Valerio, Luca, De centro gravitatis solidorvm libri tres

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/021.jpg" pagenum="13"/>
              EF. quæ ſuntin latera homologa duorum triangulorum
                <lb/>
              ABC, DEF. </s>
              <s>Ex definitione igitur, duo puncta G, H,
                <lb/>
              in triangulis ABC, DEF, ſimiliter poſita erunt. </s>
              <s>At
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              enim ſi fieri poteſt ſit aliud punctum K, in triangulo
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              DEF, ſimiliter poſitum puncto G. </s>
              <s>Vel igitur punctum
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              K in aliquo triangulorum, quorum eſt communis vertex
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              H, vel in aliquo eorundem latere cadet. </s>
              <s>cadat in latere
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              FH, & iungatur DK: triangulum ergo DFK, ſimile
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              erit triangulo ACG. </s>
              <s>Sed & triangulum EDF, ſimile
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              eſt triangulo BAC; vtraque igitur horum ad illorum ſi­
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              bi reſpondens triangulorum duplicatam eorundem late­
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              rum homologorum AC, DF, habebunt proportionem:
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              vt igitur eſt triangulum EDF, ad triangulum BAC, ita
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              erit triangulum DFK, ad triangulum ACG: & per­
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              mutando, vt triangulum ACG, ad triangulum ABC,
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              ita triangulum DFK, ad triangulum EDF: eadem ra­
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              tione, vt triangulum ACG, ad triangulum ABC, ita
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              erit triangulum DFH, ad triangulum DEF: vt igitur
                <lb/>
              triangulum DFK, ad triangulum EDF; ita erit trian­
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              gulum DFH, ad triangulum EDF; triangulum ergo
                <lb/>
              DFK, triangulo DFH, æquale erit, pars toti, quod eſt
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              abſurdum: idem autem abſurdum ſequeretur, ſi punctum
                <lb/>
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              , poneretur in aliquo prædictorum triangulorum, vt in
                <lb/>
              triangulo DFH; Non igitur aliud punctum à puncto H,
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              in triangulo EDF, ſimiliter poſitum erit puncto G.
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              </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO V.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Cuilibet figuræ planæ rectangulum æquale
                <lb/>
              poteſt eſſe. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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