Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ QT, eſt vt omnes eiſdem circumferentiæ ad omnes illius circumf
etiam figura, AFN, ad circulum, NOQT, & conſequenter etiam
ad quẽcumq; illius ſectorem per anteced. Prop. & Cor. erit vt om-
nes circumfer. ad omnes circumferentias: Vel, niſi omnes circũ. ferentiæ, QAR, æquantur omnibus circumferentijs figuræ, AFN,
erunt eiſdem maiores, vel minores, ſint primò maiores, qua ntita-
te omnium circumferentiarum ſectoris, AST, intellecta autem à
centro, A, ducta ipſa, AO, tan-
gente curuam, AFN, in puncto,
A, quæ circumferentiæ incidat
in, O, ſecetur circumferentia, O
N, bifariam in, L, & rurſus par-
tes, OL, LN, bifariam in pun-
ctis, P, M, & hoc ſemper fiat
donec ad circumferentias deuẽ-
tum ſit, quarum vna quæque ſit
minor, ST, ſcilicet iplæ, OP, P
L, LM, MN, & à centro, A, ad
puncta, P, L, M, extendantur re-
ctæ, AP, AL, AM, quæ ſecaburt curuam, AFN, earum enim por-
tiones inter centrum, & curuam interceptæ, ex hypoteſi cadunt
intra ſpatium, ANFA, ſecent in, C, F, I, & centro, A, interuallis,
AC, AF, AI, arcus deſcribantur, BCD, EFG, HIK, incidẽtes pro-
ximis rectis lineis, à centro eductis, in punctis, B, D; E, G; H, k. Quoniam ergo omnes circumferentiæ ſectoris, QAR, ſuperant
omnes circumferentias figuræ, AFN, quantitate omnium circum. ferentiarum ſectoris, AST, omnes autem circumferentiæ figuræ
compoſitæ ex ſectoribus, NAM, IAH, FAE, CAB, ideſt figuræ
ſpatio, AFN, circumſcriptæ, ſuperant omnes circumferentias fi-
guræ compoſitæ ex ſectoribus, KAI, GAF, DAC, ideſt figuræ ei-
dem ſpatio inſcriptæ, quantitate omnium circumferentiarum fe-
ſectoris, BAC, & quadrilineorum, ECDF, HFGI, MIkN, quæ ſi-
mul adæquantur omnibus circumfèrentijs ſectoris, MAN, vt fa-
cilè oſtendi poteſt, propterea omnes circumferentiæ figuræ circũ-
ſcriptæ ſuperant omnes circumferentias inſcriptæ quantitate om-
nium circumferentiarum ſectoris, MAN, quæ cum ſint minores
omnibus circumferentijs ſectoris, TAS, ideò omnes circumferen-
tiæ figuræ, circumſcriptæ ſuperabunt omnes circumferentias in-
ſcriptæ minori quantitate, & eædem multò minori quantitate ſu-
perabunt omnes circumferentias ſpatij, AFN, quam omnes circũ-
ferentiæ ſectoris, AQR, ſuperent omnes circumferentias ſpatij, A

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