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# Title: [Ps. 1] (shelfmarks Leibn. Marg. 178, Stück 1; Leibn. Marg. 178)
# Folio 141, page id 175905688X:0163
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=175905688X&page=163
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# Model: FoNDUE-GD_v2_ft_Leibniz, run 74, 2026-09-06T16:05:13Z — 52 lines, status machine
# Lines: 52 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.
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# After the first blank line: the recognised lines in reading order, one per line.

2CB.
Oradt
etrat
laeo
eu
NC CON
Everie
muSP
DEa
e
a rell
B. 12
11 1d
N O F A B R E V E 8.
nea BC. Acqui cubus lincae AB, ec triplum productum linea-
ruIM AC, BC, AB Cinul, aequantur eidem differentix q. (siqui-
dem. cum cubo linex BC componune cubum linex AC). Frit
itaque Z3, cubus ridelicet linea AB, una cum triplo produetoli-
nearum AC, BC, AB, aequalis g.
Veaucem habeatur hoc productumi mulciplicandum est bino-
mium YC. + 39. + V + 49. +
ErP quod aquatur linex AC.
per reliduumm V C.  = 9. V +44 L, P3, quod aequale elt
linea BC. Hlinc cum V = 99. F = p3 in se mulciplicarum Faciae
44 + 2, P3, dc - F = g in = = g taciat = = gq; qux productn
simul addica Faciune,, p3 (liguidem - = 9 gX - = 99 addendo
cranelcune): e porro producta, quae tiunt ex f =98 -  g in
= 44 +  p3, seMutuo destruant: Fric eorum productum
V C. 2, P Seu; p, radix scilicet cubica ex,; p3. quandoquidem
quaestio erat de mulciplicandis radicibus cubicis. Vnde criplum
productum eritp, quod (i mulciplicetur per AB, hoc cAt, per Z.
tictpZ, aquale eriplo producto linearum A C, BC, AB. LF per
conlequens Z3.
monstrandum.
∞ 9, velZ3∞ = pZ-+9. Quoderat de
Sic jam secundo loco
∞YC. F =9 F V +49- , P3 + V C. + : q - V : 49 - 2P
ee lupponatur prima radix cubica (quae binomium est) in figura
praecedente aequalis linex A B; secunda autem (quae residuum
CAt) aequalis linex B C; erit que lumma cuborum utriusque linca
aequalisque. Porro supponendo lineam A C ∞ Z, auterendoque ex
ejuldem cubo23, criplum productum linearum AB, BC, XZ.
relinquentur cubilinearum AB d B C, qui quidem limul sumpri
ipli q sune aequales. F.st aurem productum ex AB, B C, hoc elt,
quodtic ex binomio in reliduum, V C. P3, Teu : p. Nam cum
mulciplicando + V : 99 -  P3 per = 1 + 99 -  P3 (una
radice existente signo - adtecta, altera vero ligno -) produ-
catur urriulvis quadracum affectum signo, nimirum - =94
L P3, ee urramque radicem per : q mulciplicando, produ-
Cta craneleant; restat tantum. L =q in Se mulciplicandum. Jua-
re cum productum illud sic - =99, _ alterum productum in-
rencum (It  : 49 + i, P3; eric eocum productum V C. 2, P