# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0190
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0190?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 133, page id 1815201908:0190
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=190
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000190.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
# Lines: 52 recognised, mean confidence 0.88
# 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.

12
d
lec
prine
leme
i
hoch
CEOMETRIC A.
Lemao
Seo linearum AB, BC)
ED progrectio cerminaca
In R, ee ex punctis A, B, C
EC. crigancur parallelE AM,
SNV, CO, _C. qua PEOPOE-
cionales sinc ipsis AB, B C
CD, XC. ducatuTq; Cx pun-
eto Madcerminum proerei.
sonis R, linCA MR. Dico
hanc per omnium parallela.
cum exccemicaress N, O, P, sec. transice.
Demonstratio.
psideremus primo lineam BN; AI EFGO HLK nON ETAnAE Per NI, Sccabie li-
neam BN supra auc infra N, in T. Cric ergO MTK vna recta. Et quoniam
cogressionis AB, BC, eC. Terminus es R per 82. huiuS, CrIE VE AK ad BR E0
AB ad BC, hoc est, ex datis AM ad BN: aequi cciam ve AK cA ad BK, siC
AM ad BIs ergO AM eAt ad BN, ve AM ad B I maiorem aucminorem quarii
BN, quod est impossibile. Non ergo secabiE MK ipsam BN lupra aUE inETa N
ergo in Nisimilicer ostendemus rectam N K (hoc est rectam MNT K. ostendimus enim
modo puncto MNK. essc in vna recta) cransire per O. dx sic de cereris in intinirum:
Parerixicur vericas temmacis.
P R O P OSITIO CZZXI.
Seoplanorum rectilineorum similium similicerque policorum leries
LMK, balibus indirectum collocaris, cerminum habens longicudinis
punctum R. Ex verriec aurem MI, ad K ducatur recta MIK.
Dicohanc per omnes omnium angulorum rocius seriei rertices N, O,
C, Q: eec. tranlic: sive coram planorum seriem ansulo AFM inferi
peam essc.
aca licprimum teriestigu.
rarum erium quacuorile
lacerum. Cum ixieur ex hypo-
ches planorum series termi-
netur in R, balium quoque
proscessionis cerminus eric R
perr24. tuius: _ quoniem pla-
nA A N, BNI. de C. Similha CunE,
Timilicergs posica, ex elemen. a
eis paret lacera BM; CN.
DO, _c. incer se para IIela cf.
sC, ipElque AB, BC, ec. proporcionalia. ergo per lemma priecedens HK eranCE
per omnes vercices W. O, P, C ec. Quoderar demonstrandum
demonstratio.
Sitar