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

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        <div xml:id="echoid-div743" type="section" level="1" n="438">
          <pb o="311" file="0331" n="331" rhead="LIBER IV."/>
        </div>
        <div xml:id="echoid-div745" type="section" level="1" n="439">
          <head xml:id="echoid-head459" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s7489" xml:space="preserve">_H_Incliquet, ſi cuilibetparallelogrammo eſt inſcriptibilis ſemip. </s>
            <s xml:id="echoid-s7490" xml:space="preserve">1.
              <lb/>
            </s>
            <s xml:id="echoid-s7491" xml:space="preserve">rabola talipacto, quo dictum eſt, quod parietates, quæ paralle-
              <lb/>
            logrammis contingunt, etiam ipſis parabolis competere poſſunt.</s>
            <s xml:id="echoid-s7492" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div746" type="section" level="1" n="440">
          <head xml:id="echoid-head460" xml:space="preserve">THEOREMA XX. PROPOS. XXI.</head>
          <p>
            <s xml:id="echoid-s7493" xml:space="preserve">O Mnia quadrata parallelogrammi in eadem baſi, & </s>
            <s xml:id="echoid-s7494" xml:space="preserve">cir-
              <lb/>
            ca eundem axim, vel diametrum cum parabola, regu-
              <lb/>
            la baſi, ſunt dupla omnium quadratorum ipſius parabolæ:
              <lb/>
            </s>
            <s xml:id="echoid-s7495" xml:space="preserve">Omnia verò quadrata parabolæ ſunt fexquialtera omnium
              <lb/>
            quadratorum trianguli in eadem baſi, & </s>
            <s xml:id="echoid-s7496" xml:space="preserve">circa eundem axim,
              <lb/>
            vel diametrum cum ipſa conſtituti.</s>
            <s xml:id="echoid-s7497" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7498" xml:space="preserve">Sit ergo parabola, cuius baſis, VF, axis, vel diameter, EM,
              <lb/>
              <figure xlink:label="fig-0331-01" xlink:href="fig-0331-01a" number="222">
                <image file="0331-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0331-01"/>
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            ſit etiam parallelogrammum,
              <lb/>
            AF, & </s>
            <s xml:id="echoid-s7499" xml:space="preserve">triangulum, EVF, in
              <lb/>
            eadem baſi, VF, & </s>
            <s xml:id="echoid-s7500" xml:space="preserve">circa eun-
              <lb/>
            dem axim, vel diametrum, EM.
              <lb/>
            </s>
            <s xml:id="echoid-s7501" xml:space="preserve">Dico, omnia quadrata, AF, re-
              <lb/>
            gula, VF, omnium quadrato-
              <lb/>
            rum parabolæ, VEF, effe du-
              <lb/>
            pla: </s>
            <s xml:id="echoid-s7502" xml:space="preserve">Omnia verò quadrata para-
              <lb/>
            bolæ, VEF, omnium quadra-
              <lb/>
            torum trianguli, VEF, effe fex-
              <lb/>
            quialtera. </s>
            <s xml:id="echoid-s7503" xml:space="preserve">Sumaturintra, EM,
              <lb/>
            vtcunque punctum, N, per quodipſi, VF, agatur parallela, ND,
              <lb/>
            ſecans curuam parabolę; </s>
            <s xml:id="echoid-s7504" xml:space="preserve">in, O; </s>
            <s xml:id="echoid-s7505" xml:space="preserve">eſt ergo quadratum, MF, vel qua-
              <lb/>
            dratum, ND, ad quadratum, NO, vt, ME, ad, EN, eſt au-
              <lb/>
            tem, EF, parallelogrammum in eadem baſi, & </s>
            <s xml:id="echoid-s7506" xml:space="preserve">altitudine cumſe-
              <lb/>
            miparabola, EMF, regula eſt, MF, & </s>
            <s xml:id="echoid-s7507" xml:space="preserve">punctum, N, ſumptum vt-
              <lb/>
            cunque, per quod regulæ parallela ducta eſt, ND, repertumq; </s>
            <s xml:id="echoid-s7508" xml:space="preserve">eſt,
              <lb/>
              <note position="right" xlink:label="note-0331-01" xlink:href="note-0331-01a" xml:space="preserve">Coroll. 3.
                <lb/>
              16. 1. 2.</note>
            vt quadratum, DN, ad quadratum, NO, ita eſte, ME, ad EN,
              <lb/>
            ergo horum quatuor ordinum magnitudines erunt proportionales
              <lb/>
            collectæ iuxta dictas quatuor magnitudines proportionales ſci-
              <lb/>
            licet omnia quadrata, EF, magnitudines primi ordinis collectæ
              <lb/>
            iuxta primam ſcilicet iuxta quadratum, ND, ad omnia quadrata
              <lb/>
            femiparabolæ, EMF, magnitudines fecundi ordims collectas
              <lb/>
            iuxta ſecundam ſcilicet iuxta quadratum, NO, erunt vt </s>
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