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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb pagenum="454"/>
              tend to the bottom: Therefore, the whole
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
              one F T O, as well in
                <lb/>
              reſpect of the part ſubmerged, as the part above water ſhall
                <lb/>
              ſcend to the bottom. </s>
              <s>But if the Altitude of the Point F N S, ſhall
                <lb/>
              be half the Altitude of the whole Cone F T O, the ſame Altitude of
                <lb/>
              the ſaid
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
              one F N S ſhall be Seſquialter to the Altitude E N: and,
                <lb/>
              therefore, E N S C ſhall be double to the Cone F N S; and as much
                <lb/>
              water in Maſs as the
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
              ylinder E N S C, would weigh as much as the
                <lb/>
              part of the
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
              one F N S. But, becauſe the other immerged part
                <lb/>
              N T O S, is double in Gravity to the water, a Maſs of water equall
                <lb/>
              to that compounded of the
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
              ylinder E N S C, and of the Solid N T O S,
                <lb/>
              ſhall weigh leſs than the
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
              one F T O, by as much as the weight of
                <lb/>
              a Maſs of water equall to the Solid N T O S: Therefore, the
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
              one
                <lb/>
              ſha l alſo deſcend. </s>
              <s>Again, becauſe the Solid N T O S, is ſeptuple
                <lb/>
              to the
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
              one F N S, to which the
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
              ylinder E S is double, the
                <lb/>
              tion of the Solid N T O S, ſhall be to the
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
              ylinder E N S C, as ſeaven
                <lb/>
              to two: Therefore, the whole Solid compounded of the
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
              ylinder
                <lb/>
              E N S C, and of the Solid N T O S, is much leſs than double the
                <lb/>
              Solid N T O S: Therefore, the ſingle Solid N T O S, is much graver
                <lb/>
              than a Maſs of water equall to the Maſs, compounded of the
                <emph type="italics"/>
              C
                <emph.end type="italics"/>
                <lb/>
              linder E N S C, and of N T O S.</s>
            </p>
            <p type="head">
              <s>COROLARY
                <lb/>
                <arrow.to.target n="marg1521"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1521"/>
              Part of the
                <lb/>
              Cones towards
                <lb/>
              the Cuſpis
                <lb/>
              ved, it ſhall ſtill
                <lb/>
              ſink.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              From whence it followeth, that though one ſhould remove and take
                <lb/>
              way the part of the Cone F N S, the ſole remainder N T O S would
                <lb/>
              go to the bottom.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="head">
              <s>COROLARY III.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              And if we ſhould more depreſs the Cone F T O, it would be ſo much the
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg1522"/>
                <lb/>
                <emph type="italics"/>
              more impoſſible that it ſhould ſuſtain it ſelf afloat, the part ſubmerged
                <lb/>
              N T O S ſtill encreaſing, and the Maſs of Air contained in the Rampart
                <lb/>
              diminiſhing, which ever grows leſs, the more the Cone ſubmergeth.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1522"/>
              The more the
                <lb/>
              Cone is
                <lb/>
              ged, the more
                <lb/>
              impoſſible is its
                <lb/>
              floating.</s>
            </p>
            <p type="main">
              <s>That Cone, therefore, that with its Baſe upwards, and its
                <lb/>
                <emph type="italics"/>
              Cuſpis
                <emph.end type="italics"/>
              downwards doth ſwimme, being dimitted with its Baſe
                <lb/>
              downward muſt of neceſſity ſinke. </s>
              <s>They have argued farre
                <lb/>
              from the truth, therefore, who have aſcribed the cauſe of Natation
                <lb/>
              to waters reſiſtance of Diviſion, as to a paſſive principle, and to the
                <lb/>
              breadth of the Figure, with which the diviſion is to be made, as the
                <lb/>
              Efficient.</s>
            </p>
            <p type="main">
              <s>I come in the fourth place, to collect and conclude the reaſon of
                <lb/>
              that which I have propoſed to the Adverſaries, namely,</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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