Commandino, Federico, Liber de centro gravitatis solidorum, 1565

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        <body>
          <chap>
            <p type="main">
              <s id="s.000618">
                <pb pagenum="30" xlink:href="023/01/067.jpg"/>
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                <lb/>
              pra demonſtratum eſt, ita eſſe cylindrum, uel cylindri por­
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              tionem ad priſma, cuius baſis rectilinea figura, & æqua­
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              lis altitudo. </s>
              <s id="s.000619">ergo per conuerſionem rationis, ut circulus,
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              uel ellipſis ad portiones, ita conus, uel coni portio ad por­
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              tiones ſolidas. </s>
              <s id="s.000620">quare conus uel coni portio ad portiones
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              ſolidas maiorem habet proportionem, quam ge ad ef: &
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              diuidendo, pyramis ad portiones ſolidas maiorem pro­
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              portionem habet, quam gf ad fe. </s>
              <s id="s.000621">fiat igitur qf ad fe
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              ut pyramis ad dictas portiones. </s>
              <s id="s.000622">Itaque quoniam a cono
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              uel coni portione, cuius grauitatis centrum eſt f, aufer­
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              tur pyramis, cuius centrum e; reliquæ magnitudinis,
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              quæ ex ſolidis portionibus conſtat, centrum grauitatis
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              erit in linea ef protracta, & in puncto q.</s>
              <s id="s.000623"> quod fieri
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              non poteſt: eſt enim centrum grauitatis intra. </s>
              <s id="s.000624">Conſtat
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              igitur coni, uel coni portionis grauitatis centrum eſſe pun
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              ctum e. </s>
              <s id="s.000625">quæ omnia demonſtrare oportebat.</s>
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              8 huius</s>
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              <s id="s.000627">THEOREMA XIX. PROPOSITIO XXIII.</s>
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            <p type="main">
              <s id="s.000628">QVODLIBET fruſtum à pyramide, quæ
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              triangularem baſim habeat, abſciſſum, diuiditur
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              in tres pyramides proportionales, in ea proportio
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              ne, quæ eſt lateris maioris baſis ad latus minoris
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              ipſi reſpondens.</s>
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            <p type="main">
              <s id="s.000629">Hoc demonſtrauit Leonardus Piſanus in libro, qui de­
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              praxi geometriæ inſcribitur. </s>
              <s id="s.000630">Sed quoniam is adhuc im­
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              preſſus non eſt, nos ipſius demonſtrationem breuiter
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              perſtringemus, rem ipſam ſecuti, non uerba. </s>
              <s id="s.000631">Sit fru­
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              ſtum pyramidis abcdef, cuius maior baſis triangulum
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              abc, minor def: & iunctis ae, cc, cd, per, line­
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              as ae, ec ducatur planum ſecans fruſtum: itemque per
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              lineas ec, cd; & per cd, da alia plana ducantur, quæ
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              diuident fruſtum in trcs pyramides abce, adce, defc. </s>
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          </chap>
        </body>
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    </archimedes>
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