# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0168
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0168?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 111, page id 1815201908:0168
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=168
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000168.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

iomu
Eopo
lim
exti
equale
cleu
ion
M
TermI
Perie
P: D
qual
L, 1d
licato;
1
cratio
DFOCC
tiones
GEOMETRIC A
PR OPOSITIO CVI.
AEx Sne dux rariones similes, AB ad L V, a DC A DF, qua
cerminis (ic alternatim politis, ContinuentuT.
AEULMLL.
Dicoveriulque rationis in in Cortuata Me Cemu
Demo.
ronam ex hypochesi AB est ad C. D, ve B C ad D F; crir permurando compo.
nendo, rullumque permucando A C aet C L DBC ad DL: similicer quia
cando, CF ad F C, vE DF ad L Cii hoc est ex hypocheli ve BC ad D F, hoc estex
iam demonstraris, ve AC ad C. P: TUnEISIEUT A C, CP, F C COnFINUIX propOrciOMA-
les. Ouodsiraciones AB a l C.D, ex B C adD F, in infinicum concinueneur, osten-
dam paricer, rarionem AC ad CB, in infinicum concinuari, per cerminos continue
proporrionales AC, C B, P. Cn eC. Inueniaturisicur a cerminus serici AC, C B, P C1, a8. huins.
Kc. licque R. Leaquenon espunctum alsignabile, incor puncta A d R, vlera quod
non cadat alignis cerminus seriei A C, CF. F. G. Ouare cumrarionum AB ad CD,
ex B C ad D E concinuatarum, cermini omnesica concincantur in serie AC, C F,
ec. vesinguli cermini seriei AC, C F, _cc. concineanernum cerminum rationis A B
ad CD, de rnum cerminum racionis BC ad DF; manitestum quoque est nullum
punctum alsignari pose incer A _e R, vlera quod non cadac aliguis cerminus, cam
rationis AB ad C D, quamracionis BC ad D F; neucraisiur leries terminabicur
inter A e R: Sed neque rili dictarum rationum cermini eran siliene K, cum perpe-
cuo concincuneur in serie AC, C R, P C, _C. (quae ex constructione non transilie
onquam K) ergo binx seriesrationum AB ad CD, e B C ad D F, cundem habENE
cerminum K. Quoderac demonstrandum.
CD Cs ad P F, VE D P ad F G, cric permurando componendo, FuRTUM GLE PErU-
V
Ronicudo AB bisecta siC LH C, DC AMICIMMB; aC DIM L; 
ADE in F; _ F F in CI; d F C in l; acque hoc semiper hac:
Dico alterna huius progrenos cel lore in puncto, quo ma-
onicudo AB, diuidicur in parces, habences rationem quam vuum ad duo,
siucrerminum progretionis ablcindere BC, certiam partem magnicudi-
nIS AB.
etbd otib.
Voniam DC dupta cst C. E, e BC dupla DC, exit BC, hoc eA A C, quadeu-
pla iplius C P: similicer Cunt LL cpia  CL, _ D L. dupla L R, Cric _E DL,
hoc es CF, quadrupla P C; lunc isitur AC, C R, F. C tres concinux in proporcione
quadcupla. Deinde cum B. D ex hypochesi dupla sic D F, ec CD dupla F. D; Cricice.
rum C D, hoc eA BD, quadrupla DF: Similicer quia CF dupla elt FI, ex F L du-
Pla GF, eric P F, hoc est D F quadrupla F L. luncigieur BD, DF, F. L concinux in
ratione guadrupla. Jeaque E alcernailla bil ectio sine Racu continuetur, consticueruE
verimque progressio in intinitium, proportionis quadruplx: _e quoniam AC qua-
drupla est CF, exic _ BC ciusdem CF. quadrupla: cA verO _ CF, quadrupla
L C, acque ua in infinicium: progrelsioisitur A C, C L., L. C, XC. endem eAt cum pro.
Bretsione