Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <pb pagenum="31" xlink:href="023/01/069.jpg"/>
            <p type="main">
              <s id="s.000644">SIT fruſtum pyramidis ae, cuius maior baſis triangu­
                <lb/>
              lum abc, minor def: & oporteat ipſum plano, quod baſi
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              æquidiſtet, ita ſecare, ut ſectio ſit proportionalis inter
                <expan abbr="triã">trian</expan>
                <lb/>
              gula abc, def. </s>
              <s id="s.000645">Inueniatur inter lineas ab, de media pro­
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              portionalis, quæ ſit bg: & à puncto g erigatur gh æquidi­
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              ſtans be,
                <expan abbr="ſecansq;">ſecansque</expan>
              ad in h: deinde per h ducatur planum
                <lb/>
              baſibus æquidiſtans, cuius ſectio ſit triangulum hkl. </s>
              <s id="s.000646">Dico
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              triangulum hKl proportionale eſſe inter triangula abc,
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                <figure id="id.023.01.069.1.jpg" xlink:href="023/01/069/1.jpg" number="61"/>
                <lb/>
              def, hoc eſt triangulum abc ad
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              triangulum hKl eandem habere
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              proportionem, quam
                <expan abbr="triãgulum">triangulum</expan>
                <lb/>
              hKl ad ipſum def. </s>
              <s id="s.000647">
                <expan abbr="Quoniã">Quoniam</expan>
              enim
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                <arrow.to.target n="marg76"/>
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              lineæ ab, hK æquidiſtantium pla
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              norum ſectiones inter ſe æquidi­
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              ſtant: atque æquidiſtant bk, gh:
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                <arrow.to.target n="marg77"/>
                <lb/>
              linea hk ipſi gb eſt æqualis: & pro
                <lb/>
              pterea proportionalis inter ab,
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              de. </s>
              <s id="s.000648">quare ut ab ad hK, ita eſt hk
                <lb/>
              ad de. </s>
              <s id="s.000649">fiat ut hk ad de, ita de
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              ad aliam lineam, in qua ſit m. </s>
              <s id="s.000650">erit
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              ex æquali ut ab ad de, ita hk ad
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                <arrow.to.target n="marg78"/>
                <lb/>
              m. </s>
              <s id="s.000651">Et quoniam triangula abc,
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              hKl, def ſimilia ſunt;
                <expan abbr="triangulũ">triangulum</expan>
                <lb/>
                <arrow.to.target n="marg79"/>
                <lb/>
              abc ad triangulum hkl eſt, ut li­
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              nea ab ad lineam de:
                <expan abbr="triangulũ">triangulum</expan>
                <lb/>
                <arrow.to.target n="marg80"/>
                <lb/>
              autem hkl ad ipſum def eſt, ut hk ad m. </s>
              <s id="s.000652">ergo triangulum
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              abc ad triangulum hkl eandem proportionem habet,
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              quam triangulum hKl ad ipſum def. </s>
              <s id="s.000653">Eodem modo in a­
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              liis fruſtis pyramidis idem demonſtrabitur.</s>
            </p>
            <p type="margin">
              <s id="s.000654">
                <margin.target id="marg76"/>
              16. unde
                <lb/>
              cimi</s>
            </p>
            <p type="margin">
              <s id="s.000655">
                <margin.target id="marg77"/>
              34. primi</s>
            </p>
            <p type="margin">
              <s id="s.000656">
                <margin.target id="marg78"/>
              9. huius
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              corol.</s>
            </p>
            <p type="margin">
              <s id="s.000657">
                <margin.target id="marg79"/>
              20. ſexti</s>
            </p>
            <p type="margin">
              <s id="s.000658">
                <margin.target id="marg80"/>
              11. quinti</s>
            </p>
            <p type="main">
              <s id="s.000659">Sit fruſtum coni, uel coni portionis ad: & ſecetur plano
                <lb/>
              per axem, cuius ſectio ſit abcd, ita ut maior ipſius baſis ſit
                <lb/>
              circulus, uel ellipſis circa diametrum ab; minor circa cd. </s>
              <lb/>
              <s id="s.000660">Rurſus inter lineas ab, cd inueniatur proportionalis be:
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              & ab e ducta ef æquidiſtante bd, quæ lineam ca in f ſecet, </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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