Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/096.jpg" pagenum="9"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO V.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Si ſit minor proportio primæ ad ſecundam,
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              quàm ſecundæ ad tertiam, ab ipſis autem æquales
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              auferantur; erit minor proportio reliquæ primæ
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              ad reliquam ſecundæ, quam reliquæ ſecundæ ad
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              reliquam tertiæ. </s>
            </p>
            <p type="main">
              <s>Sit minor proportio AB, ad CD, quam CD, ad EF.
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              </s>
              <s>Sitque AB, minima. </s>
              <s>ablatæ autem æquales fint AG, CH,
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              EK. </s>
              <s>Dico reliquarum minorem eſse proportionem BG,
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              ad DH, quam BH, ad FH. </s>
              <s>Ponatur enim CL, æqua­
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              lis AB, & EM, æqualis CD. </s>
              <s>Quoniam igitur maior eſt
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              proportio DL ad LH, quam DL, ad LC;
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              erit componendo maior proportio DH ad
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              HL, quam DC ad CL. hoc eſt, maior
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              proportio DH, ad BG, quam DC,
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              ad AB: & conuertendo, minor proportio
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              BG ad DH, quam AB, ad CD: hoc eſt
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              maior proportio AB, ad CD, quam BG,
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              ad DH. Rurſus, quoniam maior eſt pro­
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              portio CD, ad EF, quam AB, ad CD:
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              hoc eſt quam CL, ad EM; erit permutan
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              do, maior proportio CD, ad CL, quam
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              FE, ad EM: & diuidendo, maior DL, ad
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              LC, quam FM, ad ME: & permutando,
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                <figure id="id.043.01.096.1.jpg" xlink:href="043/01/096/1.jpg" number="70"/>
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              maior DL, ad FM, quam CL, ad EM: hoc eſt quam
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              AB, ad CD. </s>
              <s>Sed maior erat proportio AB, ad CD,
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              quam BG ad DH; multo igitur maior proportio erit DL,
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              ad FM, quam BG, ad DH: hoc eſt quam LH, ad MK:
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              & permutando, maior proportio DL, ad LH, quam FM,
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              ad MK: & componendo, maior DH, ad HL, quam FK, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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