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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            guli, ad portionem parabolæ dicto parallelogrammo inſcri-
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            ptam ratio nota erit.</s>
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          <p>
            <s xml:id="echoid-s7030" xml:space="preserve">Sit parabola, cuius baſis, FG, ad axim, vel diametrum, CX, or-
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            dinatim applicata; </s>
            <s xml:id="echoid-s7031" xml:space="preserve">ad baſim autem, FG, ſit etiam ordinatim appli-
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            cata, AN, vtcunq; </s>
            <s xml:id="echoid-s7032" xml:space="preserve">diuidens baſim, FG, in puncto, N, ſiat autem
              <lb/>
            parallelogrammum, RN, & </s>
            <s xml:id="echoid-s7033" xml:space="preserve">triangulum, AFN, ſublateribus, A
              <lb/>
            N, NF, vel ſub, AN, NG; </s>
            <s xml:id="echoid-s7034" xml:space="preserve">Vel ſint duæ vtcunque ad baſim, FG,
              <lb/>
            ordinatim applicatæ, AN, CX, ſiat autem parallelogrammum, & </s>
            <s xml:id="echoid-s7035" xml:space="preserve">
              <lb/>
            triangulum ſub, AN, NX, vel ſub, CX, XN. </s>
            <s xml:id="echoid-s7036" xml:space="preserve">Dico parallelogram-
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              <figure xlink:label="fig-0309-01" xlink:href="fig-0309-01a" number="203">
                <image file="0309-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0309-01"/>
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            mum, RN, veltrian-
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            gulum, FAN, ad
              <lb/>
            portionem, AFN,
              <lb/>
            parabole, FCG, pa-
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            rallelogrammo, RN,
              <lb/>
            inſcriptam, eſſe in ra-
              <lb/>
            tione nota. </s>
            <s xml:id="echoid-s7037" xml:space="preserve">Similiter
              <lb/>
            parallelogrammum,
              <lb/>
            ZX, & </s>
            <s xml:id="echoid-s7038" xml:space="preserve">triangulum,
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            NCX, ad portio-
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            nem, ACXN, habe-
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            re rationem notam.
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            </s>
            <s xml:id="echoid-s7039" xml:space="preserve">Producatur, CX, vt-
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            cunque in, E, & </s>
            <s xml:id="echoid-s7040" xml:space="preserve">cir-
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            ca ſemiaxes, vel ſemi-
              <lb/>
            diametros coniuga-
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            tas, FX, XE, intel-
              <lb/>
            ligatur deſcriptus ſe-
              <lb/>
            micirculus, velſemi-
              <lb/>
            ellipſis, FEG, pro-
              <lb/>
            ducantur deinde, RF, ZN, indeſinitè, ſecetque, ZN, curuam ſe-
              <lb/>
            micirculi, vel ſemiellipſis, FEG, in puncto, O, & </s>
            <s xml:id="echoid-s7041" xml:space="preserve">compleantur pa-
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            rallelogramma, VN, RX, ſumatur deindein, FN, vtcunq; </s>
            <s xml:id="echoid-s7042" xml:space="preserve">pun-
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            ctum, S, per quodipſi, CE, parallela ducatur, YT, ſecans curnam
              <lb/>
            parabolæ in, I, curuam autem, FEG, in, M; </s>
            <s xml:id="echoid-s7043" xml:space="preserve">eſt ergo, AN, ad, I
              <lb/>
              <note position="right" xlink:label="note-0309-01" xlink:href="note-0309-01a" xml:space="preserve">Exantec.</note>
            S, vt rectangulum, GNF, ad rectangulum, GSF, eſt autem etiam
              <lb/>
              <note position="right" xlink:label="note-0309-02" xlink:href="note-0309-02a" xml:space="preserve">40. Et
                <lb/>
              Sch. 1. 1.</note>
            quadratum, ON, ad quadratum, SM, vt rectangulum, GNF, ad
              <lb/>
            rectangulum, GSF, ergo, AN, vel, YS, ad, SI, erit vt quadra
              <lb/>
            tum, NO, vel vt quadratum, TS, ad quadratum, SM, ſunt au-
              <lb/>
            tem, RN, NV, parallelogramma in eiſdem baſibus, & </s>
            <s xml:id="echoid-s7044" xml:space="preserve">altitudini-
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              <note position="right" xlink:label="note-0309-03" xlink:href="note-0309-03a" xml:space="preserve">Coroll.3.
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              26. lib. 2.</note>
            bus cum portionibus, AFN, NFO, & </s>
            <s xml:id="echoid-s7045" xml:space="preserve">punctum, S, ſumptum eſt
              <lb/>
            vtcunque, repertumque eſt, vt, YS, ad, SI, ita eſſe quadratum, </s>
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