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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 337, page id 1815201908:0394
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=394
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 38 lines, status machine
# Lines: 38 recognised, mean confidence 0.77
# 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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mon
O
SLLIPSFS.
DROPOSITIO CLZKVIII
Ececellipsim una ex diameeris coniusaris aequalibus AB, ad quam
Dieo quadraca AC, A D mu pla  esatt ualilatis IF, F H s.
mullumpris.
Dponacur recta C D ordinarim; iunganEuTG AC, AD; cum CuPeF F P
xequalticce b amesprepecenuet ma i Bacictibatutc-
culus E. FK: actaque per oan lansale LL, LIL.
Demornio.
Vadraca AC, AB limul lumpea =GuaIa IBNCGHaaACS a C, C A  B1 TurPIIS, L +. BCM.
Lee quadeata TE, F K b aqualia sunc quadraris LFI, HI bislupeie pelpiae.
are
cedencem C O, IEI quadraca sune xequalia, luncque lcem xequalia incer se quadraca 17. primo.
AG, B HI, quod AC, F. E recte aequales sinc ex constructione, quadracaigitur CC.
AC bis sumpra aquantur quadratis GHI, P Hbis sumpris; lgitur ec quadraca duo
C A A D simul Cumpea equalia lunc quadraris LP. F. K simul lumpris. uod exat de.
monttrandum.
3t
lkdeOdItLata.
IncAbMpSaSAB C . C ao C CeC.
LEcribacur C F. D; Polucis EL ordinacim ad arem C.D, qua circulo oc.
currant in F  MI, axi aurem in I ee ellipE in L; ducancur Cx IF por O)
centrum, FHoccurrentes circulo in H de H, ellips aurem in FI.Ii
Dicoeltevequadrarum L. L ad quadracum F I, sic P R. II rectangulum
ad rectangulura FKHI. . l3
il 180 Demonstratio.
ix lcholio quarie huius libri pacer has
Lduas proportiones FF ad F F, _ F L
2d F L. caldem ehe com CattoC L. L, al
FP quare cum ratio rectanguli F P. L ad
rectangulu LP. L; componacur ex rario-
mibus FI 2d F F; _ D L ad F L, erit
racio rectagulifi P L. ad reccangulu F P L,
duplicaca racionis F I ad FI, ac proinde
eadem que quadeaci E Lad quadracum F. L. lc a teclat Ba FL. L u elatiBula
t