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

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6646GEOMETRIÆ quæ ita inuicem ſuperponantur, vt, BC, FG, ſibi congruant, &
11D. Defin.
10. 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
22Coroll. 1.
huius. G, ipſæ, EM, PN, quarum figurarum, ac oppoſitarum tangen-
tium ſint quoque incidentes ipſę, DQ, MN, productis verò, BC,
33B. Def. 10. 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,
44D. Defin.
10. 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,
55A. Def. 10. 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,

33[Figure 33]& 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-
66C. Defin.
10. les cum ſint, vt incidentes, DQ, MN, quæ ſunt ęquales, necnon
æquales reliquæ vſq; ad incidentes, nempè, SZ, IZ, quod eſt ab-
77A. Defin.
10. 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.

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,

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