# Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

LIBER IV. E, & iungatur, AG. Dico trilineum, ABH, ad trilineum, AM
H, eſſe vt, BH, cum, CE, ad ipſam, AM, cum, CE: Prius au-
tem dico portionculam, ASB, eſſe æqualem portionculæ, MIH,
& enim trapezium, ABOR, æquatur trapezio, ROHM, & quadrilineum, RASBO, ipſi quadrilineo, RMIHO, cum, A
O, axis, vel diameter bifariam diuidat omnes æquidiſtantes ipſi, B
H, & ideò omnes lineæ quadrilinei, RASBO, æquentur omni-
ęqualia, & ideo portionculæ, ASB, MIH, inter ſe ſunt æquales: Quoniam vero portio, ASBC, ad triangulum, ABC, eſt vt com-
poſita ex {1/3}, BC, & ex, CH, ad, CH, ideò, diuidendo, portion-
cula, ASB, ad triangulum, ABC, erit vt {1/3}, BC, ad, CH, vel
vt, BC, ad triplam, CH, . i. ſumpta, BC, communi altitudine, vt
ideſt (ſumpta communi altitudine tripla, CH,) vt rectangulum
ſub, BC, & tripla, CH, ad rectangulum ſub, BH, & tripla, CH,
ergo ex æquali portioncula, ASB,
ad triangulum, ABH, erit vt qua-
BH, & tripla, HC, quoniam vero,
BC, eſt media proportionalis inter
triplam, HC, & ipſam, CE, ideò
gulo ſub tripla, HC, & ſub, CE,
vnde portioncula, ASB, ad triangulum, ABH, erit vt rectangu-
lum ſub, CE, & tripla, CH, ad rectangulum ſub, BH, & tripla,
CH, ideſt erit, vt baſis, CE, ad baſim, BH, ergo, componendo,
trilineum, ASBH, ad triangulum, ABH, erit vt, CE, cum, B
eſt vero triangulum, AGM, æquale triangulo, AHM, ergo tri-
lineum, ASBH, ad triangulum, AMH, erit vt, CE, cum, BH,
vel, MIH, illi æqualem, per conuerſionem rationis, vt, BH,
cum, CE, ad ipſam, CE, ergo, colligendo, trilineum, ASBH,
AMIH, erit vt, BH, cum, CE, ad ipſam, AM, cum, CE,
quod oſtendere oportebat.

3.2.
8. huius.
5. l. 2.
Elicitur
ex 12. 1. 2.

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