Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/037.jpg" pagenum="29"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XIII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Cuilibet figuræ ſolidæ
                <expan abbr="parallelepipedũ">parallelepipedum</expan>
              æqua­
                <lb/>
              le poteſt eſſe. </s>
            </p>
            <p type="main">
              <s>Sit quælibet figura ſolida A. </s>
              <s>Dico ſolido A, parallele­
                <lb/>
              pipedum æquale poſse exiſtere. </s>
              <s>Exponatur enim paral­
                <lb/>
              lelepipedum BC, cuius baſis BG. </s>
              <s>Quoniam igitur eſt vt
                <lb/>
              ſolidum BC, ad ſolidum A, ita recta linea, ſiue latus BD,
                <lb/>
              ad aliam rectam lineam; producto latere BD, ſit vt BC,
                <lb/>
              ad A, ita recta BD, ad rectam DE, & compleatur pa­
                <lb/>
              rallelepipedum CE. </s>
              <s>Quoniam itaque eſt vt BD, ad DE,
                <lb/>
              ita parallelogrammum ſiue baſis BG, ad parallelogram­
                <lb/>
                <figure id="id.043.01.037.1.jpg" xlink:href="043/01/037/1.jpg" number="20"/>
                <lb/>
              mum, ſiue baſim EG; hoc eſt parallelepipedum BC, ad
                <lb/>
              parallelepipedum CE: ſed vt BD, ad DE, ita eſt paral­
                <lb/>
              lelepipedum BC, ad ſolidum A; vt igitur parallelepipe­
                <lb/>
              dum BC, ad ſolidum A, ita erit parallelepipedum BC,
                <lb/>
              ad parallelepipedum CE; parallelepipedum igitur CE
                <lb/>
              æquale erit ſolido A. </s>
              <s>Quod fieri poſse propoſuimus. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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