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

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            <s xml:id="echoid-s5291" xml:space="preserve">
              <pb o="218" file="0238" n="238" rhead="GEOMETRIÆ"/>
            EF, ducta, vtcunque quadratum, EI, detractum à rectangulo ſub,
              <lb/>
            IE, EF, relinquit rectangulum ſub, EI, IF, ita in cæteris ſequitur;
              <lb/>
            </s>
            <s xml:id="echoid-s5292" xml:space="preserve">& </s>
            <s xml:id="echoid-s5293" xml:space="preserve">illis ſimul collectis ſequitur etiam, quod detractis omnibus qua-
              <lb/>
              <note position="left" xlink:label="note-0238-01" xlink:href="note-0238-01a" xml:space="preserve">Iux. dicta
                <lb/>
              pro C.23.
                <lb/>
              lib.2.</note>
            dratis ſemiportionis, OCD, à rectangulis ſub parallelogrammo, O
              <lb/>
            V, & </s>
            <s xml:id="echoid-s5294" xml:space="preserve">ſemiportione, OCD, relinquantur rectangula ſub ſemipor-
              <lb/>
            tione, OCD, & </s>
            <s xml:id="echoid-s5295" xml:space="preserve">trilineo, DCV, ad hæc igitur, quæ ſunt dictum
              <lb/>
              <figure xlink:label="fig-0238-01" xlink:href="fig-0238-01a" number="149">
                <image file="0238-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0238-01"/>
              </figure>
            reſiduum, omnia quadrata parallelo-
              <lb/>
            grammi, OV erunt vt parallelogram-
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            mum, OV, adreſiduum ſemiportio-
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            nis, OCD, ab ea demptis, {2/3}, paral-
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            lelogrammi, OV; </s>
            <s xml:id="echoid-s5296" xml:space="preserve">eadem autem om-
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            nia quadrata parallelogrammi, OV,
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            ad rectangula ſub parallelogrammo.
              <lb/>
            </s>
            <s xml:id="echoid-s5297" xml:space="preserve">OV, & </s>
            <s xml:id="echoid-s5298" xml:space="preserve">ſemiportione, OCD, .</s>
            <s xml:id="echoid-s5299" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5300" xml:space="preserve">ad
              <lb/>
              <note position="left" xlink:label="note-0238-02" xlink:href="note-0238-02a" xml:space="preserve">Per C.23.
                <lb/>
              lib.2.</note>
            omnia quadrata ſemiportionis, OC
              <lb/>
            D, vna cum rectangulis ſub ſemipor-
              <lb/>
            tione, OCD, & </s>
            <s xml:id="echoid-s5301" xml:space="preserve">trilineo, CVD,
              <lb/>
            ſunt vt parallelogrammum, OV, ad
              <lb/>
            ſemiportionem, OCD, vt paulò ſupra in hac demonſtratione oſten-
              <lb/>
            dimus, ergo, colligendo, omnia quadrata parallelogrammi, OV,
              <lb/>
            ad omnia quadrata ſemiportionis, OCD, vna cum rectangu is bis
              <lb/>
            ſub ſemiportione, OCD, & </s>
            <s xml:id="echoid-s5302" xml:space="preserve">trilineo, CVD, ſumptis, erunt vt pa-
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            rallelogrammum, OV, ad ſemiportionem, OCD, vna cum exceſ-
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            ſu, quo dicta ſemiportio, OCD, excedit, {2/3}, parallelogrammi, O
              <lb/>
            V, ergo, perconuerſionem rationis, omnia quadrata parallelogram-
              <lb/>
            mi, OV, ad omnia quadrata trilinei, DCV, quæ remanent detra-
              <lb/>
              <note position="left" xlink:label="note-0238-03" xlink:href="note-0238-03a" xml:space="preserve">Per D.23.
                <lb/>
              lib. 2.</note>
            ctis omnibus quadratis ſemiportionis, OCD, vna cum rectangulis
              <lb/>
            ſub illa, & </s>
            <s xml:id="echoid-s5303" xml:space="preserve">ſub trilineo, DCV, bis ſumptis, ab omnibus quadratis
              <lb/>
            parallelogrammi, OV; </s>
            <s xml:id="echoid-s5304" xml:space="preserve">(veluti detracto quadrato, EI, vna cum re-
              <lb/>
            ctangulo bis ſub, EI, IF, remanet quadratum, IF,) ad omnia qua-
              <lb/>
            dratatrilinei, DCV, erunt vt parallelogrammum, OV, adreſiduum,
              <lb/>
            detracta ſemiportione, OCD, vna cum exceſſu, quoipſa ſuperat
              <lb/>
            duas tertias parallelogrammi, OV, à dicto parallelogrammo,
              <lb/>
            OV.</s>
            <s xml:id="echoid-s5305" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5306" xml:space="preserve">Eſt verò parallelogrammum, OV, ad dictum ſpatium reſiduum
              <lb/>
            proximè, vt 21. </s>
            <s xml:id="echoid-s5307" xml:space="preserve">ad 2. </s>
            <s xml:id="echoid-s5308" xml:space="preserve">nam ſi ſupponamus parallelogrammum, OV,
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            eſſe 21. </s>
            <s xml:id="echoid-s5309" xml:space="preserve">erit ſemiportio, OCD, earumdem partium proximè 16. </s>
            <s xml:id="echoid-s5310" xml:space="preserve">{1/2},
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            eſt .</s>
            <s xml:id="echoid-s5311" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5312" xml:space="preserve">adeam, ſicut rectangulum, quod eſſet circulo, vel ellipſi, A
              <lb/>
              <note position="left" xlink:label="note-0238-04" xlink:href="note-0238-04a" xml:space="preserve">11.huius.</note>
            BCD, circumſcriptum, habens latera ipſis, AC, BD, axibus pa-
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            rallela ad eundem circulum, vel ellipſim .</s>
            <s xml:id="echoid-s5313" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5314" xml:space="preserve">vt 14. </s>
            <s xml:id="echoid-s5315" xml:space="preserve">ad 11. </s>
            <s xml:id="echoid-s5316" xml:space="preserve">proximè, vt
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            oſtendit Archimedes lib. </s>
            <s xml:id="echoid-s5317" xml:space="preserve">de Dimenſione Circuli, eſt .</s>
            <s xml:id="echoid-s5318" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5319" xml:space="preserve">vt 14. </s>
            <s xml:id="echoid-s5320" xml:space="preserve">ad 11.
              <lb/>
            </s>
            <s xml:id="echoid-s5321" xml:space="preserve">ita 21. </s>
            <s xml:id="echoid-s5322" xml:space="preserve">ad 16. </s>
            <s xml:id="echoid-s5323" xml:space="preserve">{1/2}, rurſus duæ tertiæ parallelogrammi, OV, ſunt 14.</s>
            <s xml:id="echoid-s5324" xml:space="preserve"/>
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