Valerio, Luca, De centro gravitatis solidorvm libri tres

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          <chap>
            <pb xlink:href="043/01/059.jpg" pagenum="51"/>
            <p type="head">
              <s>
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              PROPOSITIO XXIV.
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              </s>
            </p>
            <p type="main">
              <s>Si duarum pyramidum triangul as baſes haben­
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              tium æqualium, & ſimilium inter ſe, tria latera
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              tribus lateribus homologis fuerint in directum
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              conſtituta, in vertice communi erit vtriuſque ſi­
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              mul centrum grauitatis. </s>
            </p>
            <p type="main">
              <s>Sint duæ pyramides ſimiles, & æquales, quarum ver­
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              tex communis G, baſes autem triangula ABC, DEF.
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              </s>
              <s>Et ſint latera homologa pyramidum in directum inter ſe
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              conſtituta: vt AG, GF: & BG, GD, & CG, GE.
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              </s>
              <s>Dico compoſiti ex duabus pyramidibus ABCG, GDEF,
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              ita conſtitut is centrum gra
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              uitatis eſse in puncto G.
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              </s>
              <s>Eſto enim H, centrum gra
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              uitatis pyramidis ABCG,
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              & ducta HGK, ponatur
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              G
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              K
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              , æqualis GH, & iun­
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              gantur EK, KD, BH,
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              CH. </s>
              <s>Quoniam igitur eſt
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              vt HG, ad GK, ita CG,
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              ad GE, & proportio eſt
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              æqualitatis: & angulus
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              HGC, æqualis angulo EG
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                <emph type="italics"/>
              K
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              , erit triangulum CGH,
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                <figure id="id.043.01.059.1.jpg" xlink:href="043/01/059/1.jpg" number="35"/>
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              ſimile, & æquale triangulo EGK. </s>
              <s>Similiter triangulum
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              BGH, trian gulo DGK; & triangulum BGC, triangu­
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              lo DGE: quare & triangulum BCH, triangulo DEK.
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              pyramis igitur BCGH, ſimilis, & æqualis eſt pyramidi
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              EDGK. </s>
              <s>Congruentibus igitur inter ſe duobus triangu­</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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