Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000688">
                <pb pagenum="33" xlink:href="023/01/073.jpg"/>
              quod diuidat fruſtum in duo fruſta triangulares baſes ha­
                <lb/>
              bentia, uidelicet in fruſtum abdefh, & in
                <expan abbr="fruſtũ">fruſtum</expan>
              bcdfgh. </s>
              <lb/>
              <s id="s.000689">erit triangulum kln proportionale inter triangula abd,
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              efh: & triangulum lmn proportionale inter bcd, fgh. </s>
              <lb/>
              <s id="s.000690">ſed pyramis æque alta, cuius baſis conſtat ex tribus trian­
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                <figure id="id.023.01.073.1.jpg" xlink:href="023/01/073/1.jpg" number="66"/>
                <lb/>
              gulis abd, klz, efh, demonſtrata
                <lb/>
              eſt fruſto abdcfh æqualis. </s>
              <s id="s.000691">& ſi­
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              militer pyramis, cuius baſis con­
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              ſtat ex triangulis bcd, lmn, fgh
                <lb/>
              æqualis fruſto bcdfgh: compo­
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              nuntur autem tria quadrilatera a
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              bcd, klmn, efgh è ſex triangu­
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              lis iam dictis. </s>
              <s id="s.000692">pyramis igitur ba­
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              ſim habens æqualem tribus qua­
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              drilateris, & altitudinem eandem
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              ipſi fruſto ag eſt æqualis. </s>
              <s id="s.000693">Eodem
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              modo illud
                <expan abbr="demõſtrabitur">demonſtrabitur</expan>
              in aliis
                <lb/>
              eiuſmodi fruſtis.</s>
            </p>
            <p type="main">
              <s id="s.000694">Sit fruſtum coni, uel coni portionis ad; cuius maior ba­
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              ſis circulus, uel ellipſis circa diametrum ab; minor circa
                <lb/>
              c d: & ſecetur plano, quod baſibus æquidiſtet,
                <expan abbr="faciatq;">faciatque</expan>
              ſe­
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              ctionem circulum, uel ellipſim circa diametrum ef, ita ut
                <lb/>
              inter circulos, uel ellipſes ab, cd ſit proportionalis. </s>
              <s id="s.000695">Dico
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              conum, uel coni portionem, cuius baſis eſt æqualis tribus
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              circulis, uel tribus ellipſibus ab, ef, cd; & altitudo eadem,
                <lb/>
              quæ fruſti ad, ipſi fruſto æqualem eſſe. </s>
              <s id="s.000696">producatur enim
                <lb/>
              fruſti ſuperficies quouſque coeat in unum punctum, quod
                <lb/>
              ſit g: & coni, uel coni portionis agb axis ſit gh, occurrens
                <lb/>
              planis ab, ef, cd in punctis hkl: circa circulum uero de­
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              ſcribatur quadratum mnop, & circa ellipſim
                <expan abbr="rectangulũ">rectangulum</expan>
                <lb/>
              mnop, quod ex ipſius diametris conſtat:
                <expan abbr="iunctisq;">iunctisque</expan>
              gm,
                <lb/>
              g n, go, gp, ex eodem uertice intelligatur pyramis baſim
                <lb/>
              habens dictum quadratum, uel rectangulum: & plana in
                <lb/>
              quibus ſunt circuli, uel ellipſes ef, cd uſque ad eius latera </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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