Full text: Angeli, Stefano: Miscellaneum Hyperbolicum et Parabolicum

axim cum portionè, cuíus baſis ſit armilla exceſſus cìrcu-
li facti in portione, ſupra circulum factum in cono à pla-
no ſecante. Hic erit ad exceſſum portionis ſupra conum
tam ſecundum totum, quam ſecundum partes propor-
tionales, vt parallelogrammum circum ſcriptum parabolæ
quadraticæ ad ipſam; dummodo hæc ſecetur ſecundum
diametro parallelas.

SIt A B C, quælibet portio ſphæræ, in qua in-
telligatur inſcriptus conus A B C, ſectoque axi
B D, bifariam in E, ducatur per E, planum F E G,
plano A D C, parallelum, faciens in cono circulum
H E I; intelligamus tubum cylindricum k L M P,
circa eundem axim B D, cuius baſis armilla N L P,
æqualis armillæ F H G: pariter in ſecunda figura
intelligamus parabolam quadraticam A B C, cuius
axis B D, baſis vero A C, ſit æqualis axi B D, por-
tionis, & ei ſit circumſcriptum parallelogrammum. Dicotubum cylindricum k L M C, eſſe ad exceſſum
portionis A B C, ſupra conum A B C, vt paralle-
logrammum E C, ad parabolam A B C. Sumatur
in B D, axi portionis arbitrariè punctum V, per
quod tiaiciatur planum Q Z, plano A C, paral-
lelum ſecans omnia ſolida vt in ſchemate; & pariter
in parabola facta A F, æquali B V, per F, ducatur
F G H, parallela D B. Quoniam enim rectangu-
lum D E B, eſt ad rectangulum D V B, vt rectan-
gulum A H B, ad rectangulum A I B, quia propor-
tiones horum rectangulorum componuntur ex ijſ-

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