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

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb pagenum="460"/>
              the height of the emergent Point ſhall be double to the height of the
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              Rampart. </s>
              <s>This that hath been demonſtrated in Cones, exactly holds
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              in Piramides, although the one or the other ſhould be very ſharp in
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                <arrow.to.target n="marg1524"/>
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              their Point or Cuſpis: From whence we conclude, that the ſame
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              Accident ſhall ſo much the more eaſily happen in all other Figures,
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              by how much the leſs ſharp the Tops ſhall be, in which they
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              mine, being aſſiſted by more ſpacious Ramparts.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1524"/>
              Natatiou
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              eſt effected in
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              Figures broad
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              toward the top.</s>
            </p>
            <p type="head">
              <s>THEOREME
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                <arrow.to.target n="marg1525"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1525"/>
              All Figures ſink
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              or ſwim, upon
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              bathing or not
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              bathing of their
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              tops.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              All Figures, therefore, of whatever greatneſſe, may
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              go, and not go, to the Bottom, according as their
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              ties or Tops ſhall be bathed or not bathed.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>And this Accident being common to all ſorts of Figures, without
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              exception of ſo much as one. </s>
              <s>Figure hath, therefore, no part
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              in the production of this Effect, of ſometimes ſinking, and
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              times again not ſinking, but only the being ſometimes conjoyned
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              to, and ſometimes ſeperated from, the ſupereminent Air: which
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              cauſe, in fine, who ſo ſhall rightly, and, as we ſay, with both his
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              Eyes, conſider this buſineſs, will find that it is reduced to, yea, that
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              it really is the ſame with, the true, Naturall and primary cauſe of
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              Natation or Submerſion; to wit, the exceſs or deficiency of the
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              Gravity of the water, in relation to the Gravity of that Solid
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              nitude, that is demitted into the water. </s>
              <s>For like as a Plate of Lead,
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              as thick as the back of a Knife, which being put into the water by it
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              ſelf alone goes to the bottom, if upon it you faſten a piece of Cork
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              four fingers thick, doth continue afloat, for that now the Solid that
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              is demitted in the water, is not, as before, more grave than the water,
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              but leſs, ſo the Board of Ebony, of its own nature more grave than
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              water; and, therefore, deſcending to the bottom, when it is
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              ted by it ſelf alone into the water, if it ſhall be put upon the water,
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              conjoyned with an Expanded vail of Air, that together with the
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              Ebony doth deſcend, and that it be ſuch, as that it doth make with
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              it a compound leſs grave than ſo much water in Maſs, as equalleth
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              the Maſs already ſubmerged and depreſſed beneath the Levell of the
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              waters Surface, it ſhall not deſcend any farther, but ſhall reſt, for
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              no other than the univerſall and moſt common cauſe, which is that
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              Solid Magnitudes, leſs grave
                <emph type="italics"/>
              inſpecie
                <emph.end type="italics"/>
              than the water, go not to the
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              bottom.</s>
            </p>
            <p type="main">
              <s>So that if one ſhould take a Plate of Lead, as for Example, a finger
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              thick, and an handfull broad every way, and ſhould attempt to make
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              it ſwimme, with putting it lightly on the water, he would loſe his
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              Labour, becauſe that if it ſhould be depreſſed an Hairs breadth </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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