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

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              <pb o="223" file="0243" n="243" rhead="LIBER III."/>
            non ſunt regula, eſſe vt parallelogrammum, HF, ad circulum, vel
              <lb/>
            ellipſim, MBEG. </s>
            <s xml:id="echoid-s5433" xml:space="preserve">Omnia .</s>
            <s xml:id="echoid-s5434" xml:space="preserve">n. </s>
            <s xml:id="echoid-s5435" xml:space="preserve">quadrata parallelogrammi, HF, ſunt
              <lb/>
              <note position="right" xlink:label="note-0243-01" xlink:href="note-0243-01a" xml:space="preserve">Coroll. 1.
                <lb/>
              huit S.</note>
            ſexquialtera omnium quadratorum circuli, vel ellipſis, MBEG, & </s>
            <s xml:id="echoid-s5436" xml:space="preserve">
              <lb/>
            ideò ſunt ad illa, vt parallelogrammum, HF, ad ſui ipſius duas ter-
              <lb/>
            tias, quod ſerua.</s>
            <s xml:id="echoid-s5437" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5438" xml:space="preserve">Quoniam verò omnia quadrata parallelogrammi, AF, ad rectan-
              <lb/>
            gula ſub eodem, & </s>
            <s xml:id="echoid-s5439" xml:space="preserve">ſub ſemiportione, AEG, ſunt vt parallelogram-
              <lb/>
              <note position="right" xlink:label="note-0243-02" xlink:href="note-0243-02a" xml:space="preserve">Coroll. 1.
                <lb/>
              26.l.2.</note>
            mum, AF, ad ſemiportionem, AEG, eadem verò ad omnia qua-
              <lb/>
            drata ſemiportionis, AEG, ſunt ſexquialtera .</s>
            <s xml:id="echoid-s5440" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5441" xml:space="preserve">ſunt vt parallelo-
              <lb/>
            grammum, AF, ad ſui ipſius, {2/3}, igitur eadem ad reliqua. </s>
            <s xml:id="echoid-s5442" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5443" xml:space="preserve">ad rectan-
              <lb/>
            gula ſub ſemiportione, AEG, & </s>
            <s xml:id="echoid-s5444" xml:space="preserve">trilineo, GEF, erunt vt parallelo-
              <lb/>
            grammum, AF, ad exceſium, quo ſemiportio, AEG, excedit, {2/3}, pa-
              <lb/>
            rallelogrammi, AF, omnia autem quadrata, BF, ſunt quadrupla om-
              <lb/>
            nium quadratorum, AF, ergo omnia quadrata, BF, ad rectangula
              <lb/>
              <note position="right" xlink:label="note-0243-03" xlink:href="note-0243-03a" xml:space="preserve">7.l.2.</note>
            ſub ſemiportione, AEG, & </s>
            <s xml:id="echoid-s5445" xml:space="preserve">trilineo, GEF, erunt vt quater paral-
              <lb/>
            lelogra nmum, AF, ad dictum exceſſum.</s>
            <s xml:id="echoid-s5446" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5447" xml:space="preserve">vt parallelogrammum, H
              <lb/>
              <figure xlink:label="fig-0243-01" xlink:href="fig-0243-01a" number="151">
                <image file="0243-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0243-01"/>
              </figure>
            F, ad dictum exceſſum, & </s>
            <s xml:id="echoid-s5448" xml:space="preserve">conſequentibus
              <lb/>
            quadruplicatis, omnia quadrata paralle
              <lb/>
            logrammi, BF, adrectangula quater ſub
              <lb/>
            ſemiportione, AEG, & </s>
            <s xml:id="echoid-s5449" xml:space="preserve">trilineo, GEF, .</s>
            <s xml:id="echoid-s5450" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s5451" xml:space="preserve">ad rectangula bis ſub portione, BEG, & </s>
            <s xml:id="echoid-s5452" xml:space="preserve">
              <lb/>
            trilineo, GEF, erunt vt, HF, ad dictum ex
              <lb/>
            ceſſum quater ſumptum, quia enim, AE,
              <lb/>
            eſt diameter bifariam diuidit in portione,
              <lb/>
            BEG, omnes ipſi, DF, æquidiſtantes, & </s>
            <s xml:id="echoid-s5453" xml:space="preserve">
              <lb/>
            ideò rectangula quater ſub ſemiportione,
              <lb/>
            AEG, & </s>
            <s xml:id="echoid-s5454" xml:space="preserve">trilineo, GEF, fiunt rectangula
              <lb/>
            bis ſub portione, BEG, & </s>
            <s xml:id="echoid-s5455" xml:space="preserve">trilineo, GEF, omnia ergo quadrata paral-
              <lb/>
            lelogrammi, BF, ad rectangula bis ſub portione, BEG, & </s>
            <s xml:id="echoid-s5456" xml:space="preserve">trilineo, G
              <lb/>
            EF, vel eorum dupla. </s>
            <s xml:id="echoid-s5457" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5458" xml:space="preserve">omnia quadrata parallelogrammi, HF, ad re-
              <lb/>
              <note position="right" xlink:label="note-0243-04" xlink:href="note-0243-04a" xml:space="preserve">10.l.2.</note>
            ctangula bis ſub circulo, vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5459" xml:space="preserve">ſub trilineis, MGN, GE
              <lb/>
            F, erunt vt parallelogrammum, HF, ad quatuor exceſſus ſemiportio-
              <lb/>
            nis, AEG, ſuper duas tertias parallelogrammi, AF, .</s>
            <s xml:id="echoid-s5460" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5461" xml:space="preserve">ad exceſſum cir-
              <lb/>
            culi, vel ellipſis, MBEG, ſuper, {2/3}, parallelogrammi, HF, erant autem
              <lb/>
            omnia quadrata parallelogrammi, HF, ad omnia quadrata circuli,
              <lb/>
            vel ellipſis, MBEG, vtidem parallelogrammum, HF, ad, {2/3}, ſui ipſius,
              <lb/>
            ergo omnia quadrata parallelogrammi, HF, ad omnia quadrata cir-
              <lb/>
            culi, vel ellipſis, MBEG, ſimul cum rectangulis bis ſub eodem circulo,
              <lb/>
            vel ellipſi, MBEG, & </s>
            <s xml:id="echoid-s5462" xml:space="preserve">ſub trilineis, MNG, GFE, erunt vt parallelo-
              <lb/>
            grammum, HF, ad ſui ipſius, {2/3}, vna cum exceſſu circuli, vel ellipſis, M
              <lb/>
            BEG, ſuper eaſdem duas tertias .</s>
            <s xml:id="echoid-s5463" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5464" xml:space="preserve">erunt vt parallelogrammum, H
              <lb/>
            F, ad circulum, vel ellipſim, MBEG, quod erat oſtendendum.</s>
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