Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/162.jpg" pagenum="75"/>
              ad GE, altera maiori extremæ FG in proportione con­
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              tinua ipſius NG ad GF. </s>
              <s>Quoniam enim ob centra gra
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              uitatis QPR eſt vt QP ad PR, ita portio ABCD ad
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              reliquum cylindri LM, erit componendo, & per conuer­
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              ſionem rationis, & conuertendo, vt PQ ad QR, ita por­
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              tio ABCD ad LM cylindrum: ſed portio ABCD ad
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              LM cylindrum eſt vt prædictus exceſſus ad axim EF;
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              vtigitur prædictus exceſſus ad axim EF, ita eſt PQ ad
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              QR. </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XLI.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis conoidis parabolici centrum grauita­
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              tis eſt punctum illud, in quo axis ſic diuiditur vt
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              pars, quæ eſt ad verticem ſit dupla reliquæ. </s>
            </p>
            <p type="main">
              <s>Sit conoides parabolicum ABC, cuius vertex B, axis
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              autem BD ſectus in puncto E ita vt EB ſit ipſius ED
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              dupla. </s>
              <s>Dico E eſse centrum grauitatis conoidis ABC.
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              </s>
              <s>Nam in ſectione per
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              axim parabola ABC,
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              cuius diameter erit B
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              D, deſcribatur rian­
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              gulum ABC; ſum­
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              ptisque ipſius BD æ­
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              qualibus DH, HO,
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              per puncta H, O, ſe­
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              centur vnà parabola
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              & triangulum ABC
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              duabus rectis FGH
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                <figure id="id.043.01.162.1.jpg" xlink:href="043/01/162/1.jpg" number="123"/>
                <lb/>
              KL, MNOPQ: & per eas rectas ſecetur conoi­
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              des ABC planis baſi parallelis, factæ autem ſe­
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              ctiones erunt circuli circa FL, MQ, & in parabola </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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