# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0990
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0990?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 933, page id 1815201908:0990
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=990
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000990.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 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.

PROPORTIONALITATES GEOMEERICE.
Demonstratio.
GtaEvE C ad F, it a F ad
LFI. Bitur ralio B L ducto
in C Frationem, cAicicara-
tionem B ad Hl, cM MMCM
C F racio Cpua Lal10.
nis BP: isiut ratio B, 24
est criplicaca racionis B ad
F. Sedracio D ad 6, simili-
extibere ratt  ad C. Quod erac deuonstrandum.
275. huius.
b:
2. Pro
ter est criplicataracionis BP. igitur parer rationem BL Auctam in rationem C F,
tROPOSTTTO CZZX.
lucoa Coe proporcionalium leries A, B, C, X, D, L, F e 6,
DIEI,Z, I, L,M: SinE autem Z X Z xquales.
Dico ( C,  , D lin CaB, C L, L. d A, C, M, F elle
in continua.
demonstratio
Acio BH, C dupt
aest rationis CF, hoc est per hypochelim rationis LL. ICa C27. Pro-
ciusdem rarionis TK duplicata cstrario HL, quod HI, I, L R, L, Uinc in conri- es
nua. Ergo B eA ad FI; vE FI adI. scd d cciam L cR ad F, vE B ad FT. ergo B,
FI. L, F. sunc in continua. Ouod erat demonst. eodem discurtu ex ijsdem illis propo-
litionibus 26. e 27. Plogreslionum demonstrabimus elle coneunlle proporctoltales
test
26. Pro:
A. C, M F, de SC in inAnitum:
P ROPOSITIO CZXKI
a getalibus X, Z
IEdemposicis: sumantur B, FI, et E, L. aequaliter distantes a mediis X.
Dico rationem BHL esse ad rationem HIB, veratio BF, cstadrario.
AeIIL.
Demonstratio.
Tac ve B ad HI, sc FF ad N, crix Crario B H ad rationem AB, vE B ad V. Hal 
deinde re E adII, Ec P ad P, cricEracio B R ad racionem ll L ve B ad L. ila huius.
aucem ex constr. I est ad FI, ve B ad P, eric permucando L. adt B, ve IF ad L. F 13. huitn
sedSre L ad F, hc B cs ad FI. ergo FI est ad P, ve B ad FL, hoc CS1b. 11
EI est ad N: aequancur isieur NV, _ P. ergo B CM ad NV, Ve B cA ad P. OuatC CMIISs
rario
oll. 18
 cn