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# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 110, page id 1815201908:0167
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=167
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 40 lines, status machine
# Lines: 40 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.

Mi uii.  p MIAIEHII
R
DGRESSTONFS
EIV
Aex Ine concinue proporrionalium series binx, AX KC V racionum
divertarum, iTa TAMeN VE A, K, L, B eriam sinECOntinUX.
cionem duleemt, o C  cl. Cllalali an Gluluta i Li
Cumpci ad A primum cerminum.
DICO SCTICM A, R, L, NI, NI, _C. CCLIMIHACALH AIS V CALH HaBCLC BIOPOT.
Semonstratio.
Odacur ips R cerminus T in directum, aequalis ips A: raeio isitur (quod ex hy-
LLPoceli colliges) Lad M cripllaca cAtracionis Y ad R. Ouia Auce A L, L. B
ponuntur continux proportionales, cric L. ad B, ve R ad L: lederiam P. cst adM, ve
29. Ouini. K ad L, ergo L, adB, et M, eandem habec racionem: adcoque a B et M xquales
lunc. Sunc vero cciam aquales AT, ergo ratio A ad B, cade est cum rarione 2
ad MI. quare rario A ad B, criplicara est rarionis Lad R. cum erso vrriulque serici
inicium, idem Cccerminus A, eric Ceries T, R, L, eC. id cA series A, R, L, M, _C.
b162. Au. B ad seriem A, B, C, D, dC. ve cres priim Termini L, R, T, hoc eAt L, R, A, Cimut
lumpri ad T, hoc est ad A, primum cerminum: quod erac demonttrandum.
iui.
R O
V
Acae Cinc bina selles concinue proportionalium magnicudinum in
diversisrarionibus, cerminaca in K _ MI; e ab xqualibus cermi
niS A B, FC incipiences. Fiat aurem secundo cermino BC, unius scrici
aequalis NO; _ C HI secundo cermino alcerius scrici, xqualis OP; Dc-
inderatio NO ad OP (vel ratio OP ad NO, Si OP maior sic quam
VO) in infnicum conrinuCeur.
Dico NO esse ad PO, VECD ad FI, e NO este ad OR vE DF ad
IC, acqueicain intinicum.
Demonstraiio.
nin. Vm LCrICS A K, F. M incipiane ab aequalibus cerminis, eric rario c C D ad  L, r2.
tions BC ad GFI, hoc est, ex constructione, rationis NO ad O P. duplicatas
Requietiam eacO NYO ad P O. duplicaca est, ex dacis, rationis HO ad OP, exdem
igitur sunc rationes CD ad HI, _ NO ad PO; similicerrario D R ad LL, irI-
plicata est rationis BC ad GFI, hoc est rarionis NO ad OP: Ouare cum et ratio
O ad OR, ciuldem racionis NO ad OP, sictriplicata, caedem crune rationes
DE ad TE, _ NO 2d O R. Arque ira in intinirum, limil deonstratione proce.
lemus. Pacecisiur Theorematis veriras.
       t   e  .    u u    e      n un  mon