# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0939
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0939?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 882, page id 1815201908:0939
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=939
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000939.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 47 lines, status machine
# Lines: 47 recognised, mean confidence 0.85
# 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.

a 7. hmius.
PROPOR FION ALIF ATFS
Demonstratio.
Acio AB ad A C racio.
nem, cam habeca pro.
porcionem quam C ad B.
racio aurem CA dd BA
.torich
uduuir demonlaau
RetOSITIO XIII
racionem clt b veC ad Bi
ergorerario AB ad AC rationem, lea quoque est rario C A ad B A rationem.
prima racionis aa aud F..
AEx Ine quale scunque rationes AB, C D: RaE aurem vED, conse-
quenssecunda racionis ad C anrecedens lecundae, ita B conlequens
Dico A ex P. esse denatoeo La alau.
Demonstratio.
Voniam cx aypo-
hCa ClCadC. H
Bad F, cric inuercendo
Lacio Ti ad B; eadem
cum ratione C ad D:
2. B
Desi
11430
ED. Quodtuir demona
E
adrationem CD, esveratio A ad B, ad rationem L ad B,; sed
ratio A ad B, ad racionem F ad B, est ve c A ad F, igicur racio A ad B, ad cario-
nem C ad D, est VE A ad F: sunc ixitur d A ee P denommatores rarionum AB, _
eR OPOSIFIO XIV
aris quibuscunque ratiBIS AB, CD, Rat vE C ad D, ita A ad E.
Dicorationu B, CD denominatores esse F, et B.
Demonsitalio.
res dacarum racionum AB, et CD.
B de R.
Z Acio AB ad A P. Pattonem.
ad B, Sedracio AH
est exhypocheli eadem cum r2
tione CD. ergo ve F ad B, ica
racio AB ad CD rarionem,
Curcixicur R ee B, denominato.
tKotostItO. XV
Onacurratio ina qualteas AB _ alEera X qua lICarIS C D.
Dicorationem AD a  rationem, habere proporrionem A
ad B, raricte tet au B rationem, habere proportionem quam
Demon.