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

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476456GEOMETRIÆ325[Figure 325] habet rationem compoſitam ex ratione trianguli, LQΣ, ad trian-
gulum, L& Σ, ideſt ex ratione, QΣ, ad, Σ& , vel ex ratione circum-
11Coroll. 1.
19. l. 2.
33. Sexti
Elem. ferentiæ, CDFBC, ad circumferentiam, CDFB, quia prædictis æ-
quatur ideſt ex ratione circuli, CDFB, ad ſectorem, vel eius reſi-
duum, ACDFBA, & ex ratione trianguli, L& Σ, ad triangulum,
LZ {13/ }, ideſt ex ratione quadrati, PL, ad quadratum, L4, ideſt ex ra-
22Coroll. 1.
19. l. 2. tione quadrati, BA, ad quadratum, AK, ideſt ex ratione ſectoris
(dicatur ſic breuitatis cauſa, ſiue ſit ſector, ſiue eius reſiduum) AC
DFB, ad ſectorem, AIR εkA, quæ duæ rationes componunt ratio-
33Coroll. 2.
3. huius.
Defin. 12.
l. 1. nem circuli, CDFB, ad ſectorem, AIR εKA, ergo triangulus, LQ
Σ, ad triangulum, LZ {13/ }, erit vt circulus, CDFB, ad ſectorem, AI
RεKA, ſed triangulus, LQΣ, eſt æqualis circulo, CDFB, ergo triã-
gulus, LZ {13/ }, ſectori, AIR εKA, æqualis erit, & eſt trilineus, LΖΩ,
44Iuxta 2.
huius. æqualis ſpatio, AISMGA, ergo ſector, AIR εKA, ad ſpatium, AIS
MGA, erit vt triangulus, LZ {13/ }, ad trilineum, LΖΩ, . i. vt quadra-
tum, 4L, ad rectangulum ſub, 4L, Lβ, cum {1/3}. quadrati, 4β, . i. vt qua-
5514. huius. dratum, IA, ad rectangulum, ſub, IA, AG, cum {1/3}. quadrati, GK,
quod erat oſtendendum.

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