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

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            <s xml:id="echoid-s5784" xml:space="preserve">
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            eadem aptata deſcriptiin ijſdem conſtitutis: </s>
            <s xml:id="echoid-s5785" xml:space="preserve">In ellipſi verò
              <lb/>
            ad eadem rectangula, erunt vt quadratum ſecundiaxis, vel
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            diametri, ad quadratum primæ.</s>
            <s xml:id="echoid-s5786" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5787" xml:space="preserve">Sit primò circulus, ABFH, & </s>
            <s xml:id="echoid-s5788" xml:space="preserve">in eo vtcunque aptata recta, AB,
              <lb/>
              <note position="right" xlink:label="note-0255-01" xlink:href="note-0255-01a" xml:space="preserve">Defin.
                <lb/>
              4. Elem.</note>
            parallela diametro, ER, & </s>
            <s xml:id="echoid-s5789" xml:space="preserve">per puncta, AB, producantur viq; </s>
            <s xml:id="echoid-s5790" xml:space="preserve">ad
              <lb/>
            circumferentiam, HF, duæ, AH, BF, parallelæ ſecundæ diame-
              <lb/>
            tro, ST, quæ ſumatur pro regula, quia autem circulus eſt, ESRT,
              <lb/>
            ideò coniugatæ diametri, ER, ST, ſeſecant ad angulos rectos, & </s>
            <s xml:id="echoid-s5791" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0255-01" xlink:href="fig-0255-01a" number="159">
                <image file="0255-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0255-01"/>
              </figure>
            ſunt coniugati axes, & </s>
            <s xml:id="echoid-s5792" xml:space="preserve">ideò, AH, BF,
              <lb/>
            ſunt perpendiculares ipſi, AB; </s>
            <s xml:id="echoid-s5793" xml:space="preserve">ſuper, A
              <lb/>
            B, ergo ſit deſcriptum quadratum, AD,
              <lb/>
            & </s>
            <s xml:id="echoid-s5794" xml:space="preserve">in eo ducta diameter, AD. </s>
            <s xml:id="echoid-s5795" xml:space="preserve">Dico er-
              <lb/>
            go rectangula ſub portione, ASB, & </s>
            <s xml:id="echoid-s5796" xml:space="preserve">
              <lb/>
            quadrilineo, AB, FH, eſſe æqualia re-
              <lb/>
            ctangulis ſub duobus triangulis, ABD,
              <lb/>
            AVD, ſumatur enim in, AB, vtcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s5797" xml:space="preserve">punctum, m, & </s>
            <s xml:id="echoid-s5798" xml:space="preserve">per, M, ducatur ipſi, B
              <lb/>
            F, parallela, CG, ſecans, AD, in, N; </s>
            <s xml:id="echoid-s5799" xml:space="preserve">
              <lb/>
            VD, in, O, & </s>
            <s xml:id="echoid-s5800" xml:space="preserve">curuam circuli in, CG,
              <lb/>
            quia ergo duæ, AB, CG, in circulo ſe
              <lb/>
              <note position="right" xlink:label="note-0255-02" xlink:href="note-0255-02a" xml:space="preserve">35. 3. ele</note>
            ſecant in puncto, M, rectangulum, G
              <lb/>
            MC, eſt æquale rectangulo, BMA, & </s>
            <s xml:id="echoid-s5801" xml:space="preserve">
              <lb/>
            quia, AM, eſt æqualis ipſi, MN, &</s>
            <s xml:id="echoid-s5802" xml:space="preserve">, M
              <lb/>
            B, ipſi, NO, rectangulum, AMB, eſt
              <lb/>
            æquale rectangulo, MNO; </s>
            <s xml:id="echoid-s5803" xml:space="preserve">ergo rectan-
              <lb/>
            gulum, CMG, erit æquale rectangulo,
              <lb/>
            MNO, idem de cæteris probabitur, er-
              <lb/>
            go rectangula ſub portione, ACB, & </s>
            <s xml:id="echoid-s5804" xml:space="preserve">
              <lb/>
            quadrilineo, ABFGH, erunt æqualia
              <lb/>
            rectangulis ſub triangulis, ABD, AVD, quod eſt propoſitum in
              <lb/>
            circulo.</s>
            <s xml:id="echoid-s5805" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5806" xml:space="preserve">Sit nunc in inferiori figura ellipſis, ESRT, centrum, X, axes,
              <lb/>
              <note position="right" xlink:label="note-0255-03" xlink:href="note-0255-03a" xml:space="preserve">Velut in
                <lb/>
              circulo.</note>
            vel diametri coniugatę, ER, prima, ST, ſecunda, ſit autem in ipſo
              <lb/>
            aptata, AB, parallela ipſi, ER, per cuius extrema puncta, AB,
              <lb/>
            productæ ſint vſque ad curuam ellipſis duæ, AH, BF, parallelę ſe-
              <lb/>
            cundæ axi, vel diametro, ST; </s>
            <s xml:id="echoid-s5807" xml:space="preserve">ſit inſuper deſcriptum quadratum,
              <lb/>
            velrhombus, AD, cuius latera diametris, ER, ST, ſint paralle-
              <lb/>
            la, & </s>
            <s xml:id="echoid-s5808" xml:space="preserve">in eo ducta diameter, AD, & </s>
            <s xml:id="echoid-s5809" xml:space="preserve">per puncta, E, S, ſint etiam du-
              <lb/>
            ctæ tangentes, EY, SY, coincidentes in, Y, quæ erunt parallelæ
              <lb/>
            diametris, ER, ST, .</s>
            <s xml:id="echoid-s5810" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s5811" xml:space="preserve">YE, ipſi, ST, &</s>
            <s xml:id="echoid-s5812" xml:space="preserve">, YS, ipſi, ER; </s>
            <s xml:id="echoid-s5813" xml:space="preserve">erit </s>
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