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

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    <archimedes>
      <text>
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          <chap>
            <pb pagenum="408"/>
            <p type="main">
              <s>That is to ſay, that by how much the one is leſs grave than the other,
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              by ſo much is it in a conſtitution of moving more ſwiftly than that.</s>
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            <p type="main">
              <s>Having prefatically explicated theſe things, we may begin to en­
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              quire, what Bodyes thoſe are which totally ſubmerge in Water, and
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              go to the Bottom, and which thoſe that by conſtraint float on the
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              top, ſo that being thruſt by violence under Water, they return to
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              ſwim, with one part of their Maſs viſible above the Surface of the
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              Water: and this we will do by conſidering the reſpective operati­
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              on of the ſaid Solids, and of Water: Which operation followes
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              the Submerſion and ſinking; and this it is, That in the Submerſion
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              that the Solid maketh, being depreſſed downwards by its proper
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              Gravity, it comes to drive away the water from the place where it
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              ſucceſſively ſubenters, and the water repulſed riſeth and aſcends
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              above its firſt levell, to which Aſcent on the other ſide it, as being a
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              grave Body of its own nature, reſiſts: And becauſe the deſcending
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              Solid more and more immerging, greater and greater quantity of
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              Water aſcends, till the whole Sollid be ſubmerged; its neceſſary to
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              compare the Moments of the Reſiſtance of the water to Aſcenſion,
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              with the Moments of the preſſive Gravity of the Solid: And if the
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              Moments of the Reſiſtance of the water, ſhall equalize the Moments
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                <arrow.to.target n="marg1405"/>
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              of the Solid, before its totall Immerſion; in this caſe doubtleſs there
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              ſhall be made an
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              Equilibrium,
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              nor ſhall the Body ſink any farther.
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              </s>
              <s>But if the Moment of the Solid, ſhall alwayes exceed the Moments
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              wherewith the repulſed water ſucceſſively makes Reſiſtance, that
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              Solid ſhall not only wholly ſubmerge under water, but ſhall deſcend
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              to the Bottom. </s>
              <s>But if, laſtly, in the inſtant of totall Submerſion,
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              the equality ſhall be made between the Moments of the prement
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              Solid, and the reſiſting Water; then ſhall reſt enſue, and the ſaid
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              Solid ſhall be able to reſt indifferently, in whatſoever part of the
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              water. </s>
              <s>By this time is manifeſt the neceſſity of comparing the
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              Gravity of the water, and of the Solid; and this compariſon might
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              at firſt ſight ſeem ſufficient to conclude and determine which are the
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              Solids that float a-top, and which thoſe that ſink to the Bottom in the
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              water, aſſerting that thoſe ſhall float which are leſſe grave
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              in ſpecie
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              than the water, and thoſe ſubmerge, which are
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              in ſpecie
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              more grave.
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              </s>
              <s>For it ſeems in appearance, that the Sollid in ſinking continually,
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              raiſeth ſo much Water in Maſs, as anſwers to the parts of its own
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              Bulk ſubmerged: whereupon it is impoſſible, that a Solid leſs grave
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                <emph type="italics"/>
              in ſpecie,
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              than water, ſhould wholly ſink, as being unable to raiſe a
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              weight greater than its own, and ſuch would a Maſs of water equall
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              to its own Maſs be. </s>
              <s>And likewiſe it ſeems neceſſary, that the graver
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              Solids do go to the Bottom, as being of a Force more than ſufficient
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              for the raiſing a Maſſe of water, equall to its own, though inferiour
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              in weight. </s>
              <s>Nevertheleſs the buſineſs ſucceeds otherwiſe: and </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>