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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