Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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FED. COMMANDINI
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          <p>
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              <pb file="0180" n="180" rhead="FED. COMMANDINI"/>
            fruſtum a d. </s>
            <s xml:space="preserve">Sed pyramis q æqualis eſt fruſto à pyramide
              <lb/>
            abſciſſo, ut dem onſtrauimus. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">conus, uel coni por-
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            tio q, cuius baſis ex tribus circulis, uel ellipſibus a b, e f, c d
              <lb/>
            conſtat, & </s>
            <s xml:space="preserve">altitudo eadem, quæ fruſti: </s>
            <s xml:space="preserve">ipſi fruſto a d eſt æ-
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            qualis. </s>
            <s xml:space="preserve">atque illud eſt, quod demonſtrare oportebat.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <note position="left" xlink:label="note-0178-01" xlink:href="note-0178-01a" xml:space="preserve">9. huius</note>
            <note position="left" xlink:label="note-0178-02" xlink:href="note-0178-02a" xml:space="preserve">2. duode-
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            cimi.</note>
            <figure xlink:label="fig-0178-01" xlink:href="fig-0178-01a">
              <image file="0178-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0178-01"/>
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            <note position="left" xlink:label="note-0178-03" xlink:href="note-0178-03a" xml:space="preserve">7. de co-
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            noidibus
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            & ſphæ-
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            roidibus</note>
            <note position="right" xlink:label="note-0179-01" xlink:href="note-0179-01a" xml:space="preserve">6. 11. duo
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            decimi</note>
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        <div type="section" level="1" n="91">
          <head xml:space="preserve">THEOREMA XXI. PROPOSITIO XXVI.</head>
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              <emph style="sc">Cvivslibet</emph>
            fruſti à pyramide, uel cono,
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            uel coni portione abſcisſi, centrum grauitatis eſt
              <lb/>
            in axe, ita ut eo primum in duas portiones diui-
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            ſo, portio ſuperior, quæ minorem baſim attingit
              <lb/>
            ad portionem reliquam eam habeat proportio-
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            nem, quam duplum lateris, uel diametri maioris
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            baſis, vnà cum latere, uel diametro minoris, ipſi
              <lb/>
            reſpondente, habet ad duplum lateris, uel diame-
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            tri minoris baſis vnà cũ latere, uel diametro ma-
              <lb/>
            ioris: </s>
            <s xml:space="preserve">deinde à puncto diuiſionis quarta parte ſu
              <lb/>
            perioris portionis in ipſa ſumpta: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">rurſus ab in-
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            ferioris portionis termino, qui eſt ad baſim maio
              <lb/>
            rem, ſumpta quarta parte totius axis: </s>
            <s xml:space="preserve">centrum ſit
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            in linea, quæ his finibus continetur, atque in eo li
              <lb/>
            neæ puncto, quo ſic diuiditur, ut tota linea ad par
              <lb/>
            tem propinquiorem minori baſi, eãdem propor-
              <lb/>
            tionem habeat, quam fruſtum ad pyramidẽ, uel
              <lb/>
            conum, uel coni portionem, cuius baſis ſit ea-
              <lb/>
            dem, quæ baſis maior, & </s>
            <s xml:space="preserve">altitudo fruſti altitudini
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            æqualis.</s>
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