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

Table of figures

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    <archimedes>
      <text>
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          <chap>
            <p type="main">
              <s>
                <pb pagenum="417"/>
              ment or ebbing of the water A C, hath to the riſe or elevation of
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              the ſaid Solid M. Therefore, by Perturbation of proportion, in the
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              aſcent of the ſaid Solid M, the abaſement of the water A B C D, to
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              the abaſement of the water E N S F, hath the ſame proportion, that the
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              Surface of the water E F, hath to the Surface of the water A D;
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              that is, that the whole Maſs of the water E N S F, hath to the whole
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              Maſs A B C D, being equally high: It is manifeſt, therefore, that
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              in the expulſion and elevation of the Solid M, the water E N S F
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              ſhall exceed in Velocity of
                <emph type="italics"/>
              M
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              otion the water A B C D, aſmuch as it
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              on the other ſide is exceeded by that in quantity: whereupon their
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              Moments in ſuch operations, are mutually equall.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              And, for ampler confirmation, and clearer explication of this, let us
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              conſider the preſent Figure, (which if I be not deceived, may ſerve to
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              detect the errors of ſome Practick Mechanitians, who upon a falſe
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              tion ſome times attempt impoſſible enterprizes,) in which, unto the large
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              Veſſell E I D F, the narrow Funnell or Pipe I C A B is continued, and
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              poſe water infuſed into them, unto the Levell L G H, which water ſhall
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              reſt in this poſition, not without admiration in ſome, who cannot conceive
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                <figure id="fig268" number="7"/>
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                <emph type="italics"/>
              how it can be, that the heavie charge of the great
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              Maſs of water G D, preſſing downwards, ſhould
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              not elevate and repulſe the little quantity of the
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              other, contained in the Funnell or Pipe C L, by
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              which the deſcent of it is reſisted and hindered:
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              But ſuch wonder ſhall ceaſe, if we begin to ſuppoſe
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              the water G D to be abaſed only to Q D, and
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              ſhall afterwards conſider, what the water C L
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              hath done, which to give place to the other, which
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              is deſcended from the Levell G H, to the Levell
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              Q O, ſhall of neceſſity have aſcended in the ſame
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              time, from the Levell Lunto A B. </s>
              <s>And the
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              aſcent L B, ſhall be ſo much greater than the
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              ſcent G Q, by how much the breadth of the Veſſell
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              G D, is greater than that of the Funnell I C;
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              which, in ſumme, is as much as the water G D,
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              is more than the water L C: but in regard that the Moment of the Velocity
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              of the Motion, in one Moveable, compenſates that of the Gravity of
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              ther, what wonder is it, if the ſwift aſcent of the leſſer Water C L, ſhall
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              reſiſt the ſlow deſcent of the greater G D
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              ?</s>
            </p>
            <p type="main">
              <s>The ſame, therefore, happens in this operation, as in the Stilliard,
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              in which a weight of two pounds counterpoyſeth an other of 200,
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              asoften as that ſhall move in the ſame time, a ſpace 100 times
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              er than this: which falleth out when one Arme of the Beam is an </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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