# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:1016
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:1016?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 959, page id 1815201908:1016
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=1016
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00001016.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 50 lines, status machine
# Lines: 50 recognised, mean confidence 0.86
# 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.

YNEYLA CFLINDRLCM
Demonstratio.
Vaa OK quae contingac circulum in C.
OccUTEAEGUC A B producta in R. AaC aM-
vulo KEC I, Equalis angulus TOFI, Factâ dein-
de rectâ TE aequali AI, delcribaneur circulo-
rum arcuS L. O, DC TemidiaMCErO AB. OuO- X,
niam LOF angulus rectus cAt, reliqui duo
KOI _ M C F, recto lunc equales. Ce d angu-
lus HIGF aequatur angulo KCFT. ergoetiam
FTOI cum MOF, Facic rectum. Sed eriam
TIOI cum HICF, Facicrectum. Igicur IIOF
angulus angulo FCM est aequalis. quare cum
AO FaNSAE CC in O, CEam FFC tangeF
arcum D C in C. Similicer demonstrabo ce
iam arcum P. C: in eodem puncto cangi ab IIC.
Ouare aequales lunc Agure IOL _ GDF.
quancicacibus AC I de GF F. Sed rectangu
Ium IF, excedichguras CTIL, D CF quanci-
caremistilinca LOD. Cadem erso quancicaro
rectangulum IF, luperacFouTaS AC, L, C+ F P.
sintisicur illa dimidio segmenci AD P mino-
res, et consequencer IF maius est dimidio eius.
dem sesmenci AGFD. Quod demonclrase oporcuit.
PR OPOSITTO IV
celarsul maximum cuinis leomento circuli ilepcu, gadu
Cemicirculum non excedir, maius est ciuldem seementi dimidio.
Dembnrado.
ex quo legmentum quoduis
demacur DBF, habens DF.
Parallelam AC diametro; eri-
Bacur deinde ex I, cenero circuli
normalicer IB, quae dividerD P
bitariam; perfecto deinde re-
etangulo lacicudinis DR, altieu-
dinis vero TTB, erit F C circu-
lum concingens, equidistat enim
DE recta FG, e diameter LB
orthogona est parallelis PC,
D Eipolica isicur quavis XL. M,
temanebic B FI MaIOE K I: quare trianoulum DBF, IAIS CEIE DK L Cag
ne proinde maximum est eorum quae legmento DB E inseribi queune: est aurem
DB F criangulum dimidio legmenti maius, eum criangulum DB F, rectanguli F
sic dimidium. criangulum izicur maximum dimidio segmenri est maius. Ouod Fuir de-
monstrandum.
DOnatur Cemicirculus ABC.
guX aequidistet BFT, Cric K M minor BL. AOTa C1GD L, L.M aequalibus lineisi
F. 0. 2 102101 , P, B
ed stie chceit
s ut pe e  e s et 1 ue a u  e e p e e sute  s  p u et i e  p  ta   u  e t e   st eu  a i  pat p et  t si ate se e este u sstes