Angeli, Stefano degli - Miscellaneum hyperbolicum et parabolicum : in quo praecipue agitur de centris grauitatis hyperbolae, partium eiusdem, atque nonnullorum solidorum, de quibus nunquam geometria locuta est, parabola nouiter quadratur dupliciter, ducuntur infinitarum parabolarum tangentes, assignantur maxima inscriptibilia, minimaque circumscriptibilia infinitis parabolis, conoidibus ac semifusis parabolicis aliaque geometrica noua exponuntur scitu digna

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ESto hyperbola A B C, cuius axis B N, diame-
ter tranſuerſa E B, centrum L, ſecunda dia-
meter k M, parallelogrammum ei circumſcriptum
ſit G C: pariter ſit parabola quadratica A O C,
cum ſibi circumſcripto parallelogrammo P C. Di-
co tubum cylindricum ex reuolutione C G, circa
k M, eſſe ad annulum latum ex reuolutione A B C,
circa eandem K M, vt parallelogrammum P C, ad
A O C, parabolam. In A C, communi baſi para-
bolæ, & hyperbolæ accipiatur arbitrariè punctum I,
per quod agatur F I T, parallela O E, ſecans om-
nia vt in ſchemate. Quoniam ex propoſit. anteced.
rectangulum A N C, e@t ad rectangulum A I C, vt
rectangulum V B N, ad rectangulum T H I; & vt
rectangulum V B N, ad rectangulum T H I, ſic
armilla circularis ex B N, reuoluta circa K M, ad
armillam circularem ex H I, reuoluta circa eandem
K M; ergo vt rectangulum A N C, ad rectangulum
A I C, ſic armilla circula is V B N, ſeù T S I, ad ar-
millam circularem T H I. Sed vt rectangulum.
A N C, ad rectangulum A I C, ſic ex ſchol. propo-
ſitionis 22. libri primi N O, ſeù F I, ad I R.
Ergo vt armilla circularis T S I, ad armillam circu-
larem T H I, ſic F I, ad I R. Sed punctum I, ſum-
ptum fuit vt cunque. Ergo vt omnes armillæ circula-
res parallelæ armillæ V B N, ex parallelogrammo
G C, re@oluto circa k M, ad omnes armillas circu-
lares parallelas eidem V B N, ex hype bola A B C,
reuoluta circa eandem k M, ſic omnes lineæ

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