Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

G D H, habet rationem compoſitam ex rationibus
A D, ad G F, & B D, ad D F. Sed B D, ad D F,
eſt ex ſchol. 2. propoſit. 54. componendo, vt nume-
rus parabolæ vnitate auctus ad numerum parabolæ,
& pariter ex natura parabolæ, cum ſit B D, ad D F,
vt poteſtas A D, eiuſdem gradus cum parabola, ad
exceſſum ipſius ſupra ſimilem poteſtatem G F, nem-
pead tot tales poteſtates. G F, quotus eſt numerus
parabolæ. Ergo ratio trianguli A B C, ad G D H,
componetur ex ratione A D, ad G F, & ex ratione
poteſtatis A D, eiuſdem gradus cum parabola ad
totſimiles poteſtates G F, quotus eſt numerus para-
bolæ Sed ex iſtis rationib s componitur quoque ra-
tio poteſtatis A D, vno gradu altioris poteſtate pa-
rabolæ, ad tot ſimiles poteſtates G F, quotus eſtnu-
merus parabolæ. Ergo triangulum A B C, erit ad
triangulum G D H, vt illa poteſtas A D, ad illas
poteſtates G F. Sedvt poteſtas A D, ad vnam po-
teſtatem G F, ſic D A, ad A Q: ergo & vt pote-
ſtas dicta A D, ad omnes illas poteſtates G F, ſic
D A, ad tot A Q. Erit ergo triangulum A B C, ad
triangulum G D H, vt D A, ad tot A Q, quotus
eſt numerus parabolæ. Quoniam vero ex propoſit. 1. lib. prim eſt conuertendo, parabola A B C, ad pa-
rallelogrammum ſibi circumſcriptum vt numerus
parabolæ ad numerum parabolæ vnitate auctum,
nempe vt duplus numerus parabolæ, ad duplum nu-
merum binario auctum; ergo parabola A B C, erit
ad triangulum A B C, dimidium parallelogrammi

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