Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

illa plana duobus tertijs rectanguli k A B. Ergo tu-
bus cylindricus A D K L, erit ad prædictum annu-
lum, vt rectangulum K A B, ad duotertia eiuſdem
rectanguli; nempe in ratione ſeſquialtera. Quod
erat oſtendendum.


Si recta linea A B, ſecetur in C, bifariam, & in D,
E, æque remotè à C, eodemque modo in F, G. Re-
ctangulum A G B, erit exceſſus rectanguli A E B, ſu-
pra rectangulum F E G.


NAm rectangulum A E B, diuiditur in rectan-
gulum A E G, & in rectangulum A F, G B. Pariter rectangulum A E G, diuiditur in rectangu-
lum F E G, & in rectangulum A F, E G, ſeù B G F,
quia A F, @xhypotheſi, @ſt æqualis G B. Ergo ex-
ceſſus rectanguli A E B, ſupra rectangulum F E G,
eſt rectangulum A E, G B, cum rectangulo E G B; quæ duo rectangula ſunt æqualia rectangulo A G B. Quare patet propoſitum.


Si in oppoſitis ſection bus, quæ hyperb læ appellantur du-
cantur lineæ lateri tranſuerſo parallelæ, occurrentes


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