Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/063.jpg" pagenum="55"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSIT'IO XXVII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Solida grauia æquiponderant à longitudini­
                <lb/>
              bus ex contraria parte reſpondentibus. </s>
            </p>
            <p type="main">
              <s>Sint ſolida grauia A, & B, quorum centra grauitatis
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              ſint A, B, ſecundum quæ ſuſpenſa intelligantur A, in
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              puncto C, & B, in puncto D, cuiuslibet rectæ GH, quæ
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              ſit ita diuiſa in puncto E, vt ſit DE, ad EC, vt eſt A,
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              ad B. </s>
              <s>Dico ſolida A, E, æquiponderare à longitudini­
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              bus DE, EC; hoc eſt vtriuſque ſimul centrum grauita­
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              tis eſse E. </s>
              <s>Nam ſi A, B, ſint æqualia, manifeſtum eſt
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              propoſitum: ſi au­
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              tem inæqualia, eſto
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              maius A: maior igi
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              tur erit DE, quam
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              EC. abſcindatur
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              DF, æqualis EC:
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              erit igitur DE, æ­
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              qualis GF: & CD,
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              vtrin que producta,
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              ponatur DH, æ­
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              qualis DF: & CG,
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              ipſi CF. & circa
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              axim, &
                <expan abbr="altitudinẽ">altitudinem</expan>
                <lb/>
              GH, eſto paralle­
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              lepipedum KL, æ­
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              quale duobus ſo­
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                <figure id="id.043.01.063.1.jpg" xlink:href="043/01/063/1.jpg" number="39"/>
                <lb/>
              lidis A, B, ſimul & parallelepipedum KL, ſecetur plano
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              per punctum F, oppoſitis planis parallelo, in duo paral­
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              lelepipeda KN, ML. </s>
              <s>Quoniam igitur eſt vt GF, ad
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              FH, ita parallelepipedum KN, ad parallelepipedum </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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