Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota

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        <div xml:id="echoid-div1248" type="section" level="1" n="754">
          <pb o="541" file="0561" n="561" rhead="LIBER VII."/>
        </div>
        <div xml:id="echoid-div1249" type="section" level="1" n="755">
          <head xml:id="echoid-head788" xml:space="preserve">THEOREMA XXVI. PROPOS. XXVI.</head>
          <p>
            <s xml:id="echoid-s14228" xml:space="preserve">IN figura prop.</s>
            <s xml:id="echoid-s14229" xml:space="preserve">46. </s>
            <s xml:id="echoid-s14230" xml:space="preserve">oſtendemus, regula eadem retenta, re-
              <lb/>
            ctangulum ſolidum ſub, HP, PE, duplum eſſe rectangu-
              <lb/>
            liſolidi ſub, BZPD, DPG.</s>
            <s xml:id="echoid-s14231" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14232" xml:space="preserve">Sumatur .</s>
            <s xml:id="echoid-s14233" xml:space="preserve">n. </s>
            <s xml:id="echoid-s14234" xml:space="preserve">de illius ſchemate
              <lb/>
              <figure xlink:label="fig-0561-01" xlink:href="fig-0561-01a" number="368">
                <image file="0561-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0561-01"/>
              </figure>
            parallelogrammum, HG, cum fru-
              <lb/>
            ſto parabolæ, BZGD, & </s>
            <s xml:id="echoid-s14235" xml:space="preserve">rectis, R
              <lb/>
            F, DP, fiat autem inſuper, AP,
              <lb/>
            æqualis, PD, & </s>
            <s xml:id="echoid-s14236" xml:space="preserve">ducta, AM, paral-
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            lela, DP, iungatur, AD, ſecans, C
              <lb/>
            T, in, N. </s>
            <s xml:id="echoid-s14237" xml:space="preserve">Cum ergo in dicta prop.
              <lb/>
            </s>
            <s xml:id="echoid-s14238" xml:space="preserve">independenter ab indiuiſibilium methodo, cõcludatur rectangulũ’,
              <lb/>
            RTF, ad, STI, eſſe vt, PD, ad, DT, idpſum & </s>
            <s xml:id="echoid-s14239" xml:space="preserve">hic tanquã demonſtra-
              <lb/>
            tũ reci piemus, ſed, PD, ad, DT, hoc eſt, CT, ad, TN, eſt vt quadra-
              <lb/>
            tum, CT, ad rectangulum, CTN, ergo rectangulum, RTF, ad, STI,
              <lb/>
            erit vt quadratum, CT, ad rectangulum, CTN, eſt autem, RF, vt-
              <lb/>
            cumq; </s>
            <s xml:id="echoid-s14240" xml:space="preserve">ducta parallela, ZG, ergo modo conſueto oſtendemus ſoli-
              <lb/>
            dum rectangulum ſub, HP, PE, eſſe proportionaliter analogum
              <lb/>
            quadrato ſolido, MP, ſicut rectangulum ſolidum ſub, BZPD, DP
              <lb/>
            G, eſſe proportionalites analogum rectangulo ſolidoſub, MP, PA
              <lb/>
            D, & </s>
            <s xml:id="echoid-s14241" xml:space="preserve">tandem concludemus hæc ſolida eſſe proportionalia, ideſt
              <lb/>
            rectangulum ſolidum ſub, HP, PE, ad rectang. </s>
            <s xml:id="echoid-s14242" xml:space="preserve">ſolidum ſub, BZPD,
              <lb/>
            DPG, eſſe vt quadratum ſolidum MP, ad rectangulum ſolidum ſub,
              <lb/>
            MP, PDA, ideſt vt, MP, ad, PDA, ideſt concludemus rectangulum
              <lb/>
            ſolidum ſub, HP, PE, duplum eſſe rectanguli ſolidi ſub, BZPD, PD
              <lb/>
              <note position="right" xlink:label="note-0561-01" xlink:href="note-0561-01a" xml:space="preserve">Cor. I. 13.
                <lb/>
              hu.u.s</note>
            G, quod oſtendendum erat.</s>
            <s xml:id="echoid-s14243" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1251" type="section" level="1" n="756">
          <head xml:id="echoid-head789" xml:space="preserve">ANNOTATIO.</head>
          <p>
            <s xml:id="echoid-s14244" xml:space="preserve">PRop.</s>
            <s xml:id="echoid-s14245" xml:space="preserve">46. </s>
            <s xml:id="echoid-s14246" xml:space="preserve">igitur reſtaurata, ſtylo noſtro ſequentium propoſitio-
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            num demonſtrationes proſequemur ab hac vſque a d 51. </s>
            <s xml:id="echoid-s14247" xml:space="preserve">inclu-
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            fiuè, quæ quidem veritatem habere comperitur ex prop.</s>
            <s xml:id="echoid-s14248" xml:space="preserve">22. </s>
            <s xml:id="echoid-s14249" xml:space="preserve">hu us.
              <lb/>
            </s>
            <s xml:id="echoid-s14250" xml:space="preserve">Scholium autem ſequens retineatur vt ib, ſubſtituendo tamen no-
              <lb/>
            mini omnium ſimilium figurarum hocaliud, nempe quotcunque
              <lb/>
            ſimiles figuras &</s>
            <s xml:id="echoid-s14251" xml:space="preserve">c. </s>
            <s xml:id="echoid-s14252" xml:space="preserve">vt in examine lib. </s>
            <s xml:id="echoid-s14253" xml:space="preserve">3. </s>
            <s xml:id="echoid-s14254" xml:space="preserve">animaduerſum eſt. </s>
            <s xml:id="echoid-s14255" xml:space="preserve">His ve-
              <lb/>
            rò prædemonſtratis ſubſequentia Corollaria vſq; </s>
            <s xml:id="echoid-s14256" xml:space="preserve">ad finem lib.</s>
            <s xml:id="echoid-s14257" xml:space="preserve">4. </s>
            <s xml:id="echoid-s14258" xml:space="preserve">ſo-
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            lita nominum mutatione facta, cuncta facillimè deducentur per
              <lb/>
            iam oſtenſa circa quadrata, ſeu rectangula ſolida ſub talibus, & </s>
            <s xml:id="echoid-s14259" xml:space="preserve"/>
          </p>
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