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

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            <s xml:id="echoid-s6914" xml:space="preserve">
              <pb o="281" file="0301" n="301" rhead="LIBER III."/>
            tem axim, TX, igitur cyhndrus genitus in reuolutione ex, AX,
              <lb/>
              <figure xlink:label="fig-0301-01" xlink:href="fig-0301-01a" number="196">
                <image file="0301-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0301-01"/>
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            dempto cylindro genito
              <lb/>
            ex, CX, ad ſolidum ge-
              <lb/>
            nitum in reuolutione ex
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            ellipſi, BDMG, erit vt,
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            AR, ad ellipſim, BDM
              <lb/>
            G; </s>
            <s xml:id="echoid-s6915" xml:space="preserve">idem accidet, ſireuo-
              <lb/>
            lutio ſiat circa axem pa-
              <lb/>
            rallelam ipſi, AC, inclu-
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            ſam duabus, FA, RC,
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            verſus, A, C, puncta pro-
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            ductis: </s>
            <s xml:id="echoid-s6916" xml:space="preserve">vocetur autem ſo-
              <lb/>
            lidum genitum inreuolu-
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            tione ex ellipſi, BDMG, anulus latus ellipticus altera parte ſtrictior.</s>
            <s xml:id="echoid-s6917" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div683" type="section" level="1" n="399">
          <head xml:id="echoid-head417" xml:space="preserve">SECTIO II.</head>
          <p>
            <s xml:id="echoid-s6918" xml:space="preserve">HInc inſimul patet, quod faſcia ſolida cylindrica (vt ita dicam)
              <lb/>
            in reuolutione circa, TX, genita ex, AR, ad anulum geni-
              <lb/>
            tum ex ellipſi, BDMG, in eadem reuolutione, eſt vt cylindrus ge-
              <lb/>
            nitus ex, AR, dum reuolutio ſit circa, CR, ad anulum ſtrictum el-
              <lb/>
            lipticum altera parte latiorem in eadem reuolutione circa, CR, at-
              <lb/>
            ellipſi, BDMG, genitum; </s>
            <s xml:id="echoid-s6919" xml:space="preserve">nam ambo ſunt, vt, AR, ad ellipſim,
              <lb/>
            BDMG, dem patet pro ſolidis ſimilaribus, &</s>
            <s xml:id="echoid-s6920" xml:space="preserve">c. </s>
            <s xml:id="echoid-s6921" xml:space="preserve">Quia verò dicta fa-
              <lb/>
            ſcia ſolida genita ab, AR, ad cylindrum ab eodem, AR, genitum
              <lb/>
            eſt, vt reſiduum quadrati, FX, dempto quadrato, RX, ad quadra-
              <lb/>
            tum, FR, eſt. </s>
            <s xml:id="echoid-s6922" xml:space="preserve">n. </s>
            <s xml:id="echoid-s6923" xml:space="preserve">cylindrus genitus ab, AX, ad cylindrum genitum
              <lb/>
            ab, AR, vt quadratum, FX, ad quadratum, FR, cylindrus item
              <lb/>
            genitusà, CX, ad eundem cy ndrum genitum ab, AR, eſt vt qua-
              <lb/>
            dratum, RX, ad quadratum, RF, ergo hoc cylindro dempto à cy-
              <lb/>
            lindro genito ab, AX, reliqua faſcia ſolida genita ex, AR, ad cy-
              <lb/>
            lindrum genitum ex eodem, AR, erit vt reſiduum quadrati, FX, ab
              <lb/>
            eo dempto quadi
              <unsure/>
            ato, RX, ad quadratum, FR, hanc ergo ratio-
              <lb/>
            nem habebit etiam anulus latus ellipticus altera parte ſtrictior ad
              <lb/>
            anulum ſtrictum ellipticum altera parte latiorem ex eadem ellipſi, B
              <lb/>
            DMG, genitum; </s>
            <s xml:id="echoid-s6924" xml:space="preserve">quia vero reſiduum quadrati, FX, dempto qua-
              <lb/>
            drato, RX, eſtrectangulum ſub, XR, RF, bis cum quadrato, FR,
              <lb/>
            ideſt rectangulum ſub, XF, FR, cum rectangulo ſub, XR, RF, .</s>
            <s xml:id="echoid-s6925" xml:space="preserve">i.
              <lb/>
            </s>
            <s xml:id="echoid-s6926" xml:space="preserve">rectangulum ſub compoſita ex, RX, XF, & </s>
            <s xml:id="echoid-s6927" xml:space="preserve">iub, FR, ideò dictus
              <lb/>
            anulus latus ad dictum anulum ſtrictum, erit vt rectangulum ſub
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            compoſita ex, RX, XF, & </s>
            <s xml:id="echoid-s6928" xml:space="preserve">ſub, FR, ad quadratum, FR, .</s>
            <s xml:id="echoid-s6929" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6930" xml:space="preserve">erit
              <lb/>
            vt compoſita ex, FX, XR, ad, RF, nempè vt, VR, ad, RF.</s>
            <s xml:id="echoid-s6931" xml:space="preserve"/>
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