Cavalieri, Buonaventura
,
Geometria indivisibilibvs continvorvm : noua quadam ratione promota
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LIBER III.
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homologa ſunt æqualia, ergo etiam, BC, æquabitur ipſi, FM, &</
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CG, ipſi, DF, eſt autem, AC, æqualis ipſi, FR, &</
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<
s
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xml:space
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">, AF, ipſi, C
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R, ergo reliqua, AB, æquabitur reliquæ, MR, & </
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<
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xml:space
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">reliqua, AD, re-
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liquæ, GR; </
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<
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xml:space
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">ſuntigitur portiones laterum parallelogrammi, AR,
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coalterne tangentes inter ſe æquales.</
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<
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</
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<
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<
s
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xml:space
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">Sumantur nunc vtcunque duæ coalternè tangentes, AD, RG,
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& </
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<
s
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xml:space
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">ab ipſis verſus puncta contactuum, DG, abſcindantur vtcunque
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duæ rectæ æquales, PD, VG, & </
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<
s
xml:id
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echoid-s6328
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xml:space
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preserve
">per puncta, PV, ducantur baſi,
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FR, parallelæ, PQ, EV, ſecantes curuam ellipſis in punctis, HI,
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ipſa, PQ, & </
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<
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xml:space
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">in punctis, NO, ipſa, EV. </
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<
s
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xml:space
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">Quoniam ergo, AB, A
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D, tangunt ellipſim, BDMG, coincidentes in puncto, A, eſt au-
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tem, QP, parallela vni tangentium. </
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<
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<
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xml:space
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lipſis in, H, & </
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<
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">aliam tangentem in, P, rectangulum ergo, IPH, ad
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<
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note
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quadratum, PD, erit vt quadratum, BA, ad quadratum, AD,. </
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<
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</
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<
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<
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xml:space
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">conſimili modo oſtende-
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mus rectangulum, NVO, ad quadratum, VG, eſſe vt quadratum,
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MR, ad quadratum, RG, . </
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<
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">i. </
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<
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xml:space
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">vt rectangulum, IPH, ad quadratum,
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PD, vel ad quadratum, VG, ergo rectangulum, IPH, eſt æquale
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rectangulo, NVO. </
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<
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xml:space
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">Nunc oſtendemus, PH, eſſe æqualem ipſi, O
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V, conſideremus duo quadrilatera, APXB, MTVR, quæ ſunt ſi-
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milia polygona, nam angulus, PAB, eſt æqualis angulo, MRV,
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&</
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<
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xml:space
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">, ABX, ipſi, RMT, tum, BXP, ipſi, MTV, & </
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<
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A, ipſi, TVR, quę facilè apparent, & </
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xml:space
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">duo latera, AB, MR, ſunt
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æqualia, vt etiam, AP, RV, ergo reliqua latera erunt æqualia, quę
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æqualibus adiacent angulis, vnde, TV, erit æqualis ipſi, PX, &</
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<
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MT, ipſi, BX, vnde rectangulum, MTB, æquabitur rectangulo,
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MXB, & </
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<
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xml:space
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">quoniam, vt rectangulum, MTB, ad rectangulum, M
<
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<
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xml:space
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">Ex 40, 1.
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lib. & eiu.
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ldẽ Scho-
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lio.</
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XB, ita quadratum, TO, ad quadratum, XI, quoniam, NO, H
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I, ſunt parallelæ tangenti, AC, & </
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metrum, BM, erit ergo quadratum, TO, æquale quadrato, XI,
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&</
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<
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">, TO, ipſi, XI, vel, HX, ergo reliqua, OV, erit æqualis reli-
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quæ, PH, & </
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<
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xml:space
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">quia rectangulum, IPH, eſt æquale rectangulo, N
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VO, erit, IP, æqualis ipſi, NV, & </
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<
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erit, HI, æqualis, NO, & </
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<
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ctangulo, NOV.</
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">Vel breuius ſic proceſſiſſet demonſtratio, dimiſſo Apollonij theo-
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remate, oſtenſo. </
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<
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<
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<
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xml:space
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">, TO, ipſi, XI,
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manet oſtenſum, NO, æquari ipſi, HI, quoniam, NO, HI, bi-
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faria diuiduntur a diametro, BM, & </
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<
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rectangulum, NOV, æquari rectangulo, IHP, quod oſtendere
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oportebat.</
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