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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb pagenum="447"/>
              Maſs I S. </s>
              <s>I ſay, that the Solid I S ſhall not
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              ſinke, but being never ſo little thicker it ſhall
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              go to the bottom: For being that as A I is
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                <figure id="fig272" number="11"/>
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              to I O, ſo is the Exceſs of the Gravity of the
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              Solid I S, above the Gravity of a Maſs of water
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              equall to the Maſs I S, to the Gravity of the
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              ſaid Maſs of water: Therefore, compounding, as A O is to O I, ſo
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              ſhall the Gravity of the Solid I S, be to the Gravity of a Maſs of water
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              equall to the Maſs I S: And, converting, as I O is to O A, ſo ſhall the
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              Gravity of a Maſs of water equall to the Maſs I S, be to the Gravity
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              of the Solid I S: But as I O is to O A, ſo is a Maſs of water I S, to a
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              Maſs of water equall to the Maſs A B S O: and ſo is the Gravity of
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              a Maſs of water I S, to the Gravity of a Maſs of water A S: Therefore
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              as the Gravity of a Maſs of water, equall to the Maſs I S, is to the
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              Gravity of the Solid I S, ſo is the ſame Gravity of a Maſs of water
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              I S, to the Gravity of a Maſs of Water A S: Therefore the
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              vity of the Solid I S, is equall to the Gravity of a Maſs of water
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              quall to the Maſs A S: But the Gravity of the Solid I S, is the ſame
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              with the Gravity of the Solid A S, compounded of the Solid I S,
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              and of the Air A B C I. </s>
              <s>Therefore the whole compounded Solid
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              A O S B, weighs as much as the water that would be compriſed in the
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              place of the ſaid Compound A O S B: And, therefore, it ſhall make
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              an
                <emph type="italics"/>
              Equilibrium
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              and reſt, and that ſame Solid I O S C ſhall ſinke no
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              farther. </s>
              <s>But if its thickneſs I O ſhould be increaſed, it would be
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              ceſſary alſo to encreaſe the Altitude of the Rampart A I, to
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              tain the due proportion: But by what hath been ſuppoſed, the
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              tude of the Rampart A I, is the greateſt that the Nature of the
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              Water and Air do admit, without the waters repulſing the Air
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              herent to the Superficies of the Solid I C, and poſſeſſing the ſpace
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              A I C B: Therefore, a Solid of greater thickneſs than I O, and of the
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              ſame Matter with the Solid I S, ſhall not reſt without ſubmerging,
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              but ſhall deſcend to the bottome: which was to be demonſtrated.
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              </s>
              <s>In conſequence of this that hath been demonſtrated, ſundry and
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              rious Concluſions may be gathered, by which the truth of my
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              cipall Propoſition comes to be more and more confirmed, and the
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              imperfection of all former Argumentations touching the preſent
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              Queſtion cometh to be diſcovered.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              And firſt we gather from the things demonstrated, that,
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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