Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/113.jpg" pagenum="26"/>
              portionis circulus, cuius diameter AC, & vt EG ad GF,
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              ita ſit GF ad S, & S ad FM, cuius ſit pars tertia FN, &
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              ponatur ipſius BG, ſubſeſquialtera GL. </s>
              <s>Dico portio­
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              nem ABC ad cylindrum KH eſse vt LN ad BF. </s>
              <s>Nam
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              vt FG ad GE, ſiue ad BG, ita ſit EG ad PQ, à qua
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              abſcindatur QR, pars tertia ipſius FG. </s>
              <s>Et plano per G
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              tranſeunte baſibus cylindri KH, & ABC portionis pa­
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              rallelo ſecentur vna cylindrus KH in duos cylindros DH,
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              EK: & portio ABC, in portionem ECAD, & DBE
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              hemiſphærium. </s>
              <s>Quoniam igitur eſt conuertendo, vt PQ
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              ad EG, ita EG
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              ad GF, & eſt ip­
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              ſius GF pars ter
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              tia QR, erit por­
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              tio DACE ad
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              cylindrum EK,
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              vt PR ad
                <expan abbr="Pq.">Pque</expan>
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              Rurſus, quia eſt
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              vt EG ad GF:
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              hoc eſt vt PQ ad
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              EG, ita GF ad
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              S, & vt EG ad
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              GF, ita eſt S ad
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              FM; erit ex æqua
                <lb/>
                <figure id="id.043.01.113.1.jpg" xlink:href="043/01/113/1.jpg" number="85"/>
                <lb/>
              li, vt PQ ad GF, ita GF ad FM. </s>
              <s>Sed vt GF ad RQ,
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              ita eſt MF ad FN, tertiam ipſius MF partem, ex æquali
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              igitur erit vt PQ ad QR, ita GF ad FN, & per conuer­
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              ſionem rationis, & conuertendo, vt PR ad PQ, ita NG ad
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              GF. </s>
              <s>Sed vt PR ad PQ, ita erat portio ECAD ad cy­
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              lindrum EK; vtigitur NG ad GF, ita erit portio EC
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              AD ad cylindrum EK. </s>
              <s>Sed vt GF ad FB, ita eſt cy­
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              lindrus EK ad cylindrum KH: ex æquali igitur vt NG
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              ad BF, ita portio ECAD, ad cylindrum KH. </s>
              <s>Similiter
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              oſtenderemus eſse, vt GL ad BF, ita DBE hemiſphæ-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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