Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb xlink:href="043/01/074.jpg" pagenum="66"/>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO XXXIII.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Omnis priſmatis triangulam baſim habentis
                <lb/>
              centrum grauitatis eſt in medio axis. </s>
            </p>
            <p type="main">
              <s>Sit priſma ABCDEF, cuius baſes oppoſitæ trian­
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              gula ABC, DEF, axis autem GH, ſectus ſit bifariam
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              in puncto K. </s>
              <s>Dico punctum K, eſse priſinatis ABCD
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              EF, centrum grauitatis. </s>
              <s>Ducantur enim rectæ FGO,
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              CHP, PO. </s>
              <s>Quoniam igitur GH, eſt axis priſmatis
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              ABCDEF, erit punctum G, centrum grauitatis trian­
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              guli DEF: ſicut & H, trian­
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              guli ABC; vtraque igitur
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              dupla eſt AG, ipſius GO,
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              & CH, ipſius PH, ſectæ­
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              que erunt AB, DE, bifa­
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              riam in punctis P, O: pa­
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              rallela igitur, & æqualis eſt
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              OP, ipſi DA, iamque ipſi
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              FC. quæ igitur illas con­
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              iungunt CP, FO, æqua­
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              les ſunt, & parallelæ, & pa­
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              rallelogrammum FP.
                <lb/>
              </s>
              <s>Nunc ſecta OP, bifariam in
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              puncto N, iungantur GN,
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              NF, AF, FH, FB, & fa­
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              cta FL, tripla ipſius LH,
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                <figure id="id.043.01.074.1.jpg" xlink:href="043/01/074/1.jpg" number="48"/>
                <lb/>
              à puncto L, per punctum K, ducatur recta LKMR.
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              </s>
              <s>Quoniam igitur eſt vt FG, ad GO, ita CH, ad HP,
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              & parallelogrammum eſt FCPO; parallelogramma
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              etiam erunt CG, GP, angulus igitur FGH, æqualis
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              erit angulo NGO, quos circa æquales angulos latera </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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