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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 113, page id 1815201908:0170
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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 0.81
# 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.

i0
verta
SC
iama
i erile
tl.
cudi.
lium
males.
cinua
CCXta,
20
cUEVI
dein-
nibus
E OMEFRICA.
CD ad DF, de DF ad F C, _C. est aureni AB ad BE, vE a AC ad B D, hoc est ; 1bid.
in rarione duplicata AC ad B C, _ CD est ad DF; ve BC est ad F D secuinda
ad quartam, hoc est inracione duplicata BC id BD, hoc eA AB ad BC, ersX
illa progressiones
demonsteandutms
imiles erunc, ec inracione duplicara AB ad BC. Ouod erac
5
C1X
Ulde pos ploscoloraque AB, BC. L.F1, dol. C  6,l
Lex alcern illa divisionenaca, cerminum hrabebic cundem in magnieu-
dinc AC.
Viac SL aQuact AC, a CapTAML CA Ca ML ES LF, MT, 1Y
DOT, ac. qu LGHalCS HHE Continue proporrionalibus B C: BLd, L D, L F, _C.
CrUnCISICUE SL) LM, MN, NO, _C. ipliSquoque AB, CD; BR, FD, 8c. Xqua-
les; cum enim EOTA A C, S T, _ ablata BC, LT, aequalia sinc i necesse est criam
reliqua AB; SI. esse xqualio: _ cursum quia cora BC, L. T, _ ablata BD, H Y
aqualia sunc, paret quoque religua C D, LM aequalia esse. Similicer octendam et
BE ipE MN. D F ipG NO, acque ica in infinicum, reliqua reliquis xqualia cHc. C
soreraque progressio A e C, prosretsioni SL, LM, Eequales Tunc simut sumpEX
_ quoniam SP, L P,MT, _C. aequancur continue proporcionalibus AC, BC
BD, Rc. etiam ip(ae erune continuxe bideoque SL, LMI, MNV, _C. Tunc concirux B L. huivs:
proportionales. acque ica sine termino concinuacurracio, S I. ad I. MI; CrgO PTO.
retsioc SL ad L M, cerminatur in Y, huc consticuic magnicudinem S Y: quare c7d huins
cum veraque progressio A d C simul sumpea, aequentur progressioni SL, LMI
eciam consticuene magnicudinem ST, hoc est AC ex constructione: cundem igi-
cur cerminum habeane in magnicudine AC necesse est. nam A diversoS habeane, TiHC
illi Y ec Z. vel inter verumque terminum Y, Z. Supererie media quaedam maoni-
cudo, que ad neucram seriem perrineae; vel aliqua crir magnicudo, verique lerieicom-
munis, exieque Z. terminus seriei A, ex Y terminus seriei C: neurrum aurem Aeri po-
ecst; nam primo daco, consticueret veraque series magnicudine minorem quam AC
e potico alcetos maiorem quam A C. Duod verumque repusnar modo demonitrats;
non ixicur diverloshabebunc cerminos dicts progressiones, sed cundem: quod crac
demonstrandun
eROPOSITIO CK
IIdempolicis, seminxe prosress L1D, VL, _CD, OF CL a
lectionenax, communis reast, Ialcudinem AC; diuidee in
racione AC adBC
Demonstratio.
DEF PFXCCdENEEM POnaEuF P CNC communis veriusque cerminus; quoniam IuF
miles sut proretsiones A ee C, erir roca series proeressiotIS A, hOC eA A P.
B. oto