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

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            <s xml:id="echoid-s5211" xml:space="preserve">
              <pb o="214" file="0234" n="234" rhead="GEOMETRIÆ"/>
            licet non ſint rectangula, tamen erunt æquiangula, vndeæquiangu-
              <lb/>
            lum erit parallelogrammi, HP, ipſi, FG, & </s>
            <s xml:id="echoid-s5212" xml:space="preserve">ellipſes, ABCD, K
              <lb/>
              <figure xlink:label="fig-0234-01" xlink:href="fig-0234-01a" number="146">
                <image file="0234-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0234-01"/>
              </figure>
            TMI, erunt circa, AC, KM,
              <lb/>
            æquales diametros, ita vt ſi ſuper-
              <lb/>
            ponerentur ad inuicem iſti ellipſes,
              <lb/>
            vt, KM, eſſet in, AC, ipſa, TI,
              <lb/>
            eſſet in, BD, & </s>
            <s xml:id="echoid-s5213" xml:space="preserve">ideò eodem mo-
              <lb/>
            do oſtendemus, vt ſupra ellipſes,
              <lb/>
            ABCD, STVI, eſſe inter ſe, vt
              <lb/>
            parallelogramma illis eircumſcri-
              <lb/>
            pta, FG, ER, & </s>
            <s xml:id="echoid-s5214" xml:space="preserve">quia illa ſunt
              <lb/>
            ęquiangula habebunt rationem ex
              <lb/>
            ratione laterum compoſitam, ſed
              <lb/>
            etiam parallelogramma rectangu-
              <lb/>
              <note position="left" xlink:label="note-0234-01" xlink:href="note-0234-01a" xml:space="preserve">6.Lib.2.</note>
            la ſub eiſdem lateribus habent ra-
              <lb/>
            tionem cõpoſitam ex ratione eo-
              <lb/>
            rundem laterum, ergo ellipſis, A
              <lb/>
            BCD, ad ellipſim, STVI, erit
              <lb/>
            vt parallelogrammum, FG, ad
              <lb/>
            parallelogrammum, ER, ſibiæ-
              <lb/>
            quiangulum. </s>
            <s xml:id="echoid-s5215" xml:space="preserve">.</s>
            <s xml:id="echoid-s5216" xml:space="preserve">vt rectangulum ſub,
              <lb/>
            FL, LG, vel ſub, BD, AC, dia-
              <lb/>
            metris, ad rectangulum ſub, TI,
              <lb/>
            SV, diametris, patetigitur circu-
              <lb/>
            lum, vel ellipſim, ABCD, ad cir-
              <lb/>
            eulum, vel cllipſim, STVI, eſſe vt rectangulum ſub axibus, vel dia-
              <lb/>
            metris, AC, BD, ad rectangulum ſub axibus, vel diametris, SV,
              <lb/>
            TI, quæ diametri æquè ad inuicem inclinantur, quod oſtendere
              <lb/>
            opuserat.</s>
            <s xml:id="echoid-s5217" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div531" type="section" level="1" n="316">
          <head xml:id="echoid-head333" xml:space="preserve">COROLLARIVM I.</head>
          <p style="it">
            <s xml:id="echoid-s5218" xml:space="preserve">_H_INC ergo colligitur, quod quando circulos comparatur ad cir-
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            culum, illi ſunt interſe, vt rectangula ſub eorum axibus. </s>
            <s xml:id="echoid-s5219" xml:space="preserve">i. </s>
            <s xml:id="echoid-s5220" xml:space="preserve">vt
              <lb/>
            quadrata axium, & </s>
            <s xml:id="echoid-s5221" xml:space="preserve">ideò ſunt in dupla ratione axium, ſiue diametro-
              <lb/>
            rum, quando verò circulus comparatur ad ellipſim, erit ad illum, vt
              <lb/>
            ſui axis quadratum adrectangulum ſub axibus ellipſis. </s>
            <s xml:id="echoid-s5222" xml:space="preserve">Denique, ſiel-
              <lb/>
            lipſis comparetur ad ellipſim, erit ad illum, vt rectangulum ſub axibus
              <lb/>
            illius ad rectangulum ſub axibus alterius, vel vt rectangulum ſub dia-
              <lb/>
            metris (coniugatis ſemper intellige, niſi aliud addatur) illius ad rectan-
              <lb/>
            gulum ſub diametris alterins, quæ vt prædicti æqualiter ad inuicem
              <lb/>
            ſunt inclinatæ; </s>
            <s xml:id="echoid-s5223" xml:space="preserve">vel tandem, vt parallelogramma illis </s>
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