Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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        <body>
          <chap>
            <p type="main">
              <s id="s.000961">
                <pb pagenum="46" xlink:href="023/01/099.jpg"/>
              ro ita demonſtrabitur. </s>
              <s id="s.000962">Ducatur à puncto b ad planum ba­
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              ſis ac perpendicularis linea bh, quæ ipſam ef in K ſecet. </s>
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              <s id="s.000963">erit bh altitudo coni, uel coni portionis abc: & bK altitu
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                <arrow.to.target n="marg111"/>
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              do efg. </s>
              <s id="s.000964">Quod cum lineæ ac, ef inter ſe æquidiſtent, ſunt
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              enim planorum æquidiſtantium ſectiones: habebit db ad
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                <arrow.to.target n="marg112"/>
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              bg proportionem eandem, quam hb ad bk quare por­
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              tio conoidis abc ad portionem efg proportionem habet
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              compoſitam ex proportione baſis ac ad baſim ef; & ex
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                <arrow.to.target n="marg113"/>
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              proportione db axis ad axem bg. </s>
              <s id="s.000965">Sed circulus, uel
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              ellipſis circa diametrum ac ad circulum, uel ellipſim
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                <arrow.to.target n="marg114"/>
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              circa ef, eſt ut quadratum ac ad quadratum ef; hoc eſt ut
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                <expan abbr="quadratũ">quadratum</expan>
              ad ad
                <expan abbr="quadratũ">quadratum</expan>
              eg. & quadratum ad ad quadra
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              tum eg eſt, ut linea db ad lineam bg. </s>
              <s id="s.000966">circulus igitur, uel el
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                <arrow.to.target n="marg115"/>
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              lipſis circa diametrum ac ad
                <expan abbr="circulũ">circulum</expan>
              , uel ellipſim circa ef,
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                <arrow.to.target n="marg116"/>
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              hoc eſt baſis ad baſim eandem proportionem habet,
                <expan abbr="quã">quam</expan>
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              db axis ad axem bg. </s>
              <s id="s.000967">ex quibus ſequitur portionem abc
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              ad portionem ebf habere proportionem duplam eius,
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              quæ eſt baſis ac ad baſim ef: uel axis db ad bg axem. </s>
              <s id="s.000968">quod
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              demonſtrandum proponebatur.</s>
            </p>
            <p type="margin">
              <s id="s.000969">
                <margin.target id="marg111"/>
              16. unde­
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              cimi.</s>
            </p>
            <p type="margin">
              <s id="s.000970">
                <margin.target id="marg112"/>
              4 sexti.</s>
            </p>
            <p type="margin">
              <s id="s.000971">
                <margin.target id="marg113"/>
              2. duode
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              cimi</s>
            </p>
            <p type="margin">
              <s id="s.000972">
                <margin.target id="marg114"/>
              7. de co­
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              noidibus
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              & ſphæ­
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              roidibus</s>
            </p>
            <p type="margin">
              <s id="s.000973">
                <margin.target id="marg115"/>
              15. quinti. </s>
              <s id="s.000974">quinti</s>
            </p>
            <p type="margin">
              <s id="s.000975">
                <margin.target id="marg116"/>
              20. primi
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                <expan abbr="conicorũ">conicorum</expan>
              </s>
            </p>
            <p type="head">
              <s id="s.000976">THEOREMA XXV. PROPOSITIO XXXI.</s>
            </p>
            <p type="main">
              <s id="s.000977">Cuiuslibet fruſti à portione rectanguli conoi
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              dis abſcisſi, centrum grauitatis eſt in axe, ita ut
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              demptis primum à quadrato, quod fit ex diame­
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              tro maioris baſis, tertia ipſius parte, & duabus
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              tertiis quadrati, quod fit ex diametro baſis mino­
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              ris: deinde à tertia parte quadrati maioris baſis
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              rurſus dempta portione, ad quam reliquum qua
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              drati baſis maioris unà cum dicta portione
                <expan abbr="duplã">duplam</expan>
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              proportionem habeat eius, quæ eſt quadrati </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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