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

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              <s>
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              pieces, according to the Lines E F, G H,
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              &c.
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              making ſeven Segments,
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              we muſt adde to the twenty ſix Palmes of the circuit of the whole
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              Board, ſeventy others; whereupon the eight little pieces ſo cut and
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              ſeperated, have to cut ninty ſix Palmes of water. </s>
              <s>And, if moreover,
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              we cur each of the ſaid pieces into five parts,
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                <figure id="fig280" number="19"/>
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              ducing them into Squares, to the circuit of ninty
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              ſix Palmes, with four cuts of eight Palmes apiece;
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              we ſhall adde alſo ſixty four Palmes, whereupon
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              the ſaid Squares to deſcend in the water, muſt
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              divide one hundred and ſixty Palmes of water,
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              but the Reſiſtance is much greater than that of
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              twenty ſix; therefore to the leſſer Superficies,
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              we ſhall reduce them, ſo much the more eaſily
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              will they float: and the ſame will happen in all
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              other Figures, whoſe Superficies are ſimular amongſt themſelves, but
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              different in bigneſs: becauſe the ſaid Superficies, being either
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              ſhed or encreaſed, always diminiſh or encreaſe their Perimeters in
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              ſubduple proportion; to wit, the Reſiſtance that they find in
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              trating the water; therefore the little pieces gradually ſwim, with more
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              and more facility as their breadth is leſſened.</s>
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            <p type="main">
              <s>
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              This is manifeſt; for keeping ſtill the ſame height of the Solid, with
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              the ſame proportion as the Baſe encreaſeth or deminiſheth, doth the ſaid
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              Solid alſo encreaſe or diminiſh; whereupon the Solid more diminiſhing
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              than the Circuit, the Cauſe of Submerſion more diminiſheth than the Cauſe
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              of Natation: And on the contrary, the Solid more encreaſing than the
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              Circuit, the Cauſe of Submerſion encreaſeth more, that of Natation
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              leſs.
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              </s>
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              <s>And this may all be dedueed out of the Doctrine of
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              Ariſtotle
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              gainſt his own Doctrine.</s>
            </p>
            <p type="main">
              <s>Laſtly, to that which we read in the latter part of the Text, that
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                <arrow.to.target n="marg1551"/>
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              is to ſay, that we muſt compare the Gravity of the Moveable with
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              the Reſiſtance of the Medium againſt Diviſion, becauſe if the force of
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              the Gravity exceed the Reſiſtance of the
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              Medium,
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              the Moveable will
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              deſcend, if not it will float. </s>
              <s>I need not make any other anſwer,
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              but that which hath been already delivered; namely, that its not
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              the Reſiſtance of abſolute Diviſion, (which neither is in Water nor
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              Air) but the Gravity of the
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              Medium
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              that muſt be compared with the
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              Gravity of the Moveables; and if that of the
                <emph type="italics"/>
              Medium
                <emph.end type="italics"/>
              be greater, the
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              Moveable ſhall not deſcend, nor ſo much as make a totall Submerſion,
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              but a partiall only: becauſe in the place which it would occupy in
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              the water, there muſt not remain a Body that weighs leſs than a like
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              quantity of water: but if the Moveable be more grave, it ſhall
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              cend to the bottom, and poſſeſs a place where it is more conformable </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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