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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 417, page id 1815201908:0474
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m Demonstratio.
P A R A BOF A.
Vncta A B OcCUTEAE R C. lineis in L.
Ouoniam POlinca in circulo AH B,
ad angulos rectos in R Cccac ciameerum
BD, recta P G in K, divila est bitariam.
Sed e FTI in parabola ABC, quoque in
X dinila est bitariam; rectae igitur P LI,
TCFIACOE SO X QUALESSUINE. RRUECUM VE AT B
tectangulum ad a rectangulum AL. B, HC
FL Er rectangulum ad rectangulu F. L C
icem FTL I rectangulum 2d. B rectangu.
lum FTL I: sed F. P. C rectangulum x qua-
le est rectangulis TIL P, B FT G, igIEUF _
F HF O rectangulum est ad rectanSuIU RHTG, vE A L B rectangulum ad rectan-
sulum ALB; id cA P R B rectangulum, ad recrangulum FR B. Duod crac demon-
Atrandum. cr
eROEOSITIO CXXIX.
Sto AB CpatabolX axis AD maior dimidio laFeTIS FECHI: CCnETOGC
sD incervallo AD, circulus deleribatUr AB F. : OCCuTTAF IS paraBOla
in B X axi in F. ducaturque ex B, linea B F ordinaeim ad axem.
Dico lineam P F. aqualem este lareri recto.
e
eise
Demonstratio.
Voniam B F ordinacim ducta est 2d axem, quadratum F B
Laquale est reccangulo super F A ex lacere recto: sed es
FB quadracum quoque aequalC CA RCCFanOUIO A F R : RCCFAN-
sulumisitur AF F. aequale est ei quod AEsUPeF A F d laFCTC
rectb. quare FP linea laceri receo es aequalis. Ouod crac
demoncrandum. l
1311. I
10me ROBOSITIO CXXX
Databolam AB C cuius aris AF concingat in B li
LneaBD, Occurrensari in D, Ponatur ducem ex B liL 
nea BH normalis ad contin-
1
genrem, occurrens exi infl. Cen cale
troque _ inceruallo FIB cirea- leuD
cillus describatur BOC: por2.
curc dd arem normales quor
cunquo lK, Occurrentes Para
Bolain OL, contingenti BDinuo LV
It FF. _ circulo inera parabol
lam incercepco in I_K.
Dico CKlrectangulum ef.
se ad rectangulum GKI, ve
quadrarum B B ad quadracuin
EB.
serter11D
Virccioslatibo
DOnatur BC aquidistans F L, OC.
eutrens parabole in C; iunctaque
2
Dhutue
0c
1.II.
111I
1111
11III