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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 584, page id 1815201908:0641
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=641
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 57 lines, status machine
# Lines: 57 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
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# After the first blank line: the recognised lines in reading order, one per line.

2LLCLLBLA.
Eperbolam ABC, cuius cenerum D, Subrendarrecta AC, divila
bitariam a diamerro DF; imegue A B, CB, ac diuilis bitariam
in F _ C; demitrantur DL, s, Ocurrences sectioni in HI ee l, iungan-
Dicorriangula AH B, B IC, xqualia eNe.
Demonstratio.
DOnatuE ex F ordinatim FTF, ad diamerrum hyper-
bolx DF. Occurrens lectioni in MI, e D C lince in
T: quoniam AB, BC in F X C, dinila lune bitariam,
FC aequidistabit A C, adeogue _ ipE FII cum IIM.
et A C ordinacim posiex sinc ad diameerum D F: qui2
vero AC in F dinita es bitarIAM, CFIE _ F C in HI; a-
deoque _ HIM in L bitariam quoque divila. Sed e
FTI in L, bissecta est. quia FC in N bisectx aequidictat;
luncigitur aquales lincae HIM, FTI, et puncta M e L
eadem: quare DF, D C diamerti in FT _E ML, prOPOr-
cionalicer sune divisx. rursus cum D F NV, D ON crian.
gula, icem E BN, G BN aequalia sinc, reliqua oriam
DFB. DOB crianoula incer (e Xqualia sunc. Vede cum
DF, D C in EI d M, proportiohalicer sine diuila, ae
qualia quoque sune rriangula D ETB, DIB; adeoque e
reliqua F HI B, BM Ci: PacCCS _ illorum dupla AFIB, BM C crianglila sinter
le aequari: d etaldemoaum lsi
Ecs a C, duxe parallelae AD, BC, innganturque
Bedciangula ntaaa s MIcripea, esse incer se aequalia.
s
Demonstratio.
I_ CeHIro E dueantur diametri PF,
F C. diuidentes rectas AB, C D bita
riam in F e C occurrences hyperbole
in H ex I, e iungancur AHI, HIB, CH
ID, cruncha ceriangulaa maxima segme,
eis AHB, CID inscripta. dueta dein
diamecro F. R, qux bifariam parciaruere.
atam AD, Ponatur FC, eric illa paral.
sela linex AD, cum AB, D C in F X 6,
dinicae sine bitariam, constimuexque sinE
inter parallelas AD, BC. ex FTigirur du-
catue ordinacim HM ad diamecrum ER.
ostendetur, Ve in priore propolcione il.
lam producam sccurrere communiin.
proporcionalicer elle dimlas. Lunctisigitur LB, LC, BN, CN; cum FG; HIL BC
agordistene; _e in E, M, N bitariam sinc divisx, aequalia sunc criangula FBN.
aqualia:
R OPOSTTIO CIV.
Furque AII, IIB; BI, CL.
PROPOSITTO CV.
CD:
BHcLI
ol3
dis.
es
nar
ACIM c
cerlectioni P: adeoque FG, FIL LGOIAMLAIC, d LE, L G diameErOS in YY e L
CC, irem N P. B, H L. C: vnde  rtu L L. D L. CC crransula quoque lune
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