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

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        <div xml:id="echoid-div607" type="section" level="1" n="352">
          <head xml:id="echoid-head369" xml:space="preserve">COROLLARIVM.</head>
          <p style="it">
            <s xml:id="echoid-s6357" xml:space="preserve">_H_Inc patet nedum rectangulum, NOV, æquari rectangulo, IHP,
              <lb/>
            ſed etiam portiones interceptas tangentibus, & </s>
            <s xml:id="echoid-s6358" xml:space="preserve">curuaellipſis eſſe
              <lb/>
            inter ſe æquales, belut, OV, ipſi, PH.</s>
            <s xml:id="echoid-s6359" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div608" type="section" level="1" n="353">
          <head xml:id="echoid-head370" xml:space="preserve">THEOREMA XXXI. PROPOS. XXXII.</head>
          <p>
            <s xml:id="echoid-s6360" xml:space="preserve">EXpoſita ellipſi, cum parallelogrammo illi circumſcripto
              <lb/>
            Theor. </s>
            <s xml:id="echoid-s6361" xml:space="preserve">antecedentis, cæteris omiſſis, oſtendemus, re-
              <lb/>
            gula, FR, omnia quadrata parallelogrammi, AR, ad om-
              <lb/>
            nia quadrata ellipſis, BDMG, cum rectangulis bis ſub ea-
              <lb/>
            dem ellipſi, & </s>
            <s xml:id="echoid-s6362" xml:space="preserve">ſub trilineis, BCG, GRM, eſſe, vt paralle-
              <lb/>
            logrammum, AR, ad ellipſim, BDMG.</s>
            <s xml:id="echoid-s6363" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6364" xml:space="preserve">Ducantur à punctis contactuum regulæ, FR, parallelę, GE, D
              <lb/>
              <note position="left" xlink:label="note-0274-01" xlink:href="note-0274-01a" xml:space="preserve">Coroll. 1.
                <lb/>
              26. lib. 2.</note>
            V; </s>
            <s xml:id="echoid-s6365" xml:space="preserve">omnia ergo quadrata, AR, ad rectangula ſub ellipſi, BDMG,
              <lb/>
            & </s>
            <s xml:id="echoid-s6366" xml:space="preserve">ſub, AR, ſunt vt, AR, ad ellipſim, BDMG; </s>
            <s xml:id="echoid-s6367" xml:space="preserve">verum rectangula
              <lb/>
            ſub ellipſi, BDMG, & </s>
            <s xml:id="echoid-s6368" xml:space="preserve">ſub, AR, ſunt æqualia rectangulis ſub el-
              <lb/>
              <note position="left" xlink:label="note-0274-02" xlink:href="note-0274-02a" xml:space="preserve">A. 23. 1. 2.</note>
            lipſi, BDMG, & </s>
            <s xml:id="echoid-s6369" xml:space="preserve">ſub duobus trilineis, BAD, DFM, item ſub el-
              <lb/>
            lipſi, BDMG, & </s>
            <s xml:id="echoid-s6370" xml:space="preserve">ſub eadem. </s>
            <s xml:id="echoid-s6371" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6372" xml:space="preserve">omnibus quadratis ellipſis, BDM
              <lb/>
            G, & </s>
            <s xml:id="echoid-s6373" xml:space="preserve">ſub eadem ellipſi, BDMG, & </s>
            <s xml:id="echoid-s6374" xml:space="preserve">ſub duobus trilineis, BCG,
              <lb/>
            GRM, verum rectangula ſub ellipſi, BDMG, & </s>
            <s xml:id="echoid-s6375" xml:space="preserve">ſub trilineis, B
              <lb/>
              <figure xlink:label="fig-0274-01" xlink:href="fig-0274-01a" number="170">
                <image file="0274-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0274-01"/>
              </figure>
            AD, DFM, æquantur rectangulis ſub ea-
              <lb/>
            dem ellipſi, & </s>
            <s xml:id="echoid-s6376" xml:space="preserve">ſub trilineis, BCG, GRM,
              <lb/>
            quod ſic patet, quoniam enim, AD, RG,
              <lb/>
              <note position="left" xlink:label="note-0274-03" xlink:href="note-0274-03a" xml:space="preserve">Exantec.</note>
            coalternè tangentes ſunt æquales, & </s>
            <s xml:id="echoid-s6377" xml:space="preserve">ductis
              <lb/>
            ipſi, FR, parallelis intra ellipſim, ex ipſis
              <lb/>
            coalternè tangentibus, AD, RG, abſcin
              <lb/>
            dentibus portiones æquales verſus puncta
              <lb/>
            contactuum, rectangula ſumpta, vt dictum
              <lb/>
            eſt in antecedenti Theor. </s>
            <s xml:id="echoid-s6378" xml:space="preserve">ſunt æqualia, ideò
              <lb/>
            & </s>
            <s xml:id="echoid-s6379" xml:space="preserve">omnia omnibus erunt æqualia. </s>
            <s xml:id="echoid-s6380" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s6381" xml:space="preserve">rectan-
              <lb/>
            gula ſub portione, OGBD, & </s>
            <s xml:id="echoid-s6382" xml:space="preserve">trilineo, BAD, erunt æqualia re-
              <lb/>
            ctangulis ſub portione, SMG, & </s>
            <s xml:id="echoid-s6383" xml:space="preserve">ſub trilineo, GMR, eadem ra-
              <lb/>
            tione rectangula ſub portione, OMD, & </s>
            <s xml:id="echoid-s6384" xml:space="preserve">trilineo, DFM, æquan-
              <lb/>
            tur rectangulis ſub portione, SBG, & </s>
            <s xml:id="echoid-s6385" xml:space="preserve">trilineo, BCG, ergo rectan-
              <lb/>
            gula ſub ellipſi, BDMG, & </s>
            <s xml:id="echoid-s6386" xml:space="preserve">duobus trilineis, BAD, DFM, ęquan-
              <lb/>
            tur rectangulis ſub ellipſi, BDMG, & </s>
            <s xml:id="echoid-s6387" xml:space="preserve">ſub trilineis, BCG, GRM;</s>
            <s xml:id="echoid-s6388" xml:space="preserve"/>
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