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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 5, page id 1815201908:0062
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POTFNELA.
In 2. fgura est FD linca in P. _ C divila media eE CXITCMA FATIONC PFOPOr.
cionali.
PROPOSITIO VITI.
IE angulus AB C dinilus bi- C.
 Fariam rectâ BD, ad quam
crecta ex B normali BF, agacur
linca quacunque P. C per pun-
CEum D.
Dico E G lineam in F _ D,
media _ extrema ratiONCPFOPOT-
cionali cediuilam.
Demonstratio.
DOnacur per D, linea A C, paralleta reCtXBB: OC.
currens anguli ABC laceribus, in A _C. Duoniam
isitur A C linea aequidistac, rectae FB. qua normalis
ponitur ad lineam BD, crunc anguli ADB. CDB rC-
cti; lunc aurem per constructionem, e anguli ABD.
CBD inter (C aequales, ec BD linea communis, igieur
criangulum ABD aeguale cscriangulo CBD, e AD
balis, aequalis bas DC: ISIEUFDETPERCCdeNLEI VE F. C
ad GD, SIC F F ad FD. Ouod erar demonstrandum.
In 2 Egura linea CD. diuila est, secundum medliam
de excremam rationem proporrionalem.
PR OeOSIFTO
ISeo ABC erian-
sgulibalis AC, in
D bitariam dunla, iun-
Atilque BD, aGATUE PCF
B linca BF, varallela
ba(I A C; dein ex C, rC-
Eta dUCAEUFC E OCCUY
rensricunquelinea BF.
in E, BD rectX inF, _
laceri AB in C. Dicoin
prima fgura: lineam
F C; in lecunda lineam
F C; intercia rectam F G extrema e
media ratione proportionali esse di-
nitam.
Demonstratio.
Onontam AC, L B. CH linex Xqui-
distanE, erie AB ad BG. VI CF ad G F;
sed eA ve AB ad CB, sC AD ad CFB
Vescur CFTlinea parallela baA AC;