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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 178r, page id 00068194:0355
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Er
E A pXAC XaVaC EgeagXb
in diario eruditorum Gallico 3 jul. 1690 proponitur
problema invenire Triangulum Reclangulum in quo
smmua cuborum laterum sit cubus. Roducit remad
has duus aequationes: Fatera ponit b, a- x, Cx: d = b
Ex natura trianguli rectanguli poodit a - 2ax + XX - ccHX + 2bC= 20
Et excoditone problematis ves( a- 3aa X + 3a xX = x + 53 1. 3b cexx + 3 lb cx 
aequari cubo. aequat autem cubo ab ae, ut aqualio possit dividi per X,
et faciendo adhuc a 3bbE - 3 aa = 0 imo c=  t d bb caetera invenit,
sed nonmnis qrodemat solum 2, 4, 5. Videtur nihi procedi posse generalius:
nempe pu aeg. 2. scubatur a - 3aaX + ha XX -X + C X - 3bcc X 13bb Cx 2 a +3a exrsae
od (4 s
eu 
et fiet - 3aa  + 3a  X  - 1 X =0 ubi sulicndo C = (bbc. d - aa,: a
c
+3bbc: d3 = 3ba. dd
.3ae -3a ee
- et
biet:  X = 34 - 3b4: dd - 3aee:,  4 1 - C. d
et ex
compendii caufam videamus an liceat facere C
E
a b, c in n, p, im + n = p et. M +N + p = 9
p p = q-m - n: el p. = n + n. et fit.
p = q - m - n: n +n. p - 4 -- 24 m- 29 7 + m - mn n
1 m a
et fiei (me rn = q - 29. n - 24. i +t m - 2m n 4 n)
et
=(M + 3m n + 3m n A nS)
1
m = 6 fr m + p = q- p
si nth. pn Mp r. qn fit Gh= p +n
.Y. (u n, M + mnt pp = E (q n q + gur)
mum t m= contr. ticto
rgn tara pp=(+ quann
et.
s
m = h, p +n = r. q. n - p
P= Fg= Tn fhs 1 b