Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000859">
                <pb xlink:href="023/01/088.jpg"/>
              grauitatis eſſe punctum m. </s>
              <s id="s.000860">patet igitur totius dodecahe­
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              dri, centrum grauitatis
                <expan abbr="idẽ">idem</expan>
              eſſe, quod & ſphæræ ipſum com
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              prehendentis centrum. </s>
              <s id="s.000861">quæ quidem omnia demonſtraſſe
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              oportebat.</s>
            </p>
            <p type="margin">
              <s id="s.000862">
                <margin.target id="marg99"/>
              corol. </s>
              <s id="s.000863">pri
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              mæ ſphæ
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              ricorum
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              Theod.
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              6. primi
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              sphærico
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              rum.</s>
            </p>
            <p type="head">
              <s id="s.000864">PROBLEMA VI. PROPOSITIO XXVIII.</s>
            </p>
            <p type="main">
              <s id="s.000865">DATA qualibet portione conoidis rectangu
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              li, abſciſſa plano ad axem recto, uel non recto; fie­
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              ri poteſt, ut portio ſolida inſcribatur, uel circum­
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              ſcribatur ex cylindris, uel cylindri portionibus,
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              æqualem habentibus altitudinem, ita ut recta li­
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              nea, quæ inter centrum grauitatis portionis, &
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              figuræ inſcriptæ, uel circumſcriptæ interiicitur,
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              ſit minor qualibet recta linea propoſita.</s>
            </p>
            <p type="main">
              <s id="s.000866">Sit portio conoidis rectanguli abc, cuius axis bd,
                <expan abbr="gra-uitatisq;">gra­
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                uitatisque</expan>
              centrum e: & ſit g recta linea propoſita. </s>
              <s id="s.000867">quam ue
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              ro proportionem habet linea be ad lineam g, eandem ha­
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              beat portio conoidis ad ſolidum h: & circumſcribatur por
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              tioni figura, ſicuti dictum eſt, ita ut portiones reliquæ ſint
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              ſolido h minores: cuius quidem figuræ centrum grauitatis
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              ſit punctum k. </s>
              <s id="s.000868">Dico
                <expan abbr="lineã">lineam</expan>
              ke minorem eſſe linea g propo­
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              ſita. </s>
              <s id="s.000869">niſi enim ſit minor, uel æqualis, uel maior erit. </s>
              <s id="s.000870">& quo­
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              niam figura circumſcripta ad reliquas portiones maiorem
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                <arrow.to.target n="marg101"/>
                <lb/>
              proportionem habet, quàm portio conoidis ad ſolidum h;
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              hoc eſt maiorem, quàm bc ad g: & be ad g non minorem
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              habet proportionem, quàm ad ke, propterea quod ke non
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              ponitur minor ipſa g: habebit figura circumſcripta ad por
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              tiones reliquas maiorem proportionem quàm be ad ek:
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                <arrow.to.target n="marg102"/>
                <lb/>
              & diuidendo portio conoidis ad reliquas portiones habe­
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              bit maiorem, quàm bk ad Ke. </s>
              <s id="s.000871">quare ſi fiat ut portio </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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