Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/164.jpg" pagenum="77"/>
              baſis vnà cum minori, ad duplum minoris, vnà
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              cum maiori. </s>
            </p>
            <p type="main">
              <s>Sit conoidis parabolici ABC, cuius axis BD fruſtum
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              AEFC, eius maior baſis circulus, cuius diameter AC, mi­
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              nor, cuius diameter EF: in eadem parabola per axem, axis
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                <expan abbr="autẽ">autem</expan>
              DG, in quo fruſti AEFC ſit centrum grauitatis H.
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              </s>
              <s>Dico eſſe vt duplum circuli AC, vnà cum circulo EF, ad
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              duplum circuli EF vna cum circulo AC, ita GH, ad HD.
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                <expan abbr="Iungãtur">Iungantur</expan>
              enim re­
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              ctæ AKB, BLC.
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              </s>
              <s>Quoniam igitur
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              qua ratione oſten
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              dimus conoides,
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              & triangulum A
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              BC, commune
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              habere in linea
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              BD centrum gra
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              uitatis,
                <expan abbr="eadẽ">eadem</expan>
              pror­
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              ſus remanet de­
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              monſtratum, fruſti
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                <figure id="id.043.01.164.1.jpg" xlink:href="043/01/164/1.jpg" number="125"/>
                <lb/>
              AEFC
                <expan abbr="centrũ">centrum</expan>
              grauitatis H, idem eſse quod trapezij AK
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              FC; erit duarum parallelarum AG, KL vt dupla ipſius
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              AC, vnà cum KL, ad duplam ipſius KL, vnà cum AC
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              ita GH ad HD: ſecat enim DG ipſas AC, KL bifa­
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              riam. </s>
              <s>Sed vt AC ad
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              L ita eſt circulus AC ad circu­
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              lum EF, ex demonſtratione antecedentis, hoc eſt vt dupla
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              ipſius AC vnà cum KL ad duplam ipſius KL vnà cum
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              AC, ita duplum circuli AC vna cum circulo KL ad du­
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              plum circuli KL vnà cum circulo AC; vt igitur eſt du­
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              plum circuli AC, vnà cum circulo EF, ad duplum circu­
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              li EF, vnà cum circulo AC; ita erit GH ad HD.
                <lb/>
              </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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