# Leibniz Legible — https://leibnizlegible.com
# Page: https://leibnizlegible.com/page/1815201908:0128
# Permalink to this reading: https://leibnizlegible.com/page/1815201908:0128?run=74
# Title: [Problema Austriacum Plus Ultra Quadratura Circuli] Problema Avstriacvm Plvs Vltra Qvadratvra Circvli (shelfmark Leibn. Marg. 230, Stück 1)
# Folio 71, page id 1815201908:0128
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=1815201908&page=128
# Source image: https://digitale-sammlungen.gwlb.de/content/1815201908/jpgs/default/00000128.jpg
# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 66 lines, status machine
# Lines: 66 recognised, mean confidence 0.82
# Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German.
# Licence: CC BY 4.0, Leibniz Legible. Machine output: do not ingest it as verified text; keep this provenance with the text.
# Wording rule: say "the machine reads it as …", never "Leibniz wrote".
# After the first blank line: the recognised lines in reading order, one per line.

210
AL.
aua
rec
n2-
 ex
ad
14.
DEa
AnC
ee
2m.
Ua
190
que
Uci-
1
D
N.
CF OMF TRIC A
Demonstratio.
Vadrarum enim F F est X
ualerectangulo sub AB 8
L; _ quadracum FG, aequale est
rectangulo sub BC d L; ver
eriam quadratum CFI, re-
aangulo sub CD et N con-
cenco: isicur ve quadraca PF,
FC CHlincer se lune, ica etiam
rectangula sub laceribus AB X
T, Tub BC X C, icem sub CD, _ N COnCenCA: LCa QuaTACZ LMMCMCOMMIMUaEa an2.
logia, (cum lacera super quibus tunc ex hypocheh   Coeu analosia) ipieur
etiam rectangula, sub laceribus AB _ I, BC _ L, CD _ NY, sune concinué prO-
porcionalia: cum aurem ipsorum bales ponancur in conrinuaca ratione AB, BC
CD; Cciam I, L, N, alcicudines erune in concinuata analogia pex prxecedente. Podem
modoquir exhypoches F F, F Ci, CFT, ex ex demonstracis modo L, L, DF, liinc con-
cinux; icemque exhypocheli F F, T, R: _ F G, L M; irem Cn FF, N, O, concintaM
Ceruanc analogiam: demonstrabimus K. MI, O esse concinuas. similiter quoquepro:
cedetur in lineis P, G. R, acqueira in infinicum. constat ergo rericas propolicionis.
P R O POSITIO ZXVI
Int leries concinux proporcionalium, habentes primum cerminum A,
LCOmMunCM, A, B, C, D, F, F, _ A, MI, N, O, P, O; continuaEEautem
Cerie veriulque, hac ve B ad A, ita A ad G, deC. d ve M ad A, ica A ad
R, GICVEOmneS F, E, D, C, B, A, G, FBI, K, L: irem omnes , P, O, N,
M, A, R, S, T, V, X Sincin concinuata analogia.
Dico este B ad ML, ve R ad
G, _C ad N, ve S ad FI
D ad0, vc Y ad 1, Xc.
Demonstratio.
Vn B, A, O, SInE EreS conti-
nux, icem NI, A, R, cric eam
brectangulum BC, quam rectan-
Sulum MR, quadrato A, idcogue
d inter se aequalia. O vare ve B ad
NIACcR ad C Similicer quoniam
C, B, R, C FF sunE ContinuX, ic2
vemediam A, xqualis verimque
proporcionalium numerus cingat:
Pacec exelementis, A ese mediam
proporcionalem, incer C ex HI:
rectansulum isitur FTC aquatur quadrato A; eodem modo rectangulum SN qua-
draco A aequale erir: ergo incer sc aequancur rectangula TTC, SN. O uarCd vEC 24d Ibid.
NV, Cic S ad FI, simili dilcursu exie ve D ad O, Ac Y 2d P, e sc de exceris. Ouod
erac demonstrandum.
117. Scieri
C1b. Seuti.