſame Matter, one long and ſmall, and the o­
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1935 <lb></lb>ther ſhert, but very broad, and let him put them in the water, not
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1936 <lb></lb>diſtended, but erect and endways: he ſhall ſee, if he diligently
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1937 <lb></lb>meaſure the parts of the one and of the other, that in each of them
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1938 <lb></lb>the part ſubmerged, retains exactly the ſame proportion to that
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1939 <lb></lb>out of the water, and that no greater part is ſubmerged of that
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1940 <lb></lb>long and ſmall one, than of the other more ſpacious and broad:
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1941 <lb></lb>howbeit, this reſts upon a very large, and that upon a very little
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1942 <lb></lb>Superficies of water: therefore the diverſity of Figure, occaſioneth
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1943 <lb></lb>neither facility, nor difficulty, in parting and penetrating the Con­
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1944 <lb></lb>tinuity of the water; and, conſequently, cannot be the Cauſe of the
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1945 <lb></lb>Natation or Submerſion. </s><s>He may likewiſe diſcover the non­
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1946 <lb></lb>operating of variety of Figures, in ariſing from the Bottom of the
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1947 <lb></lb>water, towards the Surface, by taking Wax, and tempering it with
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1948 <lb></lb>a competent quantity of the filings of Lead, ſo that it may become
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1949 <lb></lb>a conſiderable matter graver than the water: then let him make
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1950
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1951
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1952 <pb pagenum="432"></pb>it into a Ball, and thruſt it unto the Bottom of the water; and
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1953 <lb></lb>faſten to it as much Cork, or other light matter, as juſt ſerveth to
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1954 <lb></lb>raiſe it, and draw it towards the Surface: for afterwards changing
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1955 <lb></lb>the ſame Wax into a thin Cake, or into any other Figure, that
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1956 <lb></lb>ſame Cork ſhall raiſe it in the ſame manner to a hair.</s></p><p type="main">
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1957
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1958 <s>This ſilenceth not my Antagoniſts, but they ſay, that all the
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1959 <lb></lb>diſcourſe hitherto made by me little importeth to them, and that it
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1960 <lb></lb>ſerves their turn, that they have demonſtrated in one only parti­
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1961 <lb></lb>cular, and in what matter, and under what Figure pleaſeth them,
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1962 <lb></lb>namely, in a Board and in a Ball of Ebony, that this put in the
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1963 <lb></lb>water, deſcends to the Bottom, and that ſtays atop to ſwim:
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1964 <lb></lb>and the Matter being the ſame, and the two Bodies differing in no­
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1965 <lb></lb>thing but in Figure, they affirm, that they have with all perſpicuity
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1966 <lb></lb>demonſtrated and ſenſibly manifeſted what they undertook; and
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1967 <lb></lb>laſtly, that they have obtained their intent. </s><s>Nevertheleſs, I believe,
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1968 <lb></lb>and thinke, I can demonſtrate, that that ſame Experiment proveth
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1969 <lb></lb>nothing againſt my Concluſion.</s></p><p type="main">
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1970
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1971 <s>And firſt, it is falſe, that the Ball deſcends, and the Board not:
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1972 <lb></lb><arrow.to.target n="marg1466"></arrow.to.target>
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1973 <lb></lb>for the Board ſhall alſo deſcend, if you do to both the Figures, as
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1974 <lb></lb>the words of our Queſtion requireth; that is, if you put them both
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1975 <lb></lb>into the water.
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1976 <lb></lb><arrow.to.target n="marg1467"></arrow.to.target></s></p><p type="margin">
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1977
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1978 <s><margin.target id="marg1466"></margin.target>In Experi­
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1979 <lb></lb>ments of Nata­
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1980 <lb></lb>tion, the Solid
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1981 <lb></lb>is to be put into,
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1982 <lb></lb>not upon the
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1983 <lb></lb>water.</s></p><p type="margin">
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1984
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1985 <s><margin.target id="marg1467"></margin.target>The Queſtion
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1986 <lb></lb>of Natation ſta­
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1987 <lb></lb>ted.</s></p><p type="main">
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1988
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1989 <s><emph type="italics"></emph>The words were theſe. </s><s>That the Antagoniſts having an opinion, that
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1990 <lb></lb>the Figure would alter the Solid Bodies, in relation to the deſcending
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1991 <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>
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1992 <lb></lb>v. </s><s>gr. <emph type="italics"></emph>in the ſame water, in ſuch ſort, that, for Example, a Solid that
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1993 <lb></lb>being of a Sphericall Figure, ſhall deſcend to the Bottom, being reduced
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1994 <lb></lb>into ſome other Figure, ſhall not deſcend: I holding the contrary, do
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1995 <lb></lb>affirm, that a Corporeall Solid Body, which reduced into a Sphericall Fi­
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1996 <lb></lb>gure, or any other, ſhall go to the Bottom, ſhall do the like under whatſoever
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1997 <lb></lb>other Figure, &amp;c.<emph.end type="italics"></emph.end></s></p><p type="main">
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1998
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1999 <s>But to be in the water, implies to be placed in the water, and by </s></p><p type="main">
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2000
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2001 <s><arrow.to.target n="marg1468"></arrow.to.target>
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2002 <lb></lb><emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> own Definition of place, to be placed, importeth to be in­
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2003 <lb></lb>vironed by the Superficies of the Ambient Body, therefore, then
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2004 <lb></lb>ſhall the two Figures be in the water, when the Superficies of the
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2005 <lb></lb>water, ſhall imbrace and inviron them: but when the Adverſaries
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2006 <lb></lb>ſhew the Board of Ebony not deſcending to the Bottom, they put it
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2007 <lb></lb>not into the water, but upon the water, where being by a certain im­
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2008 <lb></lb>pediment (as by and by we will ſhew) retained, it is invironed, part
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2009 <lb></lb>by water, and part by air, which thing is contrary to our agreement,
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2010 <lb></lb>that was, that the Bodies ſhould be in the water, and not part in
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2011 <lb></lb>water, and part in air.</s></p>
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2012
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2013
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2014 <pb pagenum="433"></pb><p type="margin">
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2015
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2016 <s><margin.target id="marg1468"></margin.target>Place defined
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2017 <lb></lb>according to
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2018 <lb></lb><emph type="italics"></emph>Ariſtotle.<emph.end type="italics"></emph.end></s></p><p type="main">
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2019
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2020 <s><emph type="italics"></emph>The which is again made manifest, by the queſtions being put as well
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2021 <lb></lb>about the things which go to the Bottom, as thoſe which ariſe from the
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2022 <lb></lb>Bottom to ſwimme, and who ſees not that things placed in the Bottom,
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2023 <lb></lb>muſt have water about them.<emph.end type="italics"></emph.end></s></p><p type="main">
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2024
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2025 <s>It is now to be noted, that the Board of Ebany and the Ball, put
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2026 <lb></lb><arrow.to.target n="marg1469"></arrow.to.target>
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2027 <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
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2028 <lb></lb>more ſlowly; and ſlower and ſlower, according as it ſhall be more
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2029 <lb></lb>broad and thin, and of this Tardity the breadth of the Figure is the
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2030 <lb></lb>true Cauſe: But theſe broad Boards that ſlowly deſcend, are the
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2031 <lb></lb>ſame, that being put lightly upon the water, do ſwimm: Therefore,
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2032 <lb></lb>if that were true which the Adverſaries affirm, the ſame numerical
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2033 <lb></lb>Figure, would in the ſame numericall water, cauſe one while Reſt, and
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2034 <lb></lb>another while Tardity of Motion, which is impoſſible: for every per­
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2035 <lb></lb><arrow.to.target n="marg1470"></arrow.to.target>
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2036 <lb></lb>ticular Figure which deſcends to the Bottom, hath of neceſſity its own
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2037 <lb></lb>determinate Tardity and ſlowneſs, proper and naturall unto it, accor­
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2038 <lb></lb>ding to which it moveth, ſo that every other Tardity, greater or leſſer
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2039 <lb></lb>is improper to its nature: if, therefore, a Board, as ſuppoſe of a foot
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2040 <lb></lb>ſquare, deſcendeth naturally with ſix degrees of Tardity, it is impoſſi­
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2041 <lb></lb>ble, that it ſhould deſcend with ten or twenty, unleſs ſome new impe­
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2042 <lb></lb>diment do arreſt it. </s><s>Much leſs can it, by reaſon of the ſame Figure
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2043 <lb></lb>reſt, and wholly ceaſe to move; but it is neceſſary, that when ever it
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2044 <lb></lb>reſteth, there do ſome greater impediment intervene than the breadth
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2045 <lb></lb>of the Figure. </s><s>Therefore, it muſt be ſomewhat elſe, and not the Fi­
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2046 <lb></lb>gure, that ſtayeth the Board of Ebany above water, of which Eigure
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2047 <lb></lb>the only Effect is the retardment of the Motion, according to which
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2048 <lb></lb>it deſcendeth more ſlowly than the Ball. </s><s>Let it be confeſſed, there­
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2049 <lb></lb>fore, rationally diſcourſing, that the true and ſole Cauſe of the Ebanys
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2050 <lb></lb>going to the Bottom, is the exceſs of its Gravity above the Gravity of
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2051 <lb></lb>the water: and the Cauſe of the greater or leſs Tardity, the breadth
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2052 <lb></lb>of this Figure, or the contractedneſs of that: but of its Reſt, it can
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2053 <lb></lb>by no means be allowed, that the quallity of the Figure, is the Cauſe
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2054 <lb></lb>thereof: aſwell, becauſe, making the Tardity greater, according as
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2055 <lb></lb>the Figure more dilateth, there cannot be ſo immenſe a Dilatation, to
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2056 <lb></lb>which there may not be found a correſpondent immence Tardity.
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2057 <lb></lb></s><s>without reduſing it to Nullity of Motion; as, becauſe the Figures
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2058 <lb></lb>produced by the Antagoniſts for effecters of Reſt, are the ſelf ſame
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2059 <lb></lb>that do alſo go to the Bottom.
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2060 <lb></lb><arrow.to.target n="marg1471"></arrow.to.target></s></p><p type="margin">
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2061
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2062 <s><margin.target id="marg1469"></margin.target>The conſutati­
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2063 <lb></lb>on of the Expe­
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2064 <lb></lb>riment in the
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2065 <lb></lb>Ebany.</s></p><p type="margin">
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2066
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2067 <s><margin.target id="marg1470"></margin.target>Every perticular
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2068 <lb></lb>Figure hath its
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2069 <lb></lb>own peculiat
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2070 <lb></lb>Tardity.</s></p><p type="margin">
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2071
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2072 <s><margin.target id="marg1471"></margin.target>* The Figure &amp;
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2073 <lb></lb>Reſiſtance of
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2074 <lb></lb>the Medium a­
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2075 <lb></lb>gainſt Diviſion,
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2076 <lb></lb>have nothing to
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2077 <lb></lb>do with the Ef­
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2078 <lb></lb>fect of Natation
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2079 <lb></lb>or Submerſion,
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2080 <lb></lb>by an Experi­
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2081 <lb></lb>ment in Wall­
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2082 <lb></lb>nut tree,</s></p><p type="main">
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2083
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2084 <s>I will not omit another reaſon, founded alſo upon Experience, and
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2085 <lb></lb>if I deceive not my ſelf, manifeſtly concluding, how that the Intro­
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2086 <lb></lb>ducton of the breadth or amplitude of Figure, and the Reſiſtance of
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2087 <lb></lb>the water againſt penetration, have nothing to do in the Effect of de­
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2088 <lb></lb>ſcending, or aſcending, or reſting in the water. ^{*}Take a piece of wood
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2089 <lb></lb>or other Matter, of which a Ball aſcends from the Bottom of the water
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2090
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2091
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2092 <pb pagenum="434"></pb>to the Surface, more ſlowly than a Ball of Ebony of the ſame bigneſſe,
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2093 <lb></lb>ſo that it is manifeſt, that the Ball of Ebony more readily divideth the
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2094 <lb></lb>water in deſcending, than the other in aſcending; as for Example, let
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2095 <lb></lb>the Wood be Walnut-tree. </s><s>Then take a Board of Walnut-tree, like
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2096 <lb></lb>and equall to that of Ebony of the Antagoniſts, which ſwims; and if
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2097 <lb></lb>it be true, that this floats above water, by reaſon of the Figure, unable
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2098 <lb></lb>through its breadth, to pierce the Craſſitude of the ſame, the other of
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2099 <lb></lb>Wallnut-tree, without all queſtion, being thruſt unto the Bottom, will
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2100 <lb></lb>ſtay there, as leſs apt, through the ſame impediment of Figure, to di­
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2101 <lb></lb>vide the ſaid Reſiſtance of the water. </s><s>But if we ſhall find, and by
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2102 <lb></lb>experience ſee, that not only the thin Board, but every other Figure
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2103 <lb></lb>of the ſame Wallnut-tree will return to float, as undoubtedly we ſhall,
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2104 <lb></lb>then I muſt deſier my oppoſers to forbear to attribute the floating of
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2105 <lb></lb>the Ebony, unto the Figure of the Board, in regard that the Reſiſtance
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2106 <lb></lb>of the water is the ſame, as well to the aſcent, as to the deſcent, and the
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2107 <lb></lb>force of the Wallnut-trees aſcenſion, is leſſe than the Ebonys force in
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2108 <lb></lb>going to the Bottom.</s></p><p type="main">
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2109
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2110
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2111 <s>Nay, I will ſay more, that if we ſhall conſider Gold in compariſon
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2112 <lb></lb><arrow.to.target n="marg1472"></arrow.to.target>
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2113 <lb></lb>of water, we ſhall find, that it exceeds it in Gravity almoſt twenty times,
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2114 <lb></lb>ſo that the Force and Impetus, wherewith a Ball of Gold goes to the
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2115 <lb></lb>Bottom, is very great. </s><s>On the contrary, there want not matters, as
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2116 <lb></lb>Virgins Wax, and ſome Woods, which are not above a fiftieth part leſs
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2117 <lb></lb>grave than water, whereupon their Aſcenſion therein is very ſlow, and
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2118 <lb></lb>a thouſand times weaker than the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> of the Golds deſcent: yet
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2119 <lb></lb>notwithſtanding, a plate of Gold ſwims without deſcending to the
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2120 <lb></lb>Bottom, and, on the contrary, we cannot make a Cake of Wax, or thin
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2121 <lb></lb>Board of Wood, which put in the Bottom of the Water, ſhall reſt there
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2122 <lb></lb>without aſcending. </s><s>Now if the Figure can obſtruct the Penetration,
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2123 <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
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2124 <lb></lb>can it chooſe but ſuffice to reſiſt the ſame Penetration of the other mat­
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2125 <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>
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2126 <lb></lb>that the Gold hath in deſcending? </s><s>Its therefore, neceſſary, that that
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2127 <lb></lb>which ſuſpends the thin Plate of Gold, or Board of Ebony, upon the
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2128 <lb></lb>water, be ſome thing that is wanting to the other Cakes and Boards of
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2129 <lb></lb>Matters leſs grave than the water; ſince that being put to the Bottom,
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2130 <lb></lb>and left at liberty, they riſe up to the Surface, without any obſtruction:
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2131 <lb></lb>But they want not for flatneſs and breadth of Figure: Therefore, the
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2132 <lb></lb>ſpaciouſneſſe of the Figure, is not that which makes the Gold and Ebony
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2133 <lb></lb>to ſwim.</s></p><p type="margin">
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2134
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2135 <s><margin.target id="marg1472"></margin.target>An Experi­
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2136 <lb></lb>ment in Gold, to
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2137 <lb></lb>prove the non­
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2138 <lb></lb>operating of Fi­
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2139 <lb></lb>gure in Natation
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2140 <lb></lb>and Submerſion.</s></p><p type="main">
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2141
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2142 <s>And, becauſe, that the exceſs of their Gravity above the Gravity of
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2143 <lb></lb>the water, is queſtionleſs the Cauſe of the ſinking of the flat piece of
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2144 <lb></lb>Ebony, and the thin Plate of Gold, when they go to the Bottom, there­
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2145 <lb></lb>fore, of neceſſity, when they float, the Cauſe of their ſtaying above
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2146 <lb></lb>water, proceeds from Levity, which in that caſe, by ſome Accident,
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2147
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2148
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2149 <pb pagenum="435"></pb>peradventure not hitherto obſerved, cometh to meet with the ſaid
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2150 <lb></lb>Board, rendering it no longer as it was before, whilſt it did fink more
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2151 <lb></lb>ponderous than the water, but leſs.</s></p><p type="main">
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2152
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2153 <s>Now, let us return to take the thin Plate of Gold, or of Silver, or the
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2154 <lb></lb>thin Board of Ebony, and let us lay it lightly upon the water, ſo that it
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2155 <lb></lb>ſtay there without ſinking, and diligently obſerve its effect. </s><s>And
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2156 <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,
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2157 <lb></lb>that it ſtayeth above water, through its unability to pierce and pene­
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2158 <lb></lb>trate the Reſiſtance of the waters Craſſitude: for it will manifeſtly
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2159 <lb></lb>appear, not only that the ſaid Plates have penetrated the water, but
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2160 <lb></lb>alſo that they are a conſiderable matter lower than the Surface of the
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2161 <lb></lb>ſame, the which continueth eminent, and maketh as it were a Rampert
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2162 <lb></lb>on all ſides, round about the ſaid Plates, the profundity of which they
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2163 <lb></lb>ſtay ſwimming: and, according as the ſaid Plates ſhall be more grave
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2164 <lb></lb>than the water, two, four, ten or twenty times, it is neceſſary, that
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2165 <lb></lb>their Superficies do ſtay below the univerſall Surface of the water, ſo
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2166 <lb></lb>much more, than the thickneſs of thoſe Plates, as we ſhal more diſtinctly
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2167 <lb></lb>ſhew anon. </s><s>In the mean ſpace, for the more eaſie underſtanding of what
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2168 <lb></lb>I ſay, obſerve with me a little the preſent
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2169 <lb></lb><figure id="fig269"></figure>
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2170 <lb></lb>Scheme: in which let us ſuppoſe the Surface
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2171 <lb></lb>of the water to be diſtended, according to the
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2172 <lb></lb>Lines F L D B, upon which if one ſhall put a
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2173 <lb></lb>board of matter ſpecifically more grave than
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2174 <lb></lb>water, but ſo lightly that it ſubmetge not, it
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2175 <lb></lb>ſhall not reſt any thing above, but ſhall enter with its whole thickneſs
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2176 <lb></lb>into the water: and, moreover, ſhall ſink alſo, as we ſee by the Board
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2177 <lb></lb>A I, O I, whoſe breadth is wholly ſunk into the water, the little Ram­
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2178 <lb></lb>perts of water L A and D O incompaſſing it, whoſe Superficies is no­
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2179 <lb></lb>tably higher than the Superficies of the Board. </s><s>See now whether it be
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2180 <lb></lb>true, that the ſaid Board goes not to the Bottom, as being of Figure
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2181 <lb></lb>unapt to penetrate the Craſſitude of the water.</s></p><p type="main">
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2182
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2183 <s>But, if it hath already penetrated, and overcome the Continuity of
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2184 <lb></lb><arrow.to.target n="marg1473"></arrow.to.target>
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2185 <lb></lb>the water, &amp; is of its own nature more grave than the ſaid water, why
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2186 <lb></lb>doth it not proceed in its ſinking, but ſtop and ſuſpend its ſelf within
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2187 <lb></lb>that little dimple or cavitie, which with its ponderoſity it hath made in
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2188 <lb></lb>the water? </s><s>I anſwer; becauſe that in ſubmerging it ſelf, ſo far as till its
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2189 <lb></lb>Superficies come to the Levell with that of the water, it loſeth a part
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2190 <lb></lb>of its Gravity, and loſeth the reſt of it as it ſubmergeth &amp; deſcends be­
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2191 <lb></lb>neath the Surface of the water, which maketh Ramperts and Banks
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2192 <lb></lb>round about it, and it ſuſtaines this loſs by means of its drawing after it,
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2193 <lb></lb>and carrying along with it, the Air that is above it, and by Contact ad­
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2194 <lb></lb>herent to it, which Air ſucceeds to fill the Cavity that is invironed by
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2195 <lb></lb>the Ramperts of water: ſo that that which in this caſe deſcends and is
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2196 <lb></lb>placed in the water, is not only the Board of Ebony or Plate of Iron,
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2197
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2198
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2199 <pb pagenum="436"></pb>but a compoſition of Ebony and Air, from which reſulteth a Solid
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2200 <lb></lb>no longer ſuperiour in Gravity to the water, as was the ſimple Ebony,
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2201 <lb></lb>or the ſimple Gold. </s><s>And, if we exactly conſider, what, and how
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2202 <lb></lb>great the Solid is, that in this Experiment enters into the water, and
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2203 <lb></lb>contraſts with the Gravity of the ſame, it will be found to be all that
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2204 <lb></lb>which we find to be beneath the Surface of the water, the which is
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2205 <lb></lb>an aggregate and Compound of a Board of Ebony, and of almoſt
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2206 <lb></lb>the like quantity of Air, or a Maſs compounded of a Plate of Lead,
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2207 <lb></lb>and ten or twelve times as much Air. </s><s>But, Genrlemen, you that
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2208 <lb></lb>are my Antagoniſts in our Queſtion, we require the Identity of
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2209 <lb></lb>Matter, and the alteration only of the Figure; therefore, you muſt
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2210 <lb></lb>remove that Air, which being conjoyned with the Board, makes it
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2211 <lb></lb>become another Body leſs grave than the Water, and put only the
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2212 <lb></lb>Ebony into the Water, and you ſhall certainly ſee the Board deſcend
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2213 <lb></lb>to the Bottom; and, if that do not happen, you have got the day.
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2214 <lb></lb><arrow.to.target n="marg1474"></arrow.to.target>
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2215 <lb></lb>And to ſeperate the Air from the Ebony, there needs no more but
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2216 <lb></lb>only to bath the Superficies of the ſaid Board with the ſame Water:
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2217 <lb></lb>for the Water being thus interpoſed between the Board and the Air,
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2218 <lb></lb>the other circumfuſed Water ſhall run together without any impedi­
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2219 <lb></lb>ment, and ſhall receive into it the ſole and bare Ebony, as it was to do.</s></p><p type="margin">
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2220
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2221 <s><margin.target id="marg1473"></margin.target>Why ſolids
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2222 <lb></lb>having penitra­
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2223 <lb></lb>ted the Water,
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2224 <lb></lb>do not proceed
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2225 <lb></lb>to a totail Sub­
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2226 <lb></lb>merſion.</s></p><p type="margin">
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2227
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2228 <s><margin.target id="marg1474"></margin.target>How to ſepe­
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2229 <lb></lb>rate the Air from
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2230 <lb></lb>Solids in demit­
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2231 <lb></lb>ting them into
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2232 <lb></lb>the water.</s></p><p type="main">
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2233
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2234 <s>But, me thinks I hear ſome of the Adverſaries cunningly oppoſing
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2235 <lb></lb>this, and telling me, that they will not yield, by any means, that
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2236 <lb></lb>their Board be wetted, becauſe the weight added thereto by the
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2237 <lb></lb>Water, by making it heavier than it was before, draws it to the
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2238 <lb></lb>Bottom, and that the addition of new weight is contrary to our a­
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2239 <lb></lb>greement, which was, that the Matter be the ſame.</s></p><p type="main">
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2240
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2241 <s>To this, I anſwer, firſt; that treating of the operation of Figure
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2242 <lb></lb>in Bodies put into the Water, none can ſuppoſe them to be put into
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2243 <lb></lb>the Water without being wet; nor do I deſire more to be done to
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2244 <lb></lb>the Board, then I will give you leave to do to the Ball. </s><s>Moreover,
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2245 <lb></lb>it is untrue, that the Board ſinks by vertue of the new Weight added
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2246 <lb></lb>to it by the Water, in the ſingle and ſlight bathing of it: for I will
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2247 <lb></lb>put ten or twenty drops of Water upon the ſame Board, whilſt it is
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2248 <lb></lb>ſuſtained upon the water, which drops, becauſe not conjoyned with
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2249 <lb></lb>the other Water circumfuſed, ſhall not ſo encreaſe the weight of it, as
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2250 <lb></lb>to make it ſink: but if the Board being taken out, and all the water
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2251 <lb></lb>wiped off that was added thereto, I ſhould bath all its Superficies
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2252 <lb></lb>with one only very ſmall drop, and put it again upon the water, with­
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2253 <lb></lb>out doubt it ſhall ſink, the other Water running to cover it, not be­
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2254 <lb></lb>ing retained by the ſuperiour Air; which Air by the interpoſition of
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2255 <lb></lb>the thin vail of water, that takes away its Contiguity unto the Ebony,
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2256 <lb></lb>ſhall without Renitence be ſeperated, nor doth it in the leaſt oppoſe
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2257 <lb></lb>the ſucceſſion of the other Water: but rather, to ſpeak better, it
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2258 <lb></lb>ſhall deſcend freely; becauſe it ſhall be all invironed and covered
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2259
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2260
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2261 <pb pagenum="437"></pb>with water, as ſoon as its ſuperiour Superficies, before vailed with
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2262 <lb></lb>water, doth arrive to the Levell of the univerſall Surface of the ſaid
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2263 <lb></lb>water. </s><s>To ſay, in the next place, that water can encreaſe the weight
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2264 <lb></lb><arrow.to.target n="marg1475"></arrow.to.target>
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2265 <lb></lb>of things that are demitted into it, is moſt falſe, for water hath no
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2266 <lb></lb>Gravity in water, ſince it deſcends not: yea, if we would well conſi­
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2267 <lb></lb>der what any immenſe Maſs of water doth put upon a grave Body;
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2268 <lb></lb><arrow.to.target n="marg1476"></arrow.to.target>
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2269 <lb></lb>that is placed in it, we ſhall find experimentally, that it, on the con­
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2270 <lb></lb>trary, will rather in a great part deminiſh the weight of it, and that
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2271 <lb></lb>we may be able to lift an huge Stone from the Bottom of the water,
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2272 <lb></lb>which the water being removed, we are not able to ſtir. </s><s>Nor let
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2273 <lb></lb>them tell me by way of reply, that although the ſuperpoſed water
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2274 <lb></lb>augment not the Gravity of things that are in it, yet it increaſeth the
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2275 <lb></lb>ponderoſity of thoſe that ſwim, and are part in the water and part
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2276 <lb></lb><arrow.to.target n="marg1477"></arrow.to.target>
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2277 <lb></lb>in the Air, as is ſeen, for Example, in a Braſs Ketle, which whilſt it
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2278 <lb></lb>is empty of water, and repleniſhed only with Air ſhall ſwim, but
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2279 <lb></lb>pouring of Water therein, it ſhall become ſo grave, that it ſhall ſink
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2280 <lb></lb>to the Bottom, and that by reaſon of the new weight added thereto.
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2281 <lb></lb></s><s>To this I will return anſwer, as above, that the Gravity of the
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2282 <lb></lb>Water, contained in the Veſſel is not that which ſinks it to the Bot­
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2283 <lb></lb>tom, but the proper Gravity of the Braſs, ſuperiour to the Specificall
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2284 <lb></lb><arrow.to.target n="marg1478"></arrow.to.target>
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2285 <lb></lb>Gravity of the Water: for if the Veſſel were leſs grave than
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2286 <lb></lb>water, the Ocean would not ſuffice to ſubmerge it. </s><s>And, give me
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2287 <lb></lb>leave to repeat it again, as the fundamentall and principall point in
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2288 <lb></lb>this Caſe, that the Air contained in this Veſſel before the infuſion of
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2289 <lb></lb>the Water, was that which kept it a-float, ſince that there was made
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2290 <lb></lb><arrow.to.target n="marg1479"></arrow.to.target>
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2291 <lb></lb>of it, and of the Braſs, a Compoſition leſs grave than an equall quanti­
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2292 <lb></lb>ty of Water: and the place that the Veſſel occupyeth in the
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2293 <lb></lb>Water whilſt it floats, is not equall to the Braſs alone, but to the
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2294 <lb></lb>Braſs and to the Air together, which filleth that part of the Veſſel
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2295 <lb></lb>that is below the Levell of the water: Moreover, when the Water
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2296 <lb></lb>is infuſed, the Air is removed, and there is a compoſition made of
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2297 <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
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2298 <lb></lb>not by vertue of the water infuſed, as having greater Specifick
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2299 <lb></lb>Gravity than the other water, but through the proper Gravity of
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2300 <lb></lb>the Braſs, and through the alienation of the Air. </s><s>Now, as he that
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2301 <lb></lb>ſhould ſay that Braſs, that by its nature goes to the Bottom, being
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2302 <lb></lb><arrow.to.target n="marg1480"></arrow.to.target>
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2303 <lb></lb>formed into the Figure of a Ketle, acquireth from that Figure a
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2304 <lb></lb>vertue of lying in the Water without ſinking, would ſay that which
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2305 <lb></lb>is falſe; becauſe that Braſs faſhioned into any whatever Figure,
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2306 <lb></lb>goeth always to the Bottom, provided, that that which is put into the
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2307 <lb></lb>water be ſimple Braſs; and it is not the Figure of the Veſſel that
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2308 <lb></lb>makes the Braſs to float, but it is becauſe that that is not purely
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2309 <lb></lb>Braſs which is put into the water, but an aggregate of Braſs and of
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2310 <lb></lb>Air: ſo is it neither more nor leſs falſe, that a thin Plate of Braſs
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2311
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2312
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2313 <pb pagenum="438"></pb>or of Ebony, ſwims by vertue of its dilated &amp; broad Figure: for the
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2314 <lb></lb>truth is, that it bares up without ſubmerging, becauſe that that which
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2315 <lb></lb>is put in the water, is not pure Braſs or ſimple Ebony, but an ag­
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2316 <lb></lb>gregate of Braſs and Air, or of Ebony and Air. </s><s>And, this is not
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2317 <lb></lb>contrary unto my Concluſion, the which, (having many a time ſeen
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2318 <lb></lb>Veſſels of Mettall, and thin pieces of diverſe grave Matters float, by
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2319 <lb></lb>vertue of the Air conjoyned with them) did affirm, That Figure
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2320 <lb></lb>was not the Cauſe of the Natation or Submerſion of ſuch Solids as
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2321 <lb></lb>were placed in the water. </s><s>Nay more, I cannot omit, but muſt tell
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2322 <lb></lb>my Antagoniſts, that this new conceit of denying that the Superfi­
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2323 <lb></lb>cies of the Board ſhould be bathed, may beget in a third perſon an
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2324 <lb></lb>opinion of a poverty of Arguments of defence on their part, ſince
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2325 <lb></lb>that ſuch bathing was never inſiſted upon by them in the beginning
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2326 <lb></lb>of our Diſpute, and was not queſtioned in the leaſt, being that the
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2327 <lb></lb>Originall of the diſcourſe aroſe upon the ſwiming of Flakes of Ice,
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2328 <lb></lb>wherein it would be ſimplicity to require that their Superficies might
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2329 <lb></lb>bedry: beſides, that whether theſe pieces of Ice be wet or dry they
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2330 <lb></lb>alwayes ſwim, and as the Adverſaries ſay, by reaſon of the Figure. </s></p><p type="margin">
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2331
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2332 <s><margin.target id="marg1475"></margin.target>Water hath
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2333 <lb></lb>no Gravity in
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2334 <lb></lb>Water.</s></p><p type="margin">
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2335
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2336 <s><margin.target id="marg1476"></margin.target>Water de­
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2337 <lb></lb>miniſheth the
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2338 <lb></lb>Gravity of So­
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2339 <lb></lb>lids immerged
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2340 <lb></lb>therein.</s></p><p type="margin">
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2341
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2342 <s><margin.target id="marg1477"></margin.target>The Experi­
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2343 <lb></lb>ment of a Braſs
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2344 <lb></lb>Ketle ſwiming
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2345 <lb></lb>when empty, &amp;
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2346 <lb></lb>ſinking when
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2347 <lb></lb>full, alledged to
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2348 <lb></lb>prove that water
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2349 <lb></lb>gravitates in
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2350 <lb></lb>water, anſwered.</s></p><p type="margin">
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2351
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2352 <s><margin.target id="marg1478"></margin.target>An Ocean ſuf­
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2353 <lb></lb>ficeth not to
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2354 <lb></lb>ſink a Veſſel ſpe­
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2355 <lb></lb>cifically leſs
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2356 <lb></lb>grave than wa­
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2357 <lb></lb>ter.</s></p><p type="margin">
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2358
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2359 <s><margin.target id="marg1479"></margin.target>Air, the Cauſe
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2360 <lb></lb>of the Natation
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2361 <lb></lb>of empty Veſſels
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2362 <lb></lb>of Matters gra­
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2363 <lb></lb>ver <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than
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2364 <lb></lb>the water.</s></p><p type="margin">
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2365
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2366 <s><margin.target id="marg1480"></margin.target>Neither Figure,
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2367 <lb></lb>nor the breadth
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2368 <lb></lb>of Figure, is the
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2369 <lb></lb>Cauſe of Nata­
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2370 <lb></lb>tion.</s></p><p type="main">
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2371
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2372 <s>Some peradventure, by way of defence, may ſay, that wetting the
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2373 <lb></lb>Board of Ebony, and that in the ſuperiour Superficies, it would,
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2374 <lb></lb>though of it ſelf unable to pierce and penetrate the water, be born
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2375 <lb></lb>downwards, if not by the weight of the additionall water, at leaſt
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2376 <lb></lb>by that deſire and propenſion that the ſuperiour parts of the water
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2377 <lb></lb>have to re-unite and rejoyn themſelves: by the Motion of which
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2378 <lb></lb>parts, the ſaid Board cometh in a certain manner, to be depreſſed
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2379 <lb></lb>downwards.
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2380 <lb></lb><arrow.to.target n="marg1481"></arrow.to.target></s></p><p type="margin">
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2381
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2382 <s><margin.target id="marg1481"></margin.target>The Bathed
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2383 <lb></lb>Solid deſcends
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2384 <lb></lb>not out of any
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2385 <lb></lb>affectation of u­
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2386 <lb></lb>nion in the upper
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2387 <lb></lb>parts of the wa­
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2388 <lb></lb>ter.</s></p><p type="main">
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2389
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2390 <s>This weak Refuge will be removed, if we do but conſider, that
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2391 <lb></lb>the repugnancy of the inferiour parts of the water, is as great against
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2392 <lb></lb>Diſ-union, as the Inclination of its ſuperiour parts is to union: nor can
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2393 <lb></lb>the uper unite themſelves without depreſſing the board, nor can it
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2394 <lb></lb>deſcend without diſuniting the parts of the nether Water: ſo that
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2395 <lb></lb>it doth follow, by neceſſary conſequence, that for thoſe reſpects, it ſhall
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2396 <lb></lb>not deſcend. </s><s>Moreover, the ſame that may be ſaid of the upper
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2397 <lb></lb>parts of the water, may with equall reaſon be ſaid of the nethe,
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2398 <lb></lb>namely, that deſiring to unite, they ſhall force the ſaid Board
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2399 <lb></lb>upwards.</s></p><p type="main">
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2400
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2401 <s>Happily, ſome of theſe Gentlemen that diſſent from me, will won­
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2402 <lb></lb>der, that I affirm, that the contiguous ſuperiour Air is able to ſuſtain
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2403 <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
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2404 <lb></lb><arrow.to.target n="marg1482"></arrow.to.target>
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2405 <lb></lb>would in a certain ſence allow the Air, a kind of Magnetick vertue
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2406 <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
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2407 <lb></lb>tisſie all I may, to all doubts, I have been conſidering how by ſome
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2408 <lb></lb>other ſenſible Experiment I might demonſtrate, how truly that little
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2409 <lb></lb>contiguous and ſuperiour Air ſuſtaines thoſe Solids, which being by
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2410
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2411
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2412 <pb pagenum="439"></pb>nature apt to deſcend to the Bottom, being placed lightly on the water
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2413 <lb></lb>ſubmerge not, unleſs they be firſt thorowly bathed; and have found,
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2414 <lb></lb>that one of theſe Bodies having deſcended to the Bottom, by conveigh­
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2415 <lb></lb>ing to it (without touching it in the leaſt) a little Air, which conjoyneth
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2416 <lb></lb>with the top of the ſame; it becometh ſufficient, not only, as before to
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2417 <lb></lb>ſuſtain it, but alſo to raiſe it, and to carry it back to the top, where it
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2418 <lb></lb>ſtays and abideth in the ſame manner, till ſuch time, as the aſſiſtance
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2419 <lb></lb>of the conjoyned Air is taken away. </s><s>And to this effect, I have taken a
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2420 <lb></lb>Ball of Wax, and made it with a little Lead, ſo grave, that it leaſurely
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2421 <lb></lb>deſcends to the Bottom, making with all its Superficies very ſmooth and
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2422 <lb></lb>pollite: and this being put gently into the water, almoſt wholly ſub­
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2423 <lb></lb><arrow.to.target n="marg1483"></arrow.to.target>
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2424 <lb></lb>mergeth, there remaining viſſible only a little of the very top, the which
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2425 <lb></lb>solong as it is conjoyned with the Air, ſhall retain the Ball a-top, but
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2426 <lb></lb>the Contiguity of the Air taken away by wetting it, it ſhall deſcend to
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2427 <lb></lb>the Bottom and there remain. </s><s>Now to make it by vertue of the Air, that
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2428 <lb></lb>before ſuſtained it to return again to the top, and ſtay there, thruſt into
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2429 <lb></lb>the water a Glaſs reverſed with the mouth downwards, the which ſhall
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2430 <lb></lb>carry with it the Air it contains, and move this towards the Ball, abaſing
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2431 <lb></lb>it till ſuch time that you ſee, by the tranſparency of the Glaſs, that the
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2432 <lb></lb><arrow.to.target n="marg1484"></arrow.to.target>
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2433 <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
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2434 <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
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2435 <lb></lb><arrow.to.target n="marg1485"></arrow.to.target>
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2436 <lb></lb>stay on the top of the water, if you carefully part the Glaſs and the water
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2437 <lb></lb>without overmuch commoving and diſturbing it. </s><s>There is, therefore, a
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2438 <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
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2439 <lb></lb>ed, ſo, that they ſeperate not without a kind of violence. </s><s>The ſame
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2440 <lb></lb><arrow.to.target n="marg1486"></arrow.to.target>
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2441 <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
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2442 <lb></lb>in it, ſo that it be thorowly bathed, in the drawing of it afterwards gent­
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2443 <lb></lb>ly out again, we ſhall ſee the water follow it, and riſe notably above its
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2444 <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
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2445 <lb></lb><arrow.to.target n="marg1487"></arrow.to.target>
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2446 <lb></lb>and alike in Superficies, ſo, that they make an exact Contact without
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2447 <lb></lb>the interpoſition of the leaſt Air, that may part them in the ſeperation
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2448 <lb></lb>and yield untill that the ambient <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end> ſucceeds to repleniſh the place,
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2449 <lb></lb>do hold very firmly conjoyned, and are not to be ſeperated without great
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2450 <lb></lb>force but, becauſe, the Air, Water, and other Liquids, very expedi­
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2451 <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
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2452 <lb></lb>Superficies do exquiſitely adopt themſelves to that of the Solids, without
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2453 <lb></lb>any thing remaining between them, therefore, the effect of this Con­
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2454 <lb></lb>junction and Adherence is more manifeſtly and frequently obſerved in
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2455 <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
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2456 <lb></lb>ly conjoyn with exactneſs of Contact. </s><s>This is therefore that Magne­
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2457 <lb></lb><arrow.to.target n="marg1488"></arrow.to.target>
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2458 <lb></lb>tick vertue, which with firm Connection conjoyneth all Bodies, that do
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2459 <lb></lb>touch without the interpoſition of flexible fluids; and, who knows, but
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2460 <lb></lb>that that a Contact, when it is very exact, may be a ſufficient Cauſe of
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2461 <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>
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2462
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2463
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2464 <pb pagenum="440"></pb><p type="margin">
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2465
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2466 <s><margin.target id="marg1482"></margin.target><emph type="italics"></emph>A<emph.end type="italics"></emph.end> Magnetiſme in
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2467 <lb></lb>the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ir, by which
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2468 <lb></lb>it bears up thoſe
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2469 <lb></lb>Solids in the wa­
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2470 <lb></lb>ter, that are con­
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2471 <lb></lb>tiguous with it.</s></p><p type="margin">
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2472
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2473 <s><margin.target id="marg1483"></margin.target>The Effect of
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2474 <lb></lb>the Airs Conti­
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2475 <lb></lb>guity in the Na­
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2476 <lb></lb>tation of Solids.</s></p><p type="margin">
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2477
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2478 <s><margin.target id="marg1484"></margin.target>The force of
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2479 <lb></lb>Contact.</s></p><p type="margin">
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2480
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2481 <s><margin.target id="marg1485"></margin.target><emph type="italics"></emph>A<emph.end type="italics"></emph.end>n affectati­
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2482 <lb></lb>on of Conjunct­
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2483 <lb></lb>ion betwixt So­
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2484 <lb></lb>lids and the Air
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2485 <lb></lb>contiguous to
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2486 <lb></lb>them.</s></p><p type="margin">
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2487
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2488 <s><margin.target id="marg1486"></margin.target>The like affect­
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2489 <lb></lb>ation of Con­
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2490 <lb></lb>junction be­
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2491 <lb></lb>twixt Solids &amp;
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2492 <lb></lb>the water.</s></p><p type="margin">
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2493
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2494 <s><margin.target id="marg1487"></margin.target>Alſo the like
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2495 <lb></lb>affectation and
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2496 <lb></lb>Conjunction be­
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2497 <lb></lb>twixt Solids
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2498 <lb></lb>themſeives.</s></p><p type="margin">
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2499
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2500 <s><margin.target id="marg1488"></margin.target>Contact may
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2501 <lb></lb>be the Cauſe of
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2502 <lb></lb>the Continuity
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2503 <lb></lb>of Naturall Bo­
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2504 <lb></lb>dies.</s></p><p type="main">
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2505
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2506 <s>Now, purſuing my purpoſe, I ſay; that it needs not, that we have
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2507 <lb></lb>recourſe to the Tenacity, that the parts of the water have amongſt them­
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2508 <lb></lb>ſelves, by which they reſiſt and oppoſe Diviſion, Diſtraction, and Seper­
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2509 <lb></lb>ration, becauſe there is no ſuch Coherence and Reſiſtance of Diviſion
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2510 <lb></lb>for if there were, it would be no leſs in the internall parts than in thoſe
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2511 <lb></lb>nearer the ſuperiour or externall Surface, ſo that the ſame Board, find­
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2512 <lb></lb>ing alwayes the ſame Reſiſtance and Renitence, would no leſs ſtop in
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2513 <lb></lb>the middle of the water than about the Surface, which is falſe. More­
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2514 <lb></lb></s><s>over, what Reſiſtance can we place in the Continuity of the water
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2515 <lb></lb>if we ſee that it is impoſſible to ſind any Body of whatſoever Matter
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2516 <lb></lb>Figure or Magnitude, which being put into the water, ſhall be obſtructed
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2517 <lb></lb>and impeded by the Tenacity of the parts of the water to one another
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2518 <lb></lb>ſo, but that it is moved upwards or downwards, according as the Cauſe
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2519 <lb></lb>of their Motion tranſports it? </s><s>And, what greater proof of it can we de­
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2520 <lb></lb>ſier, than that which we daily ſee in Muddy waters, which being put into
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2521 <lb></lb>Veſſels to be drunk, and being, after ſome hours ſetling, ſtill, as we ſay
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2522 <lb></lb><arrow.to.target n="marg1489"></arrow.to.target>
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2523 <lb></lb>thick in the end, after four or ſix dayes they are wholly ſetled, and be­
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2524 <lb></lb>come pure and clear? </s><s>Nor can their Reſiſtance of Penetration ſtay thoſe
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2525 <lb></lb>impalpable and inſenſible Atomes of Sand, which by reaſon of their
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2526 <lb></lb>exceeding ſmall force, ſpend ſix dayes in deſcending the ſpace of half
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2527 <lb></lb>a yard.</s></p><p type="margin">
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2528
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2529 <s><margin.target id="marg1489"></margin.target><emph type="italics"></emph>T<emph.end type="italics"></emph.end>he ſettlement
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2530 <lb></lb>of <emph type="italics"></emph>M<emph.end type="italics"></emph.end>uddy Wa­
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2531 <lb></lb>ter, proveth that
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2532 <lb></lb>that Element
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2533 <lb></lb>hath no averſi­
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2534 <lb></lb>on to Diviſion.</s></p><p type="main">
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2535
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2536 <s><emph type="italics"></emph>Nor let them ſay, that the ſeeing of ſuch ſmall Bodies, conſume ſix dayes in
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2537 <lb></lb>deſcending ſo little a way, is a ſufficient Argument of the Waters Reſiſtance
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2538 <lb></lb>of Diviſion; becauſe that is no reſiſting of Diviſion, but a retarding of<emph.end type="italics"></emph.end>
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2539 <lb></lb><arrow.to.target n="marg1490"></arrow.to.target>
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2540 <lb></lb><emph type="italics"></emph>Motion; and it would be ſimplicity to ſay, that a thing oppoſeth Diviſion
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2541 <lb></lb>and that in the ſame inſtant, it permits it ſelf to be divided: nor doth the
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2542 <lb></lb>Retardation of Motion at all favour the Adverſaries cauſe, for that they are
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2543 <lb></lb>to inſtance in a thing that wholly prohibiteth Motion, and procureth Reſt;
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2544 <lb></lb>it is neceſſary, therefore, to find out Bodies that ſtay in the water, if one would
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2545 <lb></lb>ſhew its repugnancy to Diviſion, and not ſuch as move in it, howbeit
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2546 <lb></lb>ſlowly.<emph.end type="italics"></emph.end></s></p><p type="margin">
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2547
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2548 <s><margin.target id="marg1490"></margin.target>Water cannot
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2549 <lb></lb>oppoſe diviſion,
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2550 <lb></lb>and at the ſame
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2551 <lb></lb>time permit it
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2552 <lb></lb>ſelf to be divi­
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2553 <lb></lb>ded.</s></p><p type="main">
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2554
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2555 <s>What then is this Craſſitude of the water, with which it reſiſteth Di­
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2556 <lb></lb>viſion? </s><s>What, I beſeech you, ſhould it be, if we (as we have ſaid above)
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2557 <lb></lb>with all diligence attempting the reduction of a Matter into ſo like a
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2558 <lb></lb>Gravity with the water, that forming it into a dilated Plate it reſts ſuſ­
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2559 <lb></lb>pended as we have ſaid, between the two waters, it be impoſſible to
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2560 <lb></lb>effect it, though we bring them to ſuch an Equiponderance, that as
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2561 <lb></lb>much Lead as the fourth part of a Grain of Muſterd-ſeed, added to the
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2562 <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
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2563 <lb></lb>or fix pounds, ſinketh it to the Bottom, and being ſubſtracted, it aſcends
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2564 <lb></lb>to the Surface of the water? </s><s>I cannot ſee, (if what I ſay be true, as it is
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2565 <lb></lb>moſt certain) what minute vertue and force we can poſſibly find or ima­
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2566 <lb></lb>gine, to which the Reſiſtance of the water againſt Diviſion and Penetra­
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2567
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2568
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2569 <pb pagenum="441"></pb>tion is not inferiour; whereupon, we muſt of neceſſity conclude
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2570 <lb></lb>that it is nothing: becanſe, if it were of any ſenſible power, ſome
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2571 <lb></lb>large Plate might be found or compounded of a Matter alike in Gra­
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2572 <lb></lb>vity to the water, which not only would ſtay between the two wa­
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2573 <lb></lb>ters; but, moreover, ſhould not be able to deſcend or aſcend with­
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2574 <lb></lb>out notable force. </s><s>We may likewiſe collect the ſame from an o­
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2575 <lb></lb><arrow.to.target n="marg1491"></arrow.to.target>
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2576 <lb></lb>ther Experiment, ſhewing that the Water gives way alſo in the ſame
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2577 <lb></lb>manner to tranſverſall Diviſion; for if in a ſetled and ſtanding water
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2578 <lb></lb>we ſhould place any great Maſs that goeth not to the bottom, draw­
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2579 <lb></lb>ing it with a ſingle (Womans) Hair, we might carry it from place to
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2580 <lb></lb>place without any oppoſition, and this whatever Figure it hath,
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2581 <lb></lb>though that it poſſeſs a great ſpace of water, as for inſtance, a great
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2582 <lb></lb>Beam would do moved ſide-ways. </s><s>Perhaps ſome might oppoſe me
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2583 <lb></lb>and ſay, that if the Reſiſtance of water againſt Diviſion, as I affirm,
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2584 <lb></lb>were nothing; Ships ſhould not need ſuch a force of Oars and Sayles
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2585 <lb></lb>for the moving of them from place to place in a tranquile Sea, or
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2586 <lb></lb>ſtanding Lake. </s><s>To him that ſhould make ſuch an objection, I would
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2587 <lb></lb><arrow.to.target n="marg1492"></arrow.to.target>
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2588 <lb></lb>reply, that the water contraſteth not againſt, nor ſimply reſiſteth
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2589 <lb></lb>Diviſion, but a ſudden Diviſion, and with ſo much greater Reni­
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2590 <lb></lb>tence, by how much greater the Velocity is: and the Cauſe of this
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2591 <lb></lb>Reſiſtance depends not on Craſſitude, or any other thing that abſo­
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2592 <lb></lb>lutely oppoſeth Diviſion, but becauſe that the parts of the water
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2593 <lb></lb>divided, in giving way to that Solid that is moved in it, are them­
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2594 <lb></lb>ſelves alſo neceſſitated locally to move, ſome to the one ſide, and ſome
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2595 <lb></lb>to the other, and ſome downwards: and this muſt no leſs be done
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2596 <lb></lb>by the waves before the Ship, or other Body ſwimming through the
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2597 <lb></lb>water, than by the poſteriour and ſubſequent; becauſe, the Ship
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2598 <lb></lb>proceeding forwards, to make it ſelf a way to receive its Bulk, it is
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2599 <lb></lb>requiſite, that with the Prow it repulſe the adjacent parts of the
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2600 <lb></lb>water, as well on one hand as on the other, and that it move them
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2601 <lb></lb>as much tranſverſly, as is the half of the breadth of the Hull: and
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2602 <lb></lb>the like removall muſt thoſe waves make, that ſucceeding the Poump
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2603 <lb></lb>do run from the remoter parts of the Ship towards thoſe of the
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2604 <lb></lb>middle, ſucceſſively to repleniſh the places, which the Ship in ad­
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2605 <lb></lb>vancing forwards, goeth, leaving vacant. </s><s>Now, becauſe, all Moti­
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2606 <lb></lb><arrow.to.target n="marg1493"></arrow.to.target>
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2607 <lb></lb>tions are made in Time, and the longer in greater time: and it being
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2608 <lb></lb>moreover true, that thoſe Bodies that in a certain time are moved
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2609 <lb></lb>by a certain power ſuch a certain ſpace, ſhall not be moved the ſame
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2610 <lb></lb>ſpace, and in a ſhorter Time, unleſs by a greater Power: therefore,
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2611 <lb></lb>the broader Ships move ſlower than the narrower, being put on by
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2612 <lb></lb>an equall Force: and the ſame Veſſel requires ſo much greater
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2613 <lb></lb>force of Wind, or Oars, the faſter it is to move.</s></p>
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2614
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2615
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2616 <pb pagenum="442"></pb><p type="margin">
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2617
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2618 <s><margin.target id="marg1491"></margin.target>An hair will
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2619 <lb></lb>draw a great
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2620 <lb></lb>Maſs thorow the
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2621 <lb></lb>Water; which
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2622 <lb></lb>proveth, that it
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2623 <lb></lb>hath no Reſiſt­
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2624 <lb></lb>ance againſt
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2625 <lb></lb>tranſverſall Di­
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2626 <lb></lb>viſion.</s></p><p type="margin">
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2627
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2628 <s><margin.target id="marg1492"></margin.target>How ſhips are
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2629 <lb></lb>moved in the
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2630 <lb></lb>water.</s></p><p type="margin">
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2631
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2632 <s><margin.target id="marg1493"></margin.target>Bodies moved
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2633 <lb></lb>a certain ſpace in
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2634 <lb></lb>a certain Time,
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2635 <lb></lb>by a certain
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2636 <lb></lb>power, cannot be
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2637 <lb></lb>moved the
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2638 <lb></lb>ſame ſpace, and
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2639 <lb></lb>in a ſhorter time,
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2640 <lb></lb>but by a greater
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2641 <lb></lb>power.</s></p><p type="main">
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2642
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2643 <s><emph type="italics"></emph>But yet for all this, any great Maſs ſwimming in a ſtanding Lake, may
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2644 <lb></lb>be moved by any petit force; only it is true, that a leſſer force more
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2645 <lb></lb>ſlowly moves it: but if the waters Reſiſtance of Diviſion, were in any
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2646 <lb></lb>manner ſenſible, it would follow, that the ſaid Maſs, ſhould, notwith­
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2647 <lb></lb>ſtanding the percuſſion of ſome ſenſible force, continue immoveable, which is<emph.end type="italics"></emph.end>
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2648 <lb></lb><arrow.to.target n="marg1494"></arrow.to.target>
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2649 <lb></lb><emph type="italics"></emph>not ſo. </s><s>Yea, I will ſay farther, that ſhould we retire our ſelves into the
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2650 <lb></lb>more internall contemplation of the Nature of water and other Fluids,
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2651 <lb></lb>perhaps we ſhould diſcover the Conſtitution of their parts to be ſuch, that
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2652 <lb></lb>they not only do not oppoſe Diviſion, but that they have not any thing in
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2653 <lb></lb>them to be divided: ſo that the Reſiſtance that is obſerved in moving<emph.end type="italics"></emph.end>
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2654 <lb></lb><arrow.to.target n="marg1495"></arrow.to.target>
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2655 <lb></lb><emph type="italics"></emph>through the water, is like to that which we meet with in paſſing through
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2656 <lb></lb>a great Throng of People, wherein we find impediment, and not by any
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2657 <lb></lb>difficulty in the Diviſion, for that none of thoſe perſons are divided
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2658 <lb></lb>whereof the Croud is compoſed, but only in moving of thoſe perſons ſide­
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2659 <lb></lb>ways which were before divided and disjoyned: and thus we find
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2660 <lb></lb>Reſiſtance in thruſting a Stick into an heap of Sand, not becauſe any part
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2661 <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>
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2662 <lb></lb><arrow.to.target n="marg1496"></arrow.to.target>
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2663 <lb></lb><emph type="italics"></emph>manners of Penetration, therefore, offer themſelves to us, one in Bodies,
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2664 <lb></lb>whoſe parts were continuall, and here Diviſion ſeemeth neceſſary; the <emph.end type="italics"></emph.end>
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2665 <lb></lb><arrow.to.target n="marg1497"></arrow.to.target>
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2666 <lb></lb><emph type="italics"></emph>other in the aggregates of parts not continuall, but contiguous only, and
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2667 <lb></lb>here there is no neceſſity of dividing but of moving only. </s><s>Now, I am
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2668 <lb></lb>not well reſolved, whether water and other Fluids may be eſteemed to
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2669 <lb></lb>be of parts continuall or contiguous only; yet I find my ſelf indeed incli­<emph.end type="italics"></emph.end>
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2670 <lb></lb><arrow.to.target n="marg1498"></arrow.to.target>
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2671 <lb></lb><emph type="italics"></emph>ned to think that they are rather contiguous (if there be in Naturno
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2672 <lb></lb>other manner of aggregating, than by the union, or by the touching of the
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2673 <lb></lb>extreams:) and I am induced thereto by the great difference that I ſee &gt;
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2674 <lb></lb>between the Conjunction of the parts of an hard or Solid Body, and the<emph.end type="italics"></emph.end>
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2675 <lb></lb><arrow.to.target n="marg1499"></arrow.to.target>
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2676 <lb></lb><emph type="italics"></emph>Conjunction of the ſame parts when the ſame Body ſhall be made Liquid
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2677 <lb></lb>and Fluid: for if, for example, I take a Maſs of Silver or other Solid
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2678 <lb></lb>and hard Mettall, I ſhall in dividing it into two parts, find not only the <emph.end type="italics"></emph.end>
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2679 <lb></lb><arrow.to.target n="marg1500"></arrow.to.target>
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2680 <lb></lb><emph type="italics"></emph>reſiſtance that is found in the moving of it only, but an other incomparably
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2681 <lb></lb>greater, dependent on that vertue, whatever it be, which holds the parts
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2682 <lb></lb>united: and ſo if we would divide again thoſe two parts into other two
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2683 <lb></lb>and ſucceſſively into others and others, we ſhould ſtill find a like Reſiſt­
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2684 <lb></lb>ance, but ever leſs by how much ſmaller the parts to be divided ſhall be;
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2685 <lb></lb>but if, laſtly, employing moſt ſubtile and acute Inſtruments, ſuch as are
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2686 <lb></lb>the moſt tenuous parts of the Fire, we ſhall reſolve it (perhaps) into its
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2687 <lb></lb>laſt and leaſt Particles, there ſhall not be left in them any longer either
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2688 <lb></lb>Reſiſtance of Diviſion, or ſo much as a capacity of being farther divi­
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2689 <lb></lb>ded, eſpecially by Inſtruments more groſſe than the acuities of Fire: and
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2690 <lb></lb>what Knife or Raſor put into well melted Silver can we finde, that will
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2691 <lb></lb>divide a thing which ſurpaſſeth the ſeparating power of Fire? </s><s>Certainly
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2692 <lb></lb>none: becauſe either the whole ſhall be reduced to the moſt minute and
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2693 <lb></lb>ultimate Diviſions, or if there remain parts capable ſtill of other Suddi­<emph.end type="italics"></emph.end>
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2694
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2695
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2696 <pb pagenum="443"></pb><emph type="italics"></emph>diviſions, they cannot receive them, but only from acuter Diviſors than
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2697 <lb></lb>Fire; but a Stick or Rod of Iron, moved in the melted Met all, is not
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2698 <lb></lb>ſuch a one. </s><s>Of a like Conſtitution and Conſiſtence, I account the parts<emph.end type="italics"></emph.end>
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2699 <lb></lb><arrow.to.target n="marg1501"></arrow.to.target>
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2700 <lb></lb><emph type="italics"></emph>of Water, and other Liquids to be, namely, incapable of Diviſion by
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2701 <lb></lb>reaſon of their Temtity; or if not abſolutely indiviſible, yet at leaſt
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2702 <lb></lb>not to be divided by a Board, or other Solid Body, palpable unto the
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2703 <lb></lb>band, the Sector being alwayes required to be more ſharp than the Solid
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2704 <lb></lb>to be cut. </s><s>Solid Bodies, therefore, do only move, and not divide the<emph.end type="italics"></emph.end>
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2705 <lb></lb><arrow.to.target n="marg1502"></arrow.to.target>
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2706 <lb></lb><emph type="italics"></emph>Water, when put into it; whoſe parts being before divided to the ex­
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2707 <lb></lb>treameſt minuity, and therefore capable of being moved, either many of
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2708 <lb></lb>them at once, or few, or very few, they ſoon give place to every ſmall Cor­
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2709 <lb></lb>puſcle, that deſcends in the ſame: for that, it being little and light, de­
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2710 <lb></lb>ſcending in the Air, and arriving to the Surface of the Water, it meets
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2711 <lb></lb>with Particles of Water more ſmall, and of leſs Reſiſtance againſt
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2712 <lb></lb>Motion and Extruſion, than is its own prement and extruſive force,
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2713 <lb></lb>whereupon it ſubmergeth, and moveth ſuch a portion of them, as is pro­
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2714 <lb></lb>portionate to its Power. </s><s>There is not, therefore, any Reſiſtance in
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2715 <lb></lb>Water againſt Diviſion, nay, there is not in it any diviſible parts. </s><s>I
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2716 <lb></lb>adde, moreover, that in caſe yet there ſbould be any ſmall Reſiſtance<emph.end type="italics"></emph.end>
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2717 <lb></lb><arrow.to.target n="marg1503"></arrow.to.target>
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2718 <lb></lb><emph type="italics"></emph>found (which is abſolutely falſe) haply in attempting with an Hair to
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2719 <lb></lb>move a very great natant Machine, or in eſſaying by the addition of one
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2720 <lb></lb>ſmall Grain of Lead to ſink, or by removall of it to raiſe a very broad
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2721 <lb></lb>Plate of Matter, equall in Gravity with Water, (which likewiſe will
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2722 <lb></lb>not happen, in caſe we proceed with dexterity) we may obſerve that that
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2723 <lb></lb>Reſiſtance is a very different thing from that which the Adverſaries pro­
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2724 <lb></lb>duce for the Cauſe of the Natation of the Plate of Lead or Board of Ebo­
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2725 <lb></lb>ny, for that one may make a Board of Ebony, which being put upon the
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2726 <lb></lb>Water ſwimmeth, and cannot be ſubmerged, no not by the addition of an
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2727 <lb></lb>bundred Grains of Lead put upon the ſame, and afterwards being ba­
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2728 <lb></lb>thed, not only ſinks, though the ſaid Lead be taken away, but though
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2729 <lb></lb>moreover a quantity of Cork, or of ſome other light Body faſtened to it,
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2730 <lb></lb>ſufficeth not to hinder it from ſinking unto the bottome: ſo that you
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2731 <lb></lb>ſee, that although it were granted that there is a certain ſmall Reſiſt­
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2732 <lb></lb>ance of Diviſion found in the ſubstance of the Water, yet this hath no­
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2733 <lb></lb>thing to do with that Cauſe which ſupports the Board above the Water,
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2734 <lb></lb>with a Reſiſtance an hundred times greater than that which men can
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2735 <lb></lb>find in the parts of the Water: nor let them tell me, that only the Sur-<emph.end type="italics"></emph.end>
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2736 <lb></lb><arrow.to.target n="marg1504"></arrow.to.target>
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diff changeset
2737 <lb></lb><emph type="italics"></emph>face of the Water hath ſuch Reſiſtance, and not the internall parts, or
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2738 <lb></lb>that ſuch Reſiſtance is found greateſt in the beginning of the Submerſion,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2739 <lb></lb>as it alſo ſeems that in the beginning, Motion meets with greater oppoſiti­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2740 <lb></lb>on, than in the continuance of it; becauſe, firſt, I will permit, that the<emph.end type="italics"></emph.end>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2741 <lb></lb><arrow.to.target n="marg1505"></arrow.to.target>
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parents:
diff changeset
2742 <lb></lb><emph type="italics"></emph>Water be ſtirred, and that the ſuperiour parts be mingled with the mid­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2743 <lb></lb>dle, and inferiour parts, or that thoſe above be wholly removed, and
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2744 <lb></lb>thoſe in the middle only made uſe off, and yet you ſhall ſee the effect for<emph.end type="italics"></emph.end>
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2745
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parents:
diff changeset
2746
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2747 <pb pagenum="444"></pb><emph type="italics"></emph>all that, to be still the ſame: Moreover, that Hair which draws a
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2748 <lb></lb>Beam through the Water, is likewiſe to divide the upperparts, and is
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2749 <lb></lb>alſo to begin the Motion, and yet it begins it, and yet it divides it: and
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2750 <lb></lb>finally, let the Board of Ebony be put in the midway, betwixt the bottome
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2751 <lb></lb>and the top of the Water, and let it there for a while be ſuſpended and
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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diff changeset
2752 <lb></lb>ſetled, and afterwards let it be left at liberty, and it will instantly begin
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2753 <lb></lb>its Motion, and will continue it unto the bottome. </s><s>Nay, more, the Board
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2754 <lb></lb>ſo ſoon as it is dimitted upon the Water, hath not only begun to move
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2755 <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">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2756
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parents:
diff changeset
2757 <s><margin.target id="marg1494"></margin.target>The parts of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2758 <lb></lb>Liquids, ſo farte
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2759 <lb></lb>from reſiſting
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2760 <lb></lb>Diviſion, that
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2761 <lb></lb>they contain not
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2762 <lb></lb>any thing that
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2763 <lb></lb>may be divided.</s></p><p type="margin">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2764
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2765 <s><margin.target id="marg1495"></margin.target>The Reſiſt­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2766 <lb></lb>ance a Solid
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2767 <lb></lb>findeth in mo­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2768 <lb></lb>ving through
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2769 <lb></lb>the water, like
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2770 <lb></lb>to that we meet
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2771 <lb></lb>with in paſſing
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parents:
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2772 <lb></lb>through a
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2773 <lb></lb>throng of peo­
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parents:
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2774 <lb></lb>ple;</s></p><p type="margin">
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2775
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2776 <s><margin.target id="marg1496"></margin.target>Or in thruſt­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2777 <lb></lb>ing a Stick into
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2778 <lb></lb>an heap of Sand.</s></p><p type="margin">
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2779
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parents:
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2780 <s><margin.target id="marg1497"></margin.target>Two kinds of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2781 <lb></lb>Penetration, one
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2782 <lb></lb>in Bodies conti­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2783 <lb></lb>nuall, the other
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2784 <lb></lb>in Bodies only
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2785 <lb></lb>contiguous.</s></p><p type="margin">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2786
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2787 <s><margin.target id="marg1498"></margin.target>Water conſiſts
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2788 <lb></lb>not of continu­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2789 <lb></lb>all, but only
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2790 <lb></lb>of contiguous
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2791 <lb></lb>parts.</s></p><p type="margin">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2792
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2793 <s><margin.target id="marg1499"></margin.target><emph type="italics"></emph>Set what ſatis­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2794 <lb></lb>faction he hath
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2795 <lb></lb>given, as to this
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2796 <lb></lb>point, in Lib. de
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2797 <lb></lb>Motu. </s><s>Dial.<emph.end type="italics"></emph.end> 2.</s></p><p type="margin">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2798
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2799 <s><margin.target id="marg1500"></margin.target>Great differ­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2800 <lb></lb>ence betwixt the
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2801 <lb></lb>Conjunction of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2802 <lb></lb>the parts of a Bo­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2803 <lb></lb>dy when Solid,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2804 <lb></lb>and when fluid.</s></p><p type="margin">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2805
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2806 <s><margin.target id="marg1501"></margin.target>Water conſiſts
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2807 <lb></lb>of parts that ad­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2808 <lb></lb>mit of no fat­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2809 <lb></lb>ther diviſion.</s></p><p type="margin">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2810
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2811 <s><margin.target id="marg1502"></margin.target>Solids dimit­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2812 <lb></lb>ted into the wa­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2813 <lb></lb>ter, do onely
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2814 <lb></lb>move, and not
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2815 <lb></lb>divide it.</s></p><p type="margin">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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2816
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2817 <s><margin.target id="marg1503"></margin.target>If there were
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2818 <lb></lb>any Reſiſtance
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2819 <lb></lb>of Diviſion in
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2820 <lb></lb>water, it muſt
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2821 <lb></lb>needs be ſmall,
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2822 <lb></lb>in that it is over­
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2823 <lb></lb>come by an
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2824 <lb></lb>Hair, a Grain of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2825 <lb></lb>Lead, or a ſlight
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2826 <lb></lb>bathing of the
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2827 <lb></lb>Solid.</s></p><p type="margin">
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
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2828
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2829 <s><margin.target id="marg1504"></margin.target>The uper parts
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2830 <lb></lb>of the Water, do
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
casties
parents:
diff changeset
2831 <lb></lb>no more reſiſt
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2832 <lb></lb>Diviſion, than
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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parents:
diff changeset
2833 <lb></lb>the middle or
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2834 <lb></lb>loweſt parts.</s></p><p type="margin">
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2835
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2836 <s><margin.target id="marg1505"></margin.target>Waters Re­
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2837 <lb></lb>ſiſtance of divi­
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2838 <lb></lb>ſion, not greater
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2839 <lb></lb>in the begin­
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2840 <lb></lb>ning of the Sub­
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2841 <lb></lb>merſion.</s></p><p type="main">
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2842
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2843 <s>Let us receive it, therefore, for a true and undoubted Concluſi­
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2844 <lb></lb>on, That the Water hath not any Renitence againſt ſimple Diviſi­
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2845 <lb></lb>on, and that it is not poſſible to find any Solid Body, be it of what
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2846 <lb></lb>Figure it will, which being put into the Water, its Motion upwards
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2847 <lb></lb>or downwards, according as it exceedeth, or ſhall be exceeded by
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2848 <lb></lb>the Water in Gravity (although ſuch exceſſe and difference be in­
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2849 <lb></lb>ſenſible) ſhall be prohibited, and taken away, by the Craſſitude of
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2850 <lb></lb>the ſaid Water. </s><s>When, therefore, we ſee the Board of Ebony, or
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2851 <lb></lb>of other Matter, more grave than the Water, to ſtay in the Con­
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2852 <lb></lb>fines of the Water and Air, without ſubmerging, we muſt have re­
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2853 <lb></lb>courſe to ſome other Originall, for the inveſting the Cauſe of that
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2854 <lb></lb>Effect, than to the breadth of the Figure, unable to overcome the
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2855 <lb></lb>Renitence with which the Water oppoſeth Diviſion, ſince there is
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2856 <lb></lb>no Reſiſtance; and from that which is not in being, we can expect
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2857 <lb></lb>no Action. </s><s>It remains moſt true, therefore, as we have ſaid before, that
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2858 <lb></lb>this ſo ſucceds, for that that which in ſuch manner put upon the wa­
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2859 <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
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2860 <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
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2861 <lb></lb>for that it is more grave than the Water, ſinketh, and that which is
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2862 <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
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2863 <lb></lb>Air, that both together are ſpecifically leſs grave than the Water,
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2864 <lb></lb>and therefore they do not deſcend.</s></p><p type="main">
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2865
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2866 <s>I will farther confirm this which I ſay. </s><s>Gentlemen, my Antago­
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2867 <lb></lb>niſts, we are agreed, that the exceſs or defect of the Gravity of the
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2868 <lb></lb>Solid, unto the Gravity of the Water, is the true and proper Cauſe
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2869 <lb></lb>of Natation or Submerſion.
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2870 <lb></lb><arrow.to.target n="marg1506"></arrow.to.target></s></p><p type="margin">
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2871
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2872 <s><margin.target id="marg1506"></margin.target>Great Caution
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2873 <lb></lb>to be had in ex­
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2874 <lb></lb>perimenting the
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2875 <lb></lb>operation of Fi­
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2876 <lb></lb>gure in Natati­
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2877 <lb></lb>on.</s></p><p type="main">
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2878
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2879 <s>Now, if you will ſhew that beſides the former Cauſe, there is ano­
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2880 <lb></lb>ther which is ſo powerfull, that it can hinder and remove the Sub­
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2881 <lb></lb>merſion of thoſe very Solids, that by their Gravity ſink, and if you
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2882 <lb></lb>will ſay, that this is the breadth or ampleneſs of Figure, you are ob­
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2883 <lb></lb>lieged, when ever you would ſhew ſuch an Experiment, firſt to make
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2884 <lb></lb>the circumſtances certain, that that Solid which you put into the
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2885 <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
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2886 <lb></lb>any one might with reaſon ſay, that not the Figure, but the Levity
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2887 <lb></lb>was the cauſe of that Natation. </s><s>But I ſay, that when you ſhall di­
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2888
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2889
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2890 <pb pagenum="445"></pb>mit a Board of Ebony into the Water, you do not put therein a Solid
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2891 <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
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2892 <lb></lb>Ebony, there is in the Water a Maſs of Air, united with the Ebony,
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2893 <lb></lb>and ſuch, and ſo light, that of both there reſults a Compoſition leſs
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2894 <lb></lb>grave than the Water: See, therefore, that you remove the Air, and
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2895 <lb></lb>put the Ebony alone into the Water, for ſo you ſhall immerge a So­
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2896 <lb></lb>lid more grave then the Water, and if this ſhall not go to the Bottom,
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2897 <lb></lb>you have well Philoſophized, and I ill.</s></p><p type="main">
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2898
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2899 <s>Now, ſince we have found the true Cauſe of the Natation of thoſe
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2900 <lb></lb>Bodies, which otherwiſe as being graver than the Water, would de­
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2901 <lb></lb>ſcend to the bottom, I think, that for the perfect and diſtinct know­
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2902 <lb></lb>ledge of this buſineſs, it would be good to proceed in a way of diſ­
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2903 <lb></lb>covering demonſtratively thoſe particular Accidents that do attend
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2904 <lb></lb>theſe effects, and,</s></p><p type="head">
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2905
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2906 <s>PROBL. I.</s></p><p type="main">
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2907
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2908 <s><emph type="italics"></emph>To finde what proportion ſeverall Figures of different<emph.end type="italics"></emph.end></s></p><p type="main">
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2909
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2910 <s><arrow.to.target n="marg1507"></arrow.to.target>
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2911 <lb></lb><emph type="italics"></emph>Matters ought to have, unto the Gravity of the
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2912 <lb></lb>Water, that ſo they may be able by vertue of the
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2913 <lb></lb>Contigucus Air to ſtay afloat.<emph.end type="italics"></emph.end></s></p><p type="margin">
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2914
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2915 <s><margin.target id="marg1507"></margin.target>To finde the
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2916 <lb></lb>proportion Fi­
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2917 <lb></lb>gures ought to
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2918 <lb></lb>have to the wa­
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2919 <lb></lb>ters Gravity,
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2920 <lb></lb>that by help of
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2921 <lb></lb>the contiguous
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2922 <lb></lb>Air, they may
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2923 <lb></lb>ſwim.</s></p><p type="main">
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2924
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2925 <s>Let, therefore, for better illuſtration, D F N E be a Veſſell,
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diff changeset
2926 <lb></lb>wherein the water is contained, and ſuppoſe a Plate or Board,
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diff changeset
2927 <lb></lb>whoſe thickneſs is comprehended between the Lines I C and
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diff changeset
2928 <lb></lb>O S, and let it be of Matter exceeding the water in Gravity, ſo that
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2929 <lb></lb>being put upon the water, it dimergeth and abaſeth below the Levell
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2930 <lb></lb>of the ſaid water, leaving the little Banks A I and B C, which are at
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diff changeset
2931 <lb></lb>the greateſt height they can be, ſo that if the Plate I S ſhould but
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diff changeset
2932 <lb></lb>deſcend any little ſpace farther, the little Banks or Ramparts would
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diff changeset
2933 <lb></lb>no longer conſiſt, but expulſing the Air A I C B, they would dif­
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diff changeset
2934 <lb></lb>fuſe themſelves over the Superficies I C, and
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diff changeset
2935 <lb></lb>would ſubmerge the Plate. </s><s>The height AIBC
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2936 <lb></lb>is therefore the greateſt profundity that the
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diff changeset
2937 <lb></lb><figure id="fig270"></figure>
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diff changeset
2938 <lb></lb>little <emph type="italics"></emph>B<emph.end type="italics"></emph.end>anks of water admit of. </s><s>Now I ſay,
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diff changeset
2939 <lb></lb>that from this, and from the proportion in Gra­
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diff changeset
2940 <lb></lb>vity, that the Matter of the Plate hath to the
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diff changeset
2941 <lb></lb>water, we may eaſily ſinde of what thickneſs, at moſt, we may make
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diff changeset
2942 <lb></lb>the ſaid Plates, to the end, they may be able to bear up above water:
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diff changeset
2943 <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
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diff changeset
2944 <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
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diff changeset
2945 <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
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2946 <lb></lb>thick as A I is high: which we will thus demonſtrate. </s><s>Lot the So­
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diff changeset
2947 <lb></lb>lid I S be donble in Gravity to the water, and let it be a regular
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2948
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2949
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2950 <pb pagenum="446"></pb>Priſme, or Cylinder, to wit, that hath its two flat Superficies, ſuperi­
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diff changeset
2951 <lb></lb>our and inferiour, alike and equall, and at Right Angles with the o­
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2952 <lb></lb>ther laterall Superficies, and let its thickneſs I O be equall to the
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2953 <lb></lb>greateſt Altitude of the Banks of water: I ſay, that if it be put upon
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2954 <lb></lb>the water, it will not ſubmerge: for the Altitude
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2955 <lb></lb>A I being equall to the Altitude I O, the Maſs
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2956 <lb></lb>of the Air A B C I ſhall be equall to the Maſs of
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2957 <lb></lb><figure id="fig271"></figure>
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2958 <lb></lb>the Solid C I O S: and the whole Maſs A O S B
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2959 <lb></lb>double to the Maſs I S; And ſince the Maſs
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2960 <lb></lb>of the Air A C, neither encreaſeth nor dimi­
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2961 <lb></lb>niſheth the Gravity of the Maſs I S, and the Solid I S was ſuppoſed
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2962 <lb></lb>double in Gravity to the water; Therefore as much water as the
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2963 <lb></lb>Maſs ſubmerged A O S B, compounded of the Air A I C B, and of
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2964 <lb></lb>the Solid I O S C, weighs juſt as much as the ſame ſubmerged Maſs
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2965 <lb></lb>A O S B: but when ſuch a Maſs of water, as is the ſubmerged part of
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2966 <lb></lb>the Solid, weighs as much as the ſaid Solid, it deſcends not farther,
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2967 <lb></lb><arrow.to.target n="marg1508"></arrow.to.target>
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2968 <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&gt;
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2969 <lb></lb>monſtrated: Therefore, I S ſhall deſcend no farther, but ſhall reſt.
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2970 <lb></lb>And if the Solid I S ſhall be Seſquialter in Gravity to the water, it
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2971 <lb></lb>ſhall float, as long as its thickneſs be not above twice as much as the
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2972 <lb></lb>greateſt Altitude of the Ramparts of water, that is, of A I. </s><s>For I S
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2973 <lb></lb>being Seſquialter in Gravity to the water, and the Altitude O I
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2974 <lb></lb>being double to I A, the Solid ſubmerged A O S B, ſhall be alſo
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2975 <lb></lb>Seſquialter in Maſs to the Solid I S. </s><s>And becauſe the Air A C,
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2976 <lb></lb>neither increaſeth nor diminiſheth the ponderoſity of the Solid I S:
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2977 <lb></lb>Therefore, as much water in quantity as the ſubmerged Maſs AOSB,
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2978 <lb></lb>weighs as much as the ſaid Maſs ſubmerged: And, therefore, that
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2979 <lb></lb>Maſs ſhall reſt. </s><s>And briefly in generall.</s></p><p type="margin">
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2980
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2981 <s><margin.target id="marg1508"></margin.target>Of Natation
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2982 <lb></lb>Lib. 1. Prop. </s><s>3.</s></p><p type="head">
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2983
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2984 <s>THEOREME. VI.</s></p><p type="main">
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2985
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2986 <s><emph type="italics"></emph>When ever the exceſs of the Gravity of the Solid above<emph.end type="italics"></emph.end>
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2987 <lb></lb><arrow.to.target n="marg1509"></arrow.to.target>
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2988 <lb></lb><emph type="italics"></emph>the Gravity of the Water, ſhall have the ſame pro­
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2989 <lb></lb>portion to the Gravity of the Water, that the Alti­
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2990 <lb></lb>tude of the Rampart, hath to the thickneſs of the
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2991 <lb></lb>Solid, that Solid ſhall not ſink, but being never ſo lit­
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2992 <lb></lb>tle thicker it ſhall.<emph.end type="italics"></emph.end></s></p><p type="margin">
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2993
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2994 <s><margin.target id="marg1509"></margin.target>The proporti­
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2995 <lb></lb>on of the great­
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2996 <lb></lb>eſt thickneſs of
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2997 <lb></lb>Solids, beyond
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2998 <lb></lb>which encrea­
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2999 <lb></lb>ſed they ſink.</s></p><p type="main">
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3000
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3001 <s>Let the Solid I S be ſuperior in Gravity to the water, and of ſuch
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3002 <lb></lb>thickneſs, that the Altitude of the Rampart A I, be in proporti­
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3003 <lb></lb>on to the thickneſs of the Solid I O, as the exceſs of the Gravi­
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3004 <lb></lb>ty of the ſaid Solid I S, above the Gravity of a Maſs of water equall
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3005 <lb></lb>to the Maſs I S, is to the Gravity of the Maſs of water equall to the
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3006
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3007
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3008 <pb pagenum="447"></pb>Maſs I S. </s><s>I ſay, that the Solid I S ſhall not
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3009 <lb></lb>ſinke, but being never ſo little thicker it ſhall
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3010 <lb></lb>go to the bottom: For being that as A I is
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3011 <lb></lb><figure id="fig272"></figure>
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3012 <lb></lb>to I O, ſo is the Exceſs of the Gravity of the
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3013 <lb></lb>Solid I S, above the Gravity of a Maſs of water
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diff changeset
3014 <lb></lb>equall to the Maſs I S, to the Gravity of the
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diff changeset
3015 <lb></lb>ſaid Maſs of water: Therefore, compounding, as A O is to O I, ſo
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diff changeset
3016 <lb></lb>ſhall the Gravity of the Solid I S, be to the Gravity of a Maſs of water
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diff changeset
3017 <lb></lb>equall to the Maſs I S: And, converting, as I O is to O A, ſo ſhall the
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diff changeset
3018 <lb></lb>Gravity of a Maſs of water equall to the Maſs I S, be to the Gravity
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diff changeset
3019 <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
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diff changeset
3020 <lb></lb>Maſs of water equall to the Maſs A B S O: and ſo is the Gravity of
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diff changeset
3021 <lb></lb>a Maſs of water I S, to the Gravity of a Maſs of water A S: Therefore
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diff changeset
3022 <lb></lb>as the Gravity of a Maſs of water, equall to the Maſs I S, is to the
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diff changeset
3023 <lb></lb>Gravity of the Solid I S, ſo is the ſame Gravity of a Maſs of water
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diff changeset
3024 <lb></lb>I S, to the Gravity of a Maſs of Water A S: Therefore the Gra­
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diff changeset
3025 <lb></lb>vity of the Solid I S, is equall to the Gravity of a Maſs of water e­
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diff changeset
3026 <lb></lb>quall to the Maſs A S: But the Gravity of the Solid I S, is the ſame
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diff changeset
3027 <lb></lb>with the Gravity of the Solid A S, compounded of the Solid I S,
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diff changeset
3028 <lb></lb>and of the Air A B C I. </s><s>Therefore the whole compounded Solid
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diff changeset
3029 <lb></lb>A O S B, weighs as much as the water that would be compriſed in the
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diff changeset
3030 <lb></lb>place of the ſaid Compound A O S B: And, therefore, it ſhall make
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diff changeset
3031 <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
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diff changeset
3032 <lb></lb>farther. </s><s>But if its thickneſs I O ſhould be increaſed, it would be ne­
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3033 <lb></lb>ceſſary alſo to encreaſe the Altitude of the Rampart A I, to main­
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3034 <lb></lb>tain the due proportion: But by what hath been ſuppoſed, the Alti­
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diff changeset
3035 <lb></lb>tude of the Rampart A I, is the greateſt that the Nature of the
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diff changeset
3036 <lb></lb>Water and Air do admit, without the waters repulſing the Air ad­
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diff changeset
3037 <lb></lb>herent to the Superficies of the Solid I C, and poſſeſſing the ſpace
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diff changeset
3038 <lb></lb>A I C B: Therefore, a Solid of greater thickneſs than I O, and of the
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diff changeset
3039 <lb></lb>ſame Matter with the Solid I S, ſhall not reſt without ſubmerging,
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diff changeset
3040 <lb></lb>but ſhall deſcend to the bottome: which was to be demonſtrated.
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diff changeset
3041 <lb></lb></s><s>In conſequence of this that hath been demonſtrated, ſundry and va­
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3042 <lb></lb>rious Concluſions may be gathered, by which the truth of my prin­
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3043 <lb></lb>cipall Propoſition comes to be more and more confirmed, and the
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3044 <lb></lb>imperfection of all former Argumentations touching the preſent
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3045 <lb></lb>Queſtion cometh to be diſcovered.</s></p><p type="main">
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3046
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3047 <s><emph type="italics"></emph>And firſt we gather from the things demonstrated, that,<emph.end type="italics"></emph.end></s></p>
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3048
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3049
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3050 <pb pagenum="448"></pb><p type="head">
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3051
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3052 <s>THEOREME VII.
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3053 <lb></lb><arrow.to.target n="marg1510"></arrow.to.target></s></p><p type="margin">
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3054
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3055 <s><margin.target id="marg1510"></margin.target>The heavieſt
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3056 <lb></lb>Bodies may
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3057 <lb></lb>ſwimme.</s></p><p type="main">
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3058
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3059 <s><emph type="italics"></emph>All Matters, how heavy ſoever, even to Gold it ſelf, the
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3060 <lb></lb>heavieſt of all Bodies, known by us, may float upon
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3061 <lb></lb>the Water.<emph.end type="italics"></emph.end></s></p><p type="main">
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3062
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3063 <s>Becauſe its Gravity being conſidered to be almoſt twenty times
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3064 <lb></lb>greater than that of the water, and, moreover, the greateſt Alti­
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3065 <lb></lb>tude that the Rampart of water can be extended to, without break
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3066 <lb></lb>ing the Contiguity of the Air, adherent to the Surface of the Solid,
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3067 <lb></lb>that is put upon the water being predetermined, if we ſhould make
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3068 <lb></lb>a Plate of Gold ſo thin, that it exceeds not the nineteenth part ofthe
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3069 <lb></lb>Altitude of the ſaid Rampart, this put lightly upon the water ſhall
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3070 <lb></lb>reſt, without going to the bottom: and if Ebony ſhall chance to be
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3071 <lb></lb>in ſeſquiſeptimall proportion more grave than the water, the greateſt
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3072 <lb></lb>thickneſs that can be allowed to a Board of Ebony, ſo that it may be
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3073 <lb></lb>able to ſtay above water without ſinking, would be ſeaven times
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3074 <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
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3075 <lb></lb>grave than water, ſhall ſwimm as oft as the thickneſs of its Plate,</s></p><p type="main">
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3076
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3077 <s><arrow.to.target n="marg1511"></arrow.to.target>
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3078 <lb></lb>exceeds not the 7th part of the Altitude of the Rampart.</s></p><p type="margin">
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3079
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3080 <s><margin.target id="marg1511"></margin.target><emph type="italics"></emph>He elſewhere
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parents:
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3081 <lb></lb>cites this as a
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parents:
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3082 <lb></lb>Propoſition, there­
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3083 <lb></lb>fore I make it of
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3084 <lb></lb>that number.<emph.end type="italics"></emph.end></s></p><p type="main">
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3085
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3086 <s>And here I will not omit to note, as a ſecond Corrollary dependent
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3087 <lb></lb>upon the things demonſtrated, that,</s></p><p type="head">
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3088
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3089 <s>THEOREME VIII.
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3090 <lb></lb><arrow.to.target n="marg1512"></arrow.to.target></s></p><p type="margin">
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3091
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3092 <s><margin.target id="marg1512"></margin.target>Natation and
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parents:
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3093 <lb></lb>Submerſion, col­
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3094 <lb></lb>lected from the
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parents:
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3095 <lb></lb>thickneſs, exclu­
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3096 <lb></lb>ding the length
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parents:
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3097 <lb></lb>and breadth of
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3098 <lb></lb>Plates.</s></p><p type="main">
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3099
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3100 <s><emph type="italics"></emph>The Expanſion of Figure not only is not the Cauſe of the
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3101 <lb></lb>Natation of thoſe grave Bodies, which otherwiſe
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3102 <lb></lb>do ſubmerge, but alſo the determining what be thoſe
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diff changeset
3103 <lb></lb>Boards of Ebony, or Plates of Iron or Gold that will
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diff changeset
3104 <lb></lb>ſwimme, depends not on it, rather that ſame determina­
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diff changeset
3105 <lb></lb>tion is to be collected from the only thickneſs of thoſe
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diff changeset
3106 <lb></lb>Figures of Ebony or Gold, wholly excluding the con­
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diff changeset
3107 <lb></lb>ſideration of length and breadth, as having no way
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diff changeset
3108 <lb></lb>any ſhare in this Effect.<emph.end type="italics"></emph.end></s></p><p type="main">
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3109
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3110 <s>It hath already been manifeſted, that the only cauſe of the Nata­
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diff changeset
3111 <lb></lb>tion of the ſaid Plates, is the reduction of them to be leſs grave
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diff changeset
3112 <lb></lb>than the water, by means of the connexion of that Air, which de­
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diff changeset
3113 <lb></lb>ſcendeth together with them, and poſſeſſeth place in the water;
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diff changeset
3114 <lb></lb>which place ſo occupyed, if before the circumfuſed water diffuſeth
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diff changeset
3115 <lb></lb>it ſelf to fill it, it be capable of as much water, as ſhall weigh equall
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diff changeset
3116 <lb></lb>with the Plate, the Plate ſhall remain ſuſpended, and ſinke no
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3117 <lb></lb>farther.</s></p>
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3118
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3119
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3120 <pb pagenum="449"></pb><p type="main">
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3121
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3122 <s>Now let us ſee on which of theſe three dimenſions of the Solid
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diff changeset
3123 <lb></lb>depends the terminating, what and how much the Maſs of that ought
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diff changeset
3124 <lb></lb>to be, that ſo the aſſiſtance of the Air contiguous unto it, may ſuffice
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parents:
diff changeset
3125 <lb></lb>to render it ſpecifically leſs grave than the water, whereupon it may
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diff changeset
3126 <lb></lb>reſt without Submerſion. </s><s>It ſhall undoubtedly be found, that the
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diff changeset
3127 <lb></lb>length and breadth have not any thing to do in the ſaid determina­
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diff changeset
3128 <lb></lb>tion, but only the height, or if you will the thickneſs: for, if we take
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diff changeset
3129 <lb></lb>a Plate or Board, as for Example, of Ebony, whoſe Altitude hath
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diff changeset
3130 <lb></lb>unto the greateſt poſſible Altitude of the Rampart, the proportion
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3131 <lb></lb>above declared, for which cauſe it ſwims indeed, but yet not if we
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3132 <lb></lb>never ſo little increaſe its thickneſs; I ſay, that retaining its thick­
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3133 <lb></lb>neſs, and encreaſing its Superficies to twice, four times, or ten times
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3134 <lb></lb>its bigneſs, or dminiſning it by dividing it into four, or ſix, or
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3135 <lb></lb>twenty, or a hundred parts, it ſhall ſtill in the ſame manner continue
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3136 <lb></lb>to float: but encreaſing its thickneſs only a Hairs breadth, it will
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3137 <lb></lb>alwaies ſubmerge, although we ſhould multiply the Superficies a
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3138 <lb></lb>hundred and a hundred times. </s><s>Now foraſmuch as that this is a
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3139 <lb></lb>Cauſe, which being added, we adde alſo the Effect, and being remo­
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3140 <lb></lb>ved, it is removed; and by augmenting or leſſening the length or
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3141 <lb></lb>breadth in any manner, the effect of going, or not going to the bot­
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3142 <lb></lb>tom, is not added or removed: I conclude, that the greatneſs and
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3143 <lb></lb>ſmalneſs of the Superficies hath no influence upon the Natation or
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3144 <lb></lb>Submerſion. </s><s>And that the proportion of the Altitude of the Ram­
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3145 <lb></lb>parts of Water, to the Altitude of the Solid, being conſtituted in
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3146 <lb></lb>the manner aforeſaid, the greatneſs or ſmalneſs of the Superficies,
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3147 <lb></lb>makes not any variation, is manifeſt from that which hath been above
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3148 <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">
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3149
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3150 <s><arrow.to.target n="marg1513"></arrow.to.target>
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3151 <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>
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3152 <lb></lb>Whence Cylinders or Prifmes, namely, the Board, be they great or
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3153 <lb></lb>little, ſo that they be all of equall thickneſs, have the ſame proportion
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3154 <lb></lb>to their Conterminall Air, which hath for Baſe the ſaid Superficies of
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3155 <lb></lb>the Board, and for height the Ramparts of water; ſo that alwayes
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3156 <lb></lb>of that Air, and of the Board, Solids are compounded, that in Gravity
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parents:
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3157 <lb></lb>equall a Maſs of water equall to the Maſs of the Solids, compounded
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3158 <lb></lb>of Air, and of the Board: whereupon all the ſaid Solids do in the
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3159 <lb></lb>ſame manner continue afloat. </s><s>We will conclude in the third place,
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parents:
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3160 <lb></lb>that,</s></p>
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3161
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parents:
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3162
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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3163 <pb pagenum="450"></pb><p type="margin">
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3164
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3165 <s><margin.target id="marg1513"></margin.target>Priſmes and
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parents:
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3166 <lb></lb>Cylinders ha­
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parents:
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3167 <lb></lb>ving the ſame
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parents:
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3168 <lb></lb>Baſe, are to one
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parents:
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3169 <lb></lb>another as their
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3170 <lb></lb>heights.</s></p><p type="head">
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3171
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3172 <s>THEOREME. IX.
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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3173 <lb></lb><arrow.to.target n="marg1514"></arrow.to.target></s></p><p type="margin">
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3174
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3175 <s><margin.target id="marg1514"></margin.target>All Figures
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parents:
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3176 <lb></lb>of all Matters,
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parents:
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3177 <lb></lb>float by hep of
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parents:
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3178 <lb></lb>the Rampart re­
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parents:
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3179 <lb></lb>pleniſhed with
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parents:
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3180 <lb></lb>Air, and ſome
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parents:
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3181 <lb></lb>but only touch
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3182 <lb></lb>the water.</s></p><p type="main">
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3183
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3184 <s><emph type="italics"></emph>All ſorts of Figures of whatſoever Matter, albeit more
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3185 <lb></lb>grave than the Water, do by Benefit of the ſaid Ram­
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3186 <lb></lb>part, not only float, but ſome Figures, though of the
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3187 <lb></lb>graveſt Matter, do ſtay wholly above Water, wetting
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3188 <lb></lb>only the inferiour Surface that toucheth the Water.<emph.end type="italics"></emph.end></s></p><p type="main">
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3189
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3190 <s>And theſe ſhall be all Figures, which from the inferiour Baſe up­
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3191 <lb></lb>wards, grow leſſer and leſſer; the which we ſhall exemplifie for
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parents:
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3192 <lb></lb>this time in Piramides or Cones, of which Figures the paſſions sre
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3193 <lb></lb>common. </s><s>We will demonſtrate therefore, that,</s></p><p type="main">
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3194
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3195 <s><emph type="italics"></emph>It is poſſible to form a Piramide, of any whatſoever Matter propoſed,
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diff changeset
3196 <lb></lb>which being put with its Baſe upon the Water, reſts not only without
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diff changeset
3197 <lb></lb>ſubmerging, but without wetting it more then its Baſe.<emph.end type="italics"></emph.end></s></p><p type="main">
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3198
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3199 <s>For the explication of which it is requiſite, that we firſt demonſtrate
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diff changeset
3200 <lb></lb>the ſubſequent Lemma, namely, that,</s></p><p type="head">
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3201
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diff changeset
3202 <s>LEMMA II.</s></p><p type="main">
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3203
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3204 <s><emph type="italics"></emph>Solids whoſe Maſſes anſwer in proportion contrarily to<emph.end type="italics"></emph.end></s></p><p type="main">
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3205
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3206 <s><arrow.to.target n="marg1515"></arrow.to.target>
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3207 <lb></lb><emph type="italics"></emph>their Specificall Gravities, are equall in Abſolute
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3208 <lb></lb>Gravities.<emph.end type="italics"></emph.end></s></p><p type="margin">
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3209
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3210 <s><margin.target id="marg1515"></margin.target>Solids whoſe
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3211 <lb></lb>Maſſes are in
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3212 <lb></lb>contrary pro­
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3213 <lb></lb>portion to their
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diff changeset
3214 <lb></lb>Specifick Gra­
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3215 <lb></lb>vities, are equall
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3216 <lb></lb>in abſolute Gra
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3217 <lb></lb>vity.</s></p><p type="main">
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3218
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3219 <s>Let A C and B be two Solids, and let the Maſs A C be to the
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3220 <lb></lb>Maſs B, as the Specificall Gravity of the Solid B, is to the Speci­
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3221 <lb></lb>ficall Gravity of the Solid A C: I ſay, the Solids A C and B are
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3222 <lb></lb>equall in abſolute weight, that is, equally grave. For
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3223 <lb></lb><figure id="fig273"></figure>
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3224 <lb></lb>if the Maſs A C be equall to the Maſs B, then, by the
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3225 <lb></lb>Aſſumption, the Specificall Gravity of B, ſhall be e­
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3226 <lb></lb>quall to the Specificall Gravity of A C, and being e­
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3227 <lb></lb>quall in Maſs, and of the ſame Specificall Gravity they
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3228 <lb></lb>ſhall abſolutely weigh one as much as another. </s><s>But
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3229 <lb></lb>if their Maſſes ſhall be unequall, let the Maſs A C be greater, and in it
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3230 <lb></lb>take the part C, equall to the Maſs B. And, becauſe the Maſſes B
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3231 <lb></lb>and C are equall; the Abſolute weight of B, ſhall have the ſame pro­
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3232 <lb></lb>portion to the Abſolute weight of C, that the Specificall Gravity of
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3233 <lb></lb>B, hath to the Specificall Gravity of C; or of C A, which is the
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3234 <lb></lb>ſame <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end>: But look what proportion the Specificall Gravity of
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3235 <lb></lb>B, hath to the Specificall Gravity of C A, the like proportion, by the
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3236 <lb></lb>Aſſumption, hath the Maſs C A, to the Maſs B; that is, to the Maſs C:
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3237
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3238
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3239 <pb pagenum="451"></pb>Therefore, the abſolute weight of B, to the abſolute weight of C, is
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3240 <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,
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3241 <lb></lb>ſo is the abſolute weight of A C, to the abſolute weight of C: There­
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3242 <lb></lb>fore the abſolute weight of B, hath the ſame proportion to the abſo­
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3243 <lb></lb>lute weight of C, that the abſolute weight of A C, hath to the ab­
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3244 <lb></lb>ſolute weight of C: Therefore, the two Solids A C and B are equall
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3245 <lb></lb>in abſolute Gravity: which was to be demonſtrated. </s><s>Having de­
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3246 <lb></lb>monſtrated this, I ſay,</s></p><p type="head">
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3247
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3248 <s>THEOREME X.</s></p><p type="main">
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3249
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3250 <s><emph type="italics"></emph>That it is poſſible of any aſſigned Matter, to form a Pi-<emph.end type="italics"></emph.end>
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3251 <lb></lb><arrow.to.target n="marg1516"></arrow.to.target>
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3252 <lb></lb><emph type="italics"></emph>ramide or Cone upon any Baſe, which being put upon
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3253 <lb></lb>the Water ſhall not ſubmerge, nor wet any more than
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3254 <lb></lb>its Baſe.<emph.end type="italics"></emph.end></s></p><p type="margin">
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3255
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3256 <s><margin.target id="marg1516"></margin.target>There may be
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3257 <lb></lb>Cones and Pira­
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3258 <lb></lb>mides of any
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3259 <lb></lb><emph type="italics"></emph>M<emph.end type="italics"></emph.end>atter, which
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3260 <lb></lb>demittedinto the
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3261 <lb></lb>water, reſt only
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3262 <lb></lb>their Baſes.</s></p><p type="main">
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3263
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3264 <s>Let the greateſt poſſible Altitude of the Rampart be the Line D B,
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3265 <lb></lb>and the Diameter of the Baſe of the Cone to be made of any Mat­
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3266 <lb></lb>ter aſſigned B C, at right angles to D B: And as the Specificall Gravity
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3267 <lb></lb>of the Matter of the Piramide or Cone to be made, is to the Specificall
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3268 <lb></lb>Gravity of the water, ſo let the Altitude of the
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3269 <lb></lb><figure id="fig274"></figure>
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3270 <lb></lb>Rampart D B, be to the third part of the Piramide
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3271 <lb></lb>or Cone A B C, deſcribed upon the Baſe, whoſe
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3272 <lb></lb>Diameter is B C: I ſay, that the ſaid Cone A B C,
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3273 <lb></lb>and any other Cone, lower then the ſame, ſhall reſt
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3274 <lb></lb>upon the Surface of the water B C without ſinking.
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3275 <lb></lb></s><s>Draw D F parallel to B C, and ſuppoſe the Priſme
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3276 <lb></lb>or Cylinder E C, which ſhall be tripple to the Cone
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3277 <lb></lb>A B C. And, becauſe the Cylinder D C hath the ſame proportion
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3278 <lb></lb>to the Cylinder C E, that the Altitude D B, hath to the Altitude B E:
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3279 <lb></lb>But the Cylinder C E, is to the Cone A B C, as the Altitude E B is to
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3280 <lb></lb>the third part of the Altitude of the Cone: Therefore, by Equality of
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3281 <lb></lb>proportion, the Cylinder D C is to the Cone A B C, as D B is to the
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3282 <lb></lb>third part of the Altitude B E: But as D B is to the third part of B E,
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3283 <lb></lb>ſo is the Specificall Gravity of the Cone A B C, to the Specificall Gra­
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3284 <lb></lb>vity of the water: Therefore, as the Maſs of the Solid D C, is to the
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3285 <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,
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3286 <lb></lb>to the Specificall Gravity of the water: Therefore, by the precedent
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3287 <lb></lb>Lemma, the Cone A B C weighs in abſolute Gravity as much as a
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3288 <lb></lb>Maſs of Water equall to the Maſs D C: But the water which by the
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3289 <lb></lb>impoſition of the Cone A B C, is driven out of its place, is as much
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3290 <lb></lb>as would preciſely lie in the place D C, and is equall in weight to the
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3291 <lb></lb>Cone that diſplaceth it: Therefore, there ſhall be an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end>
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3292 <lb></lb>and the Cone ſhall reſt without farther ſubmerging. </s><s>And its ma­
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3293 <lb></lb>nifeſt,</s></p>
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3294
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3295
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3296 <pb pagenum="452"></pb><p type="head">
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3297
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3298 <s>COROLARY I.
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3299 <lb></lb><arrow.to.target n="marg1517"></arrow.to.target></s></p><p type="margin">
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3300
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3301 <s><margin.target id="marg1517"></margin.target>Amongſt Cones
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3302 <lb></lb>of the ſame Baſe,
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3303 <lb></lb>thoſe of leaſt Al­
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3304 <lb></lb>titude ſhall ſink
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3305 <lb></lb>the leaſt.</s></p><p type="main">
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3306
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3307 <s><emph type="italics"></emph>That making upon the ſame Baſis, a Cone of a leſs Altitude, it ſhall be
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3308 <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">
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3309
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3310 <s>COROLARY II.</s></p><p type="main">
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3311
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3312 <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">
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3313
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3314 <s><arrow.to.target n="marg1518"></arrow.to.target>
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3315 <lb></lb><emph type="italics"></emph>whatſoever, more grave than the water, which being put into the
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3316 <lb></lb>water, with the Apix or Point downwards, reſt without Submerſion. <emph.end type="italics"></emph.end></s></p><p type="margin">
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3317
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3318 <s><margin.target id="marg1518"></margin.target>There may be
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3319 <lb></lb>Cones and Pira­
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3320 <lb></lb>mides of any
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3321 <lb></lb>Matter, which
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3322 <lb></lb>demitted with
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3323 <lb></lb>the Point down­
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3324 <lb></lb>wards do float a­
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3325 <lb></lb>top.</s></p><p type="main">
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3326
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3327 <s>Becauſe if we reaſſume what hath been above demonſtrated, of
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3328 <lb></lb>Priſms and Cylinders, and that on Baſes equall to thoſe of the
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3329 <lb></lb>ſaid Cylinders, we make Cones of the ſame Matter, and thrree
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3330 <lb></lb>times as high as the Cylinders, they ſhall reſt afloat, for that in Maſs
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3331 <lb></lb>and Gravity they ſhall be equall to thoſe Cylinders, and by having
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3332 <lb></lb>their Baſes equall to thoſe of the Cylinders, they ſhall leave equall
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3333 <lb></lb>Maſſes of Air included within the Ramparts. </s><s>This, which for Exam­
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3334 <lb></lb>ple ſake hath been demonſtrated, in Priſms, Cylinders, Cones and
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3335 <lb></lb>Piramids, might be proved in all other Solid Figures, but it would
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3336 <lb></lb>require a whole Volume (ſuch is the multitude and variety of their
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3337 <lb></lb>Symptoms and Accidents) to comprehend the particuler demonſtration
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3338 <lb></lb>of them all, and of their ſeverall Segments: but I will to avoid prolixity
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3339 <lb></lb>in the preſent Diſcourſe, content my ſelf, that by what I have declared
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3340 <lb></lb>every one of ordinary Capacity may comprehend, that there is not
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3341 <lb></lb>any Matter ſo grave, no not Gold it ſelf, of which one may not form
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3342 <lb></lb>all ſorts of Figures, which by vertue of the ſuperiour Air adherent to
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3343 <lb></lb>them, and not by the Waters Reſiſtance of Penetration, do remain
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3344 <lb></lb>afloat, ſo that they ſink not. </s><s>Nay, farther, I will ſhew, for removing
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3345 <lb></lb>that Error, that,</s></p><p type="head">
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3346
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3347 <s>THEOREME XI.
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3348 <lb></lb><arrow.to.target n="marg1519"></arrow.to.target></s></p><p type="margin">
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3349
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3350 <s><margin.target id="marg1519"></margin.target>A Piramide or
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3351 <lb></lb>Cone, demitted
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3352 <lb></lb>with the Point
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3353 <lb></lb>downwards ſhal
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3354 <lb></lb>ſwim, with its
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3355 <lb></lb>Baſe downward
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3356 <lb></lb>ſhall ſink.</s></p><p type="main">
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3357
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3358 <s><emph type="italics"></emph>A Piramide or Cone put into the Water, with the Point
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3359 <lb></lb>downward ſhall ſwimme, and the ſame put with the
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3360 <lb></lb>Baſe downwards ſhall ſinke, and it ſhall be impoſſible
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3361 <lb></lb>to make it float.<emph.end type="italics"></emph.end></s></p><p type="main">
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3362
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3363 <s>Now the quite contrary would happen, if the difficulty of Pene­
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3364 <lb></lb>trating the water, were that which had hindred the deſcent, for
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3365 <lb></lb>that the ſaid Cone is far apter to pierce and penetrate with its ſharp
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3366 <lb></lb>Point, than with its broad and ſpacious Baſe.</s></p><p type="main">
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3367
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3368 <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
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3369 <lb></lb>as the water, and let its height be tripple to the height of the Rampart
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3370 <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
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3371
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3372
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3373 <pb pagenum="453"></pb>Point downwards, it ſhall not deſcend to the bot­
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3374 <lb></lb>tom: for the Aeriall Cylinder contained betwixt
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3375 <lb></lb><figure id="fig275"></figure>
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3376 <lb></lb>the Ramparts <emph type="italics"></emph>D A C E,<emph.end type="italics"></emph.end> is equall in Maſs to the
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diff changeset
3377 <lb></lb>Cone <emph type="italics"></emph>A B C<emph.end type="italics"></emph.end>; ſo that the whole Maſs of the Solid
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3378 <lb></lb>compounded of the Air <emph type="italics"></emph>D A C E,<emph.end type="italics"></emph.end> and of the Cone
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3379 <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,
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3380 <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
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3381 <lb></lb>vity to the water, therefore as much water as the whole Maſſe
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3382 <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
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3383 <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>
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3384 <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,
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3385 <lb></lb>that the ſame Cone placed with the Baſe downwards, ſhall ſink to
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3386 <lb></lb>the bottom, without any poſſibility of returning again, by any means
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3387 <lb></lb>to ſwimme.</s></p><p type="main">
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3388
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3389 <s>Let, therefore, the Cone be <emph type="italics"></emph>A B D,<emph.end type="italics"></emph.end> double in Gravity to the
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3390 <lb></lb>water, and let its height be tripple the height
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3391 <lb></lb><figure id="fig276"></figure>
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3392 <lb></lb>of the Rampart of water L B: It is already
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3393 <lb></lb>manifeſt, that it ſhall not ſtay wholly out of
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3394 <lb></lb>the water, becauſe the Cylinder being com­
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3395 <lb></lb>prehended betwixt the Ramparts <emph type="italics"></emph>L B D P,<emph.end type="italics"></emph.end>
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3396 <lb></lb>equall to the Cone <emph type="italics"></emph>A B D,<emph.end type="italics"></emph.end> and the Matter of
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3397 <lb></lb>the Cone, beig double in Gravity to the
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3398 <lb></lb>water, it is evident that the weight of the ſaid
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3399 <lb></lb>Cone ſhall be double to the weight of the Maſs of water equall to the
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3400 <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
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3401 <lb></lb>ſhall deſcend.</s></p><p type="head">
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3402
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3403 <s>COROLARY I.</s></p><p type="main">
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3404
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3405 <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">
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3406
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3407 <s><arrow.to.target n="marg1520"></arrow.to.target>
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3408 <lb></lb><emph type="italics"></emph>immerge a part thereof.<emph.end type="italics"></emph.end></s></p><p type="margin">
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3409
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3410 <s><margin.target id="marg1520"></margin.target>Much leſs ſhall
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3411 <lb></lb>the ſaid Cone
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3412 <lb></lb>ſwim, if one im­
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3413 <lb></lb>merge a part
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3414 <lb></lb>thereof.</s></p><p type="main">
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3415
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3416 <s>Which you may ſee, comparing with the water as well the part
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3417 <lb></lb>that ſhall immerge as the other above water. </s><s>Let us therefore
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3418 <lb></lb>of the Cone A B D, ſubmergeth part N T O S, and advance the
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3419 <lb></lb>Point N S F above water. </s><s>The Altitude of the Cone F N S, ſhall
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3420 <lb></lb>either be more than half the whole Altitude of the Cone F T O, or
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3421 <lb></lb>it ſhall not be more: if it ſhall be more than half, the Cone F N S
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3422 <lb></lb>ſhall be more than half of the Cylinder E N S C: for the Altitude
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3423 <lb></lb>of the Cone F N S, ſhall be more than Seſquialter of the Altitude
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3424 <lb></lb>of the Cylinder E N S C: And, becauſe the Matter of the Cone is
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3425 <lb></lb>ſuppoſed to be double in Specificall Gravity to the water, the water
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3426 <lb></lb>which would be contained within the Rampart E N S C, would be
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3427 <lb></lb>leſs grave abſolutely than the Cone F N S; ſo that the whole Cone
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3428 <lb></lb>F N S cannot be ſuſtained by the Rampart: But the part immerged
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3429 <lb></lb>N T O S, by being double in Specificall Gravity to the water, ſhall
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3430
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3431
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3432 <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
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3433 <lb></lb>reſpect of the part ſubmerged, as the part above water ſhall de­
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3434 <lb></lb>ſcend to the bottom. </s><s>But if the Altitude of the Point F N S, ſhall
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3435 <lb></lb>be half the Altitude of the whole Cone F T O, the ſame Altitude of
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3436 <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,
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3437 <lb></lb>therefore, E N S C ſhall be double to the Cone F N S; and as much
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3438 <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
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3439 <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
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3440 <lb></lb>N T O S, is double in Gravity to the water, a Maſs of water equall
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3441 <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,
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3442 <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
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3443 <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
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3444 <lb></lb>ſha l alſo deſcend. </s><s>Again, becauſe the Solid N T O S, is ſeptuple
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3445 <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
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3446 <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
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3447 <lb></lb>to two: Therefore, the whole Solid compounded of the <emph type="italics"></emph>C<emph.end type="italics"></emph.end>ylinder
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3448 <lb></lb>E N S C, and of the Solid N T O S, is much leſs than double the
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3449 <lb></lb>Solid N T O S: Therefore, the ſingle Solid N T O S, is much graver
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3450 <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
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3451 <lb></lb>linder E N S C, and of N T O S.</s></p><p type="head">
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3452
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3453 <s>COROLARY II.
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3454 <lb></lb><arrow.to.target n="marg1521"></arrow.to.target></s></p><p type="margin">
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3455
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3456 <s><margin.target id="marg1521"></margin.target>Part of the
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3457 <lb></lb>Cones towards
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3458 <lb></lb>the Cuſpis remo­
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3459 <lb></lb>ved, it ſhall ſtill
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3460 <lb></lb>ſink.</s></p><p type="main">
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3461
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3462 <s><emph type="italics"></emph>From whence it followeth, that though one ſhould remove and take a­
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3463 <lb></lb>way the part of the Cone F N S, the ſole remainder N T O S would
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3464 <lb></lb>go to the bottom.<emph.end type="italics"></emph.end></s></p><p type="head">
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3465
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diff changeset
3466 <s>COROLARY III.</s></p><p type="main">
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3467
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3468 <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">
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3469
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3470 <s><arrow.to.target n="marg1522"></arrow.to.target>
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3471 <lb></lb><emph type="italics"></emph>more impoſſible that it ſhould ſuſtain it ſelf afloat, the part ſubmerged
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diff changeset
3472 <lb></lb>N T O S ſtill encreaſing, and the Maſs of Air contained in the Rampart
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3473 <lb></lb>diminiſhing, which ever grows leſs, the more the Cone ſubmergeth.<emph.end type="italics"></emph.end></s></p><p type="margin">
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3474
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3475 <s><margin.target id="marg1522"></margin.target>The more the
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3476 <lb></lb>Cone is immer­
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3477 <lb></lb>ged, the more
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3478 <lb></lb>impoſſible is its
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3479 <lb></lb>floating.</s></p><p type="main">
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3480
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3481 <s>That Cone, therefore, that with its Baſe upwards, and its
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3482 <lb></lb><emph type="italics"></emph>Cuſpis<emph.end type="italics"></emph.end> downwards doth ſwimme, being dimitted with its Baſe
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3483 <lb></lb>downward muſt of neceſſity ſinke. </s><s>They have argued farre
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3484 <lb></lb>from the truth, therefore, who have aſcribed the cauſe of Natation
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3485 <lb></lb>to waters reſiſtance of Diviſion, as to a paſſive principle, and to the
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3486 <lb></lb>breadth of the Figure, with which the diviſion is to be made, as the
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3487 <lb></lb>Efficient.</s></p><p type="main">
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3488
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3489 <s>I come in the fourth place, to collect and conclude the reaſon of
22d6a63640c6 moved texts from SVN https://it-dev.mpiwg-berlin.mpg.de/svn/mpdl-project-content/trunk/texts/eXist/
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3490 <lb></lb>that which I have propoſed to the Adverſaries, namely,</s></p>
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3491
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3492
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3493 <pb pagenum="455"></pb><p type="head">
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3494
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3495 <s>THE OREME XII.</s></p><p type="main">
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3496
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3497 <s><emph type="italics"></emph>That it is poſſible to fo m Solid Bodies, of what Figure<emph.end type="italics"></emph.end>
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3498 <lb></lb><arrow.to.target n="marg1523"></arrow.to.target>
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3499 <lb></lb><emph type="italics"></emph>and greatneſs ſoever, that of their own Nature goe
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3500 <lb></lb>to the Bottome; But by the help of the Air con­
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3501 <lb></lb>tained in the Rampart, reſt without ſubmerging.<emph.end type="italics"></emph.end></s></p><p type="margin">
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3502
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3503 <s><margin.target id="marg1523"></margin.target>Solids of any
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3504 <lb></lb>Figure &amp; great­
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3505 <lb></lb>neſſe, that natu­
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3506 <lb></lb>rally ſink, may
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3507 <lb></lb>by help of the
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3508 <lb></lb>Air in the Ram­
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3509 <lb></lb>part ſwimme.</s></p><p type="main">
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3510
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3511 <s>The truth of this Propoſition is ſufficiently manifeſt in all thoſe
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3512 <lb></lb>Solid Figures, that determine in their uppermoſt part in a plane
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3513 <lb></lb>Superficies: for making ſuch Figures of ſome Matter ſpecifi­
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3514 <lb></lb>cally as grave as the water, putting them into the water, ſo that the
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3515 <lb></lb>whole Maſs be covered, it is manifeſt, that they ſhall reſt in all
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3516 <lb></lb>places, provided, that ſuch a Matter equall in weight to the water,
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3517 <lb></lb>may be exactly adjuſted: and they ſhall by conſequence, reſt or
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3518 <lb></lb>lie even with the Levell of the water, without making any Rampart.
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3519 <lb></lb></s><s>If, therefore, in reſpect of the Matter, ſuch Figures are apt to reſt
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3520 <lb></lb>without ſubmerging, though deprived of the help of the Rampart,
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3521 <lb></lb>it is manifeſt, that they may admit ſo much encreaſe of Gravity,
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3522 <lb></lb>(without encreaſing their Maſſes) as is the weight of as much water
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3523 <lb></lb>as would be contained within the Rampart, that is made about their
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3524 <lb></lb>upper plane Surface: by the help of which being ſuſtained, they
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3525 <lb></lb>ſhall reſt afloat, but being bathed, they ſhall deſcend, having been
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3526 <lb></lb>made graver than the water. </s><s>In Figures, therefore, that determine
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3527 <lb></lb>above in a plane, we may cleerly comprehend, that the Rampart
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3528 <lb></lb>added or removed, may prohibit or permit the deſcent: but in thoſe
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3529 <lb></lb>Figures that go leſſening upwards towards the top, ſome Perſons
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3530 <lb></lb>may, and that not without much ſeeming Reaſon, doubt whether
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3531 <lb></lb>the ſame may be done, and eſpecially by thoſe which terminate in a
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3532 <lb></lb>very acute Point, ſuch as are your Cones and ſmall Piramids. </s><s>Touch­
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3533 <lb></lb>ing theſe, therefore, as more dubious than the reſt, I will endeavour
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3534 <lb></lb>to demonſtrate, that they alſo lie under the ſame Accident of going,
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3535 <lb></lb>or not going to the Bottom, be they of any whatever bigneſs. </s><s>Let
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3536 <lb></lb>therefore the Cone be A B D, made of a matter
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3537 <lb></lb>ſpecifically as grave as the water; it is manifeſt
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3538 <lb></lb><figure id="fig277"></figure>
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3539 <lb></lb>that being put all under water, it ſhall reſt in
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3540 <lb></lb>all places (alwayes provided, that it ſhall weigh
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3541 <lb></lb>exactly as much as the water, which is almoſt
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3542 <lb></lb>impoſſible to effect) and that any ſmall weight
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3543 <lb></lb>being added to it, it ſhall ſink to the bottom:
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3544 <lb></lb>but if it ſhall deſcend downwards gently, I ſay,
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3545 <lb></lb>that it ſhall make the Rampart E S T O, and
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3546 <lb></lb>that there ſhall ſtay out of the water the point A S T, tripple in
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3547 <lb></lb>height to the Rampart E S: which is manifeſt, for the Matter of the
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3548
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3549
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3550 <pb pagenum="456"></pb>Cone weighing equally with the water, the part ſubmerged S B D T,
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3551 <lb></lb>becomes indifferent to move downwards or upwards; and the Cone
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3552 <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
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3553 <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
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3554 <lb></lb>Gravity: and, therefore, there ſhall be a perfect <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> and,
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3555 <lb></lb>conſequently, a Reſt. </s><s>Now here ariſeth a doubt, whether the
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3556 <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
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3557 <lb></lb>wholly under water, it goes to the bottom, but yet not in ſuch ſort,
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3558 <lb></lb>as to take from the Rampart the vertue of ſuſtaining it that it ſink not,
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3559 <lb></lb>and, the reaſon of the doubt is this: that although at ſuch time as
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3560 <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
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3561 <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
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3562 <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
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3563 <lb></lb>part is above water; [for although in the Deſcent of the Cone the
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3564 <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
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3565 <lb></lb>Rampart <emph type="italics"></emph>E S T O,<emph.end type="italics"></emph.end> yet the Point diminiſheth in
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3566 <lb></lb><figure id="fig278"></figure>
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3567 <lb></lb>greater proportion than the Rampart, in that
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3568 <lb></lb>it diminiſheth according to all the three Di­
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3569 <lb></lb>menſions, but the Rampart according to two
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3570 <lb></lb>only, the Altitude ſtill remaining the ſame;
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3571 <lb></lb>or, if you will, becauſe the Cone <emph type="italics"></emph>S T<emph.end type="italics"></emph.end> goes di­
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3572 <lb></lb>miniſhing, according to the proportion of the
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3573 <lb></lb>cubes of the Lines that do ſucceſſively become
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3574 <lb></lb>the Diameters of the Baſes of emergent Cones,
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3575 <lb></lb>and the Ramparts diminiſh according to the proportion of the
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3576 <lb></lb>Squares of the ſame Lines; whereupon the proportions of the Points
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3577 <lb></lb>are alwayes Seſquialter of the proportions of the Cylinders, con­
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3578 <lb></lb>tained within the Rampart; ſo that if, for Example, the height of
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3579 <lb></lb>the emergent Point were double, or equall to the height of the
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3580 <lb></lb>Rampart, in theſe caſes, the Cylinder contained within the Ram­
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3581 <lb></lb>part, would be much greater than the ſaid Point, becauſe it would be
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3582 <lb></lb>either ſeſquialter or tripple, by reaſon of which it would perhaps
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3583 <lb></lb>ſerve over and above to fuſtain the whole Cone, ſince the part ſub­
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3584 <lb></lb>merged would no longer weigh any thing;] yet, nevertheleſs, when
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3585 <lb></lb>any Gravity is added to the whole Maſs of the Cone, ſo that alſo the
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3586 <lb></lb>part ſubmerged is not without ſome exceſſe of Gravity above the
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3587 <lb></lb>Gravity of the water, it is not manifeſt, whether the Cylinder con­
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3588 <lb></lb>tained within the Rampart, in the deſcent that the Cone ſhall make,
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3589 <lb></lb>can be reduced to ſuch a proportion unto the emergent Point, and to
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3590 <lb></lb>ſuch an exceſſe of Maſs above the Maſs of it, as to compenſate the
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3591 <lb></lb>exceſſe of the Cones Specificall Gravity above the Gravity of the wa­
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3592 <lb></lb>ter: and the Scruple ariſeth, becauſe that howbeit in the deſcent
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3593 <lb></lb>made by the Cone, the emergent Point <emph type="italics"></emph>A S T<emph.end type="italics"></emph.end> diminiſheth, whereby
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3594 <lb></lb>there is alſo a diminution of the exceſs of the Cones Gravity above
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3595
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3596
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3597 <pb pagenum="459"></pb>the Gravity of the water, yet the caſe ſtands ſo, that the Rampart
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3598 <lb></lb>doth alſo contract it ſelf, and the Cylinder contained in it doth de­
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3599 <lb></lb>miniſh. </s><s>Nevertheleſs it ſhall be demonſtrated, how that the Cone
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3600 <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
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3601 <lb></lb>Matter exactly equall in Gravity to the Water, if there may
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3602 <lb></lb>be affixed to it ſome Weight, by means of which it may deſcend to
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3603 <lb></lb>the bottom, when ſubmerged under water, it may alſo by vertue of
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3604 <lb></lb>the Rampart ſtay above without ſinking.</s></p><p type="main">
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3605
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3606 <s>Let, therefore, the Cone <emph type="italics"></emph>A B D<emph.end type="italics"></emph.end> be of any ſuppoſed greatneſſe,
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3607 <lb></lb>and alike in ſpecificall Gravity to the water. </s><s>It is manifeſt, that
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3608 <lb></lb>being put lightly into the water, it ſhall reſt without deſcending;
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3609 <lb></lb>and it ſhall advance above water, the Point
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3610 <lb></lb><figure id="fig279"></figure>
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3611 <lb></lb><emph type="italics"></emph>AS T,<emph.end type="italics"></emph.end> tripple in height to the height of the
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3612 <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>
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3613 <lb></lb>more depreſſed, ſo that it advance above wa­
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3614 <lb></lb>ter, only the Point <emph type="italics"></emph>A I R,<emph.end type="italics"></emph.end> higher by half than
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3615 <lb></lb>the Point <emph type="italics"></emph>A S T,<emph.end type="italics"></emph.end> with the Rampart about it
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3616 <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
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3617 <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>
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3618 <lb></lb>is to the cube of the Line <emph type="italics"></emph>I R,<emph.end type="italics"></emph.end> but the Cylin­
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3619 <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
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3620 <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
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3621 <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>:
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3622 <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,
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3623 <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
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3624 <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
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3625 <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,
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3626 <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>:
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3627 <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
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3628 <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
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3629 <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
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3630 <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:
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3631 <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
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3632 <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
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3633 <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
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3634 <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
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3635 <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
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3636 <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
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3637 <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>
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3638 <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
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3639 <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
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3640 <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
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3641 <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
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3642 <lb></lb>more then its ſeventh part, it alſo ſhall continue to ſwimme, and
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3643
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3644
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3645 <pb pagenum="460"></pb>the height of the emergent Point ſhall be double to the height of the
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3646 <lb></lb>Rampart. </s><s>This that hath been demonſtrated in Cones, exactly holds
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3647 <lb></lb>in Piramides, although the one or the other ſhould be very ſharp in
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3648 <lb></lb><arrow.to.target n="marg1524"></arrow.to.target>
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3649 <lb></lb>their Point or Cuſpis: From whence we conclude, that the ſame
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3650 <lb></lb>Accident ſhall ſo much the more eaſily happen in all other Figures,
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3651 <lb></lb>by how much the leſs ſharp the Tops ſhall be, in which they deter­
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3652 <lb></lb>mine, being aſſiſted by more ſpacious Ramparts.</s></p><p type="margin">
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3653
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3654 <s><margin.target id="marg1524"></margin.target>Natatiou eaſi­
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3655 <lb></lb>eſt effected in
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3656 <lb></lb>Figures broad
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3657 <lb></lb>toward the top.</s></p><p type="head">
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3658
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3659 <s>THEOREME XIII.
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3660 <lb></lb><arrow.to.target n="marg1525"></arrow.to.target></s></p><p type="margin">
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3661
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3662 <s><margin.target id="marg1525"></margin.target>All Figures ſink
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3663 <lb></lb>or ſwim, upon
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3664 <lb></lb>bathing or not
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3665 <lb></lb>bathing of their
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3666 <lb></lb>tops.</s></p><p type="main">
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3667
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3668 <s><emph type="italics"></emph>All Figures, therefore, of whatever greatneſſe, may
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3669 <lb></lb>go, and not go, to the Bottom, according as their Sumi­
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3670 <lb></lb>ties or Tops ſhall be bathed or not bathed.<emph.end type="italics"></emph.end></s></p><p type="main">
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3671
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3672 <s>And this Accident being common to all ſorts of Figures, without
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3673 <lb></lb>exception of ſo much as one. </s><s>Figure hath, therefore, no part
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3674 <lb></lb>in the production of this Effect, of ſometimes ſinking, and ſome­
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3675 <lb></lb>times again not ſinking, but only the being ſometimes conjoyned
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3676 <lb></lb>to, and ſometimes ſeperated from, the ſupereminent Air: which
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3677 <lb></lb>cauſe, in fine, who ſo ſhall rightly, and, as we ſay, with both his
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3678 <lb></lb>Eyes, conſider this buſineſs, will find that it is reduced to, yea, that
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3679 <lb></lb>it really is the ſame with, the true, Naturall and primary cauſe of
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3680 <lb></lb>Natation or Submerſion; to wit, the exceſs or deficiency of the
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3681 <lb></lb>Gravity of the water, in relation to the Gravity of that Solid Mag­
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3682 <lb></lb>nitude, that is demitted into the water. </s><s>For like as a Plate of Lead,
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3683 <lb></lb>as thick as the back of a Knife, which being put into the water by it
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3684 <lb></lb>ſelf alone goes to the bottom, if upon it you faſten a piece of Cork
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3685 <lb></lb>four fingers thick, doth continue afloat, for that now the Solid that
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3686 <lb></lb>is demitted in the water, is not, as before, more grave than the water,
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3687 <lb></lb>but leſs, ſo the Board of Ebony, of its own nature more grave than
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3688 <lb></lb>water; and, therefore, deſcending to the bottom, when it is demit­
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3689 <lb></lb>ted by it ſelf alone into the water, if it ſhall be put upon the water,
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3690 <lb></lb>conjoyned with an Expanded vail of Air, that together with the
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3691 <lb></lb>Ebony doth deſcend, and that it be ſuch, as that it doth make with
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3692 <lb></lb>it a compound leſs grave than ſo much water in Maſs, as equalleth
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3693 <lb></lb>the Maſs already ſubmerged and depreſſed beneath the Levell of the
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3694 <lb></lb>waters Surface, it ſhall not deſcend any farther, but ſhall reſt, for
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3695 <lb></lb>no other than the univerſall and moſt common cauſe, which is that
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3696 <lb></lb>Solid Magnitudes, leſs grave <emph type="italics"></emph>inſpecie<emph.end type="italics"></emph.end> than the water, go not to the
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3697 <lb></lb>bottom.</s></p><p type="main">
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3698
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3699 <s>So that if one ſhould take a Plate of Lead, as for Example, a finger
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3700 <lb></lb>thick, and an handfull broad every way, and ſhould attempt to make
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3701 <lb></lb>it ſwimme, with putting it lightly on the water, he would loſe his
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3702 <lb></lb>Labour, becauſe that if it ſhould be depreſſed an Hairs breadth be­
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3703
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3704
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3705 <pb pagenum="461"></pb>yond the poſſible Altitude of the Ramparts of water, it would dive
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3706 <lb></lb>and ſink; but if whilſt it is going downwards, one ſhould make
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3707 <lb></lb>certain Banks or Ramparts about it, that ſhould hinder the do fuſion
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3708 <lb></lb>of the water upon the ſaid Plate, the which Banks ſhould riſe ſo
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3709 <lb></lb>high, as that they might be able to contain as much water, as ſhould
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3710 <lb></lb>weigh equally with the ſaid Plate, it would, without all Queſtion,
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3711 <lb></lb>deſcend no lower, but would reſt, as being ſuſtained by vertue of
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3712 <lb></lb>the Air contained within the aforeſaid Ramparts: and, in ſhort,
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3713 <lb></lb>there would be a Veſſell by this means formed with the bottom of
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diff changeset
3714 <lb></lb>Lead. </s><s>But if the thinneſs of the Lead ſhall be ſuch, that a very
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diff changeset
3715 <lb></lb>ſmall height of Rampart would ſuffice to contain ſo much Air, as might
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diff changeset
3716 <lb></lb>keep it afloat, it ſhall alſo reſt without the Artificiall Banks or Ram­
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diff changeset
3717 <lb></lb>parts, but yet not without the Air, becauſe the Air by it ſelf makes
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diff changeset
3718 <lb></lb>Banks ſufficient for a ſmall height, to reſiſt the Superfuſion of the
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diff changeset
3719 <lb></lb>water: ſo that that which in this caſe ſwimmes, is as it were a
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diff changeset
3720 <lb></lb>Veſſell filled with Air, by vertue of which it continueth afloat.</s></p><p type="main">
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3721
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3722 <s>I will, in the laſt place, with an other Experimeut, attempt to
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3723 <lb></lb>remove all difficulties, if ſo be there ſhould yet be any doubt leſt in
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diff changeset
3724 <lb></lb>any one, touching the opperation of this ^{*}Continuity of the Air, with </s></p><p type="main">
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3725
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3726 <s><arrow.to.target n="marg1526"></arrow.to.target>
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3727 <lb></lb>the thin Plate which ſwims, and afterwards put an end to this part of
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diff changeset
3728 <lb></lb>my diſcourſe.</s></p><p type="margin">
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3729
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3730 <s><margin.target id="marg1526"></margin.target>*Or rather Cor­
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3731 <lb></lb>tiguity,</s></p><p type="main">
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3732
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3733 <s>I ſuppoſe my ſelf to be queſtioning with ſome of my Oponents.</s></p><p type="main">
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3734
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3735 <s>Whether Figure have any influence upon the encreaſe or diminu­
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3736 <lb></lb><arrow.to.target n="marg1527"></arrow.to.target>
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3737 <lb></lb>tion of the Reſiſtance in any Weight againſt its being raiſed in the
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3738 <lb></lb>Air, and I ſuppoſe, that I am to maintain the Affirmative, aſſert­
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3739 <lb></lb>ing that a Maſs of Lead, reduced to the Figure of a Ball, ſhall be
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3740 <lb></lb>raiſed with leſs force, then if the ſame had been made into a thinne
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3741 <lb></lb>and broad Plate, becauſe that it in this ſpacious Figure, hath a great
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3742 <lb></lb>quantity of Air to penetrate, and in that other, more compacted and
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3743 <lb></lb>contracted very little: and to demonſtrate the truth of ſuch my O­
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3744 <lb></lb>pinion, I will hang in a ſmall thred firſt the Ball or Bullet, and put
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3745 <lb></lb>that into the water, tying the thred that upholds it to one end of
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3746 <lb></lb>the Ballance that I hold in the Air, and to the other end I by degrees
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3747 <lb></lb>adde ſo much Weight, till that at laſt it brings up the Ball of Lead
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3748 <lb></lb>out of the water: to do which, ſuppoſe a Gravity of thirty Ounces
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3749 <lb></lb>ſufficeth; I afcerwards reduce the ſaid Lead into a flat and thinne
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3750 <lb></lb>Plate, the which I likewiſe put into the water, ſuſpended by three
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3751 <lb></lb>threds, which hold it parallel to the Surface of the water, and put­
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3752 <lb></lb>ting in the ſame manner, Weights to the other end, till ſuch time as
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3753 <lb></lb>the Place comes to be raiſed and drawn out of the water: I finde
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3754 <lb></lb>that thirty ſix ounces will not ſuffice to ſeperate it from the water,
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3755 <lb></lb>and raiſe it thorow the Air: and arguing from this Experiment, I af­
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3756 <lb></lb>firm, that I have fully demonſtrated the truth of my Propoſition.
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3757 <lb></lb></s><s>He re my Oponents deſires me to look down, ſhewing me a thing
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3758
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3759
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3760 <pb pagenum="462"></pb>which I had not before obſerved, to wit, that in the Aſcent of the
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3761 <lb></lb>Plate out of the water, it draws after it another Plate <emph type="italics"></emph>(if I may ſo
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3762 <lb></lb>call it)<emph.end type="italics"></emph.end> of water, which before it divides and parts from the inferiour
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parents:
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3763 <lb></lb>Surface of the Plate of Lead, is raiſed above the Levell of the other
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3764 <lb></lb>water, more than the thickneſs of the back of a Knife: Then he
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3765 <lb></lb>goeth to repeat the Experiment with the Ball, and makes me ſee,
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3766 <lb></lb>that it is but a very ſmall quantity of water, which cleaves to its
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3767 <lb></lb>compacted and contracted Figure: and then he ſubjoynes, that its
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3768 <lb></lb>no wonder, if in ſeperating the thinne and broad Plate from the
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3769 <lb></lb>water, we meet with much greater Reſiſtance, than in ſeperating the
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parents:
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3770 <lb></lb>Ball, ſince together with the Plate, we are to raiſe a great quantity of
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3771 <lb></lb>water, which occurreth not in the Ball: He telleth me moreover,
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3772 <lb></lb>how that our Queſtion is, whether the Reſiſtance of Elevation be
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parents:
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3773 <lb></lb>greater in a dilated Plate of Lead, than in a Ball, and not whether
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parents:
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3774 <lb></lb>more reſiſteth a Plate of Lead with a great quantity of water, or a
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3775 <lb></lb>Ball with a very little water: He ſheweth me in the cloſe, that the
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parents:
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3776 <lb></lb>putting the Plate and the Ball firſt into the water, to make proofe
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parents:
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3777 <lb></lb>thereby of their Reſiſtance in the Air, is beſides our caſe, which
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parents:
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3778 <lb></lb>treats of Elivating in the Air, and of things placed in the Air, and
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parents:
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3779 <lb></lb>not of the Reſiſtance that is made in the Confines of the Air and
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parents:
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3780 <lb></lb>water, and by things which are part in Air and part in water: and
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parents:
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3781 <lb></lb>laſtly, they make me feel with my hand, that when the thinne Plate
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parents:
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3782 <lb></lb>is in the Air, and free from the weight of the water, it is raiſed with
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parents:
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3783 <lb></lb>the very ſame Force that raiſeth the Ball. </s><s>Seeing, and underſtand­
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3784 <lb></lb>ing theſe things, I know not what to do, unleſs to grant my ſelf con­
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3785 <lb></lb>vinced, and to thank ſuch a Friend, for having made me to ſee that
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3786 <lb></lb>which I never till then obſerved: and, being advertiſed by this ſame
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parents:
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3787 <lb></lb>Accident, to tell my Adverſaries, that our Queſtion is, whether a
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parents:
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3788 <lb></lb>Board and a Ball of Ebony, equally go to the bottom in water, and
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parents:
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3789 <lb></lb>not a Ball of Ebony and a Board of Ebony, joyned with another
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parents:
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3790 <lb></lb>flat Body of Air: and, farthermore, that we ſpeak of ſinking, and
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parents:
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3791 <lb></lb>not ſinking to the bottom, in water, and not of that which happeneth
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parents:
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3792 <lb></lb>in the Confines of the water and Air to Bodies that be part in the
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parents:
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3793 <lb></lb>Air, and part in the water; nor much leſs do we treat of the greater
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parents:
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3794 <lb></lb>or leſſer Force requiſite in ſeperating this or that Body from the Air;
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3795 <lb></lb>not omitting to tell them, in the laſt place, that the Air doth reſiſt,
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parents:
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3796 <lb></lb>and gravitate downwards in the water, juſt ſo much as the water (if
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parents:
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3797 <lb></lb>I may ſo ſpeak) gravitates and reſiſts upwards in the Air, and that the
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3798 <lb></lb>ſame force is required to ſinke a Bladder under water, that is full of
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3799 <lb></lb>Air, as to raiſe it in the Air, being full of water, removing the con­
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3800 <lb></lb>ſideration of the weight of that Filme or Skinne, and confidering the
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3801 <lb></lb>water and the Air only. </s><s>And it is likewiſe true, that the ſame Force
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3802 <lb></lb>is required to ſink a Cup or ſuch like Veſſell under water, whilſt it is
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3803 <lb></lb>full of Air, as to raiſe it above the Superficies of the water, keeping
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3804
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3805
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3806 <pb pagenum="463"></pb>it with the mouth downwards; whilſt it is full of water, which is
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3807 <lb></lb>conſtrained in the ſame manner to follow the Cup which contains it,
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3808 <lb></lb>and to riſe above the other water into the Region of the Air, as the
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3809 <lb></lb>Air is forced to follow the ſame Veſſell under the Surface of the wa­
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3810 <lb></lb>ter, till that in this caſe the water, ſurmounting the brimme of the
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3811 <lb></lb>Cup, breaks in, driving thence the Air, and in that caſe, the ſaid
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3812 <lb></lb>brimme coming out of the water, and arriving to the Confines of the
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3813 <lb></lb>Air, the water falls down, and the Air ſub-enters to fill the cavity of
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3814 <lb></lb>the Cup: upon which enſues, that he no leſs tranſgreſſes the Arti­
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3815 <lb></lb>cles of the <emph type="italics"></emph>Convention,<emph.end type="italics"></emph.end> who produceth a Plate conjoyned with much
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3816 <lb></lb>Air, to ſee if it de ſeend to the bottom in water, then he that makes
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3817 <lb></lb>proof of the Reſiſtance againſt Elevation in Air with a Plate of Lead,
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3818 <lb></lb>joyned with a like quantity of water.</s></p><p type="margin">
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3819
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3820 <s><margin.target id="marg1527"></margin.target>An Experi­
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3821 <lb></lb>ment of the op­
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3822 <lb></lb>peration of Fi­
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3823 <lb></lb>gures, in en­
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3824 <lb></lb>creaſing or leſ­
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3825 <lb></lb>ſening of the
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3826 <lb></lb>Airs Reſiſtance
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3827 <lb></lb>of Diviſion.</s></p><p type="main">
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3828
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3829 <s>I have ſaid all that I could at preſent think of, to maintain the
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3830 <lb></lb><arrow.to.target n="marg1528"></arrow.to.target>
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3831 <lb></lb>Aſſertion I have undertook. </s><s>It remains, that I examine that which
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3832 <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>;
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3833 <lb></lb>wherein I ſhall note two things: the one that it being true as hath
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3834 <lb></lb><arrow.to.target n="marg1529"></arrow.to.target>
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3835 <lb></lb>been demonſtrated, that Figure hath nothing to do about the moving
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3836 <lb></lb>or not moving it ſelf upwards or downwards, it ſeemes that <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end>
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3837 <lb></lb>at his firſt falling upon this Sp. </s><s>culation, was of the ſame opinion, as
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3838 <lb></lb>in my opinion may be collected from the examination of his words.
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3839 <lb></lb></s><s>Tis true, indeed, that in eſſaying afterwards to render a reaſon of
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3840 <lb></lb>ſuch effect, as not having in my conceit hit upon the right, (which
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3841 <lb></lb>in the ſecond place I will examine) it ſeems that he is brought to
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3842 <lb></lb>admit the largeneſſe of Figure, to be intereſſed in this operation.
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3843 <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">
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3844
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3845 <s><margin.target id="marg1528"></margin.target><emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> opi­
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3846 <lb></lb>nion touching
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3847 <lb></lb>the Operation
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3848 <lb></lb>of Figure ex­
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3849 <lb></lb>amined.</s></p><p type="margin">
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3850
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3851 <s><margin.target id="marg1529"></margin.target><emph type="italics"></emph>Ariſtot de Cælo,<emph.end type="italics"></emph.end>
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3852 <lb></lb>Lib. 4. Cap.
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3853
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3854 66.</s></p><p type="main">
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3855
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3856 <s><emph type="italics"></emph>Figures are not the Cauſes of moving ſimply upwards or downwards,<emph.end type="italics"></emph.end>
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3857 <lb></lb><arrow.to.target n="marg1530"></arrow.to.target>
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3858 <lb></lb><emph type="italics"></emph>but of moving more ſlowly or ſwiftly, and by what means this comes to
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3859 <lb></lb>paſs, it is not difficult to ſee.<emph.end type="italics"></emph.end></s></p><p type="margin">
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3860
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3861 <s><margin.target id="marg1530"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> makes
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3862 <lb></lb>not Figure the
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3863 <lb></lb>cauſe of Motion
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3864 <lb></lb>abſolutely, but
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3865 <lb></lb>of ſwiſt or ſlow
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3866 <lb></lb>motion,</s></p><p type="main">
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3867
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3868 <s>Here firſt I note, that the terms being four, which fall under the
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3869 <lb></lb>preſent conſideration, namely, Motion, Reſt, Slowly and Swiftly:
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3870 <lb></lb><arrow.to.target n="marg1531"></arrow.to.target>
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3871 <lb></lb>And <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> naming Figures as Cauſes of Tardity and Velocity, ex­
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3872 <lb></lb>cluding them from being the Cauſe of abſolute and ſimple Motion,
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3873 <lb></lb>it ſeems neceſſary, that he exclude them on the other ſide, from being
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3874 <lb></lb>the Cauſe of Reſt, ſo that his meaning is this. </s><s>Figures are not the
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3875 <lb></lb>Cauſes of moving or not moving abſolutely, but of moving quickly
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3876 <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
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3877 <lb></lb>exclude Figures from being Cauſes of Motion, but yet not from
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3878 <lb></lb>being Cauſes of Reſt, ſo that the ſence would be to remove from
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3879 <lb></lb>Figures, there being the Cauſes of moving ſimply, but yet not there
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3880 <lb></lb>being Cauſes of Reſt, I would demand, whether we ought with
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3881 <lb></lb><emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> to underſtand, that all Figures univerſally, are, in ſome
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3882 <lb></lb>manner, the cauſes of Reſt in thoſe Bodies, which otherwiſe would
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3883 <lb></lb>move, or elſe ſome particular Figures only, as for Example, broad
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3884
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3885
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3886 <pb pagenum="464"></pb>and thinne Figures: If all indifferently, then every Body ſhall reſt:
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3887 <lb></lb>becauſe every Body hath ſome Figure, which is falſe: but if ſome
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3888 <lb></lb>particular Figures only may be in ſome manner a Cauſe of Reſt, as,
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3889 <lb></lb>for Example, the broad, then the others would be in ſome manner
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3890 <lb></lb>the Cauſes of Motion: for if from ſeeing ſome Bodies of a contracted
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3891 <lb></lb>Figure move, which after dilated into Plates reſt, may be inferred,
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3892 <lb></lb>that the Amplitude of Figure hath a part in the Cauſe of that Reſt;
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3893 <lb></lb>ſo from ſeeing ſuch like Figures reſt, which afterwards contracted
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3894 <lb></lb>move, it may with the ſame reaſon be affirmed, that the united and
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3895 <lb></lb>contracted Figure, hath a part in cauſing Motion, as the remover of
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3896 <lb></lb>that which impeded it: The which again is directly oppoſite to what
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3897 <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſaith, namely, that Figures are not the Cauſes of Motion.
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3898 <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
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3899 <lb></lb>ing Cauſes of not moving in ſome Bodies, which moulded into ano­
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3900 <lb></lb>ther Figure would move, he would have impertinently propounded
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3901 <lb></lb>in a dubitative manner, in the words immediately following, whence
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3902 <lb></lb>it is, that the large and thinne Plates of Lead or Iron, reſt upon the
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3903 <lb></lb>water, ſince the Cauſe was apparent, namely, the Amplitude of
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3904 <lb></lb>Figure. </s><s>Let us conclude, therefore, that the meaning of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>
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3905 <lb></lb>in this place is to affirm, that Figures are not the Cauſes of abſolutely
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3906 <lb></lb>moving or not moving, but only of moving ſwiftly or ſlowly: which
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3907 <lb></lb>we ought the rather to believe, in regard it is indeed a meſt true con­
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3908 <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
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3909 <lb></lb>pearing by conſequence, rather contrary at the firſt ſight, then fa­
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3910 <lb></lb>vourable to the aſſertion of the Oponents, it is neceſſary, that their
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3911 <lb></lb>Interpretation be not exactly the ſame with that, but ſuch, as being
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3912 <lb></lb>in part underſtood by ſome of them, and in part by others, was ſet
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3913 <lb></lb>down: and it may eaſily be indeed ſo, being an Interpretation
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3914 <lb></lb>conſonent to the ſence of the more famous Interpretors, which is,
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3915 <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
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3916 <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
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3917 <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
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3918 <lb></lb>Cauſes abſolutely of moving or not moving, but yet are Cauſes <emph type="italics"></emph>Se­
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3919 <lb></lb>cundum quid, viz<emph.end type="italics"></emph.end> in ſome ſort; by which means, they are called
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3920 <lb></lb>Auxiliary and Concomitant Cauſes: and this Propoſition is received
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3921 <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
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3922 <lb></lb>thus writes. <emph type="italics"></emph>There are other Cauſes concomitant, by which ſome
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3923 <lb></lb>things float, and others ſink, among which the Figures of Bodies hath
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3924 <lb></lb>the firſt place,<emph.end type="italics"></emph.end> &amp;c.</s></p><p type="margin">
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3925
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3926 <s><margin.target id="marg1531"></margin.target>Lib. 4. Cap.
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3927
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3928 61
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3929 <lb></lb>Text. </s><s>42.</s></p><p type="main">
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3930
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3931 <s>Concerning this Propoſition, I meet with many doubts and diffi­
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3932 <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
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3933 <lb></lb>ſuch a conſtruction and ſence, and the difficulties are theſe.</s></p><p type="main">
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3934
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3935 <s>Firſt in the order and diſpoſure of the words of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> the par­
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3936 <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
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3937
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3938
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3939 <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
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3940 <lb></lb>preſumption in my favour, ſeeing that the writing and the Text
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3941 <lb></lb>ſaith, Figures are not the Cauſe of moving ſimply upwards or
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3942 <lb></lb>downwards, but of quicker or ſlower Motion: and, ſaith not,
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3943 <lb></lb>Figures are not ſimply the Cauſes of moving upwards or down­
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3944 <lb></lb>wards, and when the words of a Text receive, tranſpoſed, a ſence
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3945 <lb></lb>different from that which they found, taken in the order wherein
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3946 <lb></lb>the Author diſpoſeth them, it is not convenient to inverte them.
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3947 <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,
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3948 <lb></lb>would diſpoſe the words in ſuch ſort, that they ſhould import a
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3949 <lb></lb>different, nay, a contrary ſence? </s><s>contrary, I ſay, becauſe under­
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3950 <lb></lb>ſtood as they are written; they ſay, that Figures are not the
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3951 <lb></lb>Cauſes of Motion, but inverted, they ſay, that Figures are the
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3952 <lb></lb>Cauſes of Motion, &amp;c.</s></p><p type="main">
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3953
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3954 <s>Moreover, if the intent of <emph type="italics"></emph>Aristotle<emph.end type="italics"></emph.end> had been to ſay, that Figures
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3955 <lb></lb>are not ſimply the Cauſes of moving upwards or downwards, but
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3956 <lb></lb>only Cauſes <emph type="italics"></emph>Secundum quid,<emph.end type="italics"></emph.end> he would not have adjoyned thoſe
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3957 <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
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3958 <lb></lb>ſubjoining this would have been not only ſuperfluous but falſe, for
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3959 <lb></lb>that the whole tenour of the Propoſition would import thus much.
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3960 <lb></lb></s><s>Figures are not the abſolute Cauſes of moving upwards or down­
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3961 <lb></lb>wards, but are the abſolute Cauſe of the ſwift or ſlow Motion;
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3962 <lb></lb>which is not true: becauſe the primary Cauſes of greater or leſſer
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3963 <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
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3964 <lb></lb>buted to the greater or leſſer Gravity of Moveables, compared a­
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3965 <lb></lb>mong themſelves, and to the greater or leſſer Reſiſtance of the
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3966 <lb></lb><emph type="italics"></emph>Medium&#039;s,<emph.end type="italics"></emph.end> depending on their greater or leſs Craſſitude: and theſe
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3967 <lb></lb>are inſerted by <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> as the primary Cauſes; and theſe two only
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3968 <lb></lb>are in that place nominated: and Figure comes afterwards to be
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3969 <lb></lb>conſidered, <emph type="italics"></emph>Text.<emph.end type="italics"></emph.end> 74. rather as an Inſtrumentall Cauſe of the force
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3970 <lb></lb>of the Gravity, the which divides either with the Figure, or with
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3971 <lb></lb>the <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end>; and, indeed, Figure by it ſelf without the force of
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3972 <lb></lb>Gravity or Levity, would opperate nothing.</s></p><p type="main">
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3973
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3974 <s>Iadde, that if <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> had an opinion that Figure had been in
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3975 <lb></lb>ſome ſort the Cauſe of moving or not moving, the inquiſition
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3976 <lb></lb>which he makes immediately in a doubtfull manner, whence it
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3977 <lb></lb>comes, that a Plate of Lead flotes, would have been impertinent;
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3978 <lb></lb>for if but juſt before he had ſaid, that Figure was in a certain ſort
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3979 <lb></lb>the Cauſe of moving or not moving, he needed not to call in
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3980 <lb></lb>Queſtion, by what Cauſe the Plate of Lead ſwims, and then aſcri­
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3981 <lb></lb>bing the Cauſe to its Figure; and framing a diſcourſe in this manner.
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3982 <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
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3983 <lb></lb>doubted, for what Cauſe a thin Plate of Lead goes not to the bottom;
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3984 <lb></lb>it ſhall be anſwered, that that proceeds from its Figure: a diſcourſe
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3985
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3986
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3987 <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
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3988 <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>
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3989 <lb></lb>had held, that Figure was in ſome ſort a Cauſe of Natation, he
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3990 <lb></lb>would without the leaſt Heſitation have writ; That Figure is in a
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3991 <lb></lb>certain ſort the Cauſe of Natation, and therefore the Plate of Lead
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3992 <lb></lb>in reſpect of its large and expatiated Figure ſwims; but if we take
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3993 <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
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3994 <lb></lb>deed it is true, the enſuing words come in very oppoſitely, as well in
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3995 <lb></lb>the introduction of ſwift and ſlow, as in the queſtion, which very
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3996 <lb></lb>pertinently offers it ſelf, and would ſay thus much.</s></p><p type="main">
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3997
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3998 <s>Figures are not the Cauſe of moving or not moving ſimply up­
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3999 <lb></lb>wards or downwards, but of moving more quickly or ſlowly: But if
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4000 <lb></lb>it be ſo, the Cauſe is doubtfull, whence it proceeds, that a Plate of
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4001 <lb></lb>Lead or of Iron broad and thin doth ſwim, &amp;c. </s><s>And the occaſion of
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4002 <lb></lb>the doubt is obvious, becauſe it ſeems at the firſt glance, that the
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4003 <lb></lb>Figure is the Cauſe of this Natation, ſince the ſame Lead, or a leſs
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4004 <lb></lb>quantity, but in another Figure, goes to the bottom, and we have
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4005 <lb></lb>already affirmed, that the Figure hath no ſhare in this effect.</s></p><p type="main">
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4006
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4007 <s>Laſtly, if the intent of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in this place had been to ſay,
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4008 <lb></lb>that Figures, although not abſolutely, are at leaſt in ſome meaſure
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4009 <lb></lb>the Cauſe of moving or not moving: I would have it conſidered,
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4010 <lb></lb>that he names no leſs the Motion upwards, than the other down­
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4011 <lb></lb>wards: and becauſe in exemplifying it afterwards, he produceth
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4012 <lb></lb>no other Experiments than of a Plate of Lead, and Board of Ebony,
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4013 <lb></lb>Matters that of their own Nature go to the bottom, but by vertue
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4014 <lb></lb>(as our Adverſaries ſay) of their Figure, reſt afloat; it is ſit that
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4015 <lb></lb>they ſhould produce ſome other Experiment of thoſe Matters, which
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4016 <lb></lb>by their Nature ſwims, but retained by their Figure reſt at the
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4017 <lb></lb>bottom. </s><s>But ſince this is impoſſible to be done, we conclude, that
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4018 <lb></lb><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in this place, hath not attributed any action to the Figure
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4019 <lb></lb>of ſimply moving or not moving.</s></p><p type="main">
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4020
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4021 <s>But though he hath exquiſitely Philoſophiz&#039;d, in inveſtigating
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4022 <lb></lb>the ſolution of the doubts he propoſeth, yet will I not undertake
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4023 <lb></lb>to maintain, rather various difficulties, that preſent themſelves
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4024 <lb></lb>unto me, give me occaſion of ſuſpecting that he hath not entirely
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4025 <lb></lb>diſplaid unto us, the true Cauſe of the preſent Concluſion: which
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4026 <lb></lb>difficulties I will propound one by one, ready to change opinion,
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4027 <lb></lb>when ever I am ſhewed, that the Truth is different from what I ſay;
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4028 <lb></lb>to the confeſſion whereof I am much more inclinable than to contra­
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4029 <lb></lb>diction.
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4030 <lb></lb><arrow.to.target n="marg1532"></arrow.to.target></s></p><p type="margin">
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4031
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4032 <s><margin.target id="marg1532"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> erred
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4033 <lb></lb>in affirming a
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4034 <lb></lb>Needle dimitted
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4035 <lb></lb>long wayes to
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4036 <lb></lb>ſink.</s></p><p type="main">
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4037
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4038 <s><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> having propounded the Queſtion, whence it proceeds,
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4039 <lb></lb>that broad Plates of Iron or Lead, float or ſwim; he addeth (as
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4040 <lb></lb>it were ſtrengthening the occaſion of doubting) foraſmuch as other
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4041 <lb></lb>things, leſs, and leſs grave, be they round or long, as for inſtance a
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4042
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4043
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4044 <pb pagenum="467"></pb>Needle go to the bottom. </s><s>Now I here doubt, or rather am certain,
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4045 <lb></lb>that a Needle put lightly upon the water, reſts afloat, no leſs than the
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4046 <lb></lb>thin Plates of Iron or Lead. </s><s>I cannot believe, albeit it hath been
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4047 <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
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4048 <lb></lb>Needle demitted not longwayes but endwayes, and with the Point
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4049 <lb></lb>downwards; nevertheleſs, not to leave them ſo much as this, though
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4050 <lb></lb>very weak refuge, and which in my judgement <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> himſelf
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4051 <lb></lb>would refuſe, I ſay it ought to be underſtood, that the Needle muſt
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4052 <lb></lb>be demitted, according to the Dimenſion named by <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> which
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4053 <lb></lb>is the length: becauſe, if any other Dimenſion than that which is
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4054 <lb></lb>named, might or ought to be taken, I would ſay, that even the Plates
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4055 <lb></lb>of Iron and Lead, ſink to the bottom, if they be put into the water
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4056 <lb></lb>edgewayes and not flatwayes. </s><s>But becauſe <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſaith, broad
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4057 <lb></lb>Figures go not to the bottom, it is to be underſtood, being demitted
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4058 <lb></lb>broadwayes: and, therefore, when he ſaith, long Figures as a
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4059 <lb></lb>Needle, albeit light, reſt not afloat, it ought to be underſtood of
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4060 <lb></lb>them when demitted longwayes.</s></p><p type="main">
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4061
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4062 <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
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4063 <lb></lb>mitted with the Point downwards, is to father upon him a great imper­
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4064 <lb></lb>tinency; for in this place he ſaith, that little Particles of Lead or Iron,
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4065 <lb></lb>if they be round or long as a Needle, do ſink to the bottome; ſo that by
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4066 <lb></lb>his Opinion, a Particle or ſmall Grain of Iron cannot ſwim: and if he
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4067 <lb></lb>thus believed, what a great folly would it be to ſubjoyn, that neither
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4068 <lb></lb>would a Needle demitted endwayes ſwim? </s><s>And what other is ſuch a
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4069 <lb></lb>Needle, but many ſuch like Graines accumulated one upon another? </s><s>It
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4070 <lb></lb>was too unworthy of ſuch a man to ſay, that one ſingle Grain of Iron could
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4071 <lb></lb>not ſwim, and that neither can it ſwim, though you put a hundred more
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4072 <lb></lb>upon it.<emph.end type="italics"></emph.end></s></p><p type="main">
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4073
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4074 <s>Laſtly, either <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> believed, that a Needle demitted long­
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4075 <lb></lb>wayes upon the water, would ſwim, or he believed that it would
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4076 <lb></lb>not ſwim: If he believed it would not ſwim, he might well ſpeak
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4077 <lb></lb>as indeed he did; but if he believed and knew that it would ſloat,
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4078 <lb></lb>why, together with the dubious Problem of the Natation of broad
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4079 <lb></lb>Figure, though of ponderous Matter, hath he not alſo introduced
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4080 <lb></lb>the Queſtion; whence it proceeds, that even long and ſlender Fi­
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4081 <lb></lb>gures, howbeit of Iron or Lead do ſwim? </s><s>And the rather, for that
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4082 <lb></lb>the occaſion of doubting ſeems greater in long and narrow Figures,
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4083 <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,
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4084 <lb></lb>is manifeſted.</s></p><p type="main">
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4085
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4086 <s>No leſſer an inconvenience would they faſten upon <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> who
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4087 <lb></lb>in his defence ſhould ſay, that he means a Needle pretty thick, and
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4088 <lb></lb>not a ſmall one; for take it for granted to be intended of a ſmall one
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4089
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4090
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4091 <pb pagenum="468"></pb>and it ſhall ſuffice to reply, that he believed that it would ſwim;
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4092 <lb></lb>and I will again charge him with having avoided a more wonderfull
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4093 <lb></lb>and intricate Probleme, and introduced the more facile and leſs
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4094 <lb></lb>wonderfull.</s></p><p type="main">
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4095
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4096 <s>We ſay freely therefore; that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> did hold, that only the
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4097 <lb></lb>broad Figure did ſwim, but the long and ſlender, ſuch as a Needle,
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4098 <lb></lb>not. </s><s>The which nevertheleſs is falſe, as it is alſo falſe in round
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4099 <lb></lb>Bodies: becauſe, as from what hath been predemonſtrated, may be ga­
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4100 <lb></lb>thered, little Balls of Lead and Iron, do in like manner ſwim.</s></p><p type="main">
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4101
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4102 <s>He propoſeth likewiſe another Concluſion, which likewiſe ſeems </s></p><p type="main">
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4103
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4104 <s><arrow.to.target n="marg1533"></arrow.to.target>
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4105 <lb></lb>different from the truth, and it is, That ſome things, by reaſon of
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4106 <lb></lb>their littleneſs fly in the Air, as the ſmall duſt of the Earth, and the
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4107 <lb></lb>thin leaves of beaten Gold: but in my Opinion, Experience ſhews
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4108 <lb></lb>us, that that happens not only in the Air, but alſo in the water, in
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4109 <lb></lb>which do deſcend, even thoſe Particles or Atomes of Earth, that
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4110 <lb></lb>diſtur be it, whoſe minuity is ſuch, that they are not deſervable, ſave
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4111 <lb></lb>only when they are many hundreds together. </s><s>Therefore, the duſt
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4112 <lb></lb>of the Earth, and beaten Gold, do not any way ſuſtain themſelves
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4113 <lb></lb>in the Air, but deſcend downwards, and only fly to and again in
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4114 <lb></lb>the ſame, when ſtrong Windes raiſe them, or other agitations of the
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4115 <lb></lb>Air commove them: and this alſo happens in the commotion of the
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4116 <lb></lb>water, which raiſeth its Sand from the bottom, and makes it muddy.
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4117 <lb></lb></s><s>But <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> cannot mean this impediment of the commotion, of
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4118 <lb></lb>which he makes no mention, nor names other than the lightneſs of
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4119 <lb></lb>ſuch Minutiæ or Atomes, and the Reſiſtance of the Craſſitudes of the
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4120 <lb></lb>Water and Air, by which we ſee, that he ſpeakes of a calme, and
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4121 <lb></lb>not diſturbed and agitated Air: but in that caſe, neither Gold nor
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4122 <lb></lb>Earth, be they never ſo ſmall, are ſuſtained, but ſpeedily deſcend.
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4123 <lb></lb><arrow.to.target n="marg1534"></arrow.to.target></s></p><p type="margin">
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4124
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4125 <s><margin.target id="marg1533"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> af­
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4126 <lb></lb>fir meth ſome
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4127 <lb></lb>Bodies volatile
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4128 <lb></lb>for their Minu­
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4129 <lb></lb>ity, Text. </s><s>42.</s></p><p type="margin">
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4130
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4131 <s><margin.target id="marg1534"></margin.target><emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> pla­
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4132 <lb></lb>ced the Cauſe of
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4133 <lb></lb>Natation in
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4134 <lb></lb>certain ſiery A­
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4135 <lb></lb>tomes.</s></p><p type="main">
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4136
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4137 <s>He paſſeth next to confute <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> which, by his Teſtimony
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4138 <lb></lb>would have it, that ſome Fiery Atomes, which continually aſcend
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4139 <lb></lb>through the water, do ſpring upwards, and ſuſtain thoſe grave Bodies,
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4140 <lb></lb>which are very broad, and that the narrow deſcend to the bottom, </s></p><p type="main">
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4141
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4142 <s><arrow.to.target n="marg1535"></arrow.to.target>
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4143 <lb></lb>for that but a ſmall quantity of thoſe Atomes, encounter and reſiſt
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4144 <lb></lb>them.</s></p><p type="margin">
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4145
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4146 <s><margin.target id="marg1535"></margin.target><emph type="italics"></emph>Ariſtot. </s><s>De Cœlo<emph.end type="italics"></emph.end>
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4147 <lb></lb>lib.
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4148
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4149 4. cap.
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4150
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4151 6.
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4152 <lb></lb>text. </s><s>43.</s></p><p type="main">
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4153
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4154 <s>I ſay, <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> confutes this poſition, ſaying, that that ſhould
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4155 <lb></lb><arrow.to.target n="marg1536"></arrow.to.target>
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4156 <lb></lb>much more occurre in the Air, as the ſame <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> inſtances a­
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4157 <lb></lb>gainſt himſelf, but after he had moved the objection, he ſlightly re­
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4158 <lb></lb>ſolves it, with ſaying, that thoſe Corpuſcles which aſcend in the Air,
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4159 <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
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4160 <lb></lb><arrow.to.target n="marg1537"></arrow.to.target>
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4161 <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
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4162 <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
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4163 <lb></lb>ſaith, that were it true, that the calid aſcending Atomes, ſhould
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4164 <lb></lb>ſuſtain Bodies grave, but very broad, it would much more be done
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4165 <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>
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4166
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4167
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4168 <pb pagenum="469"></pb>the ſaid calid Atomes aſcend with much greater Force and Velocity
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4169 <lb></lb>through the Air, than through the water. </s><s>And if this be ſo, as I veri­
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4170 <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
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4171 <lb></lb>give occaſion of ſuſpecting, that he may poſſibly be deceived in more
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4172 <lb></lb>than one particular: Firſt, becauſe thoſe calid Atomes, (whether
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4173 <lb></lb>they be Fiery Corpuſcles, or whether they be Exhalations, or in
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4174 <lb></lb>ſhort, whatever other matter they be, that aſcends upwards through
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4175 <lb></lb>the Air) cannot be believed to mount faſter through Air, than
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4176 <lb></lb>through water: but rather on the contrary, they peradventure move
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4177 <lb></lb>more impetuouſly through the water, than through the Air, as hath
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4178 <lb></lb>been in part demonſtrated above. </s><s>And here I cannot finde the rea­
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4179 <lb></lb>ſon, why <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſeeing, that the deſeending Motion of the ſame
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4180 <lb></lb>Moveable, is more ſwift in Air, than in water, hath not advertiſed
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4181 <lb></lb>us, that from the contrary Motion, the contrary ſhould neceſſarily
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4182 <lb></lb>follow; to wit, that it is more ſwift in the water, than in the Air: for
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4183 <lb></lb>ſince that the Moveable which deſcendeth, moves ſwifter through
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4184 <lb></lb>the Air, than through the water, if we ſhould ſuppoſe its Gravity
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4185 <lb></lb>gradually to diminiſh, it would firſt become ſuch, that deſcending
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4186 <lb></lb>ſwiftly through the Air, it would deſcend but ſlowly through the
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4187 <lb></lb>water: and then again, it might be ſuch, that deſcending in the
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4188 <lb></lb>Air, it ſhould aſcend in the water: and being made yet leſs grave,
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4189 <lb></lb>it ſhall aſcend ſwiftly through the water, and yet deſcend likewiſe
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4190 <lb></lb>through the Air: and in ſhort, before it can begin to aſcend, though
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4191 <lb></lb>but ſlowly through the Air, it ſhall aſcend ſwiftly through the water:
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4192 <lb></lb>how then is it true, that aſcending Moveables move ſwifter through
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4193 <lb></lb>the Air, than through the water?</s></p><p type="margin">
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4194
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4195 <s><margin.target id="marg1536"></margin.target><emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> con­
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4196 <lb></lb>futed by <emph type="italics"></emph>Ari­
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4197 <lb></lb>ſtotle,<emph.end type="italics"></emph.end> text 43.</s></p><p type="margin">
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4198
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4199 <s><margin.target id="marg1537"></margin.target><emph type="italics"></emph>Ariſtotles<emph.end type="italics"></emph.end> con­
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4200 <lb></lb>futation of <emph type="italics"></emph>De­
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4201 <lb></lb>mocritus<emph.end type="italics"></emph.end> refuted
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4202 <lb></lb>by the Author.</s></p><p type="main">
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4203
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4204 <s>That which hath made <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> believe, the Motion of Aſcent to be
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4205 <lb></lb>ſwifter in Air, than in water, was firſt, the having referred the
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4206 <lb></lb>Cauſes of ſlow and quick, as well in the Motion of Aſcent, as of
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4207 <lb></lb>Deſcent, only to the diverſity of the Figures of the Moveable, and to
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4208 <lb></lb>the more or leſs Reſiſtance of the greater or leſſer Craſſitude, or Ra­
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4209 <lb></lb>rity of the <emph type="italics"></emph>Medium<emph.end type="italics"></emph.end>; not regarding the compariſon of the Exceſſes
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4210 <lb></lb>of the Gravities of the Moveables, and of the <emph type="italics"></emph>Mediums<emph.end type="italics"></emph.end>: the which
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4211 <lb></lb>notwithſtanding, is the moſt principal point in this affair: for if the
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4212 <lb></lb>augmentation and diminution of the Tardity or Velocity, ſhould
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4213 <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
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4214 <lb></lb>that deſcends in Air, would deſcend in water: becauſe whatever
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4215 <lb></lb>difference is found between the Craſſitude of the water, and that of
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4216 <lb></lb>the Air, may well be found between the Velocity of the ſame Move­
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4217 <lb></lb>able in the Air, and ſome other Velocity: and this ſhould be its
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4218 <lb></lb>proper Velocity in the water, which is abſolutely falſe. </s><s>The other
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4219 <lb></lb>occaſion is, that he did believe, that like as there is a poſitive and in­
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4220 <lb></lb>trinſecall Quality, whereby Elementary Bodies have a propenſion
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4221 <lb></lb>of moving towards the Centre of the Earth, ſo there is another like­
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4222
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4223
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4224 <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
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4225 <lb></lb><arrow.to.target n="marg1538"></arrow.to.target>
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4226 <lb></lb>flying the Centre, and moving upwards: by Vertue of which in­
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4227 <lb></lb>trinſe call Principle, called by him Levity, the Moveables which have
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4228 <lb></lb>that ſame Motion more eaſily penetrate the more ſubtle <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end>
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4229 <lb></lb>than the more denſe: but ſuch a Propoſition appears likewiſe un­
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4230 <lb></lb>certain, as I have above hinted in part, and as with Reaſons and
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4231 <lb></lb>Experiments, I could demonſtrate, did not the preſent Argument im­
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4232 <lb></lb>portune me, or could I diſpatch it in few words.</s></p><p type="margin">
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4233
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4234 <s><margin.target id="marg1538"></margin.target>Lib. 4. Cap.
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4235
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4236 5.</s></p><p type="main">
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4237
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4238 <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
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4239 <lb></lb>he ſaith, that if the Fiery aſcending Atomes ſhould ſuſtain Bodies
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4240 <lb></lb>grave, but of a diſtended Figure, it would be more obſervable in
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4241 <lb></lb>the Air than in the water, becauſe ſuch Corpuſcles move ſwifter in
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4242 <lb></lb>that, than in this, is not good; yea the contrary would evene, for
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4243 <lb></lb>that they aſcend more ſlowly through the Air: and, beſides their
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4244 <lb></lb>moving ſlowly, they aſcend, not united together, as in the water,
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4245 <lb></lb>but diſcontinue, and, as we ſay, ſcatter: And, therefore, as
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4246 <lb></lb><emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> well replyes, reſolving the inſtance they make not their
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4247 <lb></lb>puſh or <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> conjunctly.</s></p><p type="main">
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4248
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4249 <s><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> in the ſecond place, deceives himſelf, whilſt he will
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4250 <lb></lb>have the ſaid grave Bodies to be more eaſily ſuſtained by the ſaid
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4251 <lb></lb>Fiery aſcending Atomes in the Air than in the Water: not obſerv­
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4252 <lb></lb>ing, that the ſaid Bodies are much more grave in that, than in this,
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4253 <lb></lb>and that ſuch a Body weighs ten pounds in the Air, which will not
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4254 <lb></lb>in the water weigh 1/2 an ounce; how can it then be more eaſily
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4255 <lb></lb>ſuſtained in the Air, than in the Water?</s></p><p type="main">
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4256
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4257 <s>Let us conclude, therefore, that <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> hath in this particular
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4258 <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>
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4259 <lb></lb><arrow.to.target n="marg1539"></arrow.to.target>
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4260 <lb></lb><emph type="italics"></emph>mocritus<emph.end type="italics"></emph.end> hath reaſon&#039;d rightly, but I rather ſay, that there is a ma­
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4261 <lb></lb>nifeſt Experiment that overthrows his Reaſon, and this it is, That
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4262 <lb></lb>if it were true, that calid aſcending Atomes ſhould uphold a Body,
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4263 <lb></lb>that if they did not hinder, would go to the bottom, it would follow,
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4264 <lb></lb>that we may find a Matter very little ſuperiour in Gravity to the
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4265 <lb></lb>water, the which being reduced into a Ball, or other contracted
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4266 <lb></lb>Figure, ſhould go to the bottom, as encountring but few Fiery A­
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4267 <lb></lb>tomes; and which being diſtended afterwards into a dilated and
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4268 <lb></lb>thin Plate, ſhould come to be thruſt upwards by the impulſion of a
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4269 <lb></lb>great Multitude of thoſe Corpuſcles, and at laſt carried to the very
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4270 <lb></lb>Surface of the water: which wee ſee not to happen; Experience
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4271 <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
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4272 <lb></lb>hardly, and with very great leaſure goeth to the bottom, will reſt
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4273 <lb></lb>there, and will alſo deſcend thither, being reduced into whatſoever
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4274 <lb></lb>other diſtended Figure. </s><s>We muſt needs ſay then, either that in the
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4275 <lb></lb>water, there are no ſuch aſcending Fiery Atoms, or if that ſuch there
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4276 <lb></lb>be, that they are not able to raiſe and lift up any Plate of a Matter,
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4277
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4278
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4279 <pb pagenum="471"></pb>that without them would go to the bottom: Of which two Pofitions,
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4280 <lb></lb>I eſteem the ſecond to be true, underſtanding it of water, conſtituted
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4281 <lb></lb>in its naturall Coldneſs. </s><s>But if we take a Veſſel of Glaſs, or Braſs,
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4282 <lb></lb>or any other hard matter, full of cold water, within which is put a
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4283 <lb></lb>Solid of a flat or concave Figure, but that in Gravity exceeds the
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4284 <lb></lb>water ſo little, that it goes ſlowly to the bottom; I ſay, that putting
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4285 <lb></lb>ſome burning Coals under the ſaid Veſſel, as ſoon as the new Fiery
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4286 <lb></lb>Atomes ſhall have penetrated the ſubſtance of the Veſſel, they ſhall
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4287 <lb></lb>without doubt, aſcend through that of the water, and thruſting a­
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4288 <lb></lb>gainſt the foreſaid Solid, they ſhall drive it to the Superficies, and
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4289 <lb></lb>there detain it, as long as the incurſions of the ſaid Corpuſcles ſhall
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4290 <lb></lb>laſt, which ceaſing after the removall of the Fire, the Solid being a­
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4291 <lb></lb>bandoned by its ſupporters, ſhall return to the bottom.</s></p><p type="margin">
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4292
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4293 <s><margin.target id="marg1539"></margin.target><emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> con­
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4294 <lb></lb>futed by the
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4295 <lb></lb>Authour.</s></p><p type="main">
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4296
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4297 <s>But <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> notes, that this Caufe only takes place when we
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4298 <lb></lb>treat of raiſing and ſuſtaining of Plates of Matters, but very little
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4299 <lb></lb>heavier than the water, or extreamly thin: but in Matters very
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4300 <lb></lb>grave, and of ſome thickneſs, as Plates of Lead or other Mettal, that
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4301 <lb></lb>ſame Effect wholly ceaſeth: In Teſtimony of which, let&#039;s obſerve
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4302 <lb></lb>that ſuch Plates, being raiſed by the Fiery Atomes, aſcend through
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4303 <lb></lb>all the depth of the water, and ſtop at the Confines of the Air, ſtill
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4304 <lb></lb>ſtaying under water: but the Plates of the Opponents ſtay not, but
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4305 <lb></lb>only when they have their upper Superficies dry, nor is there any
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4306 <lb></lb>means to be uſed, that when they are within the water, they may
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4307 <lb></lb>not ſink to the bottom. </s><s>The cauſe, therefore, of the Supernatation
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4308 <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
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4309 <lb></lb>natation of the things of which we ſpeak is another. </s><s>But, returning
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4310 <lb></lb><arrow.to.target n="marg1540"></arrow.to.target>
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4311 <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>
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4312 <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
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4313 <lb></lb>the Objection which he maketh againſt him, and oppoſed him with
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4314 <lb></lb>ſaying, that if the calid aſcendent Corpuſcles were thoſe that raiſed
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4315 <lb></lb>the thin Plate, much more then would ſuch a Solid be raiſed and
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4316 <lb></lb>born upwards through the Air, it ſheweth that the deſire in <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end>
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4317 <lb></lb>to detect <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> was predominate over the exquiſiteneſs of Solid
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4318 <lb></lb>Philoſophizing: which deſire of his he hath diſcovered in other oc­
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4319 <lb></lb>caſions, and that we may not digreſs too far from this place, in the
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4320 <lb></lb>Text precedent to this Chapter which we have in hand; where he
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4321 <lb></lb><arrow.to.target n="marg1541"></arrow.to.target>
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4322 <lb></lb>attempts to confute the ſame <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> for that he, not content­
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4323 <lb></lb>ing himſelf with names only, had eſſayed more particularly to de­
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4324 <lb></lb>clare what things Gravity and Levity were; that is, the Cauſes of
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4325 <lb></lb>deſcending and aſcending, (and had introduced Repletion and Va­
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4326 <lb></lb>cuity) aſcribing this to Fire, by which it moves upwards, and that to
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4327 <lb></lb>the Earth, by which it deſcends; afterwards attributing to the
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4328 <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>
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4329 <lb></lb>deſiring a poſitive Cauſe, even of aſcending Motion, and not as <emph type="italics"></emph>Plato,<emph.end type="italics"></emph.end>
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4330
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4331
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4332 <pb pagenum="472"></pb>or theſe others, a ſimple negation, or privation, ſuch as Vacuity
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4333 <lb></lb><arrow.to.target n="marg1542"></arrow.to.target>
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4334 <lb></lb>would be in reference to Repletion, argueth againſt <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> and
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4335 <lb></lb>ſaith: If it be true, as you ſuppoſe, then there ſhall be a great Maſs
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4336 <lb></lb>of water, which ſhall have more of Fire, than a ſmall Maſs of Air,
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4337 <lb></lb>and a great Maſs of Air, which ſhall have more of Earth than a lit­
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4338 <lb></lb>tle Maſs of water, whereby it would enſue, that a great Maſs of Air,
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4339 <lb></lb>ſhould come more ſwiftly downwards, than a little quantity of
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4340 <lb></lb>water: But that is never in any caſe ſoever: Therefore <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end>
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4341 <lb></lb>diſcourſeth erroneouſly.</s></p><p type="margin">
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4342
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4343 <s><margin.target id="marg1540"></margin.target><emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſhews
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4344 <lb></lb>his deſire of
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4345 <lb></lb>finding <emph type="italics"></emph>Demo­
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4346 <lb></lb>critus<emph.end type="italics"></emph.end> in an Er­
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4347 <lb></lb>ror, to exceed
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4348 <lb></lb>that of diſco­
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4349 <lb></lb>veting Truth.</s></p><p type="margin">
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4350
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4351
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4352 <s><margin.target id="marg1541"></margin.target>Cap.
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4353
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4354
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4355 5. Text 41.</s></p><p type="margin">
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4356
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4357 <s><margin.target id="marg1542"></margin.target>Id. </s><s>ibid.</s></p><p type="main">
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4358
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4359 <s>But in my opinion, the Doctrine of <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> is not by this alle­
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4360 <lb></lb>gation overthrown, but if I erre not, the manner of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> deduction
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4361 <lb></lb>either concludes not, or if it do conclude any thing, it may with e­
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4362 <lb></lb>quall force be reſtored againſt himſelf. <emph type="italics"></emph>Democritus<emph.end type="italics"></emph.end> will grant to
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4363 <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
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4364 <lb></lb>tains more Earth, than a ſmall quantity of water, but yet will deny,
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4365 <lb></lb>that ſuch a Maſs of Air, ſhall go faſter downwards than a little water,
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4366 <lb></lb>and that for many reaſons. </s><s>Firſt, becauſe if the greater quantity
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4367 <lb></lb>of Earth, contained in the great Maſs of Air, ought to cauſe a greater
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4368 <lb></lb>Velocity than a leſs quantity of Earth, contained in a little quantity
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4369 <lb></lb>of water, it would be neceſſary, firſt, that it were true, that a
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4370 <lb></lb>greater Maſs of pure Earth, ſhould move more ſwiftly than a leſs:
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4371 <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:
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4372 <lb></lb>becauſe not the greater abſolute, but the greater ſpecificall Gravity,
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4373 <lb></lb><arrow.to.target n="marg1543"></arrow.to.target>
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4374 <lb></lb>is the cauſe of greater Velocity: nor doth a Ball of Wood, weigh­
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4375 <lb></lb>ing ten pounds, deſcend more ſwiftly than one weighing ten Ounces,
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4376 <lb></lb>and that is of the ſame Matter: but indeed a Bullet of Lead of four
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4377 <lb></lb>Ounces, deſcendeth more ſwiftly than a Ball of Wood of twenty
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4378 <lb></lb>Pounds: becauſe the Lead is more grave <emph type="italics"></emph>in ſpecie<emph.end type="italics"></emph.end> than the Wood.
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4379 <lb></lb></s><s>Therefore, its not neceſſary, that a great Maſs of Air, by reaſon of
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4380 <lb></lb>the much Earth contained in it, do deſcend more ſwiftly than a little
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4381 <lb></lb><arrow.to.target n="marg1544"></arrow.to.target>
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4382 <lb></lb>Maſs of water, but on the contrary, any whatſoever Maſs of water,
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4383 <lb></lb>ſhall move more ſwiftly than any other of Air, by reaſon the partici­
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4384 <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
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4385 <lb></lb>Air. </s><s>Let us note, in the ſecond place, how that in multiplying the
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4386 <lb></lb>Maſs of the Air, we not only multiply that which is therein of terrene,
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4387 <lb></lb>but its Fire alſo: whence the Cauſe of aſcending, no leſs encreaſeth,
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4388 <lb></lb>by vertue of the Fire, than that of deſcending on the account of its
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4389 <lb></lb>multiplied Earth. </s><s>It was requiſite in increaſing the greatneſs of the
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4390 <lb></lb>Air, to multiply that which it hath of terrene only, leaving its Fire
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4391 <lb></lb>in its firſt ſtate, for then the terrene parts of the augmented Air,
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4392 <lb></lb>overcoming the terrene parts of the ſmall quantity of water, it might
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4393 <lb></lb>with more probability have been pretended, that the great quanti­
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4394 <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
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4395 <lb></lb>quantity of water.</s></p>
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4396
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4397
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4398 <pb pagenum="467"></pb><p type="margin">
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4399
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4400 <s><margin.target id="marg1543"></margin.target>The greater
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4401 <lb></lb>Specificall, not
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4402 <lb></lb>the greater ab­
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4403 <lb></lb>ſolute Gravity,
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4404 <lb></lb>is the Cauſe of
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4405 <lb></lb>Velocity.</s></p><p type="margin">
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4406
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4407 <s><margin.target id="marg1544"></margin.target>Any Maſs of
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4408 <lb></lb>water ſhal move
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4409 <lb></lb>more ſwiftly,
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4410 <lb></lb>than any of Air,
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4411 <lb></lb>and why.</s></p><p type="main">
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4412
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4413 <s>Therefore, the Fallacy lyes more in the Diſcourſe of <emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> than
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4414 <lb></lb>in that of <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> who with ſeverall other Reaſons might oppoſe
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4415 <lb></lb><emph type="italics"></emph>Ariſtotle,<emph.end type="italics"></emph.end> and alledge; If it be true, that the extreame Elements be
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4416 <lb></lb>one ſimply grave, and the other ſimply light, and that the mean
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4417 <lb></lb>Elements participate of the one, and of the other Nature; but the
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4418 <lb></lb>Air more of Levity, and the water more of Gravity, then there ſhall
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4419 <lb></lb>be a great Maſs of Air, whoſe Gravity ſhall exceed the Gravity of a
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4420 <lb></lb>little quantity of water; and therefore ſuch a Maſs of Air ſhall de­
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4421 <lb></lb>ſcend more ſwiftly than that little water: But that is never ſeen to
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4422 <lb></lb>occurr: Therefore its not true, that the mean Elements do partici­
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4423 <lb></lb>pate of the one, and the other quality. </s><s>This argument is fallacious,
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4424 <lb></lb>no leſs than the other againſt <emph type="italics"></emph>Democritus.<emph.end type="italics"></emph.end></s></p><p type="main">
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4425
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4426 <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>
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4427 <lb></lb>were true, it would follow, that a great Maſs of Air ſhould move
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4428 <lb></lb>more ſwiftly than a ſmall Maſs of water, and afterwards ſubjoyned,
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4429 <lb></lb>that that is never ſeen in any Caſe: methinks others may become de­
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4430 <lb></lb>ſirous to know of him in what place this ſhould evene, which he de­
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4431 <lb></lb>duceth againſt <emph type="italics"></emph>Democritus,<emph.end type="italics"></emph.end> and what Experiment teacheth us, that
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4432 <lb></lb>it never falls out ſo. </s><s>To ſuppoſe to ſee it in the Element of water,
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4433 <lb></lb>or in that of the Air is vain, becauſe neither doth water through
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4434 <lb></lb>water, nor Air through Air move, nor would they ever by any
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4435 <lb></lb>whatever participation others aſſign them, of Earth or of Fire: the
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4436 <lb></lb>Earth, in that it is not a Body fluid, and yielding to the mobility of
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4437 <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
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4438 <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
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4439 <lb></lb>is none, and were there, nothing would move in it: there remaine
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4440 <lb></lb>the Region of Fire, but being ſo far diſtant from us, what Experi­
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4441 <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
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4442 <lb></lb>ſhould as of a thing moſt obvious to ſence, affirm what he produ­
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4443 <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,
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4444 <lb></lb>is moved no ſwifter than a little one of water? </s><s>But I will dwell no
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4445 <lb></lb>longer upon this matter, whereon I have ſpoke ſufficiently: but
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4446 <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
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4447 <lb></lb>goes about to render the true reaſon, how it comes to paſs, that the
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4448 <lb></lb>thin Plates of Iron or Lead do ſwim on the water; and, moreover,
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4449 <lb></lb>that Gold it ſelf being beaten into thin Leaves, not only ſwims in
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4450 <lb></lb>water, but flyeth too and again in the Air. </s><s>He ſuppoſeth that of
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4451 <lb></lb><arrow.to.target n="marg1545"></arrow.to.target>
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4452 <lb></lb>Continualls, ſome are eaſily diviſible, others not: and that of the
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4453 <lb></lb>eaſily diviſible, ſome are more ſo, and ſome leſs: and theſe he
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4454 <lb></lb>affirms we ſhould eſteem the Cauſes. </s><s>He addes that that is eaſily
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4455 <lb></lb>diviſible, which is well terminated, and the more the more diviſible,
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4456 <lb></lb>and that the Air is more ſo, than the water, and the water than the
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4457 <lb></lb>Earth. </s><s>And, laſtly, he ſuppoſeth that in each kind, the leſſe quan­
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4458 <lb></lb>tity is eaſlyer divided and broken than the greater.</s></p>
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4459
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4460
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4461 <pb pagenum="474"></pb><p type="margin">
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4462
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4463 <s><margin.target id="marg1545"></margin.target><emph type="italics"></emph>De Cœlo<emph.end type="italics"></emph.end> l. </s><s>4. c.
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4464 <lb></lb></s><s>6. t. </s><s>44.</s></p><p type="main">
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4465
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4466 <s>Here I note, that the Concluſions of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> in generall are all
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4467 <lb></lb>true, but methinks, that he applyeth them to particulars, in which
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4468 <lb></lb>they have no place, as indeed they have in others, as for Example,
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4469 <lb></lb>Wax is more eaſily diviſible than Lead, and Lead than Silver, in­
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4470 <lb></lb>aſmuch as Wax receives all the terms more eaſiler than Lead, and
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4471 <lb></lb>Lead than Silver. </s><s>Its true, moreover, that a little quantity of Sil­
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4472 <lb></lb>ver is eaſlier divided than a great Maſs: and all theſe Propoſitions
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4473 <lb></lb>are true, becauſe true it is, that in Silver, Lead and Wax, there
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4474 <lb></lb>is ſimply a Reſiſtance againſt Diviſion, and where there is the abſo­
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4475 <lb></lb>lute, there is alſo the reſpective. </s><s>But if as well in water as in Air,
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4476 <lb></lb>there be no Renitence againſt ſimple Diviſion, how can we ſay, that
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4477 <lb></lb>the water is eaſlier divided than the Air? </s><s>We know not how to ex­
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4478 <lb></lb>tricate our ſelves from the Equivocation: whereupon I return to
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4479 <lb></lb>anſwer, that Reſiſtance of abſolute Diviſion is one thing, and Re­
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4480 <lb></lb>ſiſtance of Diviſion made with ſuch and ſuch Velocity is another.
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4481 <lb></lb></s><s>But to produce Reſt, and to abate the Motion, the Reſiſtance of
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4482 <lb></lb>abſolute Diviſion is neceſſary; and the Reſiſtance of ſpeedy Di­
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4483 <lb></lb>viſion, cauſeth not Reſt, but ſlowneſs of Motion. </s><s>But that as well
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4484 <lb></lb>in the Air, as in water, there is no Reſiſtance of ſimple Diviſion, is
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4485 <lb></lb>manifeſt, for that there is not found any Solid Body which divides
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4486 <lb></lb>not the Air, and alſo the water: and that beaten Gold, or ſmall
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4487 <lb></lb>duſt, are not able to ſuperate the Reſiſtance of the Air, is contrary
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4488 <lb></lb>to that which Experience ſhews us, for we ſee Gold and Duſt to go
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4489 <lb></lb>waving to and again in the Air, and at laſt to deſcend down­
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4490 <lb></lb>wards, and to do the ſame in the water, if it be put therein, and ſe­
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4491 <lb></lb>parated from the Air. </s><s>And, becauſe, as I ſay, neither the water,
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4492 <lb></lb>nor the Air do reſiſt ſimple Diviſion, it cannot be ſaid, that the water
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4493 <lb></lb>reſiſts more than the Air. </s><s>Nor let any object unto me, the Exam­
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4494 <lb></lb>ple of moſt light Bodies, as a Feather, or a little of the pith of El­
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4495 <lb></lb>der, or water-reed that divides the Air and not the water, and from
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4496 <lb></lb>this infer, that the Ait is eaſlier diviſible than the water; for I ſay
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4497 <lb></lb>unto them, that if they do well obſerve, they ſhall ſee the ſame
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4498 <lb></lb><arrow.to.target n="marg1546"></arrow.to.target>
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4499 <lb></lb>Body likewiſe divide the Continuity of the water, and ſubmerge in
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4500 <lb></lb>part, and in ſuch a part, as that ſo much water in Maſs would weigh
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4501 <lb></lb>as much as the whole Solid. </s><s>And if they ſhal yet perſiſt in their doubt,
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4502 <lb></lb>that ſuch a Solid ſinks not through inability to divide the water, I will
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4503 <lb></lb>return them this reply, that if they put it under water, and then let it
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4504 <lb></lb>go, they ſhall ſee it divide the water, and preſently aſcend with no leſs
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4505 <lb></lb>celerity, than that with which it divided the Air in deſcending: ſo that
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4506 <lb></lb>to ſay that this Solid aſcends in the Air, but that coming to the water,
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4507 <lb></lb>it ceaſeth its Motion, and therefore the water is more difficult to be
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4508 <lb></lb>divided, concludes nothing: for I, on the contrary, will propoſe them
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4509 <lb></lb>a piece of Wood, or of Wax, which riſeth from the bottom of the
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4510 <lb></lb>water, and eaſily divides its Reſiſtance, which afterwards being arri­
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4511
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4512
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4513 <pb pagenum="475"></pb>ved at the Air, ſtayeth there, and hardly toucheth it; whence I may
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4514 <lb></lb>aswell ſay, that the water is more eaſier divided than the Air</s></p><p type="margin">
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4515
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4516 <s><margin.target id="marg1546"></margin.target><emph type="italics"></emph>Archimed. </s><s>De
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4517 <lb></lb>Inſident, humi<emph.end type="italics"></emph.end> lib.
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4518 <lb></lb></s><s>2. prop.
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4519
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4520 1.</s></p><p type="main">
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4521
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4522 <s>I will not on this occaſion forbear to give warning of another fal­
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4523 <lb></lb>lacy of theſe perſons, who attribute the reaſon of ſinking or ſwimming
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4524 <lb></lb>to the greater or leſſe Reſiſtance of the Craſſitude of the water againſt
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4525 <lb></lb>Diviſion, making uſe of the example of an Egg, which in ſweet water
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4526 <lb></lb>goeth to the bottom, but in ſalt water ſwims; and alledging for the
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4527 <lb></lb>cauſe thereof, the faint Reſiſtance of freſh water againſt Diviſion, and
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4528 <lb></lb>the ſtrong Reſiſtance of ſalt water But if I miſtake not, from the ſame
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4529 <lb></lb>Experiment, we may aswell deduce the quite contrary; namely, that
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4530 <lb></lb>the freſh water is more denſe, and the ſalt more tenuous and ſubtle,
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4531 <lb></lb>ſince an Egg from the bottom of ſalt water ſpeedily aſcends to the
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4532 <lb></lb>top, and divides its Reſiſtance, which it cannot do in the freſh, in whoſe
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4533 <lb></lb>bottom it ſtays, being unable to riſe upwards. </s><s>Into ſuch like perplex­
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4534 <lb></lb>ities, do falſe Principles Lead men: but he that rightly Philoſophating,
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4535 <lb></lb>ſhall acknowledge the exceſſes of the Gravities of the Moveables and
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4536 <lb></lb>of the Mediums, to be the Cauſes of thoſe effects, will ſay, that the
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4537 <lb></lb>Egg ſinks to the bottom in freſh water, for that it is more grave than
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4538 <lb></lb>it, and ſwimeth in the ſalt, for that its leſs grave than it: and ſhall
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4539 <lb></lb>without any abſurdity, very ſolidly eſtabliſh his Concluſions.</s></p><p type="main">
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4540
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4541 <s>Therefore the reaſon totally ceaſeth, that <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> ſubjoyns in the
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4542 <lb></lb><arrow.to.target n="marg1547"></arrow.to.target>
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4543 <lb></lb>Text ſaying; The things, therefore, which have great breadth remain
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4544 <lb></lb>above, becauſe they comprehend much, and that which is greater,
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4545 <lb></lb>is not eaſily divided. </s><s>Such diſcourſing ceaſeth, I ſay, becauſe its not
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4546 <lb></lb>true, that there is in water or in Air any Reſiſtance of Diviſion; be­
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4547 <lb></lb>ſides that the Plate of Lead when it ſtays, hath already divided and
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4548 <lb></lb>penetrated the Craſſitude of the water, and profounded it ſelf ten or
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4549 <lb></lb>twelve times more than its own thickneſs: beſides that ſuch Reſiſtance
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4550 <lb></lb>of Diviſion, were it ſuppoſed to be in the water, could not rationally
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4551 <lb></lb>be affirmed to be more in its ſuperiour parts than in the middle, and
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4552 <lb></lb>lower: but if there were any difference, the inferiour ſhould be the
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4553 <lb></lb>more denſe, ſo that the Plate would be no leſs unable to penetrate
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4554 <lb></lb>the lower, than the ſuperiour parts of the water; nevertheleſs we ſee
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4555 <lb></lb>that no ſooner do we wet the ſuperious Superficies of the Board or
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4556 <lb></lb>thin Piece of Wood, but it precipitatly, and without any retenſion,
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4557 <lb></lb>deſcends to the bottom.</s></p><p type="margin">
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4558
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4559 <s><margin.target id="marg1547"></margin.target>Text 45.</s></p><p type="main">
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4560
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4561 <s>I believe not after all this, that any (thinking perhaps thereby to
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4562 <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
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4563 <lb></lb>ſiſts more than the little, the ſaid Board being put lower deſcendeth,
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4564 <lb></lb>becauſe there remaineth a leſs Maſs of water to be divided by it: be­
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4565 <lb></lb>cauſe if after the having ſeen the ſame Board ſwim in four Inches of
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4566 <lb></lb>water, and alſo after that in the ſame to ſink, he ſhall try the ſame
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4567 <lb></lb>Experiment upon a profundity of ten or twenty fathom water, he
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4568 <lb></lb>ſhall ſee the very ſelf ſame effect. </s><s>And here I will take occaſion to
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4569
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4570
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4571 <pb pagenum="476"></pb>remember, for the removall of an Error that is too common; That
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4572 <lb></lb>that Ship or other whatſoever Body, that on the depth of an hundred
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4573 <lb></lb>or a thouſand fathom, ſwims with ſubmerging only ſix fathom of its
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4574 <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
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4575 <lb></lb>ſwim in the ſame manner in water, that hath but ſix fathom and half
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4576 <lb></lb><arrow.to.target n="marg1548"></arrow.to.target>
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4577 <lb></lb>an Inch of depth. </s><s>Nor do I on the other ſide, think that it can be
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4578 <lb></lb>ſaid, that the ſuperiour parts of the water are the more denſe, al­
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4579 <lb></lb>though a moſt grave Authour hath eſteemed the ſuperiour water in
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4580 <lb></lb>the Sea to be ſo, grounding his opinion upon its being more ſalt, than
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4581 <lb></lb>that at the bottom: but I doubt the Experiment, whether hitherto
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4582 <lb></lb>in taking the water from the bottom, the Obſervatour did not light
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4583 <lb></lb>upon ſome ſpring of freſh water there ſpouting up: but we plainly
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4584 <lb></lb>ſee on the contrary, the freſh Waters of Rivers to dilate themſelves
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4585 <lb></lb>for ſome miles beyond their place of meeting with the ſalt water of
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4586 <lb></lb>the Sea, without deſcending in it, or mixing with it, unleſs by the
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4587 <lb></lb>intervention of ſome commotion or turbulency of the Windes.</s></p><p type="margin">
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4588
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4589 <s><margin.target id="marg1548"></margin.target>A Ship that
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4590 <lb></lb>in 100 Fathome
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4591 <lb></lb>water draweth
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4592 <lb></lb>6 Fathome, ſhall
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4593 <lb></lb>float in 6 Fa­
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4594 <lb></lb>thome and 1/2 an
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4595 <lb></lb>Inch of depth.</s></p><p type="main">
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4596
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4597 <s>But returning to <emph type="italics"></emph>Aristotle,<emph.end type="italics"></emph.end> I ſay, that the breadth of Figure hath
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4598 <lb></lb>nothing to do in this buſineſs more or leſs, becauſe the ſaid Plate of
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4599 <lb></lb><arrow.to.target n="marg1549"></arrow.to.target>
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4600 <lb></lb>Lead, or other Matter, cut into long Slices, ſwim neither more nor
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4601 <lb></lb>leſs; and the ſame ſhall the Slices do, being cut anew into little
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4602 <lb></lb>pieces, becauſe its not the breadth but the thickneſs that operates in
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4603 <lb></lb>this buſineſs. </s><s>I ſay farther, that in caſe it were really true, that the
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4604 <lb></lb><arrow.to.target n="marg1550"></arrow.to.target>
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4605 <lb></lb>Renitence to Diviſion were the proper Cauſe of ſwimming, the Fi­
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4606 <lb></lb>gures more narrow and ſhort, would much better ſwim than the more
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4607 <lb></lb>ſpacious and broad, ſo that augmenting the breadth of the Figure,
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4608 <lb></lb>the facility of ſupernatation will be deminiſhed, and decreaſing, that
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4609 <lb></lb>this will encreaſe.</s></p><p type="margin">
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4610
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4611 <s><margin.target id="marg1549"></margin.target>Thickneſs not
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4612 <lb></lb>breadth of Fi­
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4613 <lb></lb>gure to be re­
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4614 <lb></lb>ſpected in Na­
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4615 <lb></lb>tation.</s></p><p type="margin">
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4616
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4617 <s><margin.target id="marg1550"></margin.target>Were Reni­
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4618 <lb></lb>tence the cauſe
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4619 <lb></lb>of Natation,
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4620 <lb></lb>breadth of Fi­
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4621 <lb></lb>gure would
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4622 <lb></lb>hinder the
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4623 <lb></lb>ſwiming of Bo­
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4624 <lb></lb>dies.</s></p><p type="main">
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4625
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4626 <s>And for declaration of what I ſay, conſider that when a thin Plate
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4627 <lb></lb>of Lead deſcends, dividing the water, the Diviſion and diſcontinu­
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4628 <lb></lb>ation is made between the parts of the water, invironing the perime­
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4629 <lb></lb>ter or Circumference of the ſaid Plate, and according to the big­
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4630 <lb></lb>neſs greater or leſſer of that circuit, it hath to divide a greater or
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4631 <lb></lb>leſſer quantity of water, ſo that if the circuit, ſuppoſe of a Board,
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4632 <lb></lb>be ten Feet in ſinking it flatways, it is to make the ſeperation and
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4633 <lb></lb>diviſion, and to ſo ſpeak, an inciſſion upon ten Feet of water; and
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4634 <lb></lb>likewiſe a leſſer Board that is four Feet in Perimeter, muſt make an
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4635 <lb></lb>inceſſion of four Feet. </s><s>This granted, he that hath any knowledge
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4636 <lb></lb>in Geometry, will comprehend, not only that a Board ſawed in many
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4637 <lb></lb>long thin pieces, will much better float than when it was entire, but
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4638 <lb></lb>that all Figures, the more ſhort and narrow they be, ſhall ſo much the
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4639 <lb></lb>better ſwim. </s><s>Let the Board ABCD be, for Example, eight
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4640 <lb></lb>Palmes long, and five broad, its circuit ſhall be twenty ſix Palmes;
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4641 <lb></lb>and ſo many muſt the inceſſion be, which it ſhall make in the water to
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4642 <lb></lb>deſcend therein: but if we do ſaw ir, as ſuppoſe into eight little
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4643
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4644
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4645 <pb pagenum="469"></pb>pieces, according to the Lines E F, G H, <emph type="italics"></emph>&amp;c.<emph.end type="italics"></emph.end> making ſeven Segments,
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4646 <lb></lb>we muſt adde to the twenty ſix Palmes of the circuit of the whole
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4647 <lb></lb>Board, ſeventy others; whereupon the eight little pieces ſo cut and
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4648 <lb></lb>ſeperated, have to cut ninty ſix Palmes of water. </s><s>And, if moreover,
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4649 <lb></lb>we cur each of the ſaid pieces into five parts, re­
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4650 <lb></lb><figure id="fig280"></figure>
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4651 <lb></lb>ducing them into Squares, to the circuit of ninty
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4652 <lb></lb>ſix Palmes, with four cuts of eight Palmes apiece;
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4653 <lb></lb>we ſhall adde alſo ſixty four Palmes, whereupon
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4654 <lb></lb>the ſaid Squares to deſcend in the water, muſt
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4655 <lb></lb>divide one hundred and ſixty Palmes of water,
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4656 <lb></lb>but the Reſiſtance is much greater than that of
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4657 <lb></lb>twenty ſix; therefore to the leſſer Superficies,
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4658 <lb></lb>we ſhall reduce them, ſo much the more eaſily
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4659 <lb></lb>will they float: and the ſame will happen in all
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4660 <lb></lb>other Figures, whoſe Superficies are ſimular amongſt themſelves, but
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4661 <lb></lb>different in bigneſs: becauſe the ſaid Superficies, being either demini­
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4662 <lb></lb>ſhed or encreaſed, always diminiſh or encreaſe their Perimeters in
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4663 <lb></lb>ſubduple proportion; to wit, the Reſiſtance that they find in pene­
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4664 <lb></lb>trating the water; therefore the little pieces gradually ſwim, with more
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4665 <lb></lb>and more facility as their breadth is leſſened.</s></p><p type="main">
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4666
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4667 <s><emph type="italics"></emph>This is manifeſt; for keeping ſtill the ſame height of the Solid, with
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4668 <lb></lb>the ſame proportion as the Baſe encreaſeth or deminiſheth, doth the ſaid
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4669 <lb></lb>Solid alſo encreaſe or diminiſh; whereupon the Solid more diminiſhing
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4670 <lb></lb>than the Circuit, the Cauſe of Submerſion more diminiſheth than the Cauſe
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4671 <lb></lb>of Natation: And on the contrary, the Solid more encreaſing than the
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4672 <lb></lb>Circuit, the Cauſe of Submerſion encreaſeth more, that of Natation
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4673 <lb></lb>leſs.<emph.end type="italics"></emph.end></s></p><p type="main">
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4674
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4675 <s>And this may all be dedueed out of the Doctrine of <emph type="italics"></emph>Ariſtotle<emph.end type="italics"></emph.end> a­
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4676 <lb></lb>gainſt his own Doctrine.</s></p><p type="main">
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4677
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4678 <s>Laſtly, to that which we read in the latter part of the Text, that
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4679 <lb></lb><arrow.to.target n="marg1551"></arrow.to.target>
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4680 <lb></lb>is to ſay, that we muſt compare the Gravity of the Moveable with
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4681 <lb></lb>the Reſiſtance of the Medium againſt Diviſion, becauſe if the force of
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4682 <lb></lb>the Gravity exceed the Reſiſtance of the <emph type="italics"></emph>Medium,<emph.end type="italics"></emph.end> the Moveable will
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4683 <lb></lb>deſcend, if not it will float. </s><s>I need not make any other anſwer,
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4684 <lb></lb>but that which hath been already delivered; namely, that its not
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4685 <lb></lb>the Reſiſtance of abſolute Diviſion, (which neither is in Water nor
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4686 <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
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4687 <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
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4688 <lb></lb>Moveable ſhall not deſcend, nor ſo much as make a totall Submerſion,
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4689 <lb></lb>but a partiall only: becauſe in the place which it would occupy in
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4690 <lb></lb>the water, there muſt not remain a Body that weighs leſs than a like
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4691 <lb></lb>quantity of water: but if the Moveable be more grave, it ſhall deſ­
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4692 <lb></lb>cend to the bottom, and poſſeſs a place where it is more conformable
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4693
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4694 <pb></pb>
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4695
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4696 for it to remain, than another Body that is leſs grave. </s><s>And this
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4697 <lb></lb>is the only true proper and abſolute Cauſe of Natation and Sub­
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4698 <lb></lb>merſion, ſo that nothing elſe hath part therein: and the Board of the
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4699 <lb></lb>Adverſaries ſwimmeth, when it is conjoyned with as much Air,
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4700 <lb></lb>as, together with it, doth form a Body leſs grave than ſo much water
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4701 <lb></lb>as would fill the place that the ſaid Compound occupyes in the
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4702 <lb></lb>water; but when they ſhall demit the ſimple Ebony into
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4703 <lb></lb>the water, according to the Tenour of our Que­
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4704 <lb></lb>ſtion, it ſhall alwayes go to the bottom,
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4705 <lb></lb>though it were as thin as a
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4706 <lb></lb>Paper.</s></p><p type="margin">
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4707
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4708 <s><margin.target id="marg1551"></margin.target>Lib. 4. c. </s><s>6.
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4709 <lb></lb>Text 45.</s></p><p type="head">
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4710
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4711 <s><emph type="italics"></emph>FINIS.<emph.end type="italics"></emph.end></s></p>
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4712
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4713 </chap> </body> <back></back> </text></archimedes>