Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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            <s xml:id="echoid-s4681" xml:space="preserve">
              <pb o="38" file="0187" n="187" rhead="DE CENTRO GRA VIT. SOLID."/>
            ad portiones ſolidas maiorem habet proportioné, quàm
              <lb/>
            n l ad l m: </s>
            <s xml:id="echoid-s4682" xml:space="preserve">& </s>
            <s xml:id="echoid-s4683" xml:space="preserve">diuidendo fruſtum pyramidis ad dictas por-
              <lb/>
            tiones maiorem proportionem habet, quàm n m ad m l.
              <lb/>
            </s>
            <s xml:id="echoid-s4684" xml:space="preserve">fiat igitur ut fruſtum pyramidis ad portiones, ita q m ad
              <lb/>
            m l. </s>
            <s xml:id="echoid-s4685" xml:space="preserve">Itaque quoniam à fruſto coni, uel coni portionis a d,
              <lb/>
            cuius grauitatis centrum eſtm, aufertur fruſtum pyrami-
              <lb/>
            dis habens centruml; </s>
            <s xml:id="echoid-s4686" xml:space="preserve">erit reliquæ magnitudinis, quæ ex
              <lb/>
            portionibus ſolidis conſtat; </s>
            <s xml:id="echoid-s4687" xml:space="preserve">grauitatis cẽtrum in linea l m
              <lb/>
            producta, atque in puncto q, extra figuram poſito. </s>
            <s xml:id="echoid-s4688" xml:space="preserve">quod
              <lb/>
            fieri nullo modo poteſt. </s>
            <s xml:id="echoid-s4689" xml:space="preserve">relinquitur ergo, ut punctum l ſit
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            fruſti a d grauitatis centrum. </s>
            <s xml:id="echoid-s4690" xml:space="preserve">quæ omnia demonſtranda
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            proponebantur.</s>
            <s xml:id="echoid-s4691" xml:space="preserve"/>
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        <div xml:id="echoid-div272" type="section" level="1" n="92">
          <head xml:id="echoid-head99" xml:space="preserve">THEOREMA XXII. PROPOSITIO XXVII.</head>
          <p>
            <s xml:id="echoid-s4692" xml:space="preserve">
              <emph style="sc">Omnivm</emph>
            ſolidorum in ſphæra deſcripto-
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            rum, quæ æqualibus, & </s>
            <s xml:id="echoid-s4693" xml:space="preserve">ſimilibus baſibus conti-
              <lb/>
            nentur, centrum grauitatis eſt idem, quod ſphæ-
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            ræ centrum.</s>
            <s xml:id="echoid-s4694" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4695" xml:space="preserve">Solida eiuſmodi corpora regularia appellare ſolent, de
              <lb/>
            quibus agitur in tribus ultimis libris elementorum: </s>
            <s xml:id="echoid-s4696" xml:space="preserve">ſunt
              <lb/>
            autem numero quinque, tetrahedrum, uel pyramis, hexa-
              <lb/>
            hedrum, uel cubus, octahedrum, dodecahedrum, & </s>
            <s xml:id="echoid-s4697" xml:space="preserve">icoſa-
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            hedrum.</s>
            <s xml:id="echoid-s4698" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4699" xml:space="preserve">Sit primo a b c d pyramis ĩ ſphæra deſcripta, cuíus ſphæ
              <lb/>
            ræ centrum ſit e. </s>
            <s xml:id="echoid-s4700" xml:space="preserve">Dico e pyramidis a b c d grauitatis eſſe
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            centrum. </s>
            <s xml:id="echoid-s4701" xml:space="preserve">Si enim iuncta d e producatur ad baſim a b c in
              <lb/>
            f; </s>
            <s xml:id="echoid-s4702" xml:space="preserve">ex iis, quæ demonſtrauit Campanus in quartodecimo li
              <lb/>
            bro elementorum, propoſitione decima quinta, & </s>
            <s xml:id="echoid-s4703" xml:space="preserve">decima
              <lb/>
            ſeptima, erit f centrum circuli circa triangulum a b c de-
              <lb/>
            ſcripti: </s>
            <s xml:id="echoid-s4704" xml:space="preserve">atque erit e f ſexta pars ipſius ſphæræ axis. </s>
            <s xml:id="echoid-s4705" xml:space="preserve">quare
              <lb/>
            ex prima huius conſtat trianguli a b c grauitatis centrum
              <lb/>
            eſſe punctum f: </s>
            <s xml:id="echoid-s4706" xml:space="preserve">& </s>
            <s xml:id="echoid-s4707" xml:space="preserve">idcirco lineam d f eſſe pyramidis axem.</s>
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