Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

æqualis conoidi A B C; ſi cylindrus I M, adda-
tur. Ergo exceſſus cum cylindro, nempe fruſtum
G I k H, erit æquale cylindro, & conoidi ſimul. Ablato ergo conoide, exceſſus fruſti ſupra conoides
remanebit æqualis cylindro.

Non alio modo oſtendetur æqualitas partium,
proportionalium, v. g. exceſſum fruſti G N P H,
ſupra fruſtum conoidis A Q T C, æqualem eſſe
cylindro R M. Quia ex dictis in præcitata propo-
ſit. 10. exceſſus fruſti G N P H, ſupra cylindrum
R M, eſt æqualis ſegmento A Q T C; addito ergo,
vt prius, cylindro R M, & ablato ſegmento A Q T C,
intentum probabitur. Quare patuit talia ſolida æ-
qualia fore tam ſecundum totum, quam ſecundum
partes.

45. SCHOLIVM.

Sed etiam præſens propoſitio poſſet immediate
per indiuiſibilia oſtendi. Sumpto enim arbitrariè
puncto O, & acto plano N O P, G H, paralle-
lo. Ex propoſit. 10. ſec. conic. rectangulum N Q P,
eſt æquale quadrato I B, ſeù quadrato R O. Et
conſequenter armilla circularis N Q P, eſt æqua-
lis circulo R O S: & omnes armillæ ęqualis omni-
b s irculis; & exceſſus prędictus ęqualis cylindro
I M. Sed hac conſtructione adhibita, demonſtratio
non reducitur ad modum Archimedeum, quia in prę-
dicto exceſſu nequeunt inſcribi tubi cylindrici.

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