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<?xml version="1.0"?>
<archimedes xmlns:xlink="http://www.w3.org/1999/xlink" >      <info>
	<author>Roberval, Gilles Personne de</author>
	<title>Letter to Fermat</title>
	<date>1665</date>
	<place>London</place>
	<translator>Thomas Salusbury</translator>
	<lang>en</lang>
	<cvs_file>rober_ferma_072_en_1665.xml</cvs_file>
	<cvs_version></cvs_version>
	<locator>072.xml</locator>
</info>      <text>          <front>          </front>          <body>            <chap>	<pb xlink:href="072/01/001.jpg"></pb><pb xlink:href="072/01/002.jpg" pagenum="325"></pb><p type="head">



<s>A <lb></lb>LETTER <lb></lb>OF <lb></lb>Monſieur de Robberval <lb></lb>TO <lb></lb>Monſieur de Fermates, <lb></lb>Counſellour of <emph type="italics"></emph>THOULOUSE,<emph.end type="italics"></emph.end><lb></lb>Containing certain Propoſitions in the <lb></lb>MECHANICKS.</s></p><p type="main">

<s>MONSIEUR,</s></p><p type="main">

<s>I have, according to my promiſe, ſent you the <lb></lb>Demonſtration of the Fundamental Propoſi­<lb></lb>tion of our Mechanicks, in which I follow the <lb></lb>common method of explaining, in the firſt <lb></lb>place, the Definitions and Principles of which <lb></lb>we make uſe.</s></p><p type="main">

<s>We in general call that Quality a Force or <lb></lb>Power, by means of which any thing whatever <lb></lb>doth tend or aſpire into another place than that in which it is, be it <lb></lb>downwards, upwards, or ſide waies, whether this Quality naturally <lb></lb>belongeth to the Body, or be communicated to it from without. <lb></lb></s>

<s>From which definition it followeth, that all Weights are a ſpecies <lb></lb>of Force, in regard that it is a Quality, by means whereof Bodies <lb></lb>do tend downwards. </s>

<s>We often alſo aſſign the name of Force to <lb></lb>that very thing to which the Force belongeth, as a ponderous Bo­<lb></lb>dy is called a Weight, but with this pre-caution, that this is in re­<lb></lb>ference to the true Force, the which augmenting or diminiſhing <lb></lb>ſhall be called a greater or leſſer Force, albeit that the thing to <lb></lb>which it belongeth do remain alwaies the ſame.</s></p><p type="main">

<s>If a Force be ſuſpended or faſtned to a Flexible Line that is <lb></lb>without Gravity, and that is made faſt by one end unto ſome <emph type="italics"></emph>Ful­<lb></lb>ciment<emph.end type="italics"></emph.end> or ſtay, in ſuch ſort as that it ſuſtain the Force, drawing <pb xlink:href="072/01/003.jpg" pagenum="326"></pb>without impediment by this Line, the Force and the Line ſhall <lb></lb>take ſome certain poſition in which they ſhall reſt, and the Line <lb></lb>ſhall of neceſſity be ſtreight, let that Line be termed <emph type="italics"></emph>the Pendant,<emph.end type="italics"></emph.end><lb></lb>or <emph type="italics"></emph>Line of Direction of the Force.<emph.end type="italics"></emph.end> And let the Point by which it is <lb></lb>faſtned to the Fulciment be called <emph type="italics"></emph>the Point of Suſpenſion<emph.end type="italics"></emph.end>: which <lb></lb>may ſometimes be the Arm of a Leaver or Ballance; and then let <lb></lb>the Line drawn from the Center of the Fulciment of the Leaver <lb></lb>or Ballance to the Point of Suſpenſion be named <emph type="italics"></emph>the Diſtance<emph.end type="italics"></emph.end> or <lb></lb><emph type="italics"></emph>the Arm of the Force<emph.end type="italics"></emph.end>: which we ſuppoſe to be a Line fixed, and <lb></lb>conſidered without Gravity. </s>

<s>Moreover, let the Angle comprehen­<lb></lb>ded betwixt the Arm of the Force and the Line of Direction be <lb></lb>termed <emph type="italics"></emph>the Angle of the Direction of the Force.<emph.end type="italics"></emph.end></s></p><p type="head">

<s>AXIOM I.</s></p><p type="main">

<s>After theſe Definitions we lay down for a Principle, that in the <lb></lb>Leaver, and in the Ballance, Equal Forces drawing by Arms <lb></lb>that are equal, and at equall Angles of Direction, do draw equal­<lb></lb>ly. </s>

<s>And if in this Poſition they draw one againſt the other they <lb></lb>ſhall make an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end>: but if they draw together, or towards <lb></lb>the ſame part, the Effect ſhall be double.</s></p><p type="main">

<s>If the Forces being equal, and the Augles of Direction alſo <lb></lb>equal, the Arms be unequal, the Force that ſhall be ſuſpended at <lb></lb>the greater Arm ſhall work the greater Effect.</s></p><p type="main">

<s>As in this Figure, the Center of the Ballance or Leaver being A, <lb></lb><figure id="id.072.01.003.1.jpg" xlink:href="072/01/003/1.jpg"></figure><lb></lb>if the Arms A B and A C are equal, <lb></lb>as alſo the Angles A B D, and A C E, <lb></lb>the equal Forces D and E ſhall <lb></lb>draw equally, and make an <emph type="italics"></emph>Equili­<lb></lb>brium.<emph.end type="italics"></emph.end> So likewiſe the Arm A F be­<lb></lb>ing equal to A B, the Angle A F G <lb></lb>to the Angle A B D, and the Force <lb></lb>G to D, theſe two Forces ^{*} G and D <lb></lb><arrow.to.target n="marg1124"></arrow.to.target><lb></lb>draw equally; and in regard that <lb></lb>they draw both one way, the Effect <lb></lb>ſhall be double.</s></p><p type="margin">

<s><margin.target id="marg1124"></margin.target>* In the M. S. <lb></lb></s>

<s>Copy it is <emph type="italics"></emph>C and <lb></lb>D.<emph.end type="italics"></emph.end></s></p><p type="main">

<s>In the ſame manner the Forces G and E ſhall make an <emph type="italics"></emph>Equilibri­<lb></lb>um<emph.end type="italics"></emph.end>; as alſo I and L ſhall counterpoiſe, if (being equal) the Arms <lb></lb>A K and A H, and the Angles A H T, and A K L be equal.</s></p><p type="main">

<s>The ſame ſhall befall in the Forces P and R, if all things be <lb></lb>diſpoſed as before. </s>

<s>And in this caſe we make no other diſtinction <lb></lb>betwixt Weights and other Forces ſave only this, that Weights all <lb></lb>tend towards the Center of Grave Bodies, and Forces may be un­<lb></lb>derſtood to tend all towards all parts of the Univerſe, with ſo <lb></lb>much greater or leſſer <emph type="italics"></emph>Impetus<emph.end type="italics"></emph.end> than Weights. </s>

<s>So that Weights and <pb xlink:href="072/01/004.jpg" pagenum="327"></pb>their parts do draw by Lines of Direction, which all concur in one <lb></lb>and the ſame Point; and Forces and their parts may be underſtood <lb></lb>to draw in ſuch ſort that all the Lines of Direction are parallel to <lb></lb>each other.</s></p><p type="head">

<s>AXIOM II.</s></p><p type="main">

<s>In the ſecond place, we ſuppoſe that a Force and its Line of Di­<lb></lb>rection abiding alwaies in the ſame poſition, as alſo the Center <lb></lb>of the Ballance or Leaver, be the Arm what it will that is drawn <lb></lb>from the Center of the Ballance to the Line of Direction, the <lb></lb>Force drawing alwaies in the ſame faſhion, will alwaies produce <lb></lb>the ſame Effect.</s></p><p type="main">

<s>As, in this ſecond Figure, the Center of the Ballance being A, <lb></lb>the Force B, and the Line of Direction <lb></lb><figure id="id.072.01.004.1.jpg" xlink:href="072/01/004/1.jpg"></figure><lb></lb>B <emph type="italics"></emph>F<emph.end type="italics"></emph.end> prolonged, as occaſion ſhall re­<lb></lb>quire, in which the Arms A G, A C, and <lb></lb>A <emph type="italics"></emph>F<emph.end type="italics"></emph.end> do determine, in this poſition let <lb></lb>the Line B <emph type="italics"></emph>F<emph.end type="italics"></emph.end> be faſtned to the Arm <lb></lb>A <emph type="italics"></emph>F,<emph.end type="italics"></emph.end> or A C, or to another Arm drawn <lb></lb>from the Center A to the Line of Di­<lb></lb>rection ^{*} B <emph type="italics"></emph>F<emph.end type="italics"></emph.end>: we ſuppoſe that this <lb></lb><arrow.to.target n="marg1125"></arrow.to.target><lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce B ſhall alwaies work the ſame <lb></lb>Effect upon the Ballance. </s>

<s>And if <lb></lb>drawing by the Arm A C it make an <lb></lb><emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> with the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce <emph type="italics"></emph>D<emph.end type="italics"></emph.end> drawing by the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rm <emph type="italics"></emph>A<emph.end type="italics"></emph.end> E, when <lb></lb>ever it ſhall draw by the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rms <emph type="italics"></emph>A F<emph.end type="italics"></emph.end> or <emph type="italics"></emph>A<emph.end type="italics"></emph.end> G, it ſhall likewiſe make <lb></lb>an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> with the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce D drawing by the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rm <emph type="italics"></emph>A E.<emph.end type="italics"></emph.end> This <lb></lb>Principle although it be not expreſly found in <emph type="italics"></emph>A<emph.end type="italics"></emph.end>uthors, yet it is <lb></lb>tacitly ſuppoſed by all thoſe that have writ on this <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rgument, and <lb></lb>Experience conſtantly confirmeth it.</s></p><p type="margin">

<s><margin.target id="marg1125"></margin.target>* In the Original <lb></lb>it is writ, but by <lb></lb>the miſtake of <lb></lb>the Tranſcriber, <lb></lb><emph type="italics"></emph>a la ligue de<emph.end type="italics"></emph.end> di­<lb></lb>rection A F.</s></p><p type="head">

<s>AXIOM III.</s></p><p type="main">

<s>I<emph type="italics"></emph>f<emph.end type="italics"></emph.end> the Arms of a Ballance or Leaver are directly placed the one to <lb></lb>the other, and that being equal they ſuſtain equal <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces, of which <lb></lb>the Angles of Direction are Right An­<lb></lb><figure id="id.072.01.004.2.jpg" xlink:href="072/01/004/2.jpg"></figure><lb></lb>gles, theſe <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces do alwaies weigh <lb></lb>equally upon the Center of the Bal­<lb></lb>lance, whether that they be near to the <lb></lb>ſame Center, or far diſtant, or both <lb></lb>conjoyned in the Center it ſelf; as in <lb></lb>this <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure the Ballance being E D, <lb></lb>the Center A, the equal Arms A D <lb></lb>and <emph type="italics"></emph>A<emph.end type="italics"></emph.end> E, let us ſuſtain equal <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces H and I, of which the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ngles <pb xlink:href="072/01/005.jpg" pagenum="328"></pb>of Direction <emph type="italics"></emph>A<emph.end type="italics"></emph.end> D H and <emph type="italics"></emph>A<emph.end type="italics"></emph.end> E I are Right <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ngles, we ſuppoſe that <lb></lb>theſe two <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces I and H weigh alike upon the Center <emph type="italics"></emph>A<emph.end type="italics"></emph.end> as if they <lb></lb>were nearer to the Center, at the equal Diſtances <emph type="italics"></emph>A<emph.end type="italics"></emph.end> B and A C, <lb></lb>and we alſo ſuppoſe the ſame if theſe very <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces were ſuſpended <lb></lb>both together in <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>ngles of Directions being ſtill Right <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end>ngles.</s></p><p type="head">

<s>PROPOSITION I.</s></p><p type="main">

<s>Theſe Principles agreed upon, we will eaſily demonſtrate, <lb></lb>in Imitation of <emph type="italics"></emph>Archimedes,<emph.end type="italics"></emph.end> that upon a ſtraight Balance <lb></lb>the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces, of which and of all their parts the Lines of Dire­<lb></lb>ction are parallel to one another, and perpendicular to the Balance, <lb></lb>ſhall couuterpoiſe and make an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> when the ſaid <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces <lb></lb>ſhall be to one another in Reciprocal proportion of their Arms, <lb></lb>which we think to be ſo manifeſt to you, that we thence ſhall de­<lb></lb>rive the Demonſtration of this Univerſal Propoſition to which we <lb></lb>haſten.</s></p><p type="head">

<s>PROPOS. II.</s></p><p type="main">

<s>In every Balance or Leaver, if the proportion of the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces is <lb></lb>reciprocal to that of the Perpendicular Lines drawn from the <lb></lb>Center or Point of the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>ulciment unto the Lines of Direction <lb></lb>of the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces, drawing the one againſt the other, they ſhall make <lb></lb>an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> and drawing on one and the ſame ſide, they ſhall <lb></lb>have a like Effect, that is to ſay, that they ſhall have as much <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce <lb></lb>the one as the other, to move the Balance.</s></p><p type="main">

<s>In this <emph type="italics"></emph>F<emph.end type="italics"></emph.end>igure let the Center of the Balance be <emph type="italics"></emph>A,<emph.end type="italics"></emph.end> the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rm <emph type="italics"></emph>A<emph.end type="italics"></emph.end> B, <lb></lb>bigger than <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C, and firſt let the <emph type="italics"></emph>L<emph.end type="italics"></emph.end>ines of Direction B D, and E C <lb></lb>be perpendicular to the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rms <emph type="italics"></emph>A<emph.end type="italics"></emph.end> B and <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C, by which Lines the <lb></lb><emph type="italics"></emph>F<emph.end type="italics"></emph.end>orces D and E (which may be made of Weights if one will) do <lb></lb>draw; and that there is the ſame rate <lb></lb><figure id="id.072.01.005.1.jpg" xlink:href="072/01/005/1.jpg"></figure><lb></lb>of the <emph type="italics"></emph>F<emph.end type="italics"></emph.end>orce D to the Force E as there <lb></lb>is betwixt the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rm <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C to the Arm <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end> B: the Forces drawing one againſt <lb></lb>the other, I ſay, that they will make an <lb></lb><emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> upon the Balance <emph type="italics"></emph>C<emph.end type="italics"></emph.end> A B. <lb></lb></s>

<s>For let the <emph type="italics"></emph>A<emph.end type="italics"></emph.end>rm C <emph type="italics"></emph>A<emph.end type="italics"></emph.end> be prolonged <lb></lb>unto F, ſo as that <emph type="italics"></emph>A<emph.end type="italics"></emph.end>F may be equal to <lb></lb><emph type="italics"></emph>A<emph.end type="italics"></emph.end> B: and let C <emph type="italics"></emph>A<emph.end type="italics"></emph.end> F be conſidered as a <lb></lb>ſtreight Balance, of which let the Center be <emph type="italics"></emph>A<emph.end type="italics"></emph.end>: and let there be <lb></lb>ſuppoſed two Forces G and H, of which and of all their parts the <lb></lb>Lines of Direction are parallel to the Line C E, and that the <lb></lb>Force G be equal to the Force D, and H to E, the one, to wit G, <pb xlink:href="072/01/006.jpg" pagenum="329"></pb>drawing upon the Arm A <emph type="italics"></emph>F,<emph.end type="italics"></emph.end> and the other, to wit H, upon the Arm <lb></lb>A C: now, by the firſt Propoſition, G and H ſhall make an <emph type="italics"></emph>Equili­<lb></lb>brium<emph.end type="italics"></emph.end> upon the Balance C A F: But, by the firſt Principle, the Force <lb></lb>D upon the Arm A B worketh the ſame effect as the Force G on <lb></lb>the Arm A F: Therefore the Force D upon the Arm A B maketh <lb></lb>an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> with the Force H upon A C: And the Force H <lb></lb>drawing in the ſame manner upon the Arm <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C as the Force E, by <lb></lb>the ſame firſt <emph type="italics"></emph>A<emph.end type="italics"></emph.end>xiom, the Force D upon the Arm <emph type="italics"></emph>A<emph.end type="italics"></emph.end> B ſhall make an <lb></lb><emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> with the Force E upon the Arm <emph type="italics"></emph>A<emph.end type="italics"></emph.end> C.</s></p><p type="main">

<s>Now, in the following Figure, let the Center of the Balance be <lb></lb><emph type="italics"></emph>A,<emph.end type="italics"></emph.end> the Arms A B and A C, the Lines of Direction B D and C E <lb></lb>which are not Perpendicular to the Arms, and the Forces D and E <lb></lb>drawing likewiſe by the Lines of Direction, upon which Perpen­<lb></lb>diculars are erected unto the Center A, that is A F upon B D, and <lb></lb>A G upon E C, and that as A F is to A G, ſo is the Force E to the <lb></lb>Force D: which Forces draw one <lb></lb><figure id="id.072.01.006.1.jpg" xlink:href="072/01/006/1.jpg"></figure><lb></lb>againſt the other: I ſay, that they will <lb></lb>make an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end> upon the Balance <lb></lb>C A B: For let the Lines A F and A G <lb></lb>be underſtood to be the two Arms of <lb></lb>a Balance G A F, upon which the For­<lb></lb>ces D and E do draw by the Lines of <lb></lb>Direction F D and G E: Theſe Forces <lb></lb>ſhall make an <emph type="italics"></emph>Equilibrium,<emph.end type="italics"></emph.end> by the firſt <lb></lb>part of this ſecond Propoſition; but, by the ſecond Axiom, the Force <lb></lb>D upon the Arm A F hath the ſame Effect as upon the Arm A B: <lb></lb>Therefore the Force D upon the Arm A B maketh an <emph type="italics"></emph>Equilibrium<emph.end type="italics"></emph.end><lb></lb>with the Force E upon the Arm A C.</s></p><p type="main">

<s>There are many Caſes, according to the Series of Perpendicu­<lb></lb>lars, but it will be eaſie for you to ſee that they have all but one <lb></lb>and the ſame Demonſtration.</s></p><p type="main">

<s>It is alſo eaſie to demonſtrate, that if the Forces draw both on <lb></lb>one ſide they ſhall make the ſame Effect one as another, and that <lb></lb>the Effect of two together ſhall be double to that of one alone.</s></p><p type="head">

<s>OF THE <lb></lb>GEOSTATICKS.</s></p><p type="main">

<s>The Principle which you demand for the <emph type="italics"></emph>Geoſtaticks<emph.end type="italics"></emph.end> is, <lb></lb>That if two equal Weights are conjoyned by a right <lb></lb>Line fixed and void of Gravity, and that being ſo di­<lb></lb>ſpoſed they may deſcend freely, they will never reſt till <lb></lb>that the middle of the Line, that is the Center of Gravitation of <lb></lb>the Ancients, unites it ſelf to the common Center of Grave Bodies.</s></p><pb xlink:href="072/01/007.jpg" pagenum="330"></pb><p type="main">

<s>This Principle ſeems at the firſt very plauſible, but when <lb></lb>the Queſtion concerneth a Principle, you know what Conditions <lb></lb>are required to it, that it may be received, the principal of which are <lb></lb>wanting in the Principle now in controverſie<emph type="italics"></emph>: ſcil.<emph.end type="italics"></emph.end> that we do not <lb></lb>know what is the radical Cauſe why Grave Bodies deſcend; and <lb></lb>whence the Original of this Gravity ariſeth: as alſo that we are to­<lb></lb>tally ignorant of that which would arrive at the Center whither <lb></lb>Grave Bodies do tend, nor to other places without the Surface of the <lb></lb>Earth, of which, in regard we inhabit upon it, we have ſome Expe­<lb></lb>riments upon which we ground our Principles.</s></p><p type="main">

<s>For it may be, that Gravity is a Quality that reſides in the Body <lb></lb>it ſelf that falleth; it may be that it is in another that attracteth <lb></lb>that which deſcends, as in the Earth: It may be, and it is very likely <lb></lb>that it is a Natural Attraction, or a Natural Deſire of two Bodies to <lb></lb>unite together, as in the Iron and Loadſtone, which are ſuch, that <lb></lb>if the Loadſtone be ſtaid, the Iron, if nothing hinder it, will go find <lb></lb>it out; and if the Iron be ſtaid the Loadſtone will go towards it; <lb></lb>and if they be both at liberty, they will reciprocally approach one <lb></lb>another, yet after ſuch a faſhion, that the ſtrongeſt of the two <lb></lb>will move the leaſt way.</s></p><p type="main">

<s>If the firſt be true, according to the common opinion, we ſee not <lb></lb>how your Principle can ſubſiſt, for Common Senſe tells us, that in <lb></lb>whatever place a Weight is, it alwaies weigheth alike, having ever­<lb></lb>more the ſame Quality that maketh it to weigh, and that then a Bo­<lb></lb>dy will repoſe at the Common Center of things Grave when the <lb></lb>parts of the Body which ſhall be on each part of the ſaid Center <lb></lb>ſhall be of equal Ponderoſity to counterpoiſe one another, without <lb></lb>having any regard whether they be little or much removed from the <lb></lb>Center. </s>

<s>Since therefore that of theſe three poſſible Cauſes of Gra­<lb></lb>vitation, we know not which is the right, nay, that we are not cer­<lb></lb>tain that it is any of them, it being poſſibly that there is a fourth <lb></lb>from which one may draw Concluſions very different, it ſeemeth to <lb></lb>me impoſſible for us to lay down other Principles in this bufineſs <lb></lb>than thoſe of which we are aſſured by a continual Experience, and <lb></lb>a ſound Judgment. </s>

<s>As for our parts, we call thoſe Bodies equally <lb></lb>or unequally Grave which have an equal or unequal Force of mo­<lb></lb>ving towards the Common Center: and a Body is ſaid to have the <lb></lb>ſame Weight when it alwaies hath this ſame Force: but if this <lb></lb>Force augmenteth or diminiſheth, then, although it be the ſame Bo­<lb></lb>dy, we conſider it no longer as the ſame Weight: Now ſince that <lb></lb>this hapneth to Bodies that recede or approach to the Common <lb></lb>Center, this is it which we deſire to know, but finding nothing that <lb></lb>giveth me content upon this Subject, I will leave the Queſtion un­<lb></lb>determined and undeſcribed.</s></p> <p type="head">

<s>&gt;FINIS.</s></p>
		</chap>		</body>		<back></back>	</text></archimedes>