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

Table of contents

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[281.] L. SECTIO XI.
Page: 206 (186)
[282.] M. SECTIO XII.
Page: 206 (186)
[283.] N. SECTIO XIII.
Page: 207 (187)
[284.] THEOREMA XXXV. PROPOS. XXXV.
Page: 207 (187)
[285.] SCHOLIV M.
Page: 208 (188)
[286.] THEOREMA XXXVI. PROPOS. XXXVI.
Page: 208 (188)
[287.] THEOREMA XXXVII. PROPOS. XXXVII.
Page: 209 (189)
[288.] COROLLARIVM.
Page: 210 (190)
[289.] THEOREMA XXXVIII. PROPOS. XXXVIII.
Page: 210 (190)
[290.] SCHOLIVM.
Page: 211 (191)
[291.] THEOREMA XXXIX. PROPOS. XXXIX:
Page: 211 (191)
[292.] THEOREMA XL. PROPOS. XL.
Page: 212 (192)
[293.] COROLLARIVM.
Page: 212 (192)
[294.] THEOREMA XLI. PROPOS. XLI.
Page: 212 (192)
[295.] THEOREMA XLII. PROPOS. XLII.
Page: 213 (193)
[296.] COROLLARIVM.
Page: 214 (194)
[297.] SCHOLIVM.
Page: 215 (195)
[298.] Finis Secundi Libri.
Page: 215 (195)
[299.] CAVALERII LIBER TERTIVS. In quo de circulo, & Ellipſi, ac ſolidis ab eiſdem genitis, traditur doctrina.
Page: 217 (197)
[300.] THEOREMA I. PROPOS. I.
Page: 217 (197)
[301.] COROLLARIVM.
Page: 219 (199)
[302.] THEOREMA II. PROPOS. II.
Page: 220 (200)
[303.] THEOREMA III. PROPOS. III.
Page: 221 (201)
[304.] THEOREMA IV. PROPOS. IV.
Page: 223 (203)
[305.] THEOREMA V. PROPOS. V.
Page: 224 (204)
[306.] COROLLARIV M.
Page: 225 (205)
[307.] THEOREMA VI. PROPOS. VI.
Page: 226 (206)
[308.] COROLLARIVM.
Page: 228 (208)
[309.] THEOREMA VII. PROPOS. VII.
Page: 228 (208)
[310.] PROBLEMA I PROPOS. VIII.
Page: 229 (209)
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            HF, ad circulum, vel ellipſim, MB, EG. </s>
            <s xml:id="echoid-s6686" xml:space="preserve">Reuoluatur, HO, cir-
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            ca manentem axem, CO, modo ſuprad cto, ex, HO, igitur fiet cy-
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            lindrus, H ℟, & </s>
            <s xml:id="echoid-s6687" xml:space="preserve">ex figura, CMBEO, fiet quoddam ſolidum ſimi-
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            lare prædicto cylindro, auferatur à cylindro, H ℟, cylindrus, NL,
              <lb/>
            defcriptus ab, NO, & </s>
            <s xml:id="echoid-s6688" xml:space="preserve">à prædicto ſolido ſimilari auferatur ſolidum
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            ſimilare genitum ex figura, MGEOC. </s>
            <s xml:id="echoid-s6689" xml:space="preserve">Dico nos iam compertum
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            habere reſiduum primum. </s>
            <s xml:id="echoid-s6690" xml:space="preserve">i. </s>
            <s xml:id="echoid-s6691" xml:space="preserve">faſciam ſolidam cylindricam (vtita di-
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              <figure xlink:label="fig-0290-01" xlink:href="fig-0290-01a" number="184">
                <image file="0290-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0290-01"/>
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            cam) HFLK, ad reſiduum ſecundum, ad ſolidum, inquam, quod
              <lb/>
            gignitur ex reuolutione circuli, vel ellipſis, MBEG, effe vt, HF,
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            ad ipſum circulum, vel ellipſim, MBEG; </s>
            <s xml:id="echoid-s6692" xml:space="preserve">quod etiam patet de re-
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            fiduis quorumlibet ſimilarium ſolidorum ex, HO, & </s>
            <s xml:id="echoid-s6693" xml:space="preserve">figura, MBE
              <lb/>
            OC, genitorum, demptis ſolidis ſimilaribus genitis ex, NO, & </s>
            <s xml:id="echoid-s6694" xml:space="preserve">fi-
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            gura, MGEOC, vt ſupra diximus. </s>
            <s xml:id="echoid-s6695" xml:space="preserve">Vocetur autem ſolidum, quod
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            in ſupradicto exemplo, & </s>
            <s xml:id="echoid-s6696" xml:space="preserve">figura gignitur ex reuolutione circuli, vel
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            ellipſis, MBEG, Anulus latus circularis, ſi, MBEG, ſit circulus,
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            vel, Anulus latus ellipticus, ſi, MBEG, ſit ellipſis.</s>
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          <head xml:id="echoid-head396" xml:space="preserve">COROLL. XV. SECTIO PRIMA.</head>
          <p>
            <s xml:id="echoid-s6698" xml:space="preserve">IN Prop. </s>
            <s xml:id="echoid-s6699" xml:space="preserve">17. </s>
            <s xml:id="echoid-s6700" xml:space="preserve">colligitur ſolidum ſimilare genitum ex, HF, ad fo-
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            lidum ſimilare genitum ex figura, NMBEF, eſſe vt, HF, ad
              <lb/>
            circulum, vel ellipſim, MBEG, vna cum reſiduo, quod remanet,
              <lb/>
            ſi à rectangulo, MG, dematur quarta circuli, vel ellipſis, MAG,
              <lb/>
            ablato inſimul exceſſu, quo eadem quarta ſuperat duas tertias rectan-
              <lb/>
            guli, MG. </s>
            <s xml:id="echoid-s6701" xml:space="preserve">Conſpiciatur ergo exemplum in figura Coroll. </s>
            <s xml:id="echoid-s6702" xml:space="preserve">13. </s>
            <s xml:id="echoid-s6703" xml:space="preserve">huius,
              <lb/>
            patebit ergo cylindrum, H ℟, ad ſolidum genitum ex figura, NM
              <lb/>
            BEF, habere ſupradictam rationem, que eſt proximè, vt 21. </s>
            <s xml:id="echoid-s6704" xml:space="preserve">ad 17.
              <lb/>
            </s>
            <s xml:id="echoid-s6705" xml:space="preserve">vt in Propof. </s>
            <s xml:id="echoid-s6706" xml:space="preserve">17. </s>
            <s xml:id="echoid-s6707" xml:space="preserve">huius oſtenditur. </s>
            <s xml:id="echoid-s6708" xml:space="preserve">Vocetur autem ſolidum </s>
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