Galilei, Galileo, Discourse concerning the natation of bodies, 1663

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb pagenum="410"/>
                <figure id="fig262" number="1"/>
                <lb/>
                <emph type="italics"/>
              Maſſe of the Solid depreſſed, namely of
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              H I K, being equall to the only part E I K,
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              which is contained under the firſt Levell
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              E F G. </s>
              <s>Which is manifeſt, becauſe if
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              the Solid H I K be taken out, the Water
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              I G ſhall return into the place occupied by
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              the Maſs E I K, where it was continuate
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              fore the ſubmerſion of the Priſme. </s>
              <s>And
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              the Maſs L G being equall to the Maſs
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              E K: adde thereto the Maſs E N, and it
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              ſhall be the whole Maſs E M, compoſed of the parts of the Priſme E N,
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              and of the Water N F, equall to the whole Solid H I K: And,
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              fore, the Maſs L G ſhall have the ſame proportion to E M, as to the
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              Maſs H I K: But the Maſs L G hath the ſame proportion to the Maſs
                <lb/>
              E M, as the Surface L M hath to the Surface M H: Therefore it is
                <lb/>
              nifeſt, that the Maſs of Water repulſed L G, is in proportion to the Maſs
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              of the Solid ſubmerged H I K; as the Surface L M, namely, that of the
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              Water ambient about the Sollid, to the whole Surface H M, compounded
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              of the ſaid ambient water, and the Baſe of the Priſme H N. </s>
              <s>But if we
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              ſuppoſe the firſt Levell of the Water the according to the Surface H M,
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              and the Priſme allready ſubmerged H I K; and after to be taken out and
                <lb/>
              raiſed to E A O, and the Water to be faln from the firſt Levell H L M as
                <lb/>
              low as E F G; It is manifeſt, that the Priſme E A O being the ſame with
                <lb/>
              H I K, its ſuperiour part H O, ſhall be equall to the inferiour E I K:
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              and remove the common part E N, and, conſequently, the Maſs of the
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              Water L G is equall to the Maſs H O; and, therefore, leſs than the
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              Solid, which is without the Water, namely, the whole Priſme E A O, to
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              which likewiſe, the ſaid Maſs of Water abated L G, hath the ſame
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              tion, that the Surface of the Waters circumfuſed L M hath to the ſame
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              circumfuſed Surface, together with the Baſe of the Priſme A O: which
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              hath the ſame demonſtration with the former caſe above.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              And from hence is inferred, that the Maſs of the Water, that riſeth in
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              the immerſion of the Solid, or that ebbeth in elevating it, is not equall to
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              all the Maſs of the Solid, which is ſubmerged or elevated, but to that
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              part only, which in the immerſion is under the firſt Levell of the Water,
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              and in the elevation remaines above the firſt Levell: Which is that
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              which was to be demonſtrated. </s>
              <s>We will now purſue the things that
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              remain.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>And firſt we will demonſtrate that,</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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