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

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          <p>
            <s xml:id="echoid-s5515" xml:space="preserve">
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            vel ellipſis, MBEG, vna cum rectangulis bis ſub eodem circulo, vel
              <lb/>
            ellipſi, & </s>
            <s xml:id="echoid-s5516" xml:space="preserve">ſub quadrilineo, MGEOC, quoniam verò oſtenſum eſt
              <lb/>
            omnia quadrata, HO, ad rectangula ſub portione, MGE, & </s>
            <s xml:id="echoid-s5517" xml:space="preserve">pa-
              <lb/>
            rallelogrammo, MO, quater ſumpta eſſe, vt quadratum, DO, ad
              <lb/>
            rectangulum ſub, OE, & </s>
            <s xml:id="echoid-s5518" xml:space="preserve">quadrupla, EI, ideò ex æquali omnia
              <lb/>
            quadrata, HO, ad omnia quadrata circuli, vel ellipſis, MBEG,
              <lb/>
            vna cum rectangulis bis ſub eodem circulo, vel ellipſi, & </s>
            <s xml:id="echoid-s5519" xml:space="preserve">ſub quadri-
              <lb/>
            lineo, MGEOC, erunt vt quadratum, DO, ad rectangulum ſub,
              <lb/>
            OE, & </s>
            <s xml:id="echoid-s5520" xml:space="preserve">ſub quadrupla, EI, quod ſerua.</s>
            <s xml:id="echoid-s5521" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5522" xml:space="preserve">Quoniam verò omnia quadrata, HF, vna cum rectangulis bis ſub
              <lb/>
              <note position="left" xlink:label="note-0246-01" xlink:href="note-0246-01a" xml:space="preserve">14.Lib.2.</note>
            parallelogrammis, HF, FC, ad omnia quadrata, HO, ſunt, vt
              <lb/>
            vnum, ad vnum .</s>
            <s xml:id="echoid-s5523" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5524" xml:space="preserve">vt quadratum, DF, vna cum rectangulo bis ſub,
              <lb/>
            DF, FO, ad quadratum, DO, omnia quadrata verò parallelogram-
              <lb/>
            mi, HO, ad omnia quadrata circuli, vel ellipſis, MBEG, vna cum
              <lb/>
            rectangulis bis ſub eodem circulo, vel ellipſi, & </s>
            <s xml:id="echoid-s5525" xml:space="preserve">ſub quadrilineo, M
              <lb/>
            GEOC, eſſe oſtenſa ſunt, vt idem quadratum, DO, ad rectangu-
              <lb/>
            lum ſub, OE, & </s>
            <s xml:id="echoid-s5526" xml:space="preserve">quadrupla, EI, ergo ex æquali omnia quadrata pa-
              <lb/>
            rallelogrammi, HF, vna cum rectangulis bis ſub parallelogrammis,
              <lb/>
            HF, FC, ad omnia quadrata circuli, vel ellipſis, MBEG, vna
              <lb/>
              <figure xlink:label="fig-0246-01" xlink:href="fig-0246-01a" number="153">
                <image file="0246-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0246-01"/>
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            cum rectangulis bis
              <lb/>
            ſub eodem circulo,
              <lb/>
            vel ellipſi, MBE
              <lb/>
            G, erunt vt quadra-
              <lb/>
            tum, DF, vna cum
              <lb/>
            rectangulo ſub, D
              <lb/>
            F, FO, bis, ad re-
              <lb/>
            ctangulum ſub, OE,
              <lb/>
            & </s>
            <s xml:id="echoid-s5527" xml:space="preserve">quadrupla, EI,
              <lb/>
            vel erunt, vt eorum
              <lb/>
            dimidia .</s>
            <s xml:id="echoid-s5528" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5529" xml:space="preserve">vt dimi-
              <lb/>
            dium quadrati, DF,
              <lb/>
            quod erit rectangulum, DFE, vna cum rectangulo ſub, DFO, ſe-
              <lb/>
            mel (ex quibus componetur rectangulum ſub, OE, FD,) ad rectan-
              <lb/>
            gulum ſub, OE, & </s>
            <s xml:id="echoid-s5530" xml:space="preserve">dupla, EI, vel, vt adhuc horum dimidia .</s>
            <s xml:id="echoid-s5531" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5532" xml:space="preserve">vt
              <lb/>
            rectangulum ſub, OE, &</s>
            <s xml:id="echoid-s5533" xml:space="preserve">, ED, ad rectangulum ſub, OE, &</s>
            <s xml:id="echoid-s5534" xml:space="preserve">, EI,
              <lb/>
              <note position="left" xlink:label="note-0246-02" xlink:href="note-0246-02a" xml:space="preserve">5. Lib.2.</note>
            .</s>
            <s xml:id="echoid-s5535" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5536" xml:space="preserve">vt, DE, ad, EI, quia, OE, altitudo eſt communis, oſtenſum
              <lb/>
            ergo eſt omnia quadrata, HF, vna cum rectangulis bis ſub paralle-
              <lb/>
            logrammis, HF, FC, ad omnia quadrata circuli, vel ellipſis, MB
              <lb/>
            EG, vna cum rectangulis bis ſub eodem, & </s>
            <s xml:id="echoid-s5537" xml:space="preserve">ſub quadrilineo, MGE
              <lb/>
            OC, eſſe, vt, DE, vel, FE, ad, EI, .</s>
            <s xml:id="echoid-s5538" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5539" xml:space="preserve">vt parallelogrammum, M
              <lb/>
            F, ad portionem, MGE, vel vt parallelogrammum, HF, ad cir-
              <lb/>
            culum, vel ellipſim, MBEG, quod erat propoſitum.</s>
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