Archimedes, Natation of bodies, 1662

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="073/01/024.jpg" pagenum="353"/>
            <p type="head">
              <s>ARCHIMEDES,
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              HIS TRACT
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                <emph type="italics"/>
              DE
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              INSIDENTIBUS HUMIDO,
                <emph.end type="italics"/>
                <lb/>
              OR,
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              Of the NATATION of BODIES Upon, or
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              Submerſion In the WATER, or other LIQUIDS.</s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              BOOK
                <emph.end type="italics"/>
              II.</s>
            </p>
            <p type="head">
              <s>PROP. I. THEOR. I.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              If any Magnitude lighter than the Liquid be demitted
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              into the ſaid Liquid, it ſhall have the ſame proporti­
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              on in Gravity to a Liquid of equal Maſſe, that the
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              part of the Magnitude demerged hath unto the
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              whole Magnitude.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>For let any Solid Magnitude, as for in­
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              ſtance F A, lighter than the Liquid, be de­
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              merged in the Liquid, which let be F A:
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              And let the part thereof immerged be A,
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              and the part above the Liquid F, It is to
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              be demonſtrated that the Magnitude F A
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              hath the ſame proportion in Gravity to a
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              Liquid of Equall Maſſe that A hath to F
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              A. </s>
              <s>Take any Liquid Magnitude, as ſup­
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              poſe N I, of equall Maſſe with F A; and let F be equall to N, and
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              A to I: and let the Gravity of the whole Magnitude F A be B, and
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              let that of the Magnitude N I be O,
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              and let that of I be R. </s>
              <s>Now the
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                <figure id="id.073.01.024.1.jpg" xlink:href="073/01/024/1.jpg" number="19"/>
                <lb/>
              Magnitude F A hath the ſame pro­
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              portion unto N I that the Gravity B
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              hath to the Gravity O R: But for
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              aſmuch as the Magnitude F A demit­
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              ted into the Liquid is lighter than
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              the ſaid Liquid, it is manifeſt that a Maſſe of the Liquid, I, equall
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              to the part of the Magnitude demerged, A, hath equall Gravity
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                <arrow.to.target n="marg1163"/>
                <lb/>
              with the whole Magnitnde, F A: For this was
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              (a)
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              above demon­
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              ſtrated: But B is the Gravity of the Magnitude F A, and R of I: </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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