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

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            <s xml:id="echoid-s7370" xml:space="preserve">
              <pb o="306" file="0326" n="326" rhead="GEOMETRIÆ"/>
            per, C, ipſi, DF, parallela, CB, & </s>
            <s xml:id="echoid-s7371" xml:space="preserve">producantur, AR, HO, vſq;
              <lb/>
            </s>
            <s xml:id="echoid-s7372" xml:space="preserve">ad, BC, in, P, Q, iunganturque, AC, HC, & </s>
            <s xml:id="echoid-s7373" xml:space="preserve">à puncto, M,
              <lb/>
            ducatur, MX, parallela axi, vel diametro, AP; </s>
            <s xml:id="echoid-s7374" xml:space="preserve">quoniam ergo, O
              <lb/>
              <note position="left" xlink:label="note-0326-01" xlink:href="note-0326-01a" xml:space="preserve">12.huius.</note>
            Q, eſt parallela ipſi, MX, & </s>
            <s xml:id="echoid-s7375" xml:space="preserve">ipſa ſecat, MC, bifariam in, O, ſe-
              <lb/>
            cabit etiam, XC, bifariam in Q; </s>
            <s xml:id="echoid-s7376" xml:space="preserve">& </s>
            <s xml:id="echoid-s7377" xml:space="preserve">quia parabola, ABC, ad pa-
              <lb/>
            rabolam, MHFC, eſt vt cubus, BC, ad cubum, CX, vel vt cu-
              <lb/>
            bus, PC, ad cubum, CQ, ideò ſemiparabola, APC, ad ſemipa-
              <lb/>
            rabolam, HOC, erit vt cubus, PC, ad cubum, CQ, & </s>
            <s xml:id="echoid-s7378" xml:space="preserve">eorun-
              <lb/>
              <note position="left" xlink:label="note-0326-02" xlink:href="note-0326-02a" xml:space="preserve">@.huius.</note>
            dem ſubſexquitertia .</s>
            <s xml:id="echoid-s7379" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7380" xml:space="preserve">triangulum, APC, ad triangulum, HOC,
              <lb/>
            erit vt cubus, PC, ad cubum, CQ: </s>
            <s xml:id="echoid-s7381" xml:space="preserve">quoniam verò triangula æqui-
              <lb/>
            angula habent interſerationem compoſitam exratione baſium, &</s>
            <s xml:id="echoid-s7382" xml:space="preserve">G
              <lb/>
            altitudinum, vel linearum à verticibus earundem ductarum æqua-
              <lb/>
              <note position="left" xlink:label="note-0326-03" xlink:href="note-0326-03a" xml:space="preserve">Coroll.1.
                <lb/>
              19. 1. 2.</note>
            liter baſibus inclinatarum; </s>
            <s xml:id="echoid-s7383" xml:space="preserve">ideò triangulum, APC, ad triangu-
              <lb/>
            lum, HOC, habebit rationem compoſitam ex ratione baſis, PA,
              <lb/>
            ad baſim, OH, vel, AR, illi æqualem, & </s>
            <s xml:id="echoid-s7384" xml:space="preserve">ex ratione, PC, ad, C
              <lb/>
            Q, quæ vel ſunt altitudines, vellineæ ductæ à communi vertice, C,
              <lb/>
            cum æquali inclinatione ad baſes, AP, &</s>
            <s xml:id="echoid-s7385" xml:space="preserve">, HO, productam, quia,
              <lb/>
              <figure xlink:label="fig-0326-01" xlink:href="fig-0326-01a" number="218">
                <image file="0326-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0326-01"/>
              </figure>
            AP, HQ, ſunt parallelæ, eſt autem vt,
              <lb/>
            PA, ad AR, ita quadratum, PC, ad
              <lb/>
            quadratum, RF, ergo triangulum, A
              <lb/>
            PC, ad triangulum, HOC, habebit
              <lb/>
            rationem compoſitam ex ea, quam ha-
              <lb/>
            bet quadratum, PC, ad quadratum, R
              <lb/>
            F, & </s>
            <s xml:id="echoid-s7386" xml:space="preserve">ex ea, quam habet, PC, ad CQ,
              <lb/>
            quia verò triangulum, APC, ad trian-
              <lb/>
            gulum, HOC, eſt vt cubus, PC, ad
              <lb/>
            cubum, CQ, ideò ad illud habet etiam rationem compoſitam ex
              <lb/>
            ea, quam habet, PC, ad CQ, & </s>
            <s xml:id="echoid-s7387" xml:space="preserve">ex ratione quadrati, PC, ad qua-
              <lb/>
            dratum, CQ, ergo iſtæ duæ rationes, ſcilicet quam habet, PC,
              <lb/>
            ad, CQ, & </s>
            <s xml:id="echoid-s7388" xml:space="preserve">quadratum, PC, ad quadratum, RF, componunt
              <lb/>
            eandem rationem, quam iſtæ duæ, ſcilicet ratio, PC, ad, CQ, & </s>
            <s xml:id="echoid-s7389" xml:space="preserve">
              <lb/>
            quadrati, PC, ad quadratum, CQ, eſt autem in his communis
              <lb/>
            ratio, quam habet, PC, ad, CQ, ergo reliqua ratio, quam habet
              <lb/>
            quadratum, PC, ad quadratum, CQ, erit eadem ei, quam habet
              <lb/>
            quadratum idem, PC, ad quadratum, RF, ergo quadratum, C
              <lb/>
              <note position="left" xlink:label="note-0326-04" xlink:href="note-0326-04a" xml:space="preserve">2.huius.</note>
            Q, erit æquale quadrato, RF, &</s>
            <s xml:id="echoid-s7390" xml:space="preserve">, CQ, erit æqualis ipſi, RF.
              <lb/>
            </s>
            <s xml:id="echoid-s7391" xml:space="preserve">Quoniam autem parabola, BAC, ad parabolam, DAF, eſt vt
              <lb/>
              <note position="left" xlink:label="note-0326-05" xlink:href="note-0326-05a" xml:space="preserve">12.huius.</note>
            cubus, BC, ad cubum, DF, .</s>
            <s xml:id="echoid-s7392" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7393" xml:space="preserve">vt cubus, PC, ad cubum, RF,
              <lb/>
            item oſtenſum eſt parabolam eandem, BAC, ad parabolam, MH
              <lb/>
            FC, eſſe vt cubum, PC, ad cubum, CQ, ideò parabola, DAF,
              <lb/>
            ad parabolam, MHFC, erit vt cubus, RF, ad cubum, QC, ſunt
              <lb/>
            autem, QC, RF, inter ſe æquales, vtoſtenſum eſt, & </s>
            <s xml:id="echoid-s7394" xml:space="preserve">ideò </s>
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