Valerio, Luca, De centro gravitatis solidorum, 1604

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      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/082.jpg" pagenum="74"/>
              igitur M, N, ſint centra grauitatis propoſiti priſmatis par
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              tium priſmatum AFG, AGH, atque obid O, totius priſ­
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              matis AFGH, in linea MN, centrum grauitatis; per pun
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              ctum O, recta MN, tranſibit. </s>
              <s>Et quoniam planum tra­
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              pezij PV, ſecatur duobus planis parallelis, erunt TV, PQ,
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              fectiones parallelæ. </s>
              <s>His demonſtratis, fiat rurſus vt AB,
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              bis vna cum EF, ad EF, bis vna cum AB, ita TY, ad
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              YP: & ſumatur T
                <foreign lang="grc">ω</foreign>
              , pars quarta ipſius TP, & YZ, pars
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              quarta ipſius PY, & ad axim KL, ducantur ipſis TV,
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              PQ, parallelæ
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                <foreign lang="grc">ω</foreign>
              S, YR, ZX,
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              quæ rectas TP,
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              KL, ſecabunt in
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                <expan abbr="eaſdẽ">eaſdem</expan>
              rationes:
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              vt igitur TY, ad
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                <foreign lang="grc">Υ</foreign>
              P, hoc eſt vt
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              AB, bis vna cum
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              EF, ad EF bis
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              vna cum AB, ita
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              erit
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              K
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              R, ad RL,
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              eritque KS, pars
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              quarta ipſius K
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              L, qualis & R
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                <figure id="id.043.01.082.1.jpg" xlink:href="043/01/082/1.jpg" number="53"/>
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              X, ipſius RL. </s>
              <s>Et quoniam M, eſt centrum grauitatis fru­
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              ſti AFG; manifeſtum eſt ex tribus prædictis axis TP, ſe­
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              ctionibus
                <foreign lang="grc">Υ, ω</foreign>
              , Z, eſse MZ, ad Z
                <foreign lang="grc">ω</foreign>
              , hoc eſt OX, ad XS,
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              vt eſt 6 ad compoſitam ex tribus deinceps proportionalibus
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              AB, EF, 6; Fruſti igitur ABCDEFGH, centrum gra
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              uitatis O, axim KL, ita diuidit, vt propoſuimus. </s>
              <s>Quod
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              ſi fruſtum propoſitum ſit pyramidis baſim habentis quin­
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              quelateram, & quotcumque plurium deinceps fuerit la­
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              terum, eadem demonſtratione ſemper deinceps, vt in priſ­
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              mate monuimus, propoſitum concluderemus. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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