Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/152.jpg" pagenum="65"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              LEMMA.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Sit data recta PO, & in ea punctum D, & punctum quod­
                <lb/>
              dam R in ipſa DO, ita vt VD ipſius PD, ad DT ipſius DO,
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              ſit vt PD, ad DO: ſit autem maior proportio PS ad SO, quàm
                <lb/>
              VR, ad RT. </s>
              <s>Dico OS, minorem eſſe quàm OR.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Fiat enim vt PS, ad SO, ita VZ ad ZT; ma­
                <lb/>
              ìor igitur erit proportio VZ, ad ZT, quàm VR, ad
                <lb/>
              RT: & componendo maior proportio VT, ad TZ,
                <lb/>
                <figure id="id.043.01.152.1.jpg" xlink:href="043/01/152/1.jpg" number="116"/>
                <lb/>
              quàm VT, ad TR; minor igitur TZ, quàm TR, ideſt
                <lb/>
              maior DZ, quàm DR. </s>
              <s>Rurſus quia componendo eſt
                <lb/>
              vt PO ad OS, ita VT ad TZ: ſed vt DO ad OP, ita
                <lb/>
              eſt DT ad TV; erit ex æquali, vt DO ad OS, ita DT,
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              ad TZ; & per conuerſionem rationis, vt OD ad DS,
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              ita TD ad DZ: & permutando, vt DO ad DT, ita DS
                <lb/>
              ad DZ: ſed DO, eſt maior quàm DT, ergo & DS, erit
                <lb/>
              maior quàm DZ: ſed DZ maior erat quàm DR; multo
                <lb/>
              ergo DS maior quàm DR, vnde minor erit OS quàm
                <lb/>
              OR. </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XXXVII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Si datæ maiori ſphæræ portioni cylindrus cir­
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              cumſcribatur circa eundem axim portionis, cen­
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              trum grauitatis reliquæ figuræ ex cylindro cir­
                <lb/>
              cumſcripto ablata portione, propinquius erit ver­
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              tici portionis, quàm
                <expan abbr="cẽtrum">centrum</expan>
              grauitatis portionis. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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