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

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        <div xml:id="echoid-div732" type="section" level="1" n="430">
          <pb o="308" file="0328" n="328" rhead="GEOMETRIÆ"/>
          <p>
            <s xml:id="echoid-s7417" xml:space="preserve">Sit ſemiparabola, AOCB, in baſi, BC, & </s>
            <s xml:id="echoid-s7418" xml:space="preserve">axis, vel diameter
              <lb/>
            integræ, AB, compleaturq; </s>
            <s xml:id="echoid-s7419" xml:space="preserve">parallelogrammum, DB, & </s>
            <s xml:id="echoid-s7420" xml:space="preserve">circa, A
              <lb/>
            B, BC, tanquam ſemiaxes, vel ſemidiametros coniugatas, deicri-
              <lb/>
            batur quarta circuli, vel ellipſis, AICB, deinde ſumatur in baſi, B
              <lb/>
            C, vtcunque punctum, P, & </s>
            <s xml:id="echoid-s7421" xml:space="preserve">per, P, ducaturipſi, AB, parallela,
              <lb/>
            PH, ſecans curuam parabolæ in, X, & </s>
            <s xml:id="echoid-s7422" xml:space="preserve">circuli, vel ellipſis, AIC,
              <lb/>
              <figure xlink:label="fig-0328-01" xlink:href="fig-0328-01a" number="220">
                <image file="0328-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0328-01"/>
              </figure>
            in, I. </s>
            <s xml:id="echoid-s7423" xml:space="preserve">Dico ergo, IP, eſſe mediam
              <lb/>
            proportionalem inter, HP, PX, pro-
              <lb/>
            ducatur, CB, verſus, B, in, Z, ita
              <lb/>
            vt, BZ, ſit æqualis, BC, eſt ergo
              <lb/>
            quadratum, AB, vel quadratum, H
              <lb/>
            P, ad quadratum, PI, vt rectangu-
              <lb/>
            lum, ZBC, ad rectangulum, ZPC,
              <lb/>
            .</s>
            <s xml:id="echoid-s7424" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7425" xml:space="preserve">vt, AB, vel, HP, ad, PX, ergo
              <lb/>
            vt, HP, ad, PI, ita erit, IP, ad, PX.</s>
            <s xml:id="echoid-s7426" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7427" xml:space="preserve">Iungantur puncta, A, C, & </s>
            <s xml:id="echoid-s7428" xml:space="preserve">ſum-
              <lb/>
              <note position="left" xlink:label="note-0328-01" xlink:href="note-0328-01a" xml:space="preserve">40.cum
                <lb/>
              Sch.l.1.
                <lb/>
              3.huius.</note>
            pto vtcunq. </s>
            <s xml:id="echoid-s7429" xml:space="preserve">puncto, V, in, AB, per ipſum ducaturipſi, BC, pa-
              <lb/>
            rallela, VF, ſecans curuam parabolæ in, O, & </s>
            <s xml:id="echoid-s7430" xml:space="preserve">rectam, AC, in, N.
              <lb/>
            </s>
            <s xml:id="echoid-s7431" xml:space="preserve">Dico ergo, vt, FV, ad, VO, ita eſſe, VO, ad, VN; </s>
            <s xml:id="echoid-s7432" xml:space="preserve">eſt enim
              <lb/>
            quadratum, BC, vel quadratum, FV, ad quadratum, VO, vt, B
              <lb/>
            A, ad, AV, .</s>
            <s xml:id="echoid-s7433" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7434" xml:space="preserve">vt, BC, vel, FV, ad, VN, ergo erit, vt, FV, ad,
              <lb/>
            VO, ſic, VO, ad, VN, quæ oſtendere oportebat.</s>
            <s xml:id="echoid-s7435" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div735" type="section" level="1" n="431">
          <head xml:id="echoid-head451" xml:space="preserve">THEOREMA XVIII. PROPOS. XIX.</head>
          <p>
            <s xml:id="echoid-s7436" xml:space="preserve">PArabolæ ſunt inter ſe, vt parallelogramma illis circum-
              <lb/>
            ſcripta latera habentia baſibus, & </s>
            <s xml:id="echoid-s7437" xml:space="preserve">eorundem axibus,
              <lb/>
            vel diametris parallela.</s>
            <s xml:id="echoid-s7438" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7439" xml:space="preserve">Patet hæc propoſitio, nam dictæ parabolæ ſunt ſubſexquialteræ
              <lb/>
              <note position="left" xlink:label="note-0328-02" xlink:href="note-0328-02a" xml:space="preserve">1.huius.</note>
            dictorum parallelogrammorum, & </s>
            <s xml:id="echoid-s7440" xml:space="preserve">ideò ſunt inter ſe, vt ipſa paral-
              <lb/>
            lelogramma.</s>
            <s xml:id="echoid-s7441" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div737" type="section" level="1" n="432">
          <head xml:id="echoid-head452" xml:space="preserve">A. COROLL. SECTIO I.</head>
          <p style="it">
            <s xml:id="echoid-s7442" xml:space="preserve">HInc patet, concluſiones, quę de parallelogrammis collectæ ſun@
              <lb/>
            in Propoſ 5.</s>
            <s xml:id="echoid-s7443" xml:space="preserve">6.</s>
            <s xml:id="echoid-s7444" xml:space="preserve">7.</s>
            <s xml:id="echoid-s7445" xml:space="preserve">8. </s>
            <s xml:id="echoid-s7446" xml:space="preserve">Lib.</s>
            <s xml:id="echoid-s7447" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7448" xml:space="preserve">ſuppoſitis quibuſdam conditionibus in
              <lb/>
            lateribus, vel in altitudine, & </s>
            <s xml:id="echoid-s7449" xml:space="preserve">baſi dictorum parallelogrammorum, poſ-
              <lb/>
            ſe colligi etiam pro parabolis eaſdem conditiones in axibus, vel diame-
              <lb/>
            tris, vel altitudinibus, & </s>
            <s xml:id="echoid-s7450" xml:space="preserve">baſtbus habentes; </s>
            <s xml:id="echoid-s7451" xml:space="preserve">quia enim tunc dictæ </s>
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