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

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        <div xml:id="echoid-div526" type="section" level="1" n="314">
          <pb o="213" file="0233" n="233" rhead="LIBER III."/>
        </div>
        <div xml:id="echoid-div528" type="section" level="1" n="315">
          <head xml:id="echoid-head332" xml:space="preserve">THEOREMAX. PROPOS. XI.</head>
          <p>
            <s xml:id="echoid-s5198" xml:space="preserve">C Irculus, vel ellipſis ad quemlibet circulum, vel ellipſim
              <lb/>
            habet eandem rationem, quam rectangulum ſub ipſius
              <lb/>
            coniugatis axibus, vel diametris, ad rectangulum ſub iſtius
              <lb/>
            coniugatis axibus, vel diametris, æquè tamen diametris ad
              <lb/>
            inuicem inclinatis.</s>
            <s xml:id="echoid-s5199" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5200" xml:space="preserve">Sit circulus, ABCD, cuius axes coniugati ſint, AC, BD, cen-
              <lb/>
            trum, O, ductis verò per puncta, A, C, parallelis ipſi, BD, FL, Q
              <lb/>
            G, & </s>
            <s xml:id="echoid-s5201" xml:space="preserve">per puncta, B, D, parallelis ipſi, AC, LG, FQ, vt ſit, FG,
              <lb/>
            rectangulum circulo, ABCD, circumſcriptum, ſit, STVI, qui-
              <lb/>
              <figure xlink:label="fig-0233-01" xlink:href="fig-0233-01a" number="145">
                <image file="0233-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0233-01"/>
              </figure>
            libet circulus, vel ellipſis, cuirectangu-
              <lb/>
            lum, ER, ſit circumſcriptum, habens
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            latera parallela coniugatis axibus, SV,
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            TI. </s>
            <s xml:id="echoid-s5202" xml:space="preserve">Dico circulum, ABCD, ad elli-
              <lb/>
            pſem, STVI, eſſe vt rectangulum, FG,
              <lb/>
            ad rectangulum, ER; </s>
            <s xml:id="echoid-s5203" xml:space="preserve">producatur, SV,
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            hinc inde, ita vt, NK, ſit æqualis, OA,
              <lb/>
            &</s>
            <s xml:id="echoid-s5204" xml:space="preserve">, NM, ipſi, OC, & </s>
            <s xml:id="echoid-s5205" xml:space="preserve">circa, KM, TI,
              <lb/>
            axes intelligatur, KT, MI, ellipſis, vel
              <lb/>
            circulus, & </s>
            <s xml:id="echoid-s5206" xml:space="preserve">productis tangentibus, TE,
              <lb/>
            IR, vt occurrantipſis, HK, MP, ſit
              <lb/>
            rectangulum, HP, circumſcriptum ipſi,
              <lb/>
            KTMI, ellipſi, vel circulo, habens la-
              <lb/>
            tera coniugatis axibus, KM, TI, paral-
              <lb/>
            lela: </s>
            <s xml:id="echoid-s5207" xml:space="preserve">Eſt ergo vt rectangulum, FG, ad
              <lb/>
              <note position="right" xlink:label="note-0233-01" xlink:href="note-0233-01a" xml:space="preserve">Exantec.</note>
            rectangulum, HP, ita circulus, ABC
              <lb/>
            D, ad circulum, vel ellipſim, KTMI,
              <lb/>
            quia ſunt ambo circa, AC, KM, axes
              <lb/>
              <note position="right" xlink:label="note-0233-02" xlink:href="note-0233-02a" xml:space="preserve">Exantec.</note>
            æquales; </s>
            <s xml:id="echoid-s5208" xml:space="preserve">item parallelogrammum, H
              <lb/>
            P, ad parallelogrammum, ER, eſt vt
              <lb/>
            circulus, vel ellipſis, KTMI, ad circu-
              <lb/>
            lum, vel ellipſim, STVI, ergo ex ęqua-
              <lb/>
            lirectangulum, FG, ad rectangulum, ER, erit vt circulus, ABC
              <lb/>
            D, ad circulum, vel ell pſim, STVI.</s>
            <s xml:id="echoid-s5209" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5210" xml:space="preserve">Sit nunc, ABCD, ellipſis, vt etiam, STVI, poterit eſſe, quod,
              <lb/>
            AC, BD, ſint non axes, ſed coniugatæ diametri, &</s>
            <s xml:id="echoid-s5211" xml:space="preserve">, FG, pa-
              <lb/>
            rallelogrammum, oportet autem ſumere in ellipſi, ST, VI,
              <lb/>
            coniugatas diametros, SV, TI, itavt æqualiter ſint inclinatæ
              <lb/>
            ac ipiæ, AC, BD, tunc enim circumſcripta </s>
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