Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/102.jpg" pagenum="15"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO X.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Si recta linea vtcumque ſecta fuerit, cubus qui
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              fit à tota æqualis eſt cubis partium, & duobus ſo­
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              lidis rectangulis, quæ partium triplis, & earun­
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              dem quadratis reciproce continentur. </s>
            </p>
            <p type="main">
              <s>Sit recta linea AB ſecta vtcumque in puncto C. </s>
              <s>Dico
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              cubum ex AB æqualem eſse duobus cubis ex AC, CB,
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              & duobus ſolidis rectangulis, quorum alterum fit ex tripla
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                <figure id="id.043.01.102.1.jpg" xlink:href="043/01/102/1.jpg" number="75"/>
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              ipſius AC, & quadrato BC; alterum autem ex tripla ip­
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              ſius BC, & quadrato AC. </s>
              <s>Quoniam enim quadratum
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              ex AB æquale eſt duobus quadratis ex AC, CB, & ei
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              quod bis fit ex AC CB: & parallelepipeda eluſdem al­
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              titudinis inter ſe ſunt vt baſes; erit rectangulorum folido­
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              rum id quod fit ex AC, & quadrato AB æquale cubo ex
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              AC, & ei, quod fit ex AC, & rectangulo ACB bis, &
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              ei, quod ex AC, & quadrato BC. </s>
              <s>Eadem ratione erit
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              quod fit ex BC, & quadrato AB æquale cubo ex BC, &
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              ei, quod fit ex BC, & rectangulo ACB, bis & ei, quod ex
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              BC, & quadrato AC. </s>
              <s>Sed cubus ex AB æqualis eſt
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              duobus ſolidis ex AC CB. & quadrato AB; cubus igi­
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              tur ex AB æqualis eſt duobus cubis ex AC CB, & ſex
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              ſolidis, quorum tres fiunt ex AC, & duobus rectangulis
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              ex AC CB, & quadrato BC: tria vero ex BC, & duo­
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              bus rectangulis ex AC CB, & quadrato AC. </s>
              <s>Sed quod
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              fit ex AC, & rectangulo ACB, eſt quod fit ex BC, & </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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