# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0234
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0234?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 177, page id 1815201908:0234
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=234
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000234.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 75 lines, status machine
# Lines: 75 recognised, mean confidence 0.83
# 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.

l
eran
C
au
Dil
H in
Cta, d
istrat
vel
DaTet D
quec
il
Cripro.
u1, 11
un
b051B
C IR
tis ariguluS F G F ipE AC B ad rercicem po-
LcuIS; igicur anguli AF C, F. G F, sune duobus
Fectis aequalesi adcoque BD, FC. parallela, de
arcuS HIF, CD, corumque subcensx aqua-
les; vnde ec anguli DHF, FTD C aequalibus
arcubus insictentes, xquales lunc: elt aurem
angulus AOB, aqualis angulo CFB.
(cum AGB, BF C segmenta reliqua sinC Si-
milia) ad eoque d celiquus F eII. aqualis ce-
liguo CF D; isicur criangula LIL C, CF D,
unc inter se aequalia; ee II C latus xequale la-
teri F. D.
Sexto, quodsrectaD per apicem acta,
per communem incerlectionem F cranseat;
sic ostendetur aequales esse rectasCF,
F D: Snc primo seomenca similia semis
circulis maiora; ductaque ex A peE
E, reCta AEF, iUnSaNCUT CF, CF.
ED, C C: Duoniamigitur sesmenta
Timilia, semicireulis sunc maioea, cric D
extra lineam A C. E enim heri pOME,
(IE CF A rna cacemqie linea cum
AC. cum ergo ob limilicudinem lc.
emencorum, anguli BR A, BF C sInC
inter se aquales, crunc etiam recti:
quodherinon pocest, cum segtmenta
surt semicirculis maiora. quare punctum P. non est in linca AC. Cum ixieur ansu-
lus AFC. vra cum angulo segmenci AI C, duobus arectis sic se quas; sicque al. d n.
pulo AD C, aqualis angulus AE B (ob ADC. AF B segmehcalimiMa) id el an-
vulus DF F ad verricem oppolicus, cricintulus AF Cs una cum ansulo DL. L.
duobus rectis aequalis; unde F C, BD, linex aequidistant; _ arcus OF, D C, adcoque
ex arCuS CC, D F corum que subrenla equales, _c. veprius.
Si vero scometa similia minora fuerine lomicirculis:
demonstrabitur repriuis, punctum t, esse extra lineam
baleos A C. quia verO AF C, A R B segmenta (uncSi-
milia, crun anguli AF B, AFC aequales; sed angulo
A EB aequalis est angulus ad verricem DF F; isirur
anguli D P F, A F C sunc aequales, e BD, F C rC-
etae aequidictanCeS; quarC _E arCUS C C, DF, corum.
que subrensa xquales sunE: dc. vei prius.
Reliquum esset casus eosdem explicare cum veriex trian-
guli ABC cadit in peripheriam vel extra aream circuli
qui supra basim A C constiturus est; se d quia omnes illi, de-
monstrationes communes habent ex constructiones cum casibus quos explicuimus, dum nimi-
rum vertex B, ipsa areacontinetur, lectorem non olterius defaricandum censeo: hoc tamer
pramoneo, vi dum B vertex trianguli, cadit extra sermentum baseos, casus excludat, quos in
medium proculimus qui BD lineam iubent earatione duci, ut cum basi trianculi non conve-
vias, quosineptos esse huic maveriae manifestum est.
12 L23 X837V CMEM2IZ
_ O. Sit Tta. Xa amivvani
Et OleBAS 
rici
denus luper A BC erian suli laceribus segmenca circulorun, sta
constructa fuerinr; ae per B verticem ponatur P. D, ad cuius extrema
ex scenero F circuli super basi descripei, alic antur PP, F.D . evlunria siro
DBIMSHLSEFC.) is CMIVF
Dico casincer sexquales e. P. Q et si w Sninnm (1 X. TEL HI CMMIIIEETS
SIEOFAS MaC