Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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            <s xml:id="echoid-s14032" xml:space="preserve">
              <pb o="538" file="0558" n="558" rhead="GEOMETRI Æ"/>
            pro alis in hac propoſitione ſit pariter regula, extendaturq; </s>
            <s xml:id="echoid-s14033" xml:space="preserve">hinc
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            indevt ſecet EC, vt in, N, HV, vt in, R, & </s>
            <s xml:id="echoid-s14034" xml:space="preserve">PV, vt in, Q, ergo, CG,
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              <figure xlink:label="fig-0558-01" xlink:href="fig-0558-01a" number="365">
                <image file="0558-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0558-01"/>
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            ad, MO, erit vt quadratum, GH,
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            ad rectangulum ſub compoſita
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            ex, HG, GO, & </s>
            <s xml:id="echoid-s14035" xml:space="preserve">ſub, OH, (hoc. </s>
            <s xml:id="echoid-s14036" xml:space="preserve">n.
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            </s>
            <s xml:id="echoid-s14037" xml:space="preserve">deducitur ex prop. </s>
            <s xml:id="echoid-s14038" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14039" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14040" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14041" xml:space="preserve">quæ
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            non dependet à prop. </s>
            <s xml:id="echoid-s14042" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14043" xml:space="preserve">neq; </s>
            <s xml:id="echoid-s14044" xml:space="preserve">indi-
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            get, quod denuò demonſtretur)
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            ideſt vt quadratum, GV, ad qua-
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            dratum, OR, ſed vt, CG, ad MO,
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            ita eſt quadratum, CG, ad rectan-
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            gulum ſub, CG, ſeu, NO, & </s>
            <s xml:id="echoid-s14045" xml:space="preserve">OM, ergo quadratum, CG, ad rectan-
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            gulum, NOM, erit vt quadratum, GV, ad quadratum, OR, & </s>
            <s xml:id="echoid-s14046" xml:space="preserve">per-
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            mutando quadratum, CG, ad quadratum, GV, erit vt rectan-
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            gulum, NOM, ad quadratum, OR, ſic ductis alijs parallelis
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            euenire oſtendemus; </s>
            <s xml:id="echoid-s14047" xml:space="preserve">ergo ſolidum rectangulum ſub, EG, paral-
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            lelogrammo, & </s>
            <s xml:id="echoid-s14048" xml:space="preserve">ſemiparabola, CHG, erit proportionaliter ana-
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            logum quadrato ſolido quadrantis, HVG, ſecundum regulam,
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            C V, ſecundum eandem autem oſtendemus etiam quadratum
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            ſolidum, EG, eſſe proportionaliter analogum quadrato ſolido, H
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            V, etenim quadratum, CG, ad quadratum, GV, eſt vt quadratum,
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            NO, ad quadratum, OQ, vnde vt quadratum, CG, ad quadratum,
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            GV, ſic erit quadratum ſolidum, EG, ad quadratum ſolidum, G
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            P, & </s>
            <s xml:id="echoid-s14049" xml:space="preserve">ſic etiam rectangulum ſolidum ſub, EG, HCG, ad quadratum
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            ſolidum, HGV, ergo quadratum ſolidum, EG, ad quadratum ſoli-
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            dum, HV, erit vt rectangulum ſolidum ſub, EG, HCG, ad quadra-
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            tum ſolidum, HGV, ergo permutando quadratum ſolidum, EG, ad
              <lb/>
            rectangulum ſolidum ſub, EG, HCG, erit vt quadratum ſolidum,
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            HV, ad quadratum ſolidum, HGV, ſed quadratum ſolidum, HV,
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              <note position="left" xlink:label="note-0558-01" xlink:href="note-0558-01a" xml:space="preserve">Elicitur
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              ex 20. hu-
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              ius.</note>
            ſequialterum eſt quadrati ſolidi, HGV, cum, VG, tranſeat per cen-
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            trum, G, ergo quadratum ſolidum, EG, ſexquialterum erit rectan-
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            guli ſolidi ſub, EG, HCG, ſed vt quadratum ſolidum, EG, ad rectan-
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            gulum ſolidum ſub, EG, HCG, ita baſis, EG, ad baſim, HCG, ergo,
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            EG, erit ſexquialtera, HCG, & </s>
            <s xml:id="echoid-s14050" xml:space="preserve">conſequenter, viſa figura prop. </s>
            <s xml:id="echoid-s14051" xml:space="preserve">1.
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            </s>
            <s xml:id="echoid-s14052" xml:space="preserve">
              <note position="left" xlink:label="note-0558-02" xlink:href="note-0558-02a" xml:space="preserve">Cor. 1. 13.
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              huius.</note>
            lib. </s>
            <s xml:id="echoid-s14053" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14054" xml:space="preserve">erit parallelogrammum, AH, ſequialterum parabolæ, FCH,
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            quod oſtendendum erat.</s>
            <s xml:id="echoid-s14055" xml:space="preserve"/>
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          <head xml:id="echoid-head783" xml:space="preserve">ANNOTATIO.</head>
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            <s xml:id="echoid-s14056" xml:space="preserve">PEr hanc autem ſuppletur prop. </s>
            <s xml:id="echoid-s14057" xml:space="preserve">1. </s>
            <s xml:id="echoid-s14058" xml:space="preserve">lib. </s>
            <s xml:id="echoid-s14059" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14060" xml:space="preserve">etenim illius poſterior
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            pars deducetur, vt ibi, hac vero demonſtrata reliqua </s>
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