Archimedes, Natation of bodies, 1662

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    <archimedes>
      <text>
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          <chap>
            <pb xlink:href="073/01/008.jpg" pagenum="337"/>
            <p type="head">
              <s>PROP. II. THEOR. II.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              The Superficies of every Liquid that is conſiſtant and
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              ſetled ſhall be of a Sphærical Figure, which Figure
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              ſhall have the ſame Center with the Earth.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Let us ſuppoſe a Liquid that is of ſuch a conſiſtance as that it
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              is not moved, and that its Superficies be cut by a Plane along
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              by the Center of the Earth, and let the Center of the Earth
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              be the Point K: and let the Section of the Superficies be the Line
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              A B G D. </s>
              <s>I ſay that the Line A B G D is the Circumference of a
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                <figure id="id.073.01.008.1.jpg" xlink:href="073/01/008/1.jpg" number="3"/>
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              Circle, and that the Center
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              thereof is the Point K And
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              if it be poſſible that it may
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              not be the Circumference
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              of a Circle, the Right­
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                <arrow.to.target n="marg1130"/>
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              Lines drawn ^{*} by the Point
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              K to the ſaid Line A B G D
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              ſhall not be equal. </s>
              <s>There­
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              fore let a Right-Line be
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              taken greater than ſome of thoſe produced from the Point K unto
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              the ſaid Line A B G D, and leſſer than ſome other; and upon the
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              Point K let a Circle be deſcribed at the length of that Line,
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              Now the Circumference of this Circle ſhall fall part without the
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              ſaid Line A B G D, and part within: it having been preſuppoſed
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              that its Semidiameter is greater than ſome of thoſe Lines that may
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              be drawn from the ſaid Point K unto the ſaid Line A B G D, and
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              leſſer than ſome other. </s>
              <s>Let the Circumference of the deſcribed
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              Circle be R B G H, and from B to K draw the Right-Line B K: and
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              drawn alſo the two Lines K R, and K E L which make a Right­
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              Angle in the Point K: and upon the Center K deſcribe the Circum­
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              ference X O P in the Plane and in the Liquid. </s>
              <s>The parts, there­
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              fore, of the Liquid that are ^{*} according to the Circumference
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                <arrow.to.target n="marg1131"/>
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              X O P, for the reaſons alledged upon the firſt
                <emph type="italics"/>
              Suppoſition,
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              are equi­
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              jacent, or equipoſited, and contiguous to each other; and both
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              theſe parts are preſt or thruſt, according to the ſecond part of the
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                <emph type="italics"/>
              Suppoſition,
                <emph.end type="italics"/>
              by the Liquor which is above them. </s>
              <s>And becauſe the
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              two Angles E K B and B K R are ſuppoſed equal [
                <emph type="italics"/>
              by the
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              26.
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              of
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              3.
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                <emph type="italics"/>
              of Euclid,
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              ] the two Circumferences or Arches B E and B R ſhall
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              be equal (foraſmuch as R B G H was a Circle deſcribed for ſatis­
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              faction of the Oponent, and K its Center:) And in like manner
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              the whole Triangle B E K ſhall be equal to the whole Triangle
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              B R K. </s>
              <s>And becauſe alſo the Triangle O P K for the ſame reaſon </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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