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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 609, page id 1815201908:0666
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sectio.
Uavio
derbe
labere
ione
ex 1
iOHR
d
em et
Talilo
qedie
ntet
6.
Der l
ide.
IIIIII
DArabola ABC.
Ke LFIO, CLI
Xis ADIlCC in Bhyperbolam F BF, CaI
HX P E R B O L. A.
605
inter A, _ B, in parabOla, pONANCuFDGF, F CH) parallelx asymptoris
IungancuIrqUe AL, AB, AA:, 12.P, 2it 5CrI(G1.
Dicomixcilincum E AB, duplum esse mixtilinei B AF.
alympeori AB, AHI angulum rectum conrineanc; ec alumpro C
Demonstratio.
smptoco AEL. cruncisiur (D, BL
ordinacim polica ad axem AD vade
Facio AD, ad AY 2 duplicaca est rario-
nis  al 23cl, F R ad. BI: ICd
emencum l. DBl adplu el ese
BIF K. est aurem P. AB d figura aequa-
Iis sesmento F DBI, l B AF, aequa-
lis BIFK segmento;  AB aupa C BAF. Ho. ABHC de.
monctrandum.
i
o Ca
nancurver D rectae FC, HIL, aequidistantes alymproris, et L. M, F. C ij(
DOnantux, BF. Ha aquidistances a-
eA vE AD ad b AL, EC BI ad F D: c2
tio isicur BI, ad P D duplicata cstra.
cionis FK ad BI; 2dcoque e c sc
Ses, ae parabola delcribarur BDF, (cuius aris BC) occurrens hyper-
CInc AB, BCasympeoti hyperbOlX P F. HI, atigulum tectum FormaH-
bolae in E, ee per assumprum punctum B in parabola, Encer B _ L; p0-
dent pacallele:
Ec
Dicomincilineum F.D F. duplum esse mixcilinei F. DHI.
Demonstralio.
Scentum est Fationem F C ad _G, esse dupculam Cdius, quatm habet R C Xd
DEtiocest MB ad F B, hocFCAHP ad F M. igicur duplum cAt scomen. er
tum E GC F; quancicaris TYL M F: sed libro ac parabola demonstracum est para-
bolXS parrem F D CC duplam esse F M I. B, igicur roliduum F. D B. duplum ost serir
reldui F.DFI. Ouodtuic demonstrandum.
Atht 3
Bar
a
e  e   t  e  p  e  a  stet  e t te e     t tat    t  p a et tet  e a ti e   t   t t   et  e     A