Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

ptus cylindrus O C. Dico hunc eſſe ad illud vt E D,
ad dimidiam E B, cum tertia parte B D. Sit F,
centrum hyperbolæ genitricis, & F G, F H, ſint
eius aſymptoti, & per B, ſit ducta I B, parallela
G D; intelligamuſque ex reuolutione trapezij
G I B D, circa B D, genitum eſſe fruſtum conicum
G I K H, cui ſit circumſcriptus cylindrus N H, & inſcriptus I M. Quoniam linea G H, diuiſa eſt ſe-
cundum conditiones propoſit. 9. nam ex propoſit. 10. 2. conic. rectangulum G A H, eſt æquale qua-
drato I B, ſeù quadrato L D. Ergo rectangulum
G L H, erit æquale quadrato A D. Ergo etiam ar-
milla circularis G L H, quæ eſt baſis tubi cylindrici
N L P, erit æqualis circulo A C, baſi cylindri O C. Cum ergo ex propoſit. anteced. exceſſus fruſti coni
G I k H, ſupra cylindrum I M, ſit æqualis conoidi
hyperbolico A B C. Ergo tubus cylindricus N L P,
ad illum exceſſum, & cylindrus O C, ad conoides
erunt in eadem ratione. At ex propoſit. 8. tubus eſt
ad exceſſum vt E D, ad F B, cum tertia parte D B. Quare patet propoſitum.

Oſten ſa ergo proportione cylindri circumſcripti
conoidi hyperbolico ad ipſum, facile docebimus in
qua linea diametro parallela ſit centrum grauitatis
ſemihyperbolæ. Sit ergo.

Note to user

Dear user,

In response to current developments in the web technology used by the Goobi viewer, the software no longer supports your browser.

Please use one of the following browsers to display this page correctly.

Thank you.

powered by Goobi viewer