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

Table of contents

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[241.] G. SECTIO VII.
Page: 177 (157)
[242.] H. SECTIO VIII.
Page: 178 (158)
[243.] I. SECTIO IX.
Page: 178 (158)
[244.] K. SECTIO X.
Page: 178 (158)
[245.] L. SECTIO XI.
Page: 178 (158)
[246.] THEOREMA XXIV. PROPOS. XXIV.
Page: 179 (159)
[247.] COROLLARIVM.
Page: 180 (160)
[248.] THEOREMA XXV. PROPOS. XXV.
Page: 181 (161)
[249.] THE OREMA XXVI. PROPOS. XXVI.
Page: 183 (163)
[250.] COROLLARIVM I.
Page: 185 (165)
[251.] COROLLARIVM II.
Page: 186 (166)
[252.] COROLLARIVM III.
Page: 186 (166)
[253.] THEOREMA XXVII. PROPOS. XXVII.
Page: 187 (167)
[254.] THEOREMA XXVIII. PROPOS. XXVIII:
Page: 188 (168)
[255.] COROLLARIVM.
Page: 189 (169)
[256.] THEOREMA XXIX. PROPOS. XXIX.
Page: 190 (170)
[257.] COROLLARIVM.
Page: 190 (170)
[258.] THEOREMA XXX. PROPOS. XXX.
Page: 191 (171)
[259.] COROLLARIVM.
Page: 192 (172)
[260.] THEOREMA XXXI. PROPOS. XXXI.
Page: 193 (173)
[261.] COROLLARIVM.
Page: 194 (174)
[262.] THEOREMA XXXII. PROPOS. XXXII.
Page: 195 (175)
[263.] COROLLARIVM.
Page: 196 (176)
[264.] THEOREMA XXXIII. PROPOS. XXXIII.
Page: 197 (177)
[265.] COROLLARIVM I.
Page: 198 (178)
[266.] COROLLARIVM II.
Page: 199 (179)
[267.] THEOREMA XXXIV. PROPOS. XXXIV.
Page: 199 (179)
[268.] COROLLARIVM I.
Page: 201 (181)
[269.] COROLLARIVM II.
Page: 201 (181)
[270.] COROLLARIVM III.
Page: 201 (181)
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            <s xml:id="echoid-s6914" xml:space="preserve">
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            tem axim, TX, igitur cyhndrus genitus in reuolutione ex, AX,
              <lb/>
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                <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
              <lb/>
            ellipſi, BDMG, erit vt,
              <lb/>
            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-
              <lb/>
            ſam duabus, FA, RC,
              <lb/>
            verſus, A, C, puncta pro-
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            ductis: </s>
            <s xml:id="echoid-s6916" xml:space="preserve">vocetur autem ſo-
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            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"/>
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        <div xml:id="echoid-div683" type="section" level="1" n="399">
          <head xml:id="echoid-head417" xml:space="preserve">SECTIO II.</head>
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            <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-
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            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-
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            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
              <lb/>
            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
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            vt compoſita ex, FX, XR, ad, RF, nempè vt, VR, ad, RF.</s>
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