Archimedes, Natation of bodies, 1662

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="073/01/015.jpg" pagenum="344"/>
              for that B G is the Gravity of the Liquid equal in Maſs unto it:
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              Therefore the Solid compounded of thoſe two Solids A and D
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              being dimerged, it ſhall, by the precedent, ſo much of it ſubmerge,
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              as that a quantity of the Liquid equal to the ſaid ſubmerged part
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              ſhall have equal Gravity with the ſaid compounded Solid. </s>
              <s>And
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                <figure id="id.073.01.015.1.jpg" xlink:href="073/01/015/1.jpg" number="8"/>
                <lb/>
              for an example of that
                <emph type="italics"/>
              Propoſition
                <emph.end type="italics"/>
              let the Su­
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              perficies of any Liquid be that which pro­
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              ceedeth according to the Circumference
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              A B G D: Becauſe now a Maſs or quantity
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              of Liquor as big as the Maſs A hath equal
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              Gravity with the whole compounded Solid
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              A D: It is manifeſt that the ſubmerged part
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              thereof ſhall be the Maſs A: and the remain­
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              der, namely, the part D, ſhall be wholly a­
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              top, that is, above the Surface of the Liquid.
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              </s>
              <s>It is therefore evident, that the part A hath ſo much virtue or
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              Force to return upwards, that is, to riſe from below above the Li­
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              quid, as that which is upon it, to wit, the part D, hath to preſs it
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              downwards, for that neither part is repulſed by the other: But D
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              preſſeth downwards with a Gravity equal to G, it having been ſup­
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              poſed that the Gravity of that part D was equal to G: Therefore
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              that is manifeſt which was to be demonſtrated.</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>This was a fine Demonſtration, and from this I perceive that you colle­
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              cted your
                <emph type="italics"/>
              Induſtrious Invention
                <emph.end type="italics"/>
              ; and eſpecially that part of it which you inſert in
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              the firſt Book for the recovering of a Ship ſunk: and, indeed, I have many Que­
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              ſtions to ask you about that, but I will not now interrupt the Diſcourſe in hand, but
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              deſire that we may go on to the ſeventh
                <emph type="italics"/>
              Propoſition,
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              the purport whereof is this.</s>
            </p>
            <p type="head">
              <s>PROP. VII. THEOR. VII.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Solid Magnitudes beavier than the Liquid, being de­
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              mitted into the [ſetled] Liquid, are boren down­
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              wards as far as they can deſcend: and ſhall be lighter
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              in the Liquid by the Gravity of a Liquid Maſs of
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              the ſame bigneſs with the Solid Magnitude.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>NIC. </s>
              <s>This ſeventh
                <emph type="italics"/>
              Propoſition
                <emph.end type="italics"/>
              hath two parts to be demonſtrated.</s>
            </p>
            <p type="main">
              <s>The firſt is, That all Solids heavier than the Liquid, being demit­
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              ted into the
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              L
                <emph.end type="italics"/>
              iquid, are boren by their Gravities downwards as far
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              as they can deſcend, that is untill they arrive at the Bottom. </s>
              <s>Which
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              firſt part is manifeſt, becauſe the Parts of the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid, which ſtill lie
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              under that Solid, are more preſſed than the others equijacent,
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              becauſe that that Solid is ſuppoſed more grave than the Liquid. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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