Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

eſſe H B, vt pars vltra B, ſit ad B H, vt numerus
parabolæ vnitate minutus, nempe vt nihil, ad vnita-
tem. Ergo H B, non eſt producenda, ſed à puncto
B, ad C, ducenda eſt linea, quæ vtique quodam-
modo poteſt dici tangere triangulum, quia ipſum
non ſecat.

105. PROPOSITIO LI.

Maximum triangulum inſcriptum in quolibet triangulo, eſt
cutus baſis bifariam diuidit diametrum
circum ſcripti.

ESto triangulum A B C, cuius diameter B D,
quæ ſecetur in F, bifariam à baſe E O, trian-
guli E D O. Dico triangulum E D O, eſſe maxi-
mum omnium inſcriptibilium in triangulo A B C. Quoniam enim triangulum A B C, ad triangulum
E D O, habet rationem compoſitam ex ratione
A C, ad E O (nempe ex ratione D B, ad B F) & ex ratione B D, ad D F; & hæ duæ rationes com-
ponunt rationem quadrati B D, ad rectangulum
B F D. Ergo triangulum A B C, erit ad E D O,
vt quadratum D B, ad rectangulum B F D. Sed
rectangulum B F D, eſt maximum omnium rectan-
gulorum factibilium ex partibus B D, in puncto di-
uifæ. Ergo etiam triangulum E D O, erit ma-
ximum omnium inſcriptibilium intra A B C. Quod
& c.

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