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

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        <div xml:id="echoid-div209" type="section" level="1" n="135">
          <p>
            <s xml:id="echoid-s2126" xml:space="preserve">
              <pb o="86" file="0106" n="106" rhead="GEOMETRIE"/>
            dem ſecantis figuram, & </s>
            <s xml:id="echoid-s2127" xml:space="preserve">alterius acti per axem recto ad pla-
              <lb/>
            num ſecans. </s>
            <s xml:id="echoid-s2128" xml:space="preserve">Archim. </s>
            <s xml:id="echoid-s2129" xml:space="preserve">ibid. </s>
            <s xml:id="echoid-s2130" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s2131" xml:space="preserve">14.</s>
            <s xml:id="echoid-s2132" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div210" type="section" level="1" n="136">
          <head xml:id="echoid-head147" xml:space="preserve">THEOREMA XLI. PROPOS. XLIV.</head>
          <p>
            <s xml:id="echoid-s2133" xml:space="preserve">SI ſphæroides plano ſecetur non recto ad axem, ſectio erit
              <lb/>
            ellipſis, diameter verò ipſius maior erit concepta in ſphę-
              <lb/>
            roide ſectio duorum planorum, eius ſcilicet, quod ſecat figu-
              <lb/>
            ram, & </s>
            <s xml:id="echoid-s2134" xml:space="preserve">eius, quod ducitur per axem recto ad planum ſecans.
              <lb/>
            </s>
            <s xml:id="echoid-s2135" xml:space="preserve">Arch. </s>
            <s xml:id="echoid-s2136" xml:space="preserve">ibid. </s>
            <s xml:id="echoid-s2137" xml:space="preserve">Propoſ. </s>
            <s xml:id="echoid-s2138" xml:space="preserve">15.</s>
            <s xml:id="echoid-s2139" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2140" xml:space="preserve">Minor verò diameter ſic habetur. </s>
            <s xml:id="echoid-s2141" xml:space="preserve">Sit Sphæroides, vel conoides
              <lb/>
            hyperbolicum, BDMF, axis, BM, centrum, A, ellipſis verò per
              <lb/>
              <figure xlink:label="fig-0106-01" xlink:href="fig-0106-01a" number="59">
                <image file="0106-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0106-01"/>
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            axem tranſiens in
              <lb/>
            ſphæroide, BDM
              <lb/>
            F, in conoide verò
              <lb/>
            hyperbola, NCO.
              <lb/>
            </s>
            <s xml:id="echoid-s2142" xml:space="preserve">Secetur autem ſphę-
              <lb/>
            roides, vel conoides
              <lb/>
            plano non recto ad
              <lb/>
            axem, ſed erecto fi-
              <lb/>
            guræ, BDMF, ex
              <lb/>
            quo fiat in ipſis ſe-
              <lb/>
            ctio, DF, hæc erit
              <lb/>
            ellipſis, cuius maior
              <lb/>
            diameter, DF. </s>
            <s xml:id="echoid-s2143" xml:space="preserve">In-
              <lb/>
            ueniatur nunc ver-
              <lb/>
            tex ellipſis, ſeu hy-
              <lb/>
            perbolæ, BDMF,
              <lb/>
            reſpectu ipſius, DF, qui ſit, C, & </s>
            <s xml:id="echoid-s2144" xml:space="preserve">iungatur, CB, ac per, B, aga-
              <lb/>
            tur, BG, tangens in, B, ipſam ellipſim, ſeu hyperbolam, tandem à
              <lb/>
            puncto, D, parallela ipſi, BG, & </s>
            <s xml:id="echoid-s2145" xml:space="preserve">à puncto, F, parallela ipſi, CB,
              <lb/>
            produc antur, DE, FE, quæ inuicem concurrent vt in, E. </s>
            <s xml:id="echoid-s2146" xml:space="preserve">Dico
              <lb/>
            igitur, quod erit, ED, minor diameter eiuſdem ellipſis, DF.</s>
            <s xml:id="echoid-s2147" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2148" xml:space="preserve">Hoc autem demonſtrat ibid. </s>
            <s xml:id="echoid-s2149" xml:space="preserve">Dauid Riualtus in Commentarijs in
              <lb/>
            Archim. </s>
            <s xml:id="echoid-s2150" xml:space="preserve">ad Propoſ. </s>
            <s xml:id="echoid-s2151" xml:space="preserve">14. </s>
            <s xml:id="echoid-s2152" xml:space="preserve">& </s>
            <s xml:id="echoid-s2153" xml:space="preserve">15.</s>
            <s xml:id="echoid-s2154" xml:space="preserve"/>
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