Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

Sed notetur, in ſemifuſis, B D, ſecari in F, ali-
qua continuata ſerie, nempe ſic vt B F, ſit ad F D,
vt vnitas ad duplum numerum fuſi. Nempe in pri-
mo vt 1, ad 2. In ſecundo vt 1, ad 4. In tertio vt 1,
ad 6. & ſic in infinitum. Quod enim in primo ſe-
mifuſo, nempe in cono ſit vt 1, ad 2, patet ex dictis. In alijs ſic patebit. Nam cum ſit E F, ad F B, com-
ponendo, vt numerus parabolæ ad vnitatem; erit
conuertendo F B, ad F E, vt vnitas ad numerum
parabolæ. Et ad D F, duplam F E, vt vnitas ad
duplum numerum parabolæ, ſeù ſemifuſi.

122. PROPOSITIO LXII.

Minimum trianguium circumſcriptum cuilibet infinitarum
p@rabolarum, eſt illud cuius latera tangunt baſim maximi
triangu [...] in parabola in ſcripti.

ESto ſemiparabola quælibet A B C, cuius dia-
meter B C, & in ipſa ſit in ſcriptum maximum
trianguium E C F (quod enim dicetur de dimidia
intelligetur etiam de tota) ſitque ei circumſcriptum
triangulum G E I C. Dico hoc eſſe minimum om-
nium circumſcriptibilium ſemiparabolæ. Si non,
ſit minimum H O k C, & per punctum E, duca-
tur L E M, parallela K H. Patet manifeſtè trian-
gulum L M C, minus eſſe triangulo k O H C, cum
L M, ſecet, k H, vero tangat parabolam. Quoniam
autem ex ſuperioribus, triangulum E F C, eſt ma-

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