# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0124
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0124?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 67, page id 1815201908:0124
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=124
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000124.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 54 lines, status machine
# Lines: 54 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.

caH.
na.
bus
H
H,
Ei
nul
am
sC.
esF.
E ex
C,
D.
c2:
AC.
H.
6
s.
GEOME tRTCF.
serius proportiones ita conuertat, que madmodum hac propositione fecimus. En infinitum repe-
siet plures ac plures subdivisiones rationum, sola praxis in propositione posita obseruatione.
PR OPOSITIO AVIII
Inc quacum que e quorcumque magnieudines A, B, C3 , L; Pona
curque F omnibus (praecer vleimam) bis sumpris, ac vlcimxe F. lemet
sumpeae aequalis; C vero aequalis omnibus simul Cumpris, denique FL
qualisvICIX F..
Dico F, C, EI arichmeticam A
analogiam continuare.
demonstratio.
IncaF, id est A, B, C, D, bis lum-
ex, una cum E semel, excedic rect a
Steet l, B, C, D, P semel sutipeas
exCCH A, B, C, D, semel sumpeis. Sed eodem excellu exceaclinea C, iplam fI,
quX aqualis pOnIEETCCtX F, igITT F, G, FT LINOX ATITHIELICAM CONCIHUANEPEOPOFL
cionem. Duod crat demonstrandum.
Scholion.
ae mirum videri non debult Frederico Commandino, P appum, cum lb. 3. ex C eometri-
Pappi desectum, ut vocat, eodem libro propositione 29. Supplerenicitur, continunale e
metricam aplenare, exqua, cum quapiam ratione Prithmelicam analoeiam deduxisset, non
ideo caeleris non proportionalibus quantitaribus commune esse, posset aemonstat: siquidem a
problematicinitoris splendore alienum videtur, certum es determinatum quid in constructio-
nem aamibere, cum obuium quoandet fuerii jufficiens. Sed hac in cratiam antiquitatis dicta
Leaproportione, analogias, ac naatats etu net. Cas nestexisse quanaoquiaeo
non ex Geometrica rantum se d quacum que quantitarum serie producatur; quou Lappl ica
reris sacacisimum latere poruisse vix crent potest:; vel certe oportuiss et C ommanutu antis
sint, quam venerart omnes dederent. Tuls hi sal drum labores, es ingeniorum parta
hucusque no diat a recentioribus acaequata.
PR ODOSITIOATA.
Atis duabus progresionibus cCotuM I Cora ratione A-
richmerica A, B, C; D, P, F; ex veriulque scriei cerminis A, D,
F in vnum conslaris constiruatur certia leries G7, FI, l.
icoeciam C,  l este in comunameliea apalogis.
ei t
Denton-