Valerio, Luca, De centro gravitatis solidorum, 1604

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/027.jpg" pagenum="19"/>
              tripla: ſed vt AF, ad FE, ita eſt CF, ad FL; tripla igi­
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              tur erit CF, ipſius FL. </s>
              <s>Similiter oſtenderemus rectas
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              AE, BM, ſecare ſe ſe in eaſdem rationes, ita vt ſegmen­
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              ta, quæ ad angulos, ſint tripla eorum, quæ ſunt ad centra
                <lb/>
              E, M, quorum AF, eſt tripla ipſius FE: in puncto igitur
                <lb/>
              F, ſecant ſe rectæ lineæ AE, BM. </s>
              <s>Eadem ratione & re
                <lb/>
              ctæ AE, DN, ſecent ſe in puncto F, neceſse erit: quare
                <lb/>
              vt AF ad FE, ita erit DF ad FN. </s>
              <s>Quatuor igitur
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              axes pyramidis ABCD, ſecantſe ſe in puncto F, in eaſ­
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              dem rationes, ita vt
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              ſegmenta ad angulos,
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              ſint
                <expan abbr="reliquorũ">reliquorum</expan>
              tripla.
                <lb/>
              </s>
              <s>Rurſus, quia compo­
                <lb/>
              nendo, & conuerten­
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              do, eſt vt FE ad EA,
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              ita FL ad LC: hoc
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              eſt, vt pyramis BCD
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              F, ad pyramidem A
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              BCD, ita pyramis
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              ABDF, ad pyrami­
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              dem CBDA, (pro­
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              pter baſium commu­
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              nitatem, & vertices in
                <lb/>
              eadem recta linea) erit
                <lb/>
                <figure id="id.043.01.027.1.jpg" xlink:href="043/01/027/1.jpg" number="14"/>
                <lb/>
              pyramis ABDF, æqualis pyramidi BCDF. </s>
              <s>Eadem ra­
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              tione tam pyramis ACDF, quàm pyramis ABCF, æqua
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              lis eſt pyramidi BCDF. </s>
              <s>Quatuor igitur pyramides, qua­
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              rum communis vertex punctum F, baſes autem triangula,
                <lb/>
              quæ ſunt circa pyramidem ABCD, inter ſe æquales
                <expan abbr="erũt">erunt</expan>
              ,
                <lb/>
              & vnaquæque pyramidis ABCD, pars quarta. </s>
              <s>Dico in
                <lb/>
              nullo alio puncto à puncto F, quatuor rectas, quæ ab an­
                <lb/>
              gulis ad triangula oppoſita pyramidis ABCD, ducantur,
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              ſecare ſe in eaſdem rationes. </s>
              <s>Si enim fieri poteſt ſecent
                <lb/>
              ſe tales rectæ in eaſdem rationes in alio puncto S. </s>
              <s>Simi­</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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