Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/151.jpg" pagenum="64"/>
              KLMN abſciſſum ijſdem planis, quibus por­
                <lb/>
              tio, & ſphæræ ſemidiameter ſit EHGS: & po­
                <lb/>
              ſita T tripla ipſius ES, & V ipſius EG tri­
                <lb/>
              pla, eſto vt V ad T ita T ad XZ: & vt GE
                <lb/>
              ad EH ita EH ad
                <foreign lang="grc">ω</foreign>
              , & ſit ZY, ipſius XZ,
                <lb/>
              æqualis tribus GE, EH,
                <foreign lang="grc">ω</foreign>
              , vt ſit exceſſus
                <lb/>
              XY: & ſecto axe GH bifariam in puncto I, in
                <lb/>
              linea GI, ſumatur O, centrum grauitatis fru­
                <lb/>
              ſti KLMN: Et vt
                <foreign lang="grc">Υ</foreign>
              X ad XZ, ita fiat IO
                <lb/>
              ad OIP. </s>
              <s>Dico portionis ABCD centrum
                <lb/>
              grauitatis eſſe P. </s>
              <s>Nam circa axim GH pla­
                <lb/>
              nis baſium portionis interceptus ſtet cylin­
                <lb/>
              drus QR, cuius baſis ſit æqualis circulo ma­
                <lb/>
              ximo. </s>
              <s>Quoniam igitur eſt vt YX ad XZ,
                <lb/>
              hoc eſt vt IO ad OP, ita portio ABCD
                <lb/>
              ad cylindrum QR, & diuidendo vt OI ad
                <lb/>
              IP, ita portio ABCD ad reliquum cylindri
                <lb/>
              QR: & I eſt cylindri QR, & O prædicti
                <lb/>
              reſidui centrum grauitatis; erit reliquæ por­
                <lb/>
                <figure id="id.043.01.151.1.jpg" xlink:href="043/01/151/1.jpg" number="115"/>
                <lb/>
              tionis ABCD centrum grauitatis P. </s>
              <s>Quod demon­
                <lb/>
              ſtrandum erat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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