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

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="452"/>
            <p type="head">
              <s>COROLARY
                <lb/>
                <arrow.to.target n="marg1517"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1517"/>
              Amongſt Cones
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              of the ſame Baſe,
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              thoſe of leaſt
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              titude ſhall ſink
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              the leaſt.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              That making upon the ſame Baſis, a Cone of a leſs Altitude, it ſhall be
                <lb/>
              alſo leſs grave, and ſhall ſo much the more reſt without Submerſion.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>COROLARY II.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              It is manifeſt, alſo, that one may make Cones and Piramids of any Matter
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg1518"/>
                <lb/>
                <emph type="italics"/>
              whatſoever, more grave than the water, which being put into the
                <lb/>
              water, with the Apix or Point downwards, reſt without Submerſion.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1518"/>
              There may be
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              Cones and
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              mides of any
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              Matter, which
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              demitted with
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              the Point
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              wards do float
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              top.</s>
            </p>
            <p type="main">
              <s>Becauſe if we reaſſume what hath been above demonſtrated,
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              Priſms and Cylinders, and that on Baſes equall to thoſe of the
                <lb/>
              ſaid Cylinders, we make Cones of the ſame Matter, and
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              times as high as the Cylinders, they ſhall reſt afloat, for that in Maſs
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              and Gravity they ſhall be equall to thoſe Cylinders, and by having
                <lb/>
              their Baſes equall to thoſe of the Cylinders, they ſhall leave equall
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              Maſſes of Air included within the Ramparts. </s>
              <s>This, which for
                <lb/>
              ple ſake hath been demonſtrated, in Priſms, Cylinders, Cones and
                <lb/>
              Piramids, might be proved in all other Solid Figures, but it would
                <lb/>
              require a whole Volume (ſuch is the multitude and variety of their
                <lb/>
              Symptoms and Accidents) to comprehend the particuler demonſtration
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              of them all, and of their ſeverall Segments: but I will to avoid prolixity
                <lb/>
              in the preſent Diſcourſe, content my ſelf, that by what I have declared
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              every one of ordinary Capacity may comprehend, that there is not
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              any Matter ſo grave, no not Gold it ſelf, of which one may not form
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              all ſorts of Figures, which by vertue of the ſuperiour Air adherent to
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              them, and not by the Waters Reſiſtance of Penetration, do remain
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              afloat, ſo that they ſink not. </s>
              <s>Nay, farther, I will ſhew, for removing
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              that Error, that,</s>
            </p>
            <p type="head">
              <s>THEOREME
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                <arrow.to.target n="marg1519"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1519"/>
              A Piramide or
                <lb/>
              Cone, demitted
                <lb/>
              with the Point
                <lb/>
              downwards ſhal
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              ſwim, with its
                <lb/>
              Baſe downward
                <lb/>
              ſhall ſink.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              A Piramide or Cone put into the Water, with the Point
                <lb/>
              downward ſhall ſwimme, and the ſame put with the
                <lb/>
              Baſe downwards ſhall ſinke, and it ſhall be impoſſible
                <lb/>
              to make it float.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Now the quite contrary would happen, if the difficulty of Pene­
                <lb/>
              trating the water, were that which had hindred the deſcent, for
                <lb/>
              that the ſaid Cone is far apter to pierce and penetrate with its ſharp
                <lb/>
              Point, than with its broad and ſpacious Baſe.</s>
            </p>
            <p type="main">
              <s>And, to demonſtrate this, let the Cone be
                <emph type="italics"/>
              A B C,
                <emph.end type="italics"/>
              twice as grave
                <lb/>
              as the water, and let its height be tripple to the height of the Rampart
                <lb/>
                <emph type="italics"/>
              D A E C
                <emph.end type="italics"/>
              : I ſay, firſt, that being put lightly into the water with the </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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