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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 1105, page id 1815201908:1162
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 46 lines, status machine
# Lines: 46 recognised, mean confidence 0.82
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2105
EV ADR A TYRA OTKCFLL
P R OE OSITIO X
Vodliracio A D duplicaca tuerie racions   L le propoo-
eo ABC, OtF.
DicoC d lGualcllates aguales e.
F Sc conuersa praecedenris, eiusque demonstracio facile elicieur ex hypocheti.
PROPOSIIIOA
Viracio AB duplicata
D Fueric racionis eius qua
continet ratio C adD, Fa-
tio vero C ad D, duplicata
liceius quam habet ratio FP.
ad F;
Dicorationem A ad B, quadruplicacam elle rationis F. ad F.
Demonstratio
ClatDe ad D, ita A 2dF; veque F 2d F, ica F ad R: erie icaque rario A 2d B,
B, hoc est duplicata R ad B, X Cx racionC Lau L, d R ad B, qua cum agualesHE
inter se et limul xqualesrationi A ad T, pacecracionem A ad B, quadruplicacam
eseK adB, sivC F. ad F. Duod tuir demonttrandum.
Est. 1 VI, 5
VInc quacuor ordines
Dquinque proportio-
nalium ABCDF, e
NOF, d ASEV, ha-
ciraces C, K, P, V, aquales
incerle.
cinetrationem quancirarum  ad I.
duplicoca racionis P ad B, vel A ad I: d rario Iad B, vel A ad J, duplicACAL
ad K, vel R ad B. Compolica aurem est ratio A ad B, ex ratione A ad L, hoc eA I ad
XII
FOFTIK. deinac L. MI
bencium vlcimas quan-
Dicorationem quanticarum AF ad L. O, rories continere rationem
quancicarum C H ad . Guorsraco Guaa CL alt 1YS, CBH
demonstratio.
Z Acio A cum F ad L. C, aequacur racioni AL, A O et l L, F O. a Similicer a vo S tum
racio quancicatum C HI ad NS, aequaturracioni CN, CS, e HIH ELSdeiri- in
admodum eriam ratio D, cum I ad OP, aequatur rarioni D9, D F, ec IO, TT.
bergo quociesrationes AL, A O, F L, F O contineneracioies C NV, CS, FTNF, FIS: B PeroAM
e quocies hx concinencraciones DO, DI, TO, PP, cories concince eciam racio dem
a de L lalionem eia a2s. cllatpla ractom e alDI.
  a . 1 . 1 11. 1 111
A 22 5
Scd
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