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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 581, page id 1815201908:0638
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=638
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 62 lines, status machine
# Lines: 62 recognised, mean confidence 0.81
# 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.

uio.
nAR.
unis
Ao
tion
10si
1B,
i8
A. AB
ue
F
ilq
ene
NC.
Jam
1
D.
HI Y PEM BO L A.
PROPOSITIO ACL.
INE AB, AC asymptori hyperbola DF F, e ducta DB, FC alym.
Dpcoto AC aquidiltenE: IUnSaNEUTG AD, A F, _DF.
Dico criangulum ADF aequale esse AglIrX
quadrilaterae DBGF.
Demonstratio.
TRiangulum BD A = xquale eAt F C A criangulo(quia
dimidia rectangulorum D A, A F aequalium): igieuE
ablaco communi triangulo A C T, rehduia sune aequalia:
Scilicer F AI criangulum, quadrilacero BD GT. addi-
ca icaque communi tigura DPF, Cric D A F criangulum
aquale quadrilacero DB CF. Ouod fuie deMton
dum.
PROPOSITIO
Tine dux hyperbolae xqua-
 les de imiles, quarum a (ym - 2521
DEOTILINE AB, BC; F.D, F. F: PO-
NANEUEaUECM AIE, L. MI, _ SF,
R Oproporrionalesinter le, e
alympeoco cuidam parallelx.
iunctisque RL, OS ac dinils
bitariam per diametros BFI,
F C, Occurrences sectionibus
in I d O. duCaMEuE IR, IL, _
D0 05.
Dico triangulum LLIL X
quari 9OS criangulo.
Demonstratio.
Donancur LH, O aGaaeS
AR, OR. quoniam AR, LM
SF, OR, in aequalibus ac similibus
Ayperbolis, proporrionales TunE:tra-
DeZIU AKL M Bxquale cAO RF S
Erapezio. & quia concinux lunE PrO.
porcionalestam SFi, cOP, OR,
quam AR, NE, ML, adcoque SnE
Proporcionales AR, NVI ipsis OR,
OP: iBitur quadrIlaTeTA ARIN, QOPR d aqualia sune inter lc. ee Similicer 3+. hu-
EFaPCZIa INML, OP F S. ablacisigitur trapeZiis AR IN, S INML agualIbuS
iplis QOPR, OPFS, remaner criangulum KIL. aequale reliduo criangulo
905. Quodtuir demonstrandum.
Ba
hains
c