Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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      <text>
        <body>
          <chap>
            <p type="main">
              <s id="s.000798">
                <pb pagenum="38" xlink:href="023/01/083.jpg"/>
              ad portiones ſolidas maiorem habet
                <expan abbr="proportionẽ">proportionem</expan>
              , quàm
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              nl ad lm: & diuidendo fruſtum pyramidis ad dictas por­
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              tiones maiorem proportionem habet, quàm nm ad ml. </s>
              <lb/>
              <s id="s.000799">fiat igitur ut fruſtum pyramidis ad portiones, ita qm ad
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              m l. </s>
              <s id="s.000800">Itaque quoniam à fruſto coni, uel coni portionis ad,
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              cuius grauitatis centrum eſt m, aufertur fruſtum pyrami­
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              dis habens centrum l; erit reliquæ magnitudinis, quæ ex
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              portionibus ſolidis conſtat; grauitatis
                <expan abbr="cẽtrum">centrum</expan>
              in linea lm
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              producta, atque in puncto q, extra figuram poſito: quod
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              fieri nullo modo poteſt. </s>
              <s id="s.000801">relinquitur ergo, ut punctum l ſit
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              fruſti ad grauitatis centrum. </s>
              <s id="s.000802">quz omnia demonſtranda
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              proponebantur.</s>
            </p>
            <p type="margin">
              <s id="s.000803">
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              22. huius</s>
            </p>
            <p type="margin">
              <s id="s.000804">
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              19. quínti</s>
            </p>
            <p type="head">
              <s id="s.000805">THEOREMA XXII. PROPOSITIO XXVII.</s>
            </p>
            <p type="main">
              <s id="s.000806">OMNIVM ſolidorum in ſphæra deſcripto­
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              rum, quæ æqualibus, & ſimilibus baſibus conti­
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              nentur, centrum grauitatis eſt idem, quod ſphæ­
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              ræ centrum.</s>
            </p>
            <p type="main">
              <s id="s.000807">Solida eiuſmodi corpora regularia appellare ſolent, de
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              quibus agitur in tribus ultimis libris elementorum: ſunt
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              autem numero quinque, tetrahedrum, uel pyramis, hexa­
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              hedrum, uel cubus, octahedrum, dodecahedrum, & icoſa­
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              hedrum.</s>
            </p>
            <p type="main">
              <s id="s.000808">Sit primo abcd pyramis
                <expan abbr="ĩ">im</expan>
              ſphæra deſcripta, cuius ſphæ
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              ræ centrum ſit e. </s>
              <s id="s.000809">Dico e pyramidis abcd grauitatis eſſe
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              centrum. </s>
              <s id="s.000810">Si enim iuncta dc producatur ad baſim abc in
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              f; ex iis, quæ demonſtrauit Campanus in quartodecimo li
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              bro elementorum, propoſitione decima quinta, & decima
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              ſeptima, erit f centrum circuli circa triangulum abc de­
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              ſcripti: atque erit ef ſexta pars ipſius ſphæræ axis. </s>
              <s id="s.000811">quare
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              ex prima huius conſtat trianguli abc grauitatis centrum
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              eſſe punctum f: & idcirco lineam df eſſe pyramidis axem. </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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