8977
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
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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