Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/083.jpg" pagenum="75"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XXXVII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Dodecaedri, & icoſaedri idem eſt centrum gra
                <lb/>
              uitatis, & figuræ. </s>
            </p>
            <p type="main">
              <s>Nam huiuſmodi figuras habere axes, qui omnes ſe ſe
                <lb/>
              bifariam ſecant; (tale autem ſectionis punctum centrum eſt)
                <lb/>
              conſtat ex talium corporum in ſphæra inſcriptione in de­
                <lb/>
              cimotertio Euclidis Elemento: nec non omnem pyrami­
                <lb/>
              dem, cuius vertex eſt dodecaedri, vel octaedri centrum
                <lb/>
              idem cum centro ſphæræ, vt conſtat ex ijſdem Euclidis in­
                <lb/>
              ſcriptionibus; baſis autem triangulum æquilaterum, vel
                <lb/>
              pentagonum, vna ex baſibus corporum prædictorum, ha­
                <lb/>
              bere pyramidem oppoſitam ſimilem ipſi, & æqualem, cuius
                <lb/>
              latera eius lateribus homologis ſunt in directum poſita,
                <lb/>
              baſis autem triangulum, vel pentagonum, quale diximus;
                <lb/>
              Eadem igitur ratione, qua vſi ſumus ad demonſtrandum
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              centrum grauitatis, & parallelepipedi, & octaedri, propo­
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              ſitum concluderemus. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XXXVIII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Data qualibet figura, cuius termini omnis
                <lb/>
              cauitas ſit interior, ſi certum in ea punctum talis
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              cius partis centrum grauitatis eſse poſsit, quæ ab
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              ca deficiat minori ſpacio quantacumque magnitu
                <lb/>
              dine propoſita; illud erit totius figuræ centrum
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              grauitatis. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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