Valerio, Luca, De centro gravitatis solidorvm libri tres

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      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/092.jpg" pagenum="5"/>
            <p type="main">
              <s>Sint quatuor magnitudines, A prima, B ſecunda, C ter­
                <lb/>
              tia, & D quarta: & aliæ duæ magnitudines E
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              F vnà maiores quàm A, B minori exceſsu
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              quantacumque magnitudine propoſita eiuſ­
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              dem generis cum ipſis A, B. </s>
              <s>Sit autem E
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              maior quàm A, ad F maiorem quàm B, vt
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              C ad D. </s>
              <s>Dico eſse A ad B, vt C ad
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              D. </s>
              <s>Eſto enim, quod fieri poteſt, alia ma­
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              gnitudo G eiuſdem generis cum EF ad
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              aliam H, vt C ad D, vel E ad F. </s>
              <s>Quoniam
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              igitur eſt permutando vt E ad G, ita F ad H,
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              & ſunt EF vnà maiores quàm AB minori ex­
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              ceſsu quantacumque magnitudine propoſi­
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              ta; erit per antecedentem, vt A ad G, ita B
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              ad H: & permutando A ad B, vt G ad H,
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              hoc eſt vt C ad D. </s>
              <s>Idem autem ſimiliter oſten
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              deremus poſitis EF minoribus quàm AB, &
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              proportionalibus vt
                <expan abbr="dictũ">dictum</expan>
              eſt. </s>
              <s>
                <expan abbr="Manifeſtũ">Manifeſtum</expan>
              eſt igitur
                <expan abbr="propoſitũ">propoſitum</expan>
              . </s>
            </p>
            <figure id="id.043.01.092.1.jpg" xlink:href="043/01/092/1.jpg" number="64"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              ALITER.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Ijſdem poſitis, ſi non eſt A ad
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              B, vt C ad D; vel igitur ma­
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              ior vel minor erit proportio A
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              ad B quàm C ad D: ſit autem
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              maior: vt igitur A ad B, ita erit
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              eadem A ad
                <expan abbr="aliã">aliam</expan>
              maiorem <34>B.
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              </s>
              <s>Eſto illa E. ſintque aliæ duæ ma
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              gnitudines, G maior quàm A
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                <figure id="id.043.01.092.2.jpg" xlink:href="043/01/092/2.jpg" number="65"/>
                <lb/>
              minori exceſsu magnitudine eiuſdem generis cum A,
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              quam quis voluerit, & F maior quàm B, & minor quàm
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              E. ſit autem G ad F vt C ad D. </s>
              <s>Quoniam igitur & vt
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              C ad D, ita eſt A ad E; erit vt G ad F, ita A ad E; &
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              permutando vt G ad A, ita F ad E: ſed G eſt maior </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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