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

Table of contents

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[431.] THEOREMA XVIII. PROPOS. XIX.
Page: 328 (308)
[432.] A. COROLL. SECTIO I.
Page: 328 (308)
[433.] B. SECTIO II.
Page: 329 (309)
[434.] C. SECTIO III.
Page: 329 (309)
[435.] D. SECTIO IV.
Page: 329 (309)
[436.] E. SECTIO V.
Page: 329 (309)
[437.] SCHOLIV M.
Page: 330 (310)
[438.] THEOREMA XIX. PROPOS. XX.
Page: 330 (310)
[439.] COROLLARIVM.
Page: 331 (311)
[440.] THEOREMA XX. PROPOS. XXI.
Page: 331 (311)
[441.] THEOREMA XXI. PROPOS. XXII.
Page: 332 (312)
[442.] THEOREMA XXII. PROPOS. XXIII.
Page: 333 (313)
[443.] COROLLARIVM.
Page: 334 (314)
[444.] THEOREMA XXIII. PROPOS. XXIV.
Page: 334 (314)
[445.] PROBLEMA II. PROPOS. XXV.
Page: 335 (315)
[446.] COROLLARIVM.
Page: 336 (316)
[447.] THEOREMA XXIV. PROPOS. XXVI.
Page: 337 (317)
[448.] THEOREMA XXV. PROPOS. XXVII.
Page: 337 (317)
[449.] COROLLARIVM I.
Page: 339 (319)
[450.] COROLLARIVM II.
Page: 339 (319)
[451.] THEOREMA XXVI. PROPOS. XXVIII.
Page: 340 (320)
[452.] COROLLARIVM.
Page: 341 (321)
[453.] THEOREMA XXVII. PROPOS. XXIX:
Page: 341 (321)
[454.] A. COROLL. SECTIO I.
Page: 341 (321)
[455.] B. SECTIO II.
Page: 342 (322)
[456.] C. SECTIO III.
Page: 342 (322)
[457.] D. SECTIO IV.
Page: 342 (322)
[458.] E. SECTIO V.
Page: 342 (322)
[459.] THEOREMA XXVIII. PROPOS. XXX.
Page: 343 (323)
[460.] A. COROLL. SECT IO I.
Page: 344 (324)
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            compoſitam ex duabus rationibus ibidem appoſitis. </s>
            <s xml:id="echoid-s10891" xml:space="preserve">Vt autem
              <lb/>
            fiat noſtrum exemplum, intelligatur in ipia (in qua dimittantur
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            aſymptoti, & </s>
            <s xml:id="echoid-s10892" xml:space="preserve">rectæ, ad, DC, OV, VX, PO, PX,) BD, eſſe axem,
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            circa quam reuoluatur figura, vt ex hypeibola, ADC, fiat conois
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              <figure xlink:label="fig-0437-01" xlink:href="fig-0437-01a" number="298">
                <image file="0437-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/05TCTFNR/figures/0437-01"/>
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            hyperbolica, ADC; </s>
            <s xml:id="echoid-s10893" xml:space="preserve">vlterius per,
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            OX, traducatur planum, OX, ere-
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            ctum plano genitricis hyperbolæ,
              <lb/>
            ADC, cuius pars in conoide con-
              <lb/>
            cepta erit ellipſis, OX, cuius maior
              <lb/>
            diameter, OX, minor autem in fi-
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            gura propoſitionis linea, PO, ha-
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            bemus igitur ex Prop. </s>
            <s xml:id="echoid-s10894" xml:space="preserve">11. </s>
            <s xml:id="echoid-s10895" xml:space="preserve">conoi-
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            dem, ADC, ad conoidem, OVX,
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            habere rationem compoſitam ex
              <lb/>
            ratione rectanguli ſub, MB, HI,
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            ad rectangulum ſub, RI, FB, & </s>
            <s xml:id="echoid-s10896" xml:space="preserve">ex
              <lb/>
              <note position="right" xlink:label="note-0437-01" xlink:href="note-0437-01a" xml:space="preserve">43. l. 1.
                <lb/>
              Coro. 44.
                <lb/>
              l. 1.</note>
            ratione parallelepipedi ſub altitu-
              <lb/>
            dine hyperbolæ, ADC, baſi qua-
              <lb/>
            drato, AC, ad parallelepipedum ſub altitudine hyperbolæ, OVX,
              <lb/>
            baſi autem rectangulo ſub, XO, OP, veluti ſunt omnia quadrata
              <lb/>
            hyperbolæ, ADC, regula, AC, ad omnia rectangula hyperbolæ,
              <lb/>
            OVX, (regula, OX,) ſimilia rectangulo ſub, XO, OP, ſiue omnes
              <lb/>
            circuli eiuſdem ad omnes ellipſes hyperbolæ, OVX, ſimiles ellipſi,
              <lb/>
              <note position="right" xlink:label="note-0437-02" xlink:href="note-0437-02a" xml:space="preserve">Corol. 2.
                <lb/>
              33. l. 2.</note>
            cuius coniugati axes, vel diametri ſunt, XO, OP, XO, maior, OP,
              <lb/>
            minor, nam omnes dicti circuli ſunt omnia plana conoidis, ADC,
              <lb/>
            regula, AC, & </s>
            <s xml:id="echoid-s10897" xml:space="preserve">dictæ omnes ellipſes ſunt omnia plana conoidis, O
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            VX, eandem autem rationem ſupradictæ comperiemus habere
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            quæcunq; </s>
            <s xml:id="echoid-s10898" xml:space="preserve">lolida non quidem ſimilaria inter ſe, ſed quorum om-
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            nia plana ſint omnes figuræ ſimiles genitricium figurarum, ADC,
              <lb/>
            OVX, a quibus genita dicuntur, quæ habeant inter ſeeandem ra-
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            tionem ei, quam habet quadratum, AC, ad rectangulum, XOP.</s>
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          <head xml:id="echoid-head611" xml:space="preserve">COR OLLARIVM XII.</head>
          <p>
            <s xml:id="echoid-s10900" xml:space="preserve">IN Propoſ. </s>
            <s xml:id="echoid-s10901" xml:space="preserve">12. </s>
            <s xml:id="echoid-s10902" xml:space="preserve">conſpecta illius figura, & </s>
            <s xml:id="echoid-s10903" xml:space="preserve">completis conoidibus,
              <lb/>
            BAD, HMQ, patet eorum rationem eſſe compoſitam ex ra-
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            tionibus ibi explicatis, vbi videri poterunt. </s>
            <s xml:id="echoid-s10904" xml:space="preserve">Quas quidem ratio-
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            nes comperiemus etiam habere quæcunq; </s>
            <s xml:id="echoid-s10905" xml:space="preserve">ſolida, licet etiam non
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            ſimilaria ad inuicem, genita tamen ex eildem figuris, quarum om-
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            nes figuræ ſimiles (inter ſe, quę ſunt vnius, vtriuſq; </s>
            <s xml:id="echoid-s10906" xml:space="preserve">tamen figuræ
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            genitricis diſſimiles) habeant eandem rationem, quam </s>
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