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

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            <s xml:id="echoid-s7069" xml:space="preserve">
              <pb o="291" file="0311" n="311" rhead="LIBER IV."/>
            &</s>
            <s xml:id="echoid-s7070" xml:space="preserve">, ZX, ad portionem, ACXN, eſſe, vt omnia quádratà, ℟ X, ad
              <lb/>
            omnia quadrata quadrilinei, NOEX, &</s>
            <s xml:id="echoid-s7071" xml:space="preserve">, AN, CX, ordinatim ad ba-
              <lb/>
            ſim, FG, applicatæ ſumptæ ſunt vtcunq; </s>
            <s xml:id="echoid-s7072" xml:space="preserve">vnde patet.</s>
            <s xml:id="echoid-s7073" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div699" type="section" level="1" n="411">
          <head xml:id="echoid-head431" xml:space="preserve">THEOREMA V. PROPOS. V.</head>
          <p>
            <s xml:id="echoid-s7074" xml:space="preserve">DVctis vtcunque ad baſim parabolæ ordinatim applica-
              <lb/>
            tis, parallelogramma ſub ipſis, & </s>
            <s xml:id="echoid-s7075" xml:space="preserve">portionibus baſis ab
              <lb/>
            ijſdem abſciſſis ad ſibi inſcriptas portiones parabolæ infra-
              <lb/>
            ſcriptam rationem habebunt.</s>
            <s xml:id="echoid-s7076" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7077" xml:space="preserve">Sit ergo parabola, HGA, in baſi, HA, circa axim, vel diame-
              <lb/>
            trum, GO, & </s>
            <s xml:id="echoid-s7078" xml:space="preserve">ſint ductæ ipſi, GO, parallelæ vtcunque, ST, EC,
              <lb/>
            compleantur autem parallelogramma, LT, BO, DC, deinde pro-
              <lb/>
            ducatur, GO, vtcunque in, M, & </s>
            <s xml:id="echoid-s7079" xml:space="preserve">circa ſemiaxes, vel ſemidiame-
              <lb/>
            tros, HO, OM, intelligatur, HMA, ſemicirculus, vel ſemiellipſis,
              <lb/>
              <figure xlink:label="fig-0311-01" xlink:href="fig-0311-01a" number="205">
                <image file="0311-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0311-01"/>
              </figure>
            cuius curuam, ST,
              <lb/>
            EC, productæ ſe-
              <lb/>
            cent in, VN, com-
              <lb/>
            pleàtur pariter pa-
              <lb/>
            rallelogramma, H
              <lb/>
            V, HM, HN, pro-
              <lb/>
            ducantur inſuper, Y
              <lb/>
            M, BG, vſque in,
              <lb/>
            & </s>
            <s xml:id="echoid-s7080" xml:space="preserve">℟, &</s>
            <s xml:id="echoid-s7081" xml:space="preserve">, SV, EN,
              <lb/>
            vſq; </s>
            <s xml:id="echoid-s7082" xml:space="preserve">ad puncta, P,
              <lb/>
            Z, Q, I, quæ ſunt
              <lb/>
            in lateribus, B ℟, Y
              <lb/>
            &</s>
            <s xml:id="echoid-s7083" xml:space="preserve">. Igitur paralle-
              <lb/>
            logrammum, LT,
              <lb/>
            ad portionem, HS
              <lb/>
            T, erit vt omnia
              <lb/>
            quadrata, HV, ad
              <lb/>
            omnia quadrata ſe-
              <lb/>
            miportionis, HT
              <lb/>
            V, (regula, GM, pro hac Propoſ. </s>
            <s xml:id="echoid-s7084" xml:space="preserve">ſumpta). </s>
            <s xml:id="echoid-s7085" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7086" xml:space="preserve">vt, TA, ad compó-
              <lb/>
            ſitam ex {1/2}, TA, &</s>
            <s xml:id="echoid-s7087" xml:space="preserve">, {1/6}, HT, vt patet in Libro de Circulo, & </s>
            <s xml:id="echoid-s7088" xml:space="preserve">Ellipſi
              <lb/>
            Propoſitione I.</s>
            <s xml:id="echoid-s7089" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7090" xml:space="preserve">Similiter oſtendemus, BO, ſemiparabolæ, HGO, eſſe ſexqui-
              <lb/>
            alterum, eſt enim vt omnia quadrata, HM, ad omnia quadrata, H
              <lb/>
            VMO, ideſt in ratione ſexquialtera, vt patet in eadem Propoſit. </s>
            <s xml:id="echoid-s7091" xml:space="preserve">I.</s>
            <s xml:id="echoid-s7092" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7093" xml:space="preserve">Pariter demonſtrabimus, DC, ad portionem, HGEC, eſſe vt,
              <lb/>
            AC, ad compoſitam ex, {1/2}, AC, &</s>
            <s xml:id="echoid-s7094" xml:space="preserve">, {1/6}, CH, ſicenim ſunt </s>
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