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

ASſumpta figura Propoſ. ant. dimiſſa recta, AG, & con-
ſtituto parallelogrammo ſuper, BH, circa axim, vel
diametrum, RO, quod ſit, PH, iunctiſque, BR, RH, o-
ſtendemus parallelogrammum, PH, ad fruſtum parabolæ,
ASBHIM, eſſe vt, BH, ad, HC, cum, CE; & trian-
gulum, RBH, ad idem fruſtum eſſe vt, BH, ad duplam,
HC, CE.

Parallelogrammum enim, PH, eſt ad triangulum, ABH, vt
dupla, BH, ad ipſam, BH, triangulum verò, ABH, ad ſection-
culam, ASB, eſt vt, BH, ad, CE, ergo, ex æquali, parallelo-
grammum, PH, ad ſectionculam, ASB, eſt vt dupia, BH, ad,
11Gorol. 11
huius.

213[Figure 213] CE, & ad duas portionculas, AS
B, MIH, erit vt dupla, BH, ad
duplam, CE, ideſt vt, BH, ad, C
22O. 1. 2. E. Item parallelogrammum, PH,
ad trapezium, ABHM, eſt vt, B
H, ad, AM, cum dimidio exceſſus,
BH, ſuper, AM, . i. ad, AM, vel,
CG, GH, ergo, colligendo, pa-
rallelogrammum, PH, ad ſectionculas, ASB, MIH, cum trape-
zio, ABHM, . i. ad fruſtum parabolæ, ASBHIM, erit vt, BH,
ad, HC, cum, CE. Quia verò triangulum, RBH, eſt dimidium
parallelogrammi, PH, ideò ad fruſtum, ASBH'IM, erit vt di-
midia, BH, ad, HC, cum, CE, . i. vt, BH, ad duplam, HC, C
E, quod erat oſtendendum.

214[Figure 214]

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