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

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          <pb o="287" file="0307" n="307" rhead="LIBER IV."/>
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        <div xml:id="echoid-div692" type="section" level="1" n="407">
          <head xml:id="echoid-head427" xml:space="preserve">THEOREMA II. PROPOS. II.</head>
          <p>
            <s xml:id="echoid-s6986" xml:space="preserve">SI intra parabolam ducantur vtcunque duæ ad axim, vel
              <lb/>
            diametrum eiuſdem ordinatim applicatę lineę, abſciſſæ
              <lb/>
            abijſdem parabolæ, erunt inter ſe, vt cubi dictarum linea-
              <lb/>
            rum ordinatim applicatarum.</s>
            <s xml:id="echoid-s6987" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6988" xml:space="preserve">Sint ergo intra parabolam circa axim, veldiametrum, CG, con-
              <lb/>
            ſtitutam, duæ adipſum ordinatim applicatæ rectæ lineæ, FH, OM,
              <lb/>
            parabolas, OCM, FCH, abſc ndentes. </s>
            <s xml:id="echoid-s6989" xml:space="preserve">Dico ergo parabolam, F
              <lb/>
            CH, ad parabolam, OCM, eſſe vt cubum, FH, ad cubum, OM;
              <lb/>
            </s>
            <s xml:id="echoid-s6990" xml:space="preserve">conſtituantur circa axes, vel diametros, CI, CG, & </s>
            <s xml:id="echoid-s6991" xml:space="preserve">in eiſdem ba-
              <lb/>
            ſibus, OM, FH, cum dictis parabolis parallelogramma, AH, RM. </s>
            <s xml:id="echoid-s6992" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0307-01" xlink:href="fig-0307-01a" number="201">
                <image file="0307-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0307-01"/>
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            Quoniam ergo ęquiangula paral
              <lb/>
              <note position="right" xlink:label="note-0307-01" xlink:href="note-0307-01a" xml:space="preserve">11. Lib. 2.</note>
            lelogramma habent rationem ex
              <lb/>
            lateribus compoſitam, ſunt au-
              <lb/>
            tem parallelogramma, AH, R
              <lb/>
            M, æquiangula, nam, OM, eſt
              <lb/>
            parallela ipſi, FH, ideò paralle-
              <lb/>
            logrammum, AH, ad parallelo-
              <lb/>
            grammum, RM, habebit ratio-
              <lb/>
            nem compoſitam ex ea, quam ha
              <lb/>
            bet, FA, ad, RO, .</s>
            <s xml:id="echoid-s6993" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6994" xml:space="preserve">GC, ad,
              <lb/>
            CI, .</s>
            <s xml:id="echoid-s6995" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6996" xml:space="preserve">quadratum, FH, ad qua-
              <lb/>
              <note position="right" xlink:label="note-0307-02" xlink:href="note-0307-02a" xml:space="preserve">38. Ec
                <lb/>
              Schol. 40.
                <lb/>
              lib. 1.</note>
            dratum, OM, & </s>
            <s xml:id="echoid-s6997" xml:space="preserve">ex ea, quam habet, FH, ad, OM, ſed etiam cu-
              <lb/>
            bus, FH, ad cubum, OM, habet rationem compoſitam ex ea, quam
              <lb/>
            habet quadratum, FH, ad quadratum, OM, & </s>
            <s xml:id="echoid-s6998" xml:space="preserve">ex ea, quam ha-
              <lb/>
              <note position="right" xlink:label="note-0307-03" xlink:href="note-0307-03a" xml:space="preserve">D. Corol.
                <lb/>
              4. Gener.
                <lb/>
              34, lib. 2.</note>
            bet, FH, ad, OM, ergo parallelogrammum, AH, ad parallelo-
              <lb/>
            grammum, RM, & </s>
            <s xml:id="echoid-s6999" xml:space="preserve">conſequenter parabola, FCH, ad parabolam,
              <lb/>
            OCM, (quia ſunt dictorum parallelogrammorum ſubſexquialterę)
              <lb/>
              <note position="right" xlink:label="note-0307-04" xlink:href="note-0307-04a" xml:space="preserve">Exantec.</note>
            erit vt cubus, FH, ad cubum, OM, quodoſtendere opus erat.</s>
            <s xml:id="echoid-s7000" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div694" type="section" level="1" n="408">
          <head xml:id="echoid-head428" xml:space="preserve">THEOREMA III. PROPOS. III.</head>
          <p>
            <s xml:id="echoid-s7001" xml:space="preserve">SI in parabola ducatur quædam recta linea ad eiuſdem
              <lb/>
            axim, vel diametrum ordinatim applicata; </s>
            <s xml:id="echoid-s7002" xml:space="preserve">agantur de-
              <lb/>
            inde ipſx
              <unsure/>
            axi, vel diametro æquidiſtantes rectæ lineævſque
              <lb/>
            ad curuam parabolicam, & </s>
            <s xml:id="echoid-s7003" xml:space="preserve">dictam ordinatim applicatam,
              <lb/>
            quæ baſis erit eiuſdem parabolæ; </s>
            <s xml:id="echoid-s7004" xml:space="preserve">Dictæ æquidiſtantes </s>
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