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

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11090GEOMETRI Æ byperbolam hic babentur, circa ſectiones oppoſitas, quirum communes
ſunt dictæ paſſiones, quoq; intelligi poſſe. Eadem verò nedum in dictis
integris ſolidis, ſed etiam in eorum portionibus, ſiue in portionibus ſe-
ctionum coni abſciſſis per line as ad earum axim, vel diametrum ordina-
tim ductas, pariter verificari manifeſtum eſt.

LEMMA.

PRopoſitis duabus quibuſcumq; ſimilibus figuris, duæ quæuis re-
ctæ lineæ earum homologę poterunt eſſe incidentes, vel in ipſis
productis reperientur ſaltem earum incidentes, & oppoſitarum tan-
gentium, quibus ipſæ incidunt ad eundem angulum ex eadem parte,
erunt autem dictæ homologæ ſemper inuentarum incidentium par-
tes proportionales.

Sint duæ quæcunq; ſimiles figuræ planæ, IQsP, 487R, in eiſ-
que duæ quælibet homologę, Is, 47. Dico has eſſe vel incidentes,
vel in eiſdem productis reperiri poſſe incidentes prædictarum figura-
rum, & oppoſitarum tangentium, quibus occurrant ipſæ homolo-
gæ, productæ, ad eundem angulum ex eadem parte, quales ſint, D
L, dO; pu, g Y. Ducantur autem vlterius oppoſitę tangentes, quę

62[Figure 62] ſunt regulæ homologarum,
ls, 47, ipſæ, Ad, Co; F
g, KZ, quarum, & dicta-
11Corol. 19.
& p. 24. rum figurarum incidentes
ſint, AC, FK, parallelæ
2223. huius. ipſis, DL, pu, hoc . n. fieri
33Coroll.
2. 19. & p.
24. poteſt; erunt autem etiam
ipſæ, d O, g Y, regulæ ho-
mologarum, cum faciant
angulos æquales cum regu-
lis, dA, gF, vt ſuppono,
& inueniri poterunt earum,
& dictarum figurarum inci-
dentes parallelæ eiſdem, A
d, Fg, ſint ipſę, LO, uY,
tales incidentes: Vel ergo
homologæ datæ, ls, 47,
terminantur ad oppofitas
tangentes, DL, dO; pu,
gY, velnon, & tunc producantur, & ipſis incidant in punctis, E,
f; ℟, & , & vlterius productæ vſque ad, AC, FK, ſecent ipſas in
punctis, B, G. Vlterius vel, Ho, XZ, tangunt ſetotis, vel

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