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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 474, page id 1815201908:0531
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E2, Ar. Bm.
P AR ABOL
Demonstratio.
Nonia BP, CF linex aequales
lune, eriangula B C F, C D F, Icem
B AF, G AF, 2C PFOPTCrCA ABC.
AC D criangula inter se aequalia lunc,
sed quoque a maxima lunc illorui quxe
seomentis ABC, ACD, inscribipol.
lunci scomenta isicur ABC, B AC D
2qualia lune. Ouod erat demonstram.
dum.
ROPOSTTIO COLIZ.
nacur L. HE axis patabola A BC, aequalis diametro BF, et ordina-
cim per I linca HII.
Dieo illam recta AD aqua C.
Demonstratio.
NIM PEF PEXCCdENEE A C D ParabO-
Ia aequalisparabole AB C id cAC FTT. P.
isitur de crianoulamaxima ACFD, dTTLI
lunc aequalia: sunc aucem ex hypoches il.
lorum alcieudines PK, F C aquales, ixi-
cur _ Bales AD, FILinceF (C X qualeS TUnE.
Ouod fuic demonstrandum.
PROPOSITIO CCLZ.
Nientoane FC applicentur ad illum
Lordinaeim lineae FIL,KL: XFTTqui-
dem SE aqualis AD; RL VerO rectX
CF: crit isitur sesmento AB c xquale
seomentum FTF I, &x seomento BC X
quale SeOMenTUM RF L. SCd FTFL SC.
Smencum ad segmentum R F I, teripli.
ed i. entam habecrarionem linea FTI ad li-
neam R L3 igIeuE SICBTMCHCU A B ad seomentum B C, criplicatam habCEFa
cionem lince HL ad _ L lincum, id ett ex lypochiesi AD ad L. C. Quod exat de
monstrandum.
Cr2L 3LI
Corollarium.
EX
240.
nius
Ed
versa 2
uins.
EcenE A BC parabolam linex quaeuis AB, BC: demisaq; ex B dia-
Dncero BD, ponantur ad illam ex A e C normales AD, CF.
Dicoleomentum AB esse ad segmentum BC in criplicacaratione li-
Demonpratio.
nex A ad CC.
112
Inclegu aucta AC, quB OCCUEFAE BD in M, A Blcomenta aa ToM
cum BC triplicaram habere ratiOneM AM ad MC. Pater, cum sierE AD ad
CL.3  A M de MC, C+8O, dC.
11
( e  s 1i        .  t        p . i . e    . 1                       e e  u    t i   e 1.  H 11