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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 136, page id 1815201908:0193
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=193
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 60 lines, status machine
# Lines: 60 recognised, mean confidence 0.82
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c
E. SSI
F
i 13
IFI
ex constructione linea
a M, BL paralscla
B0 aM Clt ad BL
V
ad BN maioret
auc minorem quaiie
quod ectablurdum. No
ABIEUF FectAMROccuF
tet tecta BI supra vet
intra N: ereso in N.
Duoniam nurem ex
cencro ad concactum
o lela sit aM, angulUS quOqUE R N B rectUS CHE: Cr5O b linea RM tansit circutum
BNC. limiliraciocinatione demonltrabimus RMl religuos criam omnes circulos
COMLISCFC, Dusd etaC demontrandum.
Corollarium.
eragin; ducta est aM angulus AM a L cuSCs GuaCu e Contructione BN paraI.
Vod in hoc Theor. de circulis demomes ausmus, etiam de similibus L. Ilipsibus, P2-
Ccabolis, Flyperbolis demonstrari pocest.
; Et 1s12C la. l5.
eROPOSITIOLEXKRI
Idem posicis duos quolcum que circulos seriei datxe circulos, verbi gra-
Aria AMB, C. OD tangac recta. MO.
Dico hanc productam cadere in cerminum longicudinis R, de reli.
quos circulosomnes ContingCrC.
Demonstratio
Eneta circutorum
AINE a, B, Y, E,C
Cum Cx a dC y adCOn-
tactus duCANEUE aM.
y O. A IgITUE nesCEuL
producta occurrer li-
nex AR cis vel vltea
K in V. de quoniam
per corollarium pro-
policionis 125. huus
aNerciO, TaNGENSMO
Jr. huius.
cB2. buins. Terminus progressionis basium est in R, CFUNEC A R, BR, CR, DK, RR, RC. 2
duo
analobia. Guare parec exaegnoctiam a l..Ea eecoasi elgacu ad
cros. hu. mus quo in praecedenri ostendimus AB esc ad B C vE a B dd B y) a HC en ad
CL. inc duplicaca racionis AB ad BC, id eAt ve AB ad CD; _ AB Cu aCV
ve a M ad 7 C7, ergo a K est ad yR, VE aM ad 7 O. Deinde cuM aN, yO ex
centris de concactus ductx line, cruncperpendiculares ad MI V, id eoque parallela
incer sc. Qarc MV crit ad OV, re aM ad. 7O, hoc est per iam demonstrata ve
a K 2c y K, quod est ablurdum. non isicuE MIO OccurrecipsI AK cis vel tala L
proinde per lemma propolicionis praecedencis cciam aR, BK, yK, in concinu
YR, ve ay ad 7E. Acqui ay est ad y E, VE AC ad C F (quod simili modo ostende
circulos continsut, demouletatio lonsc cric tacilior, quam proinde omilimus.
(ed in K. Ouod eracprimum. Ouo demonstrato, parex per pra cedenrem secunda
Pars; guix cranc demonstranda.
Ouodsiloco circuli COD altumatur circulus B N C, ita ve linea alos HEMS
Cdrol.
   ap si ae  M 1 ) e s . i.  a  )1 .    1 1    1       p 1     1 .   1    p u    u     m a u mau