Full text: Cavalieri, Bonaventura: Geometria indivisibilibvs continvorvm

427. THEOREMA XV. PROPOS. XVI.

INeadem ſupradicti Theorematis figura oſtendemus tri-
lineum, VNAI, ad trilineum, VNABX, eſſe vt pa-
rallelepipedum ter ſub, EI, & quadrato, IA, cum cubo,
IA, ad parallelepipedum ter ſub, CX, & quadrato, XB,
cum cubo, XB. Similiter trilineum, VEI, ad trilineum,
VECX, eſſe vt parallelepipedum ter ſub, AI, & quadra-
to, IE, cum cubo, IE, ad parallelepipedum terſub, BX, & quadrato, XC, cum cubo, XC.

Trilineum enim, VNAI, ad parabolam, ANE, eſt vt paral-
lelepipedum ter ſub, EI, & quadrato, IA, cum cubo, IA, ad cu-
bum, AE, item parabola, ANE, ad parabolam, BNC, eſt vt
cubus, AE, ad cubum, BC, & tandem parabola, BNC, ad trili-
neum, VABX, eſt vt cubus, CB, ad parallelepipedum ter ſub, C
X, & quadrato, XB, cum cubo, BX, ergo, ex æquali, trilineum,
VNAI, ad trilineum, VNBX, erit vt parallelepipedum ter ſub,
EI, & quadrato, IA, cum cubo, IA, ad parallelepipedum ter
ſub, CX, & quadrato, XB, cum cubo, XB. Eodem modo o-
ſtendemus trilineum, VIE, ad trilineum, VXC, eſſe vt paralle-
lepipedum ter ſub, AI, & quadrato, IE, cum cubo, IE, ad pa-
rallelepipedum ter ſub, BX, & quadrato, XC, cum cubo, XC,
quod, & c.

427.1.

6.huius.
2.huius.
6.huius.

428. THEOREMA XVI. PROPOS. XVII.

SI duæ intra curuam parabolicam ducantur rectæ lineæ
axem ſecantes, fuerint autem conſtitua@um ab eiſdem
parabolarum diametri, vel axis, & diameter æquales, & ipſe
parabolæ erunt æquales.

Sit curua parabolica, BAC, intra quam ducantur vtcunque duę,
DF, MC, axem ſecantes, ideſt non parallelæ axi, ſint autem, A
R, HO, diametri, vel axis, & diameter inter ſe æquales. Dico
parabolam, DAF, eſſe æqualem parabolæ, MHFC; ducatur

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