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

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            <s xml:id="echoid-s10890" xml:space="preserve">
              <pb o="417" file="0437" n="437" rhead="LIBER V."/>
            compoſitam ex duabus rationibus ibidem appoſitis. </s>
            <s xml:id="echoid-s10891" xml:space="preserve">Vt autem
              <lb/>
            fiat noſtrum exemplum, intelligatur in ipia (in qua dimittantur
              <lb/>
            aſymptoti, & </s>
            <s xml:id="echoid-s10892" xml:space="preserve">rectæ, ad, DC, OV, VX, PO, PX,) BD, eſſe axem,
              <lb/>
            circa quam reuoluatur figura, vt ex hypeibola, ADC, fiat conois
              <lb/>
              <figure xlink:label="fig-0437-01" xlink:href="fig-0437-01a" number="298">
                <image file="0437-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0437-01"/>
              </figure>
            hyperbolica, ADC; </s>
            <s xml:id="echoid-s10893" xml:space="preserve">vlterius per,
              <lb/>
            OX, traducatur planum, OX, ere-
              <lb/>
            ctum plano genitricis hyperbolæ,
              <lb/>
            ADC, cuius pars in conoide con-
              <lb/>
            cepta erit ellipſis, OX, cuius maior
              <lb/>
            diameter, OX, minor autem in fi-
              <lb/>
            gura propoſitionis linea, PO, ha-
              <lb/>
            bemus igitur ex Prop. </s>
            <s xml:id="echoid-s10894" xml:space="preserve">11. </s>
            <s xml:id="echoid-s10895" xml:space="preserve">conoi-
              <lb/>
            dem, ADC, ad conoidem, OVX,
              <lb/>
            habere rationem compoſitam ex
              <lb/>
            ratione rectanguli ſub, MB, HI,
              <lb/>
            ad rectangulum ſub, RI, FB, & </s>
            <s xml:id="echoid-s10896" xml:space="preserve">ex
              <lb/>
              <note position="right" xlink:label="note-0437-01" xlink:href="note-0437-01a" xml:space="preserve">43. l. 1.
                <lb/>
              Coro. 44.
                <lb/>
              l. 1.</note>
            ratione parallelepipedi ſub altitu-
              <lb/>
            dine hyperbolæ, ADC, baſi qua-
              <lb/>
            drato, AC, ad parallelepipedum ſub altitudine hyperbolæ, OVX,
              <lb/>
            baſi autem rectangulo ſub, XO, OP, veluti ſunt omnia quadrata
              <lb/>
            hyperbolæ, ADC, regula, AC, ad omnia rectangula hyperbolæ,
              <lb/>
            OVX, (regula, OX,) ſimilia rectangulo ſub, XO, OP, ſiue omnes
              <lb/>
            circuli eiuſdem ad omnes ellipſes hyperbolæ, OVX, ſimiles ellipſi,
              <lb/>
              <note position="right" xlink:label="note-0437-02" xlink:href="note-0437-02a" xml:space="preserve">Corol. 2.
                <lb/>
              33. l. 2.</note>
            cuius coniugati axes, vel diametri ſunt, XO, OP, XO, maior, OP,
              <lb/>
            minor, nam omnes dicti circuli ſunt omnia plana conoidis, ADC,
              <lb/>
            regula, AC, & </s>
            <s xml:id="echoid-s10897" xml:space="preserve">dictæ omnes ellipſes ſunt omnia plana conoidis, O
              <lb/>
            VX, eandem autem rationem ſupradictæ comperiemus habere
              <lb/>
            quæcunq; </s>
            <s xml:id="echoid-s10898" xml:space="preserve">lolida non quidem ſimilaria inter ſe, ſed quorum om-
              <lb/>
            nia plana ſint omnes figuræ ſimiles genitricium figurarum, ADC,
              <lb/>
            OVX, a quibus genita dicuntur, quæ habeant inter ſeeandem ra-
              <lb/>
            tionem ei, quam habet quadratum, AC, ad rectangulum, XOP.</s>
            <s xml:id="echoid-s10899" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div984" type="section" level="1" n="586">
          <head xml:id="echoid-head611" xml:space="preserve">COR OLLARIVM XII.</head>
          <p>
            <s xml:id="echoid-s10900" xml:space="preserve">IN Propoſ. </s>
            <s xml:id="echoid-s10901" xml:space="preserve">12. </s>
            <s xml:id="echoid-s10902" xml:space="preserve">conſpecta illius figura, & </s>
            <s xml:id="echoid-s10903" xml:space="preserve">completis conoidibus,
              <lb/>
            BAD, HMQ, patet eorum rationem eſſe compoſitam ex ra-
              <lb/>
            tionibus ibi explicatis, vbi videri poterunt. </s>
            <s xml:id="echoid-s10904" xml:space="preserve">Quas quidem ratio-
              <lb/>
            nes comperiemus etiam habere quæcunq; </s>
            <s xml:id="echoid-s10905" xml:space="preserve">ſolida, licet etiam non
              <lb/>
            ſimilaria ad inuicem, genita tamen ex eildem figuris, quarum om-
              <lb/>
            nes figuræ ſimiles (inter ſe, quę ſunt vnius, vtriuſq; </s>
            <s xml:id="echoid-s10906" xml:space="preserve">tamen figuræ
              <lb/>
            genitricis diſſimiles) habeant eandem rationem, quam </s>
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