Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000631">
                <pb xlink:href="023/01/068.jpg"/>
              Dico eas proportionales eſſe in proportione, quæ eſt la­
                <lb/>
              teris ab adlatus de, ita ut earum maior ſit abce, me­
                <lb/>
              dia adce, & minor defc. </s>
              <s id="s.000632">Quoniam enim lineæ de,
                <lb/>
              ab æquidiſtant; & inter ipſas ſunt triangula abe, ade;
                <lb/>
                <arrow.to.target n="marg72"/>
                <lb/>
                <figure id="id.023.01.068.1.jpg" xlink:href="023/01/068/1.jpg" number="60"/>
                <lb/>
              erit triangulum abe
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              ad triangulum abe,
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              ut linea ab ad lineam
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              de. </s>
              <s id="s.000633">ut autem triangu
                <lb/>
              lum abe ad triangu­
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                <arrow.to.target n="marg73"/>
                <lb/>
              lum abe, ita pyramis
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              abec ad pyramidem
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              adec: habent enim
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              altitudinem eandem,
                <lb/>
              quæ eſtà puncto cad
                <lb/>
              planum, in quo qua­
                <lb/>
                <arrow.to.target n="marg74"/>
                <lb/>
              drilaterum abed. </s>
              <s id="s.000634">er­
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              go ut ab ad de, ita pyramis abec ad pyramidem adec. </s>
              <lb/>
              <s id="s.000635">Rurſus quoniam æquidiſtantes ſunt ac, df; erit eadem
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                <arrow.to.target n="marg75"/>
                <lb/>
              ratione pyramis adce ad pyramidem cdfe, ut ac ad
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              df. </s>
              <s id="s.000636">Sed ut ac ad df, ita ab ad de, quoniam triangula
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              abc, def ſimilia ſunt, ex nona huius. </s>
              <s id="s.000637">quare ut pyramis
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              abce ad pyramidem abce, ita pyramis adce ad ipſam
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              defc. fruſtum igitur abcdef diuiditur in tres pyramides
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              proportionales in ea proportione, quæ eſt lateris ab ad de
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              latus, & earum maior eſt cabe, media adce, & minor
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              defc. quod demonſtrare oportebat.</s>
            </p>
            <p type="margin">
              <s id="s.000638">
                <margin.target id="marg72"/>
              1. ſexti.</s>
            </p>
            <p type="margin">
              <s id="s.000639">
                <margin.target id="marg73"/>
              5. duodeci
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              mi.</s>
            </p>
            <p type="margin">
              <s id="s.000640">
                <margin.target id="marg74"/>
              11. quinti.</s>
            </p>
            <p type="margin">
              <s id="s.000641">
                <margin.target id="marg75"/>
              4 ſexti.</s>
            </p>
            <p type="head">
              <s id="s.000642">PROBLEMA V. PROPOSITIO XXIIII.</s>
            </p>
            <p type="main">
              <s id="s.000643">QVODLIBET fruſtum pyramidis, uel coni,
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              uel coni portionis, plano baſi æquidiſtanti ita ſe­
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              care, ut ſectio ſit proportionalis inter maiorem,
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              & minorem baſim.</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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