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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 273, page id 1815201908:0330
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listane
1D
et
Iee
perc
1
recta
E L L IPSIS.
Demonstratio.
Vnoancur OB, BFE, F A, AF, FTT. Ouoniam AB,
GF lincx aequidictane, CrunE GB, 2 F A SCGMEHCA
aequalia: sed G B segmento est aequale legmentum HIB.
(nam Scomencudinex CFR B aequaEuT SCGMENEO FTRB,
ee criangulum GB K criangulo HIBK) ex L A segmen-
100b candem caulam aequacur segmentum AI: igieur d
TTB scgmencum eAt ae quale lcgmenco AI, ex TIIxqui-
distac blincae AB, hoc ek FC. quare eocum legmentum
OBHI, Equale eA cori legmento L AI: adeoque per
pracedencem AC, BD diamecri in R ee I. Similicer
lunc dinilx. Quod erac demonstrandum.
PROPOSITIO LY
Vellipsi data sic quacunque diamerrorum coniugario AB, CB, e
iutSatuE AC, cui parallela lic quaenis E D, ex punctis aurem D, ec F.
ducantur ordinatim ad diamerros DF, P HI, D G, F. I, cruncisitur EgurX
ODFBG, EIBHI parallelogramma.
Dicoparallelogramma illa aequalia esse.
Demonstratio.
Via per praecedentem B A, BC proporcionaliter
Lsune diuilx, erie AB ad BF, ve C B ad BFT: _E Per.
mucando ve AB ad C B, Sc BF 2 d B FT. Smilicor AB
pet praecedencem est ad B L ve CB ad B CF, ee permu-
cando ve AB ad CB, SC BI ad BG. ergo B F cst 2d
BTI, ve BI ad BC. orgoeparallelogramma AC, FII
aqualia lunc. Ouod ctac demonstrandum
e
D ROPOSITTO IT V
10l
Aester
InE AB, BC diamerri coniusaces innetis pun-
Dais AC, ducacux F. D pacallela rectae AC
cum ex D e E recte ponantur E L, DF, B C, F. H
Ordinarim ad diamerros AB, C B, iungancurque out ciin c
EB, DB.
vctiluru
Dico FBD sectorem, aequaritigura F IFD K F.
Demonstratio.
DEr praeccaencem parallelosramma FG, FII: a illorum dimidia, triangula D FB,
F TB incer se sunexequalias ablaco igicur communi DIB, eric F P B crianoulum
aqualetrapeZIO DF LL. quare addica AgUTA ComuNIVF. L DR E, sectOE EBD
aequalis est AgUEA F IF D K Fi. Quod cracdemonstrandum.
PROP OSIT IOILV
a
huins
ins
huins.
d GL. haius.
C2+ sex1t
1p16 53
cclabe clbla clla ucltolce aB.L E Oddc 
aud parallelam ducere, que legmenrum auterat xquale lesmenro AHB.
Mt m
Coesltn