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

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          <p>
            <s xml:id="echoid-s2074" xml:space="preserve">
              <pb o="84" file="0104" n="104" rhead="GEOMETRI Æ"/>
            nitè ſecat baſis productum planum in recta, 2, Z, perpendiculari
              <lb/>
            triangulo per axem, ACF, & </s>
            <s xml:id="echoid-s2075" xml:space="preserve">ſint adhuc per puncta, N, S, ipſi, C
              <lb/>
            F, ductæ parallelæ, TL, HR, igitur quadratum, ℟ S, erit ęquale
              <lb/>
              <note position="left" xlink:label="note-0104-01" xlink:href="note-0104-01a" xml:space="preserve">14. Secunn.
                <lb/>
              Elem.</note>
              <figure xlink:label="fig-0104-01" xlink:href="fig-0104-01a" number="58">
                <image file="0104-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0104-01"/>
              </figure>
            rectangulo, TSL, & </s>
            <s xml:id="echoid-s2076" xml:space="preserve">quadra-
              <lb/>
            tum, MN, æquale rectangulo,
              <lb/>
              <note position="left" xlink:label="note-0104-02" xlink:href="note-0104-02a" xml:space="preserve">Ex Sexta
                <lb/>
              lib. 2. feq.
                <lb/>
              velex 23.
                <lb/>
              Sext. El.</note>
            HNR, at rectangulum, TSL,
              <lb/>
            ad, HNR, habet rationem com-
              <lb/>
            poſitam ex ea, quam habet, T
              <lb/>
            S, ad, HN, .</s>
            <s xml:id="echoid-s2077" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2078" xml:space="preserve">SB, ad, BN,
              <lb/>
            quia trianguli, BTS, BHN,
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            ſunt æquianguli, & </s>
            <s xml:id="echoid-s2079" xml:space="preserve">ex ea, quam
              <lb/>
            habet, SL, ad, NR, .</s>
            <s xml:id="echoid-s2080" xml:space="preserve">i. </s>
            <s xml:id="echoid-s2081" xml:space="preserve">SV,
              <lb/>
            ad, VN, quia pariter trianguli,
              <lb/>
            SVL, NVR, ſunt æquiangu-
              <lb/>
            li, duę autem rationes, SB, ad,
              <lb/>
            BN, &</s>
            <s xml:id="echoid-s2082" xml:space="preserve">, SV, ad, VN, componunt rationem rectanguli, BSV,
              <lb/>
              <note position="left" xlink:label="note-0104-03" xlink:href="note-0104-03a" xml:space="preserve">Ex Sexta
                <lb/>
              lib. 2. feq.
                <lb/>
              vel ex 23.
                <lb/>
              Sexti El.</note>
            ad rectangulum, BNV, ergo rectangulum, TSL, ad, HNR, .</s>
            <s xml:id="echoid-s2083" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s2084" xml:space="preserve">quadratum, ℟ S, ad quadratum, MN, vel quadratum, ℟ D, ad
              <lb/>
            quadratum, MO, erit vt rectangulum, VSB, ad rectangulum, V
              <lb/>
            NB, quod oſtendere opu erat; </s>
            <s xml:id="echoid-s2085" xml:space="preserve">hæc autem ab Apollonio vocatur
              <lb/>
            Ellipſis.</s>
            <s xml:id="echoid-s2086" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div205" type="section" level="1" n="132">
          <head xml:id="echoid-head143" xml:space="preserve">SCHOLIVM.</head>
          <p style="it">
            <s xml:id="echoid-s2087" xml:space="preserve">_H_Aec circa ſectiones conicas appoſui, tum vt quod menti meæ ſuc-
              <lb/>
            currit in lucem proferrem, tum vt eluceſcat, quam facilè paſſio-
              <lb/>
            nes, quæ ab. </s>
            <s xml:id="echoid-s2088" xml:space="preserve">Apollonio in Elementis conicis circa earundem diametros,
              <lb/>
            vel axes quoſcumque demonſtrantur, circa eos, qui axes, vel diametri
              <lb/>
            princibales, ſiue ex generatione vocantur modo ſupradicto oſtendantur.
              <lb/>
            </s>
            <s xml:id="echoid-s2089" xml:space="preserve">His tamen contenti ex Apollonio recipiemus pro dictarum ſectionum
              <lb/>
            axibus, vel diametris quibuſcumq; </s>
            <s xml:id="echoid-s2090" xml:space="preserve">quod ipſe colligit ad finem Trop. </s>
            <s xml:id="echoid-s2091" xml:space="preserve">51. </s>
            <s xml:id="echoid-s2092" xml:space="preserve">
              <lb/>
            primi Conicorum, ſcilicet.</s>
            <s xml:id="echoid-s2093" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2094" xml:space="preserve">In Parabola vnamquamque rectarum linearum, quę diametro ex
              <lb/>
            generatione ducuntur æquidiſtantes, diametrum eſſe: </s>
            <s xml:id="echoid-s2095" xml:space="preserve">In hyperbola
              <lb/>
            verò, & </s>
            <s xml:id="echoid-s2096" xml:space="preserve">ellipſi, & </s>
            <s xml:id="echoid-s2097" xml:space="preserve">oppoſitis ſectionibus vnamquamque earum, quę
              <lb/>
            per centrum ducuntur, & </s>
            <s xml:id="echoid-s2098" xml:space="preserve">in parabola quidem applicatas ad vnam-
              <lb/>
            quamq; </s>
            <s xml:id="echoid-s2099" xml:space="preserve">diametrum, ęquidiſtantes contingentibus, poſte rectangula
              <lb/>
            ipſi adiacentia: </s>
            <s xml:id="echoid-s2100" xml:space="preserve">In hyperbola, & </s>
            <s xml:id="echoid-s2101" xml:space="preserve">oppoſitis poſſe rectangula adiacen-
              <lb/>
            tia ipſi, quę excedunt eadem figura: </s>
            <s xml:id="echoid-s2102" xml:space="preserve">In ellipſi autem, quę eadem de-
              <lb/>
            ficiunt: </s>
            <s xml:id="echoid-s2103" xml:space="preserve">Poſt@@mò quęcumque circa ſectiones adhibitis principalibus
              <lb/>
            diametris demonſtrata ſunt, & </s>
            <s xml:id="echoid-s2104" xml:space="preserve">alijs diametris aſſumptis eadem con-
              <lb/>
            tingere.</s>
            <s xml:id="echoid-s2105" xml:space="preserve"/>
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