Archimedes, Natation of bodies, 1662

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="073/01/016.jpg" pagenum="345"/>
              But now that that Solid is lighter in the Liquid than out of it, as
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              is affirmed in the ſecond part, ſhall be demonſtrated in this man­
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              ner. </s>
              <s>Take a Solid, as ſuppoſe A, that is more grave than the Li­
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              quid, and ſuppoſe the Gravity of that ſame Solid A to be BG.
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              </s>
              <s>And of a Maſs of
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquor of the ſame bigneſs with the Solid A, ſup­
                <lb/>
              poſe the Gravity to be B: It is to be demonſtrated that the Solid
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              A, immerged in the Liquid, ſhall have a Gravity equal to G. </s>
              <s>And
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              to demonſtrate this, let us imagine another Solid, as ſuppoſe D,
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              more light than the Liquid, but of ſuch a quality as that its Gravi­
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              ty is equal to B: and let this D be of ſuch a Magnitude, that a
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              Maſs of
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquor equal to it hath its Gravity equal to the Gravity
                <lb/>
              B G. </s>
              <s>Now theſe two Solids D and A being compounded toge­
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              ther, all that Solid compounded of theſe two ſhall be equally
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              Grave with the Water: becauſe the Gravity of theſe two Solids
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              together ſhall be equal to theſe two Gravities, that is, to B G, and
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                <figure id="id.073.01.016.1.jpg" xlink:href="073/01/016/1.jpg" number="9"/>
                <lb/>
              to B; and the Gravity of a Liquid that hath its
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              Maſs equal to theſe two Solids A and D, ſhall be
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              equal to theſe two Gravities B G and B.
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              et
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              theſe two Solids, therefore, be put in the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid,
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                <arrow.to.target n="marg1136"/>
                <lb/>
              and they ſhall ^{*} remain in the Surface of that
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              i­
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              quid, (that is, they ſhall not be drawn or driven
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              upwards, nor yet downwards:) For if the Solid
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              A be more grave than the Liquid, it ſhall be
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              drawn or born by its Gravity downwards to­
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              wards the Bottom, with as much Force as by the Solid D it is thruſt
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              upwards: And becauſe the Solid D is lighter than the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid, it
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              ſhall raiſe it upward with a Force as great as the Gravity G: Be­
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              cauſe it hath been demonſtrated, in the ſixth
                <emph type="italics"/>
              Propoſition,
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              That So­
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              lid Magnitudes that are lighter than the Water, being demitted in
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              the ſame, are repulſed or driven upwards with a Force ſo much the
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              greater by how much a
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid of equal Maſs with the Solid is more
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              Grave than the ſaid Solid: But the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid which is equal in Maſs
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              with the Solid D, is more grave than the ſaid Solid D, by the Gra­
                <lb/>
              vity G: Therefore it is manifeſt, that the Solid A is preſſed or
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              born downwards towards the Centre of the World, with a Force
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              as great as the Gravity G: Which was to be demonſtrated.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1136"/>
              * Or, according to
                <lb/>
                <emph type="italics"/>
              Commandine,
                <emph.end type="italics"/>
              ſhall
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              be equall in Gravi­
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              ty to the Liquid,
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              neither moving up­
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              wards or down­
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              wards.</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>This hath been an ingenuous Demonſtration; and in regard I do ſuffici­
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              ently underſtand it, that we may loſe no time, we will proceed to the ſecond
                <emph type="italics"/>
              Suppo­
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              ſition,
                <emph.end type="italics"/>
              which, as I need not tell you, ſpeaks thus.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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