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

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6343LIBERI. E, ad, BD, ita, CA, ad, AB, ergo vt, CM, ad, MB, ita erit, C
A, ad, AB, diuidendo, CB, ad, BM, erit vt, CB, ad, BA, er-
go, MB, erit æqualis ipſi, BA, totum parti, quod eſt abiurdum,
non igitur, ED, producta tranſit ſupra, A, eodem modo oſtende-
mus non tranfire infra, A, ergo tranſibit per, A, ergo tria puncta,
A, D, E, erunt in recta linea, AE, quod erat oſtendendum.

THEOREMA XX. PROPOS. XXIII.

SI duarum quarumlibet ſimilium figurarum habeamus
homologas cum duabus quibuſdam regulis, habebi-
mus etiam homologas earundem cum duabus quibuſuis a-
lijs, cum prædictis angulos æquales ad eandem partem fa-
cientibus.

Patet hęc propoſitio, nam quæcunq; figuræ planę ſimiles, ſi ſint
æquales, & ſimiliter poſitæ, poſſunt eſſe cuiuſdam cylindrici oppo-
1114. Huius. ſitæ baſes, ſi ſint inæquales, oppoſitæ bales fruſti conici, in his au-
2222. Huius tem contingit, ſi habeamus homologas cum duabus quibuſdam re-
33Corol. 9.
& 11. hus
ius. gulis, nos eaſdem habere cum alijs duabus quibuſcumque cum præ-
dictis angulos æquales ad eandem partem conſtituentibus, ergo hoc
in quibuſcumque planis ſimilibus figuris verificatur, quod eſt pro-
poſitum.

COROLLARIVM.

_E_T quia incidentes ad homologarum ſimilium figurarum regulas an-
44_B. Def. 10._ gulos ad eandem partem efficiunt æquales, ideò & ipſæ incidentes
erunt homologarum earundem ſimilium figurarum regulæ, & vice verſa
in quibuſdam regulis homologarum poterunt ſumi earum incidentes.

THEOREMA XXI. PROPOS. XXIV.

SI in duarum ſimilium figurarum oppoſitas tangentes, quę
earundem homologarum ſint regulæ, incidant duæ re-
ctæ lineæ ad eundem angulum ex eadem parte eaſdem ſe-
cantes, ductis verò quibuſdam duabus, prædictis tangenti-
bus parallelis, in dictis figuris, quæ ſecantes diuidant ſimi-
liter ad eandem partem, vel aſſumptis ipſis oppoſitis tangen-
tibus, reperiamus harum portiones inter incidentes, &

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