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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 563, page id 1815201908:0620
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 63 lines, status machine
# Lines: 63 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.
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# After the first blank line: the recognised lines in reading order, one per line.

n
ctio.
60.
CO10,
X
IEt
BV.
1bV.
AOE.
OB
(den
OP
eaM
HIY P E R B O L A
PROPOSITIO LYII.
Ent alymptori AB, AC, hyperbola DLF: &
binx aquidistanes F C, BC, de BC quidem
hyperbolae OccUTTaF D XC F, PONaNEUTG; AL
DicOFK, HIO aquales esse lincas.
Demonstratio.
Scendimus enim BD, 2F B aequales esse; ipieur
C aquidiltet Be, eriam sunc b xquases F. R, C
eROFOSFF1O
L V. I, +I.
Vinchyperbolae coniusacx ABO, DF F, qua
Prum cenerum 6, de diamerri coniugate FIB,
E: 2d quas sINE ordinatim pOLIEX AC, DF, OCCUETONTES aLYMMPEOTO
CormunI, In M.
Dico rectansulo HIKEB, aequari quadrarum L. F: rectangulo vero
IL F aequari quadracum AIE.
Demonstratio.
Vadratum OK equale est quadearis G B,
LBK, vnac cum G B R rectanvulo bis Tum-
peo: id. est GK quadracum, aquacur IIKB
rectangulo, una cum quadraco +B id eA F. NV:
id es dMF O rectanoulo: Sed _x CTK, id cA
LM quadratum, xe quale est rectanguloM FO
vna cum c quadraco LF; aequalia igieur (UnE,
quadrarum CB ona cum rectangulo HIKB,
_ L F quadrarum, rna cum rectangulo M F O: UI
etu
rectanoulo e quadraco CB, aequalia remanene TIKB cectanoulum; d quadia-
cum L. F. Similicer ostendetur PP P. rectangulum, aequari quadraro AK: Ouod
fuir demonstrandum.
IIdem posiris;
PROBOSTTIO LLX.
Dico HIKB rectangulum cAC ad rectangulum lL. L, ve quadra
cum HIB, ad quadratum LF.
2 Coroll. 155
hi
B eerele
Ct
valibus MIFO
A E Occurrences in IE, FI, rectX FC.
Demonstratio.
Ectangulum YE F vna cum quadrato DE, aequale eAE quadratO C.F ; ex F per ct-
HIRB fectangulum, cum C B Guacaco, a guate Cn Guacato rk. Cn aue mm.
ioicur _ TL. L. rectangulum est ad rectangulum AR B sreliauum ad relauum, e huiun
Co F. quadrarum ad quadearum GB, id ellve IF. quadrarum ad quadracum EB:
Quod erat demonstrandum.
VE GL Guaccacur Salt Guattracum C R, HC CF. Guaoratum da Guaalu B, 83
Corolla
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