Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/069.jpg" pagenum="61"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XXXI.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis pyramidis triangulam baſim habentis
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              idem eſt centrum grauitatis, & figuræ. </s>
            </p>
            <p type="main">
              <s>Sit pyramis ABCD, cuius baſis triangulum ABC,
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              centrum autem E. </s>
              <s>Dico E, eſſe centrum grauitatis pyra­
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              midis ABCD. </s>
              <s>Secta enim ABCD, pyramide in quatuor
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              pyramides, ſimiles, & æquales inter ſe, & toti pyramidi
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              ABCD, & vnum octaedrum, ſint eæ pyramides DKLM,
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              MGCH, LBGF,
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              AKFH. </s>
              <s>Octaedrum
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              autem FGHKLM,
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              quod dimidium erit
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              pyramidis ABCD, &
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              ſint axes pyramidum
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              DSN, DS, KO, LP,
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              MQ: & ARG, iunga
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              tur. </s>
              <s>Quoniam igitur
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              FH, eſt parallela ipſi
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              BC, & ſecta eſt BC,
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              bifariam in puncto G,
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                <expan abbr="trãſibit">tranſibit</expan>
              recta AG, per
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              centra
                <expan abbr="triangulorũ">triangulorum</expan>
              O,
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              & N, ad quæ axes KO,
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                <figure id="id.043.01.069.1.jpg" xlink:href="043/01/069/1.jpg" number="45"/>
                <lb/>
              DN, terminantur; manifeſtum hoc eſt ex ſuperioribus:
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              eritque dupla AO, ipſius OR, nec non AN, dupla ipſius
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              NG, componendo igitur erit vt AG, ad GN, ita AR,
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              ad RO, & permutando, vt AG, ad AR, ita GN, ad
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              RO: ſed AG, eſt dupla ipſius AR, quoniam & AB, ip­
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              ſius AF; igitur & GN, erit dupla ipſius RO: ſed & GN,
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              eſt dupla ipſius NR, nam N, eſt centrum trianguli GFH;
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              æqualis eſt igitur NR, ipſi RO, atque hinc dupla NO, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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