Archimedes, Natation of bodies, 1662

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    <archimedes>
      <text>
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          <chap>
            <p type="main">
              <s>
                <pb xlink:href="073/01/009.jpg" pagenum="338"/>
              ſhall be equal to the Triangle O X K; Therefore (by common
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              Notion) ſubſtracting thoſe two ſmall Triangles O P K and O X K
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              from the two others B E K and B R K, the two Remainders ſhall
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              be equal: one of which Remainders ſhall be the Quadrangle
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              B E O P, and the other B R X O. </s>
              <s>And becauſe the whole Quadran­
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              gle B E O P is full of Liquor, and of the Quadrangle B R X O,
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              the part B A X O only is full, and the reſidue B R A is wholly void
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              of Water: It followeth, therefore, that the Quadrangle B E O P
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              is more ponderous than the Quadrangle B R X O. </s>
              <s>And if the ſaid
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              Quadrangle B E O P be more Grave than the Quadrangle
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              B R X O, much more ſhall the Quadrangle B L O P exceed in Gra­
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              vity the ſaid Quadrangle B R X O: whence it followeth, that the
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              part O P is more preſſed than the part O X. But, by the firſt part
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              of the Suppoſition, the part leſs preſſed ſhould be repulſed by the
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              part more preſſed: Therefore the part O X muſt be repulſed by
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              the part O P: But it was preſuppoſed that the Liquid did not
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              move: Wherefore it would follow that the leſs preſſed would not
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              be repulſed by the more preſſed: And therefore it followeth of
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              neceſſity that the Line A
                <emph type="italics"/>
              B
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              G D is the Circumference of a Circle,
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              and that the Center of it is the point K. </s>
              <s>And in like manner ſhall
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              it be demonſtrated, if the Surface of the Liquid be cut by a Plane
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              thorow the Center of the Earth, that the Section ſhall be the Cir­
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              cumference of a Circle, and that the Center of the ſame ſhall be
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              that very Point which is Center of the Earth. </s>
              <s>It is therefore mani­
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              feſt that the Superficies of a Liquid that is conſiſtant and ſetled
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              ſhall have the Figure of a Sphære, the Center of which ſhall be
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              the ſame with that of the Earth, by the firſt
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              Propoſition
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              ; for it is
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              ſuch that being ever cut thorow the ſame Point, the Section or Di­
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              viſion deſcribes the Circumference of a Circle which hath for Cen­
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              ter the ſelf-ſame Point that is Center of the Earth: Which was to
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              be demonſtrated.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1130"/>
              * O: through.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1131"/>
              *
                <emph type="italics"/>
              i.e.
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              Parallel.</s>
            </p>
            <p type="main">
              <s>RIC. </s>
              <s>I do thorowly underſtand theſe your Reaſons, and ſince there is in them
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              no umbrage of Doubting, let us proceed to his third
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              Propoſition.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>PROP. III. THEOR. III.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Solid Magnitudes that being of equal Maſs with the
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              Liquid are alſo equal to it in Gravity, being demit-
                <emph.end type="italics"/>
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                <arrow.to.target n="marg1132"/>
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                <emph type="italics"/>
              ted into the [^{*} ſetled] Liquid do ſo ſubmerge in the
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              ſame as that they lie or appear not at all above the
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              Surface of the Liquid, nor yet do they ſink to the
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              Bottom.
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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