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

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              <pb o="351" file="0371" n="371" rhead="LIBER IV."/>
            genitricium figurarum, quales ſunt parabolæ, BDF, CEG, dicta ex
              <lb/>
            ijſdem genita iolida iuxta regulas baſes abſciſſarum parabolarum,
              <lb/>
            ſi dictæ figuræ ſimiles fuerint inter ſe, vt prædicti circuli, vel ſimi-
              <lb/>
            les e lipſes, vel vt omnia quadrata, & </s>
            <s xml:id="echoid-s8808" xml:space="preserve">rectangula ſub abſciſſis pa-
              <lb/>
            rabolis, & </s>
            <s xml:id="echoid-s8809" xml:space="preserve">figuris diſtantiarum earundem, regulis ſemper pro vna-
              <lb/>
            quaque earundem parabolarum baſibus ſumptis, erunt inter ſe, vt
              <lb/>
            quadrata diametrorum abſciſſarum per ducta plana parabolarum,
              <lb/>
            intellige tamen reſecantia plana ſemper in ſupradictis eſſe erecta
              <lb/>
            plano genitricium figurarum, vt planum per, CG, erectum para-
              <lb/>
            bolæ, ADH, plano, ſimiſiter & </s>
            <s xml:id="echoid-s8810" xml:space="preserve">quod per, BF, ſiue in conoide, ſiue
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            in alijsiam dictis ſolidis, vt ſupradictum eſt genitis.</s>
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        <div xml:id="echoid-div844" type="section" level="1" n="499">
          <head xml:id="echoid-head519" xml:space="preserve">APPENDIX.</head>
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            <s xml:id="echoid-s8812" xml:space="preserve">EXponatur parabola, ACE, circa axim, CM, in baſi, AE, cui
              <lb/>
            paraliela ducatur vtcunque, BD, intra ipſam, & </s>
            <s xml:id="echoid-s8813" xml:space="preserve">iungatur, BE,
              <lb/>
              <figure xlink:label="fig-0371-01" xlink:href="fig-0371-01a" number="253">
                <image file="0371-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0371-01"/>
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            ducaturque, RS, diameter parabolæ,
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            BRE, & </s>
            <s xml:id="echoid-s8814" xml:space="preserve">vt fiat noſtrum exemplum
              <lb/>
            reuo uatur parabola, ACE, circa axim
              <lb/>
            manentem, CM, vt fiant conoides
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            parabolicæ, ACE, BCD, & </s>
            <s xml:id="echoid-s8815" xml:space="preserve">per BE,
              <lb/>
            ducatur planum erectum plano para-
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            bolæ, ACE, ſcindens fruſtum conoi-
              <lb/>
            dis, BAED, in duas portiones, ſcilicer,
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            BAE, BDE. </s>
            <s xml:id="echoid-s8816" xml:space="preserve">Dico ergo portionem, BAE, ad portionem, BDE,
              <lb/>
            (reſecta, CO, æquali ipſi, RS,) eſſe vt quadratũ, MO, cũ rectangulo
              <lb/>
            bis ſub, MOC, ad quadratum, ON, cum rectangulo bis ſub, ONC.</s>
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            <s xml:id="echoid-s8818" xml:space="preserve">Nam conois, ACE, ad conoidem, BRE, eſt vt quadratum, MC,
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            ad quadratum, SR, vel ad quadratum, OC, ergo, per conuerſionem
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            rationis, & </s>
            <s xml:id="echoid-s8819" xml:space="preserve">conuertendo, portio ſolida, BAE, ad conoidem para-
              <lb/>
            bolicam, ACE, erit vt reſiduum quadrati, MC, dempto quadrato,
              <lb/>
            OC, ad quadratum, MC, .</s>
            <s xml:id="echoid-s8820" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8821" xml:space="preserve">vt quadratum, MO, cum rectangulo
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            bis ſub, MOC, ad quadratum, MC, quod ſerua. </s>
            <s xml:id="echoid-s8822" xml:space="preserve">Item quia conoi-
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            dem, ACE, ad conoidem, BRE, diximus eſſe vt quadratum, MC,
              <lb/>
            ad quadratum, CO, eadem autem conois, ACE, ad conoidem, BCD,
              <lb/>
            eſt vt quadratum, MC, ad quadratum. </s>
            <s xml:id="echoid-s8823" xml:space="preserve">CN, ergo conois, ACE, ad
              <lb/>
            reliquum dempta conoide, BCD, à conoide, BRE, erit vt idem qua-
              <lb/>
            dratum, MC, ad reliquum, dempto quadrato, CN, à quadrato, CO,
              <lb/>
            .</s>
            <s xml:id="echoid-s8824" xml:space="preserve">i. </s>
            <s xml:id="echoid-s8825" xml:space="preserve">ad quadratum, ON, cum rectangulo bis ſub, ONC, eſt ergo co-
              <lb/>
            nois, ACE, ad portionem ſolidam, BDE, vt quadratum, MC, ad
              <lb/>
            quadratum, ON, cum rectangulo bis ſub, ONC, erat autem </s>
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