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

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          <p>
            <s xml:id="echoid-s7094" xml:space="preserve">
              <pb o="292" file="0312" n="312" rhead="GEOMETRIÆ"/>
            quadrata, HN, ad omnia quadrata ſemiportionis, HMNC, vt
              <lb/>
            patet in eiuſdem Lib. </s>
            <s xml:id="echoid-s7095" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s7096" xml:space="preserve">I.</s>
            <s xml:id="echoid-s7097" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7098" xml:space="preserve">Quod ſi velimus comparare parallelogramma, quæ ſunt in baſi-
              <lb/>
            bus æqualibus axi, vel diametro, inueniemus infraſcriptas rationes
              <lb/>
            ſcilicet parallelogrammum, BT, ad portionem, HST, eſſe vt re-
              <lb/>
            ctangulum ſub, HO, & </s>
            <s xml:id="echoid-s7099" xml:space="preserve">tripla, OA, ad rectangulum ſub, HT, & </s>
            <s xml:id="echoid-s7100" xml:space="preserve">
              <lb/>
            ſub compoſita ex, TA, &</s>
            <s xml:id="echoid-s7101" xml:space="preserve">, AO, ſicuti ſunt omnia quadrata, HZ,
              <lb/>
            ad omnia quadrata ſemiportionis, HTV. </s>
            <s xml:id="echoid-s7102" xml:space="preserve">Eadem ratione, BC, ad
              <lb/>
              <figure xlink:label="fig-0312-01" xlink:href="fig-0312-01a" number="206">
                <image file="0312-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0312-01"/>
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            portionem, HGE
              <lb/>
            C, erit vt rectangu-
              <lb/>
            lum ſub, HO, & </s>
            <s xml:id="echoid-s7103" xml:space="preserve">
              <lb/>
            tripla, OA, ad re-
              <lb/>
            ctangulum ſub, H
              <lb/>
            C, & </s>
            <s xml:id="echoid-s7104" xml:space="preserve">ſub compoſi-
              <lb/>
            ta ex, CA, &</s>
            <s xml:id="echoid-s7105" xml:space="preserve">, AO,
              <lb/>
            ſic enim ſunt om-
              <lb/>
            nia quadrata, HI,
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            ad omnia quadrata
              <lb/>
            ſemiportionis, HM
              <lb/>
            NC, vt patet in eo-
              <lb/>
            dem Lib. </s>
            <s xml:id="echoid-s7106" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7107" xml:space="preserve">Prop. </s>
            <s xml:id="echoid-s7108" xml:space="preserve">2.</s>
            <s xml:id="echoid-s7109" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7110" xml:space="preserve">Sitandem ſuma-
              <lb/>
            musparallelogram-
              <lb/>
            mum, PC, cui in-
              <lb/>
            ſcripta eſt parabolę
              <lb/>
            portio, TSGEC,
              <lb/>
            incluſa duabus, ST,
              <lb/>
            EC, ad baſim, HA, vtcunq; </s>
            <s xml:id="echoid-s7111" xml:space="preserve">ordinatim applicatis, ſiue intercipiant
              <lb/>
            axem, vel diametrum, GO, ſiue non, ſiue axis, vel diameter, GO,
              <lb/>
            ſit altera harum duarum ad baſim, HA, ordinatim applicatarum,
              <lb/>
            ſiue non; </s>
            <s xml:id="echoid-s7112" xml:space="preserve">reperiemus parallelogrammum, PC, ad portionem, TS
              <lb/>
            GEC, eſſe vt rectangulum, HOA, ad rectangulum ſub, AC, & </s>
            <s xml:id="echoid-s7113" xml:space="preserve">
              <lb/>
            ſub compoſita ex, {1/2}, CT, & </s>
            <s xml:id="echoid-s7114" xml:space="preserve">tota, TH, vna cum rectangulo ſub, T
              <lb/>
            C, & </s>
            <s xml:id="echoid-s7115" xml:space="preserve">ſub compoſita ex, {1/6}, TC, &</s>
            <s xml:id="echoid-s7116" xml:space="preserve">, {1/2}, TH, ſic enim eſſe inuenie-
              <lb/>
            mus omnia quadrata, TI, ad omnia quadrata quadrilinei, TVM
              <lb/>
            NC, vt patet eodem Lib. </s>
            <s xml:id="echoid-s7117" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s7118" xml:space="preserve">4.</s>
            <s xml:id="echoid-s7119" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div702" type="section" level="1" n="412">
          <head xml:id="echoid-head432" xml:space="preserve">COROLLARIV M.</head>
          <p style="it">
            <s xml:id="echoid-s7120" xml:space="preserve">_H_Inc habetur ſi fiant triangulæ, ductis, SH, PH, GH, QT, hæc
              <lb/>
            ad portiones, quibus inſcribuntur habere eaſdem rationes, quas
              <lb/>
            habent dimidia antecedentium ad eadem conſequentia ſuperius expoſita,
              <lb/>
            ſunt enim & </s>
            <s xml:id="echoid-s7121" xml:space="preserve">ipſa triangula dictorum parallelogrammorum dimedia.</s>
            <s xml:id="echoid-s7122" xml:space="preserve"/>
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