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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 118, page id 1815201908:0175
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 44 lines, status machine
# Lines: 44 recognised, mean confidence 0.84
# 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.

2
P R O G R F SSTONFS
erro sectio ipsius F B, in rarione V ad Z, Cadic vlera D, versus B: ergo cum criam vlera
R versuS A CadaC, InCEFD e K, continsaenecesse cA, nempe in F; similicer lectionell
ipsius F Aincer I _ F, Fucuram in C demonstrabimus, acque ica in infinicum; alleu
P A RS SE CVND A.
IIdem positis: ( C CadaCinEeF L _ R (NZ RInCeF B _E K caderet, Forer casus prima
parcis) simili plane dilcurtis demonstrabimus eadem omnia contingere que prius,
lus enim idem omnibus diuiliomibus sequencibus quadrat.
hoc lolum mucaco, quod ligna divitionum en Cn LoR, ex C. D F, FIM, e C. ad alcerum
acus orde Conaeu.
2
TF
Aca (ic proporrio V de Les emascsao AB ita lectain le R, n
 ia au B, aD alA, HelCV elt ad X. Alicer deinde di-
uidacet B L GuoClgue tandem loco cadac C, modo noninci-
FiaE aurem C B ad D B, vEV ad Z; ee D A ad F A, ve V ad Z: icen
EB ad FB, dF AL Aa GA, _ GB ad BEB, _ FI A ad L A, Fucrincin.
cer sc reV, eltad X: Arquehoc Cemper concinuetur.
Dico alcerna huius progrestioniscerminos, Forein L et K, ubi AB, di-
vidicur inratione V ad X.
dat in I auE R .
omomratio.
Voniam est ex constructione C D au DB, M L. B ad F B (luncenim veraque 2d
arg. Guin. Linvicem in ratione V ad X) criam C B reliquum, D F reliquum, erie ve CB ad
D B, id est sicuE V ad Z: _ quia D A cA ad F A, vE F A ad C A (nempe inracio-
AC V ad Z) rurtum eric D F 2d F G, VE F R ad E A, hoc est ve V ad X: sunc igi-
TuT C E, D F, F Cntres continux proporcionalesinrarione V ad X. ergo racio C F
ad FC uupmeala eh laliono V dd a. Smmer olendems L. bHL. CL CMC
continuas in ratione V ad Z, idcoquerationem F. C ad C L, duplicatam cAC r2-
tionis V ad X. Cum ergo criamrario CF ad F C, Sc racionis V ad Z duplicaca,
CrUNE CF, F, C, CFL, in continua analogia; aeque ica continuando (ine Aaru alcer.
nam illam divilionem, demonstrabimus consticui progreltionem magnirudinum C B,
EC, OL, LN. ac. concinue proporrionalium in ratione duplicara V ad Z. ab alce.
ravoro parre, eodem plane discurlis ostendemus D F, F FI, FIM, _C. eNe continuas
inracione duplicata V ad Z; ac proinde sic quoque constirui progresionem pro-
porcionis duplicaex V ad X. vlcerius quia A R est ad R B, ve B Lad L A, componen-
do AB cric ad R B, ve AB ad A I; ideoque K B, AI aequantur: addicaqi IR com
muni, aegualeS CrUNE IB, A R: ErSOVE AK ad R B, id elt ex costructione ve V ad Z,
b1g. 6 uin- RB. AItaCt C1BO FB, RB, CP erir b ad DR, reC B ad D B religuum ad reliquum,
hoc est ex costructione ve V ad X. similicer demostrabimusD K ese ad L G VEV ad X,
Crun
sc IB ad KB: Dunre cum e CB al DB. Hee ad L.cciam CB cric adD B, velB
u u     as es  p  e  e  pt         1 . i         .      . i t  u     1u a  aa iuo u