Archimedes, Natation of bodies, 1662

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="073/01/012.jpg" pagenum="341"/>
            <p type="head">
              <s>PROP. IV. THEOR. IV.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Solid Magnitudes that are lighter than the Liquid,
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              being demitted into the ſetled Liquid, will not total­
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              ly ſubmerge in the ſame, but ſome part thereof will
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              lie or ſtay above the Surface of the Liquid.
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              </s>
            </p>
            <p type="main">
              <s>NIC. </s>
              <s>In this fourth
                <emph type="italics"/>
              Propoſition
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              it is concluded, that every Body or Solid that is
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              lighter (as to Specifical Gravity) than the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid, being put into the
                <lb/>
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid, will not totally ſubmerge in the ſame, but that ſome part of it
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              will ſtay and appear without the
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              iquid, that is above its Surface.</s>
            </p>
            <p type="main">
              <s>For ſuppoſing, on the contrary, that it were poſſible for a Solid
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              more light than the Liquid, being demitted in the Liquid to ſub­
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              merge totally in the ſame, that is, ſo as that no part thereof re­
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              maineth above, or without the ſaid Liquid, (evermore ſuppoſing
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              that the Liquid be ſo conſtituted as that it be not moved,) let us
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              imagine any Plane produced thorow the Center of the Earth, tho­
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              row the Liquid, and thorow that Solid Body: and that the Surface
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              of the Liquid is cut by this Plane according to the Circumference
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              A
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              B
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              G, and the Solid
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              B
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              ody according to the Figure R; and let the
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              Center of the Earth be K. </s>
              <s>And let there be imagined a Pyramid
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                <figure id="id.073.01.012.1.jpg" xlink:href="073/01/012/1.jpg" number="6"/>
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              that compriſeth the Figure
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              R, as was done in the pre.
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              </s>
              <s>cedent, that hath its Ver­
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              tex in the Point K, and let
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              the Superficies of that
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              Pyramid be cut by the
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              Superficies of the Plane
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              A
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              G, according to A K
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              and K
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              B
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              . </s>
              <s>And let us ima­
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              gine another Pyramid equal and like to this, and let its Superficies
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              be cut by the Superficies A
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              B
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              G according to K
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              B
                <emph.end type="italics"/>
              and K
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              G
                <emph.end type="italics"/>
              ; and let
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              the Superficies of another Sphære be deſcribed in the Liquid, upon
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              the Center K, and beneath the Solid R; and let that be cut by the
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              ſame Plane according to
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              X
                <emph.end type="italics"/>
              O P. And, laſtly, let us ſuppoſe ano­
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              ther Solid taken ^{*} from the Liquid, in this ſecond Pyramid, which
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                <arrow.to.target n="marg1133"/>
                <lb/>
              let be H, equal to the Solid R. </s>
              <s>Now the parts of the Liquid, name­
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              ly, that which is under the Spherical Superficies that proceeds ac­
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              cording to the Superficies or Circumference
                <emph type="italics"/>
              X
                <emph.end type="italics"/>
              O, in the firſt Py­
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              ramid, and that which is under the Spherical Superficies that pro­
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              ceeds according to the Circumference O P, in the ſecond Pyramid,
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              are equijacent, and contiguous, but are not preſſed equally; for </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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