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

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            <s xml:id="echoid-s7668" xml:space="preserve">
              <pb o="319" file="0339" n="339" rhead="LIBER IV."/>
            autem vt, OC, ad, CQ, ita, ſumpta, QC, communi altitudine,
              <lb/>
            rectangulum ſub OC, CQ, ad quadratum, QC, ergo ratio com-
              <lb/>
            poſita ex ea, quam habet, OC, ad, CQ, & </s>
            <s xml:id="echoid-s7669" xml:space="preserve">quadratum, QC, ad
              <lb/>
            quadratum, CO, eſt eadem compoſitæ ex ea, quam habet rectan-
              <lb/>
            gulum ſub, OC, CQ, ad quadratum, CQ, & </s>
            <s xml:id="echoid-s7670" xml:space="preserve">quadratum, CQ,
              <lb/>
            ad quadratum, CO, . </s>
            <s xml:id="echoid-s7671" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7672" xml:space="preserve">eademei, quam habet rectangulum ſub,
              <lb/>
            QC, CO, ad quadratum, CO, . </s>
            <s xml:id="echoid-s7673" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7674" xml:space="preserve">eadem ei, quam habet, QC, ad,
              <lb/>
            CO; </s>
            <s xml:id="echoid-s7675" xml:space="preserve">ergo omnia quadrata trianguli, DAF, ad omnia quadrata
              <lb/>
            trianguli, MHC, vel omnia quadrata parabolæ, DAF, ad om-
              <lb/>
            nia quadrata parabolæ, MHC, regulis iam dictis, erunt vt, QC,
              <lb/>
            ad, CO, quod ſerua.</s>
            <s xml:id="echoid-s7676" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7677" xml:space="preserve">Vlterius omnia quadrata parabolæ, MHC, ad rectangula ſub
              <lb/>
              <note position="right" xlink:label="note-0339-01" xlink:href="note-0339-01a" xml:space="preserve">Exantec.</note>
            parabola, MHC, & </s>
            <s xml:id="echoid-s7678" xml:space="preserve">trilineo, HRC, regula, MC, ſunt vt, M
              <lb/>
            C, ad, CR, vel ad, CX, . </s>
            <s xml:id="echoid-s7679" xml:space="preserve">i. </s>
            <s xml:id="echoid-s7680" xml:space="preserve">vt, OC, ad, CQ, ergo omnia qua-
              <lb/>
            drata parabolæ, DAF, regula, DF, ad rectangula ſub parabola,
              <lb/>
            MHC, & </s>
            <s xml:id="echoid-s7681" xml:space="preserve">trilineo, HRC, regula, MC, habebunt rationem
              <lb/>
            compoſitam ex ea, quam habet, QC, ad, CO, & </s>
            <s xml:id="echoid-s7682" xml:space="preserve">ex ea quam
              <lb/>
            habet, CO, ad, QC, ideſt habebunt eandem rationem, quam
              <lb/>
            habet, QC, ad, QC, ideſt eruntillis æqualia, quod oſtende-
              <lb/>
            re opus erat.</s>
            <s xml:id="echoid-s7683" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div763" type="section" level="1" n="449">
          <head xml:id="echoid-head469" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s7684" xml:space="preserve">_H_Inc patet omnia quadrata parabolæ, DAF, regula, DF, ad om-
              <lb/>
            nta quadrata parabolæ, MHC, regula, MC, eſſe vt QC, ad,
              <lb/>
            CO, vel, XC, ad CM, vel, DF, (quæ eſt æqualis ipſi, XC,) ad, MC,
              <lb/>
            dumdiametri, AZ, HO, ſunt æquales, vt in Theoremate oſtenſum eſt.</s>
            <s xml:id="echoid-s7685" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div764" type="section" level="1" n="450">
          <head xml:id="echoid-head470" xml:space="preserve">COROLLARIVM II.</head>
          <p style="it">
            <s xml:id="echoid-s7686" xml:space="preserve">_P_Atet vlterius, ſi intra cùruam parabolicam duæ vtcunq; </s>
            <s xml:id="echoid-s7687" xml:space="preserve">rectæ li-
              <lb/>
            neæ obliquè axem ſecantes, & </s>
            <s xml:id="echoid-s7688" xml:space="preserve">in ipſam terminantes, ductæ fue-
              <lb/>
            rint, regula pro qualibetparabola ſumpta earum baſi, quod rectangula
              <lb/>
            ſub dictis parabolis per eaſdem conſtitutis, & </s>
            <s xml:id="echoid-s7689" xml:space="preserve">ſub figura diſtantiarum
              <lb/>
            earundem parabolarum, inter ſe erunt æqualia, quotieſcunq diametri
              <lb/>
            earundem ſint æquales, vtraq; </s>
            <s xml:id="echoid-s7690" xml:space="preserve">enim ſingillatim æquabuntur omnibus
              <lb/>
            qu dratis parabolæ, cuius baſis ſecet perpendeculariter axem eiuſdem
              <lb/>
            qui ſit æqualis diametris dictarum parabolarum, & </s>
            <s xml:id="echoid-s7691" xml:space="preserve">pro, qua ſit regula
              <lb/>
            eiuſdem baſis.</s>
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