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

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        <div xml:id="echoid-div841" type="section" level="1" n="497">
          <p>
            <s xml:id="echoid-s8794" xml:space="preserve">
              <pb o="350" file="0370" n="370" rhead="GEOMETRIÆ"/>
            nia plana dictarum conoidum, alijs figuris ſimilibus ſeorſim in
              <lb/>
            vnoquoque ſolido aſsumptis, inter ſe eandem rationem, quam prę-
              <lb/>
            dictæ ſimiles ellipſes habentibus, quod ea ſolida, quorum aſsum-
              <lb/>
            ptæ fimiles figuræ ſunt omnia plana, erunt inter ſe æ qualia, dum
              <lb/>
            diametri genitricium eorundem figurarum, quæ ſunt abſciſsæ pa-
              <lb/>
            rabolæ, inter ſe quoq; </s>
            <s xml:id="echoid-s8795" xml:space="preserve">æquales fuerint.</s>
            <s xml:id="echoid-s8796" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div842" type="section" level="1" n="498">
          <head xml:id="echoid-head518" xml:space="preserve">COROLLARIVM VI.</head>
          <p>
            <s xml:id="echoid-s8797" xml:space="preserve">IN Propoſ. </s>
            <s xml:id="echoid-s8798" xml:space="preserve">28. </s>
            <s xml:id="echoid-s8799" xml:space="preserve">& </s>
            <s xml:id="echoid-s8800" xml:space="preserve">eius Coroll. </s>
            <s xml:id="echoid-s8801" xml:space="preserve">aſsum pta illius figura, & </s>
            <s xml:id="echoid-s8802" xml:space="preserve">facto ſo-
              <lb/>
            lito exemplo per reuolutionem, ADH, parabolæ circa axim,
              <lb/>
              <figure xlink:label="fig-0370-01" xlink:href="fig-0370-01a" number="252">
                <image file="0370-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0370-01"/>
              </figure>
            DO, habetur, quod ſi conois paraboli-
              <lb/>
            ca, ADH, in reuolutione deſcripta
              <lb/>
            ſecetur quomodocunque planis ſiue
              <lb/>
            ad axem rectis, ſiue obliquis, quod ab-
              <lb/>
            fcifsæ conoides erunt inter ſe, vt qua-
              <lb/>
            drata diametrorum eorundem, Nam
              <lb/>
            vt omnia quadrata, BDF, regula, BF,
              <lb/>
            quæ axim, DO, rectè ſecat, ad rectan-
              <lb/>
            gula ſub parabola, CEG, & </s>
            <s xml:id="echoid-s8803" xml:space="preserve">figura di-
              <lb/>
            ftantiarum, ERG, ita eſse omnes circulos, BDF, diametros in ea ſi-
              <lb/>
            tas habentes, ſumptos iuxta regulam, BF, ad omnes ſimiles elli-
              <lb/>
            pſes figuræ genitricis, CEG, ſumptas iuxta regulam, CG, quarum
              <lb/>
            diametri maiores ſunt in figura, CEG, minores verò in figura di-
              <lb/>
            ſtantiarum, REG, oſtendemus, methodo antecedentis, ergo dicti
              <lb/>
            omnes circuli parabolæ, BDF, ad dictas omnes ellipſes parabolæ,
              <lb/>
            CEG, erunt vt quadratum, DN, ad quadratum, EM, ergo & </s>
            <s xml:id="echoid-s8804" xml:space="preserve">co-
              <lb/>
            nois parabolica, BDF, ad conoidem parabolicam, CEG, erit vt
              <lb/>
            quadratum, DN, ad quadratum, EM, vnde, conuertendo, conois
              <lb/>
            parabolica, GEC, ad conoidem parabolicam, FDB, erit vt qua-
              <lb/>
            dratum, EM, ad quadratum, DN, ſi ergo aliud planum, vtcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s8805" xml:space="preserve">obliquè axem, DO, ſecauerit, erit conois parabolica, BDF, ad
              <lb/>
            hanc conoidem vltimò reſectam, vt quadratum, DN, ad quadra-
              <lb/>
            tum diametri huius reſectæ conodis, ergo ex æquali conois pa-
              <lb/>
            rabolica, CEG, ad hanc conoidem vltimò reſectam, cuius baſis
              <lb/>
            pariter obliquè ſecat axim, DO, erit vt quadratum, EM, ad huius
              <lb/>
            diametri quadratum, quomodocunque igitur reſecetur conois pla-
              <lb/>
            nis axem ſecantibus, reſecta ſegmenta ſunt, vt diametrorum qua-
              <lb/>
            drata. </s>
            <s xml:id="echoid-s8806" xml:space="preserve">Sed vniuerſaliter, ſi, vice circulorum, vel dictarum ellipſium,
              <lb/>
            ſummamus alias figuras ſimiles in vnoquoq; </s>
            <s xml:id="echoid-s8807" xml:space="preserve">ſolido ſeorſim, quo-
              <lb/>
            rum ſunt omnia plana, ijs exiſtentibus omnibus figuris </s>
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