Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

natim applicatarum parabolæ congruentes, ęquales
ſint poteſtatibus factis ſub prędictis abſciſſis ab or-
dinatim applicatis, & ſub poteſtate talis lineæ vno
gradu depreſſiore poteſtate parabolę. Sit ergo.

101. PROPOSITIO XLIX.

Si fiat vt diameter parabolæ ad ſemibaſim, ſic buius po-
testas vno gradu depreſſior poteſtate parabolæ ad ſimi-
lem poteſtatem lineæ inueniendæ. Potestates applicata-
rum ordinatim in parabola eiuſdem gradus cum parabo-
la, æquales erunt factis ſub abſciſſis diametri verſus
verticem ab ordinatim applicatis, & ſub poteſtate li-
neæ inuentæ, vno gradu depreſſiore poteſtate para-
bolæ.

Esto quælibet parabola B A C, in qua fiat vt dia-
meter A D, ad ſemibaſim D B, ſic poteſtas
huius vnogradu depreſſior poteſtate parabolæ, ad
fimilem poteſtatem A H: v. g. ſi parabola eſt qua-
dratica, ſic D B, ad A H; ſi eſt cubica, ſic quadra-
tum D B, ad quædratum A H: ſi eſt quadratoqua-
dratica, ſic cubus D B, ad cubum A H. Dico, quod
ſi ordinatim applicentur G L, E k, poteſtas G L,
eiuſdem gradus cum parabola ęqualis erit facto ſub
L A, & ſub poteſtate A H, vno gradu depreſſiore
poteſtate parabolæ, & ſic de cæteris. Quoniam e-
nim vt A D, ad D B, ſic poteſtas D B, vno gradu
depreſſior poteſtate parabolæ, ad ſimilem poteſta-

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