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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 189, page id 1815201908:0246
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=246
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000246.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 70 lines, status machine
# Lines: 70 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.

exun
ualen
dle
D
12
ve
alita
Ci
trane
BBenS
D.
Ar
tam.
AC
19an
e
C. IR C V LVE
Demonsnto.
iX F Cehiro potratur F. F. Ouo-
Loniam PONIEUE VE AD ad AC)
ACDB ad CB; CrUnE AF, CFs
B F linca : in continua rarionc. 191-
cur cum FFCc aequalis medix CF,
CA AC b ad B. C, vE A F ad FB:
Est hac conuer sa rricesimae cerriae hu-
ius.
P ROPOSITIO XLVI.
IE AD linea vecunque dinila in C: de seripeoq super C D circulo,
D Ponacur ex A linea AP. Occurrens circulo in F: duCaTUT aUTCM FB,
ve AF, FB proporcionales sint, lineis AC, CB, d ex B crecta normalis
occurrac circulo in C.
Dico AO lineam circulum contingere.
Demonstratio.
Vm sc A F ad FB, BE AC
ad CB, erie angulus AFB
divisus cbitariam: quia vero linca
FHI, rectae CH aequalis est,
erune AIB dCFB BE in conei
nua ratione: Unde e G A circu-
lum cconcingir. Quod fuit de
monstrandum.
PROPOSITIO XXXVII.
Irculi ABC diamerer AC, verimque producta lic in D ee F. pun-
cta, aqualiter a CeHErO FT dictantia, Polca deinde DB contingen.
rein B, demissague normalicer B G, ad C A diamerrum, AAEO F, aqua-
lis AG: ductisque rectis DI, TE. innoaneur IG; IF.
Dico DI, IE, iplis LO, LP proporrionales esse.
vngacae Al. Guolicacu
DB concingir ciecu.
tum ee BC normalis po.
nicur ad diaMETEUM, OFHNE
FDEL, AHI, BHin con-
cinua analosia veile BII,
CFI LHlicltaucem f1L
IPA ALL LGuacoS BIEUE
adIF. lcdveL CadC l,
iins
B22. Lib. dC
non
du
et
C27. hnins.
c3.
ve EC ad C F ica 5 F. I
ita D A ad AG, hoc eAt
Demonstratio.
ronibum
DF ad I6, quareve B L ad IF, ita D F ad IO. ee permurando inuerrendo DL2d
Llve LC ad 165
PRO