Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/101.jpg" pagenum="14"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO IX.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Si recta linea vtcumque ſecta fuerit, cubus qui
                <lb/>
              fit à tota æqualis eſt duobus ſolidis rectangulis,
                <lb/>
              quæ ex partibus, & totius quadrato fiunt. </s>
            </p>
            <p type="main">
              <s>Sit recta linea AB ſecta in puncto C vtcumque. </s>
              <s>Di­
                <lb/>
              co cubum ex AB æqualem eſse duobus ſolidis rectangu­
                <lb/>
              lis, quæ fiunt ex AC CB, & quadrato AB. </s>
              <s>Quoniam
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                <figure id="id.043.01.101.1.jpg" xlink:href="043/01/101/1.jpg" number="74"/>
                <lb/>
              enim communi altitudine AB, eſt vt rectangulum BAC
                <lb/>
              ad quadratum AB, ita ſolidum ex AB, & rectangulo
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              BAC ad cubum ex AB, eademque ratione vt rectangu­
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              lum ABC, ad quadratum AB, ita ſolidum eſt AB, &
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              rectangulo ABC ad cubum ex AB; erunt vt duo rectan­
                <lb/>
              gula BAC, ABC ad quadratum AB, ita duo ſolida
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              ex AB, & rectangulis BAC, ABC ad cubum ex AB.
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              </s>
              <s>Sed duo rectangula BAC, ABC ſunt æqualia quadrato
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              AC; duo igitur ſolida ex AB, & rectangulis BAC, CBA,
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              æqualia ſunt cubo ex AB. </s>
              <s>Sed ſolidum ex AB & rectan­
                <lb/>
              gulo BAC eſt id quod fit ex AC, & AC & quadrato
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              AB; duo igitur ſolida ex AC, CB, & quadrato AB ſi­
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              mul ſumpta æqualia ſua cubo ex AB. </s>
              <s>Si igitur recta linea
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              vtcumque ſecta fuerit, &c. </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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