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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1086, page id 1815201908:1143
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1086
a r73. BH-
B Cora
77. huints
CONOIDES MXPERDOLLCNM.
Demonstratio.
InC ABC, D F F sectiones conoideos
paranelx producentes hyperbolas. Di-
coillas incer se similes ese: perfecto enim
conoalmpeorico L. R MI producatur plana
ABC, DPP doncc occurrentia con
Formenchrperbolas NBO, PF O, Osten.
sum cs : hyperbolam NBO parallelam
PF O, similem quoque cidem cAc. de-
monstratu incuper eAb hyperbolas NBO,
PFO similes esse hyperbolis ABC.
DF I. igicur etiam hyperbola ABC
DE. P lune similes incer le. Ouod demon-
IxareOPOTEUIE.
PROPOSITIO CLXXXVIII.
TIEcOnUS ABC rectus sectus pla-
no per axem exhribence sectio-
nem hxperbolicam DF F cum a-
symproris ciu(dem AB, AC. AaRE
sectiones C, FIN per verricem D, e
aliae BIC qua line rectae ad B AC,
planum per axem, aequidictances
contingenri G DH e exhibeane in
plano BAC sectiones ON, BF. F C:
erisantur denique FI normales ad
CB.
Dicorecras F L aequAlES CNCFCCEX
Demonstratio.
roE enim rellangula BFC aquali
Dcquadraco D N, sed criam rectangula
BF C aquantur quadratis F I, quod F L
Einc recta ad circulares diamerros BC
FE quadrata aequalia quadra-
eis DN. ergo rectae FI, DNcriam aqua
lessune. Ouod erac demonstrandum.
DEDSITIO CLXXXIK.
Udem politis:
ri cylindro cuius balis eA circulus C HN, ee alcirudo D L.
Dicolpacumeve condices hyperbolicum cingens aequa
bo