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

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        <div xml:id="echoid-div844" type="section" level="1" n="499">
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            <s xml:id="echoid-s8825" xml:space="preserve">
              <pb o="352" file="0372" n="372" rhead="GEOMETRIÆ"/>
            ſolida, BAE, ad conoidem parabolicam, ACE, vt quadratum, MO,
              <lb/>
            cum rectangulo bis ſub, MOC, ad quadratum, MC, ergo, ex æqua-
              <lb/>
            li, portio ſolida, ABE, ad portionem ſolidam, BDE, erit vt qua-
              <lb/>
            dratum, MO, cum rectangulo bis ſub, MOC, ad quad. </s>
            <s xml:id="echoid-s8826" xml:space="preserve">ON, cum re-
              <lb/>
            ctang. </s>
            <s xml:id="echoid-s8827" xml:space="preserve">bis ſub, ONC, quod &</s>
            <s xml:id="echoid-s8828" xml:space="preserve">c.</s>
            <s xml:id="echoid-s8829" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8830" xml:space="preserve">Sed vniuerſaliter ſi ſint ſolida ſimilaria genita ex parabolis, ACE,
              <lb/>
            BCD, iuxta communem regulam, AE, & </s>
            <s xml:id="echoid-s8831" xml:space="preserve">ducatur planum per, BE,
              <lb/>
            rectum plano parabolæ, ACE, ſcindens ſolidum ſimilare genitum
              <lb/>
            ex, BDEA, in duas portiones ſolidas, BAE, BDE, adhuc, conſe-
              <lb/>
            quenter ſupradictis, inueniemus has duas portiones ſolidas eſſe in
              <lb/>
            eadem ratione, vt portiones ſolidæ productæ ex ſectione fruſti co-
              <lb/>
            noidis parabolicæ, BAED, .</s>
            <s xml:id="echoid-s8832" xml:space="preserve">ſ. </s>
            <s xml:id="echoid-s8833" xml:space="preserve">eſſe vt quadratum, MO, cum rectan-
              <lb/>
            gulo bis ſub, MOC, ad quadrat, ũON, cum rectangulo bis ſub, ONC,
              <lb/>
            quod ex ſupradictis erui facilè poteſt; </s>
            <s xml:id="echoid-s8834" xml:space="preserve">quæ demonſtratio currit etiã,
              <lb/>
            ſi, CM, non ſit axis, ſed tantum diameter, vt confideranti clarè
              <lb/>
            patebit.</s>
            <s xml:id="echoid-s8835" xml:space="preserve"/>
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        <div xml:id="echoid-div846" type="section" level="1" n="500">
          <head xml:id="echoid-head520" xml:space="preserve">A. COROLL. VII. SECTIO I.</head>
          <note position="left" xml:space="preserve">A.</note>
          <p>
            <s xml:id="echoid-s8836" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s8837" xml:space="preserve">29. </s>
            <s xml:id="echoid-s8838" xml:space="preserve">& </s>
            <s xml:id="echoid-s8839" xml:space="preserve">Cor. </s>
            <s xml:id="echoid-s8840" xml:space="preserve">Sect. </s>
            <s xml:id="echoid-s8841" xml:space="preserve">1. </s>
            <s xml:id="echoid-s8842" xml:space="preserve">& </s>
            <s xml:id="echoid-s8843" xml:space="preserve">2. </s>
            <s xml:id="echoid-s8844" xml:space="preserve">colligimus ſolida ſimilaria geni-
              <lb/>
            ta ex parabolis in eadem altitudine conſtitutis, genita inquam
              <lb/>
            iuxta regulas ipſarum baſes, eſſe inter ſe, vt quadrata baſium, & </s>
            <s xml:id="echoid-s8845" xml:space="preserve">in
              <lb/>
            ijſdem baſibus conſtitutis, vt earum altitudines, vel vt diametros
              <lb/>
            æqualiter baſibus inclinatas; </s>
            <s xml:id="echoid-s8846" xml:space="preserve">hoc igitur nedum concluditur de co-
              <lb/>
            noidibus parabolicis in eadem altitudine ſtantibus, quod ſit, vt qua-
              <lb/>
            drata baſium, vel in eadem baſi exiſtentium, quod ſint, vt altitu-
              <lb/>
            dines, ſed de cæteris ſimilaribus ſolidis ex ipſis parabolis genitis
              <lb/>
            iuxta regulas baſes, vt dictum eſt.</s>
            <s xml:id="echoid-s8847" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div847" type="section" level="1" n="501">
          <head xml:id="echoid-head521" xml:space="preserve">B. SECTIO II.</head>
          <note position="left" xml:space="preserve">B.</note>
          <p>
            <s xml:id="echoid-s8848" xml:space="preserve">ITem habemus conoides parabolicas, & </s>
            <s xml:id="echoid-s8849" xml:space="preserve">cætera ſolida ſimilaria
              <lb/>
            ex parabolis genita iuxta regulas baſes, habere inter ſe ratio-
              <lb/>
            nem eompoſitam ex ratione quadratorum baſium, & </s>
            <s xml:id="echoid-s8850" xml:space="preserve">altitudi-
              <lb/>
            num, vel diametrorum æqualiter baſibus inclinatarum.</s>
            <s xml:id="echoid-s8851" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div848" type="section" level="1" n="502">
          <head xml:id="echoid-head522" xml:space="preserve">C. SECTIO III.</head>
          <note position="left" xml:space="preserve">C.</note>
          <p>
            <s xml:id="echoid-s8852" xml:space="preserve">ITem eadem ſolida, quarum baſes altitudinibus, vel diametris
              <lb/>
            æqualiter baſibus inclinatis reciprocantur, eſſe æqualia, & </s>
            <s xml:id="echoid-s8853" xml:space="preserve">
              <lb/>
            quæ ſunt æqualia habere baſes altitudinibus, vel diametris æqua-
              <lb/>
            liter baſibus inclinatis, reciprocas.</s>
            <s xml:id="echoid-s8854" xml:space="preserve"/>
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