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

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

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8666GEOMETRIÆ ad, PI, vt, dY, ad, dX, ergo ex æquali, KP, ad, PI, erit vt, u
d, ad, dX, eſt autem, PI, ad, IK, vt, dX, ad, Xu, ergo trian-
gula quoque, PKI, duX, pariter ſimilia erunt, vnde anguli, LP
I, YdX; PIK, dXu, & , IKL, XuY, æquales erunt. Ducantur
nunc in planis figurarum, LHMP, YVZd, à punctis, L, Y, pa-

45[Figure 45] rallelæ, KN, ug, ipſæ, L3,
Y4. Cum igitur anguli, LK
I, YuX, ſint ęquales, etiam,
KL3, uY4, æquales erunt,
11Corol. 27
huius. ſed & , KLP, uYd, ſuntæ-
quales, ergo reſidui quoque, 3
LP, 4Yd, erunt ęquales, vn-
de cum ipſæ, L3, Y4, con-
tineant cum lateribus homo-
logis, LP, Yd, ad eandem
partem angulos æquales, e-
runt regulę homologarum ſi-
milium figurarum, LHMP,
YVZd, vnde etiam ipſæ, K
N, ug, velipſæ OS, fp, e-
runt regulæ homologarum
earundem, ſunt. n. OS, KN,
parallelæ, vt etiam, ug, fp,
vnde omnes homologæ ſimi-
lium figurarum, LHMP, Y
VZd, ipſis regulis, OS, fp,
æquidiſtabunt, quod & de cę-
teris eodem modo oſtende-
tur, dumſectio fiet in figuris,
AESo, Tlps. Quod ſi fi-
guris, AESO, Tlps, aliæ
figuræ planæ continuarentur
citra cõtactum planorum ba-
ſibus oppoſitorum, cum his
in lateribus homologis, AE,
Tl, conuenientes, quibus eſ-
ſent inclinatę, parum diſſimili
methodo, producentes, OB,
fQ, vſq; ad tangentia plana, & occurſuum puncta cum ipſis, S, p,
iungentes, necnon extrema laterum homologorum, qualia fuerunt,
LP, Yd, cum extremis rectarum in triangulis (qualia fuerunt, BO
S, Qfp,) productarum, panter iungentes, vt fecimus cum ipſis,

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