Cavalieri, Buonaventura, Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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            <s xml:id="echoid-s5558" xml:space="preserve">
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            illius reſidui .</s>
            <s xml:id="echoid-s5559" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5560" xml:space="preserve">vt, HF, ad vnum illud reſiduum ; </s>
            <s xml:id="echoid-s5561" xml:space="preserve">omnia autem qua-
              <lb/>
            drata eiuſdem, HF, ad omnia quadrata circuli, vel ellipſis, MBE
              <lb/>
            G, ſimul cum rectangulis bis ſub eodem, & </s>
            <s xml:id="echoid-s5562" xml:space="preserve">ſub trilineis, MNG, G
              <lb/>
            FE, ſunt vt, HF, ad circulum, vel ellipſim, MBEG, ergo, col-
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            ligendo, omnia quadrata, HF, ad omnia quadrata circuli, vel elli-
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            pſis, MBEG, & </s>
            <s xml:id="echoid-s5563" xml:space="preserve">ad omnia quadrata trilineorum, MNG, GFE,
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            ſimul cum rectangulis bis ſub circulo, vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5564" xml:space="preserve">trili-
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            neis, MNG, GFE, ideſt ad omnia quadrata figuræ, NMBEF,
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            erunt vt, HF, ad circulum, vel ellipſim, MBEG, ſimul cum reſi-
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              <note position="left" xlink:label="note-0248-01" xlink:href="note-0248-01a" xml:space="preserve">Per D.23.
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              lib.2.</note>
            duo, dempto à parallelogrammo, MG, quadrante, MAG, & </s>
            <s xml:id="echoid-s5565" xml:space="preserve">eo
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            ſpatio, quo idem excedit duas tertias parallelogrammi, MG.</s>
            <s xml:id="echoid-s5566" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5567" xml:space="preserve">Dico nunc hanc rationem eſſe, vt 21. </s>
            <s xml:id="echoid-s5568" xml:space="preserve">ad 17. </s>
            <s xml:id="echoid-s5569" xml:space="preserve">proximè, parallelo-
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            grammum enim, MG, ad dictum reſiduum eſt, vt 21. </s>
            <s xml:id="echoid-s5570" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s5571" xml:space="preserve">proxi-
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            mè, vt oſtendimus Theor. </s>
            <s xml:id="echoid-s5572" xml:space="preserve">12. </s>
            <s xml:id="echoid-s5573" xml:space="preserve">parallelogrammum vero, HF, qua-
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            druplum eſt ipſius, MG, ergo, HF, ad illud reſiduum eſt, vt 84. </s>
            <s xml:id="echoid-s5574" xml:space="preserve">ad 2.
              <lb/>
            </s>
            <s xml:id="echoid-s5575" xml:space="preserve">proximè, eſt autem idem, HF, ad circulum, vel ellipſim, MBEG,
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            vt 14. </s>
            <s xml:id="echoid-s5576" xml:space="preserve">ad 11. </s>
            <s xml:id="echoid-s5577" xml:space="preserve">proximè .</s>
            <s xml:id="echoid-s5578" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5579" xml:space="preserve">vt 84. </s>
            <s xml:id="echoid-s5580" xml:space="preserve">ad 66. </s>
            <s xml:id="echoid-s5581" xml:space="preserve">ergo parallelogrammum, H
              <lb/>
            F, ad compoſitum ex circulo, vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5582" xml:space="preserve">dicto reſiduo
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            eſt, vt 84. </s>
            <s xml:id="echoid-s5583" xml:space="preserve">ad 68. </s>
            <s xml:id="echoid-s5584" xml:space="preserve">proximè .</s>
            <s xml:id="echoid-s5585" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5586" xml:space="preserve">vt 21. </s>
            <s xml:id="echoid-s5587" xml:space="preserve">ad 17. </s>
            <s xml:id="echoid-s5588" xml:space="preserve">proximè, ideò omnia qua-
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            drata, HF, ad omnia quadrata figuræ, NMBEF, ſunt proximè,
              <lb/>
            vt 21. </s>
            <s xml:id="echoid-s5589" xml:space="preserve">ad 17. </s>
            <s xml:id="echoid-s5590" xml:space="preserve">patet ergo propoſitum.</s>
            <s xml:id="echoid-s5591" xml:space="preserve"/>
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          <head xml:id="echoid-head349" xml:space="preserve">COROLLARIVM I.</head>
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            <s xml:id="echoid-s5592" xml:space="preserve">_H_INC patet, quoniam omnia quadrata, HF, omnium quadrato-
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              <note position="left" xlink:label="note-0248-02" xlink:href="note-0248-02a" xml:space="preserve">_@. Lib. 8._</note>
            rum, MF, ſunt quadrupla, quod ſunt ad illa, vt, HF, ad, MG,
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            & </s>
            <s xml:id="echoid-s5593" xml:space="preserve">ideò, ſi dempſeris omnia quadrata, MF, ab omnibus quadratis ſigu-
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            ræ, NMBEF, omnia quadrata, HF, ad reſiduum erunt, vt, HF, ad
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            illud, quod relinquitur, dempto, MG, à circulo, vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5594" xml:space="preserve">
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            reſiduo ſæpius dicto .</s>
            <s xml:id="echoid-s5595" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5596" xml:space="preserve">quod remanet ablato ab, MG, quadrante, MAG,
              <lb/>
            & </s>
            <s xml:id="echoid-s5597" xml:space="preserve">eo exceſſu, quo idem ſuperat, {2/3}, MG, eſt autem, HF, ad bac rema-
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            nentia ſpatia proximè, vt 84.</s>
            <s xml:id="echoid-s5598" xml:space="preserve">ad 47.</s>
            <s xml:id="echoid-s5599" xml:space="preserve"/>
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            <s xml:id="echoid-s5600" xml:space="preserve">Conſtitue .</s>
            <s xml:id="echoid-s5601" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5602" xml:space="preserve">HF, 84. </s>
            <s xml:id="echoid-s5603" xml:space="preserve">erit circulus, vel ellipſis, MBEG, 66. </s>
            <s xml:id="echoid-s5604" xml:space="preserve">& </s>
            <s xml:id="echoid-s5605" xml:space="preserve">di-
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            ctum reſiduum 2. </s>
            <s xml:id="echoid-s5606" xml:space="preserve">vt ſupra oſtendimus (proximè ſemper intellige) eſt au-
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            tem, MG, 21. </s>
            <s xml:id="echoid-s5607" xml:space="preserve">demas ergo 21. </s>
            <s xml:id="echoid-s5608" xml:space="preserve">à compoſito ex 66. </s>
            <s xml:id="echoid-s5609" xml:space="preserve">& </s>
            <s xml:id="echoid-s5610" xml:space="preserve">2. </s>
            <s xml:id="echoid-s5611" xml:space="preserve">ideſt à 68. </s>
            <s xml:id="echoid-s5612" xml:space="preserve">re-
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            manent 47. </s>
            <s xml:id="echoid-s5613" xml:space="preserve">eſt ergo, HF, ad remanentia ſpatia, vt 84. </s>
            <s xml:id="echoid-s5614" xml:space="preserve">ad 47. </s>
            <s xml:id="echoid-s5615" xml:space="preserve">vnde om-
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            nia quadrata, HF, ad reſiduum, dempt is omnibus quadratis, MF, ab
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            omnibus quadratis ſiguræ, NMBEF, erunt, proximè, vt 84. </s>
            <s xml:id="echoid-s5616" xml:space="preserve">ad 47.
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            </s>
            <s xml:id="echoid-s5617" xml:space="preserve">quod eſt propoſitum.</s>
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