Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ quæ ita inuicem ſuperponantur, vt, BC, FG, ſibi congruant, & ipſæ ſint ſimiliter poſitæ. Dico etiam ipſas figuras ad inuicem fore
congruentes. Sint oppoſitæ tangentes ductæ pro figura, ABXC,
ipſæ, AD, XQ, regula, BC, & pro figura, EFPG, regula, F
G, ipſæ, EM, PN, quarum figurarum, ac oppoſitarum tangen-
tium ſint quoque incidentes ipſę, DQ, MN, productis verò, BC,
FG, verſus, DQ, MN, illis incidant in punctis, O, R, & ſuper-
ponatur figura, ABXC, figuræ, EFPG, ita vt, BC, congruat
ipſi, FG, & ſint ſimiliter poſitę: Erunt ergo ipſæ incidentes, DQ,
MN, ad eandem partem figurarum iam ſuperpoſitarum, & inuicem
parallelæ, vel congruentes, ſed in noſtro caſu erunt congruentes,
cum enim vt, BC, ad, FG, ita ſit, DQ, ad, MN, ipſæ verò, B
C, FG, ſint ęquales, etiam, DQ, MN, ęquales erunt, ſicut etiam,
CO, GR, (quæ ſunt inter ſe vt, DQ, MN,) ergo cum punctus,
B, poſitus ſit in, F, erit, O, in, R, & DQ, extenſa ſuper, MN,
& cum etiam, DO, MR, ſint ęquales
punctus, D, erit in, M, ſic autem oſten-
demus quoque punctum, Q, cadere in,
N, & conſequenter, XQ, cadere ſuper,
PN, & , AD, ſuper, EM, ſi ergo figu-
ra, ABXC, cadens ſuper, EFPG, non
congruit illi, eſto quod ceciderit, ſi poſ-
ſibile eſt vt, FVIG, ita vt ambitus ex-
tra ambitum cadat, ſumpto autem quo-
cunque puncto, I, qui ſit in ambitu fi-
guræ, VFPGI, ſed cadens non in am-
bitu figuræ, EFPG, per ipſum duca-
tur, TZ, parallela, EM, ſecans, MN,
in, Z, ambitum figuræ, VPI, in, V, I, & ambitum figuræ, EF
PG, in, T, S, erunt autem homologę, VI, TS, & inter ſe ęqua-
les cum ſint, vt incidentes, DQ, MN, quæ ſunt ęquales, necnon
æquales reliquæ vſq; ad incidentes, nempè, SZ, IZ, quod eſt ab-
ſurdum, punctus enim, I, non eſt in S, non ergo cadet ambitus fi-
guræ, ABXC, ſuperpoſitę, ipſi, EFPG, vt dictum eſt, extra am-
bitum eiuſdem figurę, EFPG, igitur cadet ſuper illius ambitum, & ipſę figurę erunt ſibi inuicem congruentes, quod oſtendendum erat.

97.1.

D. Defin.
10.
Coroll. 1.
huius.
B. Def. 10.
D. Defin.
10.
A. Def. 10.
0066-01
C. Defin.
10.
A. Defin.
10.

98. COROLLARIVM.

EX hoc inſuper colligitur figuras quaſcumq; planas ſimiles ab æqua-
libus rectis lineis, tanquam ab bomologis, deſcriptas interfé æqua-
les eſſe, cum ita ad inuicem ſuperponi poſſint, vt ſibi congruant, velut

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