## Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ T, & cęteris vt ibidem conſtructis, eodem modo prius oſtende-
mus vt ibitriangula, AFE, KZT, necnon, AFG, KZY, EFG, TZ
Y, & AGE, KYT, eſſe inter ſe ſimilia, & angulum, PGE, æquari
angulo, XYT. Hoc ſuppoſito, cum, PG, ad, GA, ſit vt, XY, ad,
YK, & , AG, ad GE, vt, KY, ad, YT, exæquali, PG, ad GE, erit vt, X
Y, ad, YT, & ſunt circa æquales angulos, PGE, XYT, ergotrian-
gula, PGE, XYT, ſunt ſimilia, ergo, PE, ad, EG, eſt vt, XT, ad,
TY, & , GE, ad, EA, vt, YT, ad, Tk, ergo, PE, ad, EA, eſt vt, X
T, ad, TH, & ſunt circa rectos, PEA, XTK, ergo triangula, PEA,
XTk, ſunt ſimilia, ergo, AP, ad, PE, erit vt, KX, ad, XT, ſed & ,
XY, & , PG, ad, GA, eſt vt, XY, ad, Yk, ergo triangula, APG, kXY,
ſunt ſimilia, rectus autem eſt angulus, AGP, cum rectus ponatur,
AGV, ergo, kYX, & , ΚΥΔ, rectus erit, vnde anguli, AGV, κΥΔ ę-
rectus erit, & conſequenter etiam rectus ipſe, XYT, vnde anguli,
AGE, kYT, erunt inclinationes ſecundorum planorum, AV, ΚΛ,
cum ſubiectis planis, HV, & Δ, & inter ſe ęquales, per quę ſuppo-
ſito caſui ſatisfieri maniſeſtum eſt.

### 692.1.

6. Sex. Ele.
6. Sex. Ele.
5. Sex. Ele.
47. Primi
Elem.
48. Primi
Elem.
Deſin. 6.
Vnd, Ele.

In Lemmate 5. poſt Prop. 8. prętermiſſa fui demonſtratio prę-
ſentis caſus, cum eadem facilis exiſtimaretur, nempè quando, FE,
FG, cum, AE, AG, & , LI, LM, cum, HI, HM, concurrere mini-
me poſſe contingat, vt cum angulos, EAF, GAF, IHL, MHL, re-
ctos, vel recto maiores acciderit eſſe: Sic autem tum hic, tum ſup-
poſitus ibi caſus poterit vniuerſaliter demonſtrari. Intelligantur
ipſę, AE, AF, AG, HI, HL, HM, inter ſe ęquales, & iungantur,
EF, FG, EG, IL, LM, IM: Cum ergo anguli, FAG, LHM, ſup-
ponantur ęquales, & latera, FA, LH, & , AG, HM, ęqualia, erunt
pariter baſes, FG, LM, æquales: Sic autem probabimus tum, EF,
IL, tum, EG, IM, inter ſe æquales eſſe. Rurſus ſuſpenſa pyrami-
de, AEFG, ponatur, F, in, L, demittaturq; FG, ſuper, LM, cui cõ-
gruet, & triangulo, EFG, cadente ſuper, ILM, punctum, E, pari-
ter erit in, I; Sed & punctum, A, dico fore in, H, tres enim ſphæ-
ricæ ſuperficies ſuper centris, I, L, M, radijs inuicem ſe ſecantibus
deſcriptæ, nempè radijs, HI, HL, HM, ſeu, AE, AF, AG, in duo-
bus tantum punctis ſeſe decuſſare poſſunt, vt facile oſtendi poteſt,
duę enim quęlibet ſphæricæ ſuperficies in circuli periphæria ſe ſe-

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