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

8868GEOMETRIÆ regulis aſſumamus iterum ipſas, OS, fp, eiſdem quoque æquidiſta-
11Fuxta def.
10. huius. bunt, ergo in eiſdem figuris habebimus etiam homologas alias ęqui-
diſtantes regulis quibuſcumque cum ipſis, OS, fp, angulos æqua-
les ad eandem partem continentibus, cum ergo ipſæ, GO, 8f, an-
22Jmin s. 2 gulos æquales cum ipſis, OS, fp, ad eandem partem contineant,

46[Figure 46] ideò omnium homologæ pa-
riter duabus, GO, 8f, tan-
quam nouis regulis ęquidiſta-
bunt, iſtis autem, quæ tan-
gunt ex vna parte figuras, G
FSO, 8 & pf, ducantur ex
alia parte oppoſitæ tangen
tes, FD, & ℟, ita vt incidant
duę, GO, FD, plano, BD,
in punctis, O, D, & duæ, 8
f, & ℟, plano, Q℟, in pun-
ctis, f, ℟, ſint autem iunctæ,
OD, f℟. Similiter figurarum,
HMPL, VZdY, ſint ductę
oppoſitæ tangentes præfatis
regulis, GO, 8f, parallelæ,
planis, BD, Q℟, occurren-
tes in punctis, K, N; ug, iun-
gantur autem, KN, ug, &
ita cæterarum ſic producibi-
lium figurarum intelligantur
ductæ oppoſitæ tangentes ip-
ſis, GO, 8f, parallelæ, &
productæ vſque ad plana, B
D, Q℟, punctaq; occurſuum
iuncta rectis lineis, per qua-
rum omnium extrema tran.
ſeant lineæ, BO, CD, Qf,
R℟. Cum ergo, GO, 8f,
ſint homologarum regulæ, ac
oppoſitę tangentes figurarum
ſimilium, OGFS, f8 & p,
incidant autem illis ad eun-
dem angulum ex eadem parte, OD, f℟, & ſit, GO, ad, f8, vt, O
D, ad, f℟, ideo, OD, f℟, erunt incidentes ſimilium figurarum,
3314. huius. OGFS, f8& p, & oppoſitarum tangentium, GO, FD, 8f, &
℟. Similiter in figuris, HMPL, VZdY, oſtendemus eſſe

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