## Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

GEOMETRIÆ per punctum extremum alterius ſecundò ductæ, parallela
primò ductæ, incluſæ dicto puncto, & alio eiuſdem paralle-
læ productæ, ſi opus ſit; in quod cadit, quæ ducitur per
aliud extremum punctum ſecundò ductæ, parallela axi, vel
diametro parabolæ per primò ductam conſtitutæ.

Sit curua parabolæ, BAEC, intra quam ſint vtcumq; ductæ in
eandem curuam hinc inde terminantes (. i. quod non ſint ductæ pa-
rallelæ axi) primò, BC, ſecundò, AD; ducatur deinde per vtrum
libet extremorum punctorum ſecundò
ductæ, vt per, A, ipſa, AF, parallela
ipſi, BC, in quam productam, ſi opus
ſit, incidat parallela axi, quæ ducitur
per punctum, D, aliud extremum
ipſius, AD, occurrat autem illi in, F. Dico parabolam, BAEC, ad para-
bolam, AED, eſſe vt cubum, BC,
ad cubum, AF. Eſt enim parabola,
item parabola, ANE, ad parabolam, ANED, eſt vt cubus, A
ED, eſt vt cubus, BC, ad cubum, AF, quod oſtendere opus
erat.

@. huius.
Exantec.

## 426.THEOREMA XIV. PROPOS. XV.

IN eadem antecedentis figura, ſi ducatur intra parabo-
lam, BNC, à puncto, V, ſumpto vtcumque in curua, B
NC, verſus baſim, BC, ipſa, VX, incidens baſi in, X, pa-
rallela axi, vel diametro eiuſdem parabolæ. Dico parabo-
lam, ANED, ad ſegmentum, VCX, eſſe vt cubum, AF,
cubo, XC.

Nam parabola, ANED, ad parabolam, BNC, conuertendo,
ſegmentum, VCX, eſt vt cubus, BC, ad parallelepipedum ter ſub
altitudine, BX, baſi quadrato, XC, cum cubo, XC, ergo, ex æ-
quali, parabola, ANED, ad ſegmentum, VXC, erit vt cubus,
bo, XC, quod oſtendere oportebat.

6.huius.

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