Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/054.jpg" pagenum="46"/>
            <p type="main">
              <s>Sed eſto polygonum æquilaterum, & æquiangulum,
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              ABCDEF, cuius laterum numerus ſit par, & centrum
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              eſto G. </s>
              <s>Dico idem G, eſse centrum grauitatis polygoni
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              ABCDEF. </s>
              <s>Iungantur enim angulorum oppoſitorum
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              puncta rectis lineis AD, BE, CF. </s>
              <s>Ex quarto igitur
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              Elem. ſecabunt ſeſe hæ rectæ omnes bifariam in vno pun­
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              cto, quod talis figuræ centrum definiuimus: ſed G poni­
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              tur centrum; in puncto igitur G. </s>
              <s>Quoniam igitur duo­
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              rum triangulorum CBG, GFE, anguli ad verticem
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              BGC, FGE, ſunt æquales; & vterlibet angulorum CBG,
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              GCB, æqualis eſt vtrilibet ipſorum EFG, GEF; ex
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              quarto Elem. & circa æquales angulos latera proportio­
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              nalia horum triangu
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              lorum ſunt æqualia;
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              ſimilia, & æqualia
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              erunt triangula BC
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              G, GFE: poſitis
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              igitur centris graui­
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              tatis K, H, duorum
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              triangulorum EFG,
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              GBC, iunctifque
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              KG, GH, erit v­
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              terlibet angulorum
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              BGH, HGC, æ­
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              qualis vtrilibet an­
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                <figure id="id.043.01.054.1.jpg" xlink:href="043/01/054/1.jpg" number="31"/>
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              gulorum CGK, KGE, propter ſimilitudinem poſitio­
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              nis centrorum K, H, in iſoſcelijs triangulis CBG,
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              GFE: (nam GH, ſi produceretur latus BC, bifariam
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              ſecaret: ſimiliter GK, latus EF) ſed CG, eſt in directum
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              poſita ipſi GF; igitur & GH ipſi GK: & ſunt æquales,
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              vtpote lateribus triangulorum BCG, GFE, æqualibus
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              homologæ; cum igitur eorundem triangulorum centra
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              grauitatis ſint K, H; centrum grauitatis duorum triangu­
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              lorum CBG, GFE, ſimul, erit punctum G. </s>
              <s>Eadem </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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