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

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            S, ad quadratum, SM, ergo horum quatuor ordinum magnitudines
              <lb/>
            erunt proportionales collectæ, iuxta quatuor iam dictas magnitudi-
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            nes proportionales .</s>
            <s xml:id="echoid-s7046" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s7047" xml:space="preserve">omnes lineæ ipſius, RN, (ſumpta pro omni-
              <lb/>
            bus communi regula, CE,) ad omnes lineas trilinei, FIAN, erunt
              <lb/>
            vt omnia quadrata, FO, ad omnia quadrata trilinei, FMON, ra-
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            tio autem, quam habent omnia quadrata, FO, ad omnia quadrata
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            trilinei, FMON, iam notiſicata eſt lib.</s>
            <s xml:id="echoid-s7048" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7049" xml:space="preserve">de circulo, & </s>
            <s xml:id="echoid-s7050" xml:space="preserve">ellipſi Pro-
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              <figure xlink:label="fig-0310-01" xlink:href="fig-0310-01a" number="204">
                <image file="0310-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0310-01"/>
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            poſit. </s>
            <s xml:id="echoid-s7051" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7052" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s7053" xml:space="preserve">ratio
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            omnium linearum, R
              <lb/>
            N, ad omnes lineas
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            trilinei, FIAN, & </s>
            <s xml:id="echoid-s7054" xml:space="preserve">
              <lb/>
            ſubinde ratio paral-
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            lelogrammi, RN, ad
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            portionem, FIAN,
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            nota erit, & </s>
            <s xml:id="echoid-s7055" xml:space="preserve">ſubinde
              <lb/>
            nota erit ratio trian-
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            guli, FAN, quod eſt
              <lb/>
            dimidium parallelo-
              <lb/>
            grammi, RN, ad
              <lb/>
              <note position="left" xlink:label="note-0310-01" xlink:href="note-0310-01a" xml:space="preserve">3. Lib. 2.</note>
            portionem, FIAN;
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            </s>
            <s xml:id="echoid-s7056" xml:space="preserve">eodem modo oſten-
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            demus parallelográ-
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            mum, ZX, ad qua-
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            drilineum, NACX,
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            eſſe vt omnia qua-
              <lb/>
            drata, RX, ad om-
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            nia quadrata quadri-
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            linei, ONXF, ratio autem, quam habent omnia quadrata, RX,
              <lb/>
            ad omnia quadrata quadrilinei, ONXE, iam notiſicata eſt in ſupra-
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            dicto Libro, Propoſit.</s>
            <s xml:id="echoid-s7057" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7058" xml:space="preserve">& </s>
            <s xml:id="echoid-s7059" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7060" xml:space="preserve">ergo ratio pamllelogrammi, ZX, ad
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            quadrilineum, ſiue portionem parabolæ, ANXC, nota erit, veluti
              <lb/>
            & </s>
            <s xml:id="echoid-s7061" xml:space="preserve">ratio trianguli, CNX, ad eandem portionem, ANXC, pariter
              <lb/>
            nota erit, quod erat oſtendendum.</s>
            <s xml:id="echoid-s7062" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div698" type="section" level="1" n="410">
          <head xml:id="echoid-head430" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s7063" xml:space="preserve">HInc colligitur dicta parallelogramma ad portiones parabolæ ſibi
              <lb/>
            inſcriptas, ordmatimque ad parabolæ baſim applicatis incluſas,
              <lb/>
            eſſe, bt omnia quadrata parallelogrammorum illis è regione reſponden-
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            tium, quibuſq; </s>
            <s xml:id="echoid-s7064" xml:space="preserve">inſcribuntur ſemiportiones circuli. </s>
            <s xml:id="echoid-s7065" xml:space="preserve">vel ellipſis iam di-
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            ctæ ad omnia quadrata dictarum ſemiportionum, regula communt axi,
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            vel diametro, CE, exiftente. </s>
            <s xml:id="echoid-s7066" xml:space="preserve">Oſtenſum .</s>
            <s xml:id="echoid-s7067" xml:space="preserve">n. </s>
            <s xml:id="echoid-s7068" xml:space="preserve">eſt, RN, ad portionera, FA
              <lb/>
            N, eſſe, bt omnia quadrata, FO, ad omnia quadrata trilmet, FMON;</s>
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