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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 64, page id 1815201908:0121
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=121
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 53 lines, status machine
# Lines: 53 recognised, mean confidence 0.77
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 . t . 11
64
L LKL 5SIOHES
AB, BC, de F, erir linea F. aequalis C E: deinde quia COnFINUX (UNE AB, AC, AD
AII. HMInS. B Aac B C xqualis CFD, CrunE quoque in continua analogia C G, DC, D A. p0.
isicur L aequalis C C: vr L L. GuC HUNC XQUDL CS, VEpOEC Ip A C C L C5.
Duod cratpropolicum demonsteare.
i
513
BAIHEAFAUECM CONFIHUX A D, DC _E F; CrUNE IgIEUE CONFINUX F, DC, AD: est
Lema.
il et coctaris3: 12.
B cob 113Z 3ea
 F.d D es CFX m F
11. ∞t12C1. 3
Demonstriov
E  5
1
cunda ad CFi cerciam, ica in ordine alcero L. prima, eAt ad B A sccundam, ergo ex
b23. Ouin. Zqu0 in proporcione perturbata, veC F, ad C F, ita Z. b ad D A: acqui ex hypochesi
CHat C A CIdC ae D H, VE CF ad G+ F, CrgOVE CA ad D A, SC L (maior vel mi-
Ld. Duinm 1 Guat C A er a D A, quod est cab surdum: non olt ixicur C. A ad B A, in alia
proxortione, quam P. F ad C F.
PR, OPOSIFIO:121
cionali AC, aqualis sic producta A G. -. l vorrog
DicOFC, FB, F C in concinuara esse proporrionE.
Aei sne duo ordines erium quancitatum C A, B A, D A _E C F, PF, GF; e
sEDE CA ad D A, AC CF ad C F, sEque icem re B A ad W A, SICC F ad FF.
Dico eriam esse C A ad B A, vE P Fssest ad ( F. P sNi
de clire
EP enimnon est C A ad, B A, VE F F ad, C: L, eric erso aliqua maior vel minor
quam C A. nempe Z ad B A, VE B F, est ad CiTis quoniam ergo ve CF prima ac
EF secundam ica in Mctooe B sebuda cst ad D A cercIam, L V L F 1C
ncprovortionales AB, AC, AB, d linca BD COMPlITa ex vEra
 que nterea De, e Mlaturbitariam in F, ac medix PrOPOF-
Demonstrati
Vn enim GC bilecta sic in A, e BD in F, eric C C ad AC, vE B alLD.
PracerCa cum AB, A C, AD Ponantur concinua, C Pet PaSB C aC
C. D, VE AB ad A C, id est A C; e componendo ve B C act LL, Ia BD al CD: Sca
ante ostenderamus esse ve C Ci ad A ∞ ita BD ad FD. Ouare per lemmapeacl
dens etiam eric ve C C ad B C; ita CD ad BF, hoc est F D; e diuidendo C B
ad BeCaLDHoCCHFB llaque mucclenao, petmulanao. d componen
docricve CL ad BF, ica BLad C L, er30 Ct hL, Ct lunt proportionules. 1dd
erac demonstrandum.
Corollarium.
X hac provolicione hoc Theorema de ducimus. Sinceres proporcionales AB, BC.
CD, diuilaque sc AB biFariam in F. DICOAE, F C _E COMPONICAM CX AF 8
Lineis BC. C D bissumpeis, esse proportionales, _C sI A R, E C, _ COIPOSIEA CK AL
de DC, CD lineis bis sumpris, sinc continux; dico AB, BC, CD esse in continua
F
2d 16B. do
Demon-
A s       i u  1 1i    M    1       ue  t    a    e   pou a m ma