# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0970
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0970?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 913, page id 1815201908:0970
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=970
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000970.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 49 lines, status machine
# Lines: 49 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.

vel
11
973
_L DALL IRIC A.
AB eA adrarionem CD, veracio F. F ad rationem O HI, criam , rario AB est ad a60 huins.
racionem GTI. netaio CD ad lachene LL ea ance ostendi A eAc ad I, vera-
tio AB est ad rarionem Cx FI, _ C esse ad R, veracio C D est ad racionem B F.
ergo A csadI, re C ad Khpcesrario AT producta, ve supra demonstraui, ex mul-
ciplicacione racionum AB, C FI, primae ec quareae eadem est cum rarione C R prO-
ducta catitutbalibum ucttraum et acteicla. a 
Arastao
Corollarium.
Vod siires Fuerinc raciones proporcionales, prima in cerciam ducta idem produ.
ccd media in sciplam. Demonttracio Palelet propbtione lam demonstra-
ia li media rario bis sumatur.
YI cacio B ad CD racio
nem, candem habeac rario-
nem quam DE rario ad racio-
nem BF.
Dico A esse ad F, vEC 2d F.
Demonstratio.
Inc primo harum racionum cermini
sexnomero, virrualicer octo conci-
nences, ve in primo schemace, cumra-
rio AB sIC ad C D raciONEMS VETA-
eio D F ad B F racionem. igicur ra
eio AB ducta in BF rarionem, aequa-
cur b racioni CD in D F. sed rario
AB in B F pacionem, cAt cracio A ad
F, de racio CD in DF, est d rario C
ad P. ixicur ratio A ad fi, cadem est
cumracione C ad F.
Sint deinde vein secundo schemare
octo cerminis invenianeure parionum
AB, CD denOMinACOTES A _ C.
icem D E, B F rarionum denominacores D d FI. Ouoniam igicur racio AB ad
CD rationem, ponicur esse rerario D F. ad B F rationem; isicur t A ad G7, habecF +2 huins.
eandem proxorcionem quam D ad FT. quare quod oritur ex ductu A in FI, aquale
cric Silli quod generatur ex ductu C in D. ergo criamracio A. ad B, ducta in FatiO- S Per corr.
nem B ad Fi peoducee aqualem rarionem cum E. D ductoin DC. Componicur 85.
aurem rario A F ex ratione AB ducta in BF, _ racio R ad C, compolica es CxF2.
tione F. D in DC; isitur cum equales sinc raciones AF eC EC, crir A ad F, VE
P ad C. Ouod Fuic demonstrandum.
PROPOSITIO LRXZVIII
Tcratio ABuCta in C D eadem cum ratione L. F ducta in leiplam.
Dicoem AD ductam in C B rationem, candem quoque
elle cam Lactore L. F ducta in (c.
EROPOSIFIO LXXXV
Demon-