# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0942
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0942?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 885, page id 1815201908:0942
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=942
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000942.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 56 lines, status machine
# Lines: 56 recognised, mean confidence 0.79
# 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.

38
A E OM L FRVC R.
PROPOSIHIO XXI.
PINCTaTIONES AB, OD ve A ad B.
 Dico quanticares CD, aequales elle intet lc. uodlratio CD, lE
ad AB rationem, ve B ad A.
Dicorurlum D X C, quancicates xquales este.
Demonstrar.V SIECB L
idcit
CIe isitur primo ratio AB ad
DCD, ve A ad B. Racque ipsi C
aequalis I: cric a Ve A ad B, ica
racio AB ad CB rarionem: (cd
ve A ad B, ica est ratio AB ad
CD ex suppolicione, CrgO VEFZ
eio AB ad rationem C F, ica eAt
cadem racio AB ad CD: quare
exdem lunerationes CP e C. D; ac proinde D, ip ( F, hoc est ipl C aequalis est:
quodcrac primum.
Sicdeinderario CB ad rationem AB, vE B ad A. Dicotimiliter C e D X GuIa-
les elle quancieares. hac enim veprilis P ipsi C aequalis, crie ve B ad A, ICa raEIO
CF ad AB cacionem, quare iterum re pruis oltenderur C de D, aquales cAlc.
Duod tuic demonctran dum. Hlac est converta i5. huius.
PROBOSITIO XXII
e ie tra et d A  monoie c
NIc rario A ad D IOr ea, quam habet C ad D, _ Rac D ad C, ve
.CVLAEt 3 LOHE. BAISBEECCLI 
Dico A maiorem esse quam ve (ic x qualis F.
Demonstratio.
Ct 
i
B. in
1012S.t EN
B ad F..
Voniam eAve D ad C, it2
B adF, crooracio AB al
CD rationem, est b VE A 2c
F. sed ex suppolicione rario
A ad B, maine est racione,
quam habet C ad D. CrgO
A maior est quatri H, pari
quoque modo quod (racio A
ad B, minorhtracione quam habet C ad D, e Aac D ad C, ve B ad F, osten-
decur A. minor esse quamm _c P.
S. L.B
MIli
n
25. buciis.
LXTEI
ROPOSITYO
b 17. tuia1.
Vod liquatuos Guamitates A, B, C. Dcandem concintene aMa10
n.
Dico rationem AB ad D C rarionem, eandem habere proporrio.
nem, cum ea quae incercedir inrex A e C.
DeMO