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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb pagenum="431"/>
              below the Levell of the water, almoſt twenty times the thickneſs
                <lb/>
              of the Plate, as I ſhall anon declare.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1464"/>
              Bodies of all
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              Figures, laid
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              on the water, do
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              penetrate its
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              Craſſitude, and
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              in what
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              tion.</s>
            </p>
            <p type="main">
              <s>But let us proceed to evince, that the water yields and ſufters it
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              ſelf to be penetrated by every the lighteſt Body; and therewithall
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              demonſtrate, how, even by Matters that ſubmerge not, we may
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              come to know that Figure operates nothing about the going or
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              not going to the Bottom, ſeeing that the water ſuffers it ſelf to be
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              penetrated equally by every Figure.</s>
            </p>
            <p type="main">
              <s>Make a Cone, or a Piramis of Cypreſs, of Firre, or of other
                <lb/>
                <arrow.to.target n="marg1465"/>
                <lb/>
              Wood of like Gravity, or of pure Wax, and let its height be
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              what great, namely a handfull, or more, and put it into the water
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              with the Baſe downwards: firſt, you ſhall ſee that it will penetrate
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              the water, nor ſhall it be at all impeded by the largeneſs of the Baſe,
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              nor yet ſhall it ſink all under water, but the part towards the point
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              ſhall lye above it: by which ſhall be manifeſt, firſt, that that Solid
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              forbeares not to ſink out of an inabillity to divide the Continuity
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              of the water, having already divided it with its broad part, that in
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              the opinion of the Adverſaries is the leſs apt to make the diviſion.
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              </s>
              <s>The Piramid being thus fixed, note what part of it ſhall be
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              merged, and revert it afterwards with the point downwards, and
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              you ſhall ſee that it ſhall not dive into the water more than before,
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              but if you obſerve how far it ſhall ſink, every perſon expert in
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              Geometry, may meaſure, that thoſe parts that remain out of the
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              water, both in the one and in the other Experiment are equall to
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              an hair: whence he may manifeſtly conclude, that the acute Figure
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              which ſeemed moſt apt to part and penetrate the water, doth not
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              part or penetrate it more than the large and ſpacious.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1465"/>
              The
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              ment of a Cone,
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              demitted with
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              its Baſe, and
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              ter with its
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              Point
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              wards.</s>
            </p>
            <p type="main">
              <s>And he that would have a more eaſie Experiment, let him take
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              two Cylinders of the ſame Matter, one long and ſmall, and the
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              ther ſhert, but very broad, and let him put them in the water, not
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              diſtended, but erect and endways: he ſhall ſee, if he diligently
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              meaſure the parts of the one and of the other, that in each of them
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              the part ſubmerged, retains exactly the ſame proportion to that
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              out of the water, and that no greater part is ſubmerged of that
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              long and ſmall one, than of the other more ſpacious and broad:
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              howbeit, this reſts upon a very large, and that upon a very little
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              Superficies of water: therefore the diverſity of Figure, occaſioneth
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              neither facility, nor difficulty, in parting and penetrating the
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              tinuity of the water; and, conſequently, cannot be the Cauſe of the
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              Natation or Submerſion. </s>
              <s>He may likewiſe diſcover the
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              operating of variety of Figures, in ariſing from the Bottom of the
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              water, towards the Surface, by taking Wax, and tempering it with
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              a competent quantity of the filings of Lead, ſo that it may become
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              a conſiderable matter graver than the water: then let him make </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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