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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 3
# Folio 10v, page id 00068000:0020
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. p
sind numeri C, m, n, differentiae l - M = Y l - n = n
 = Y + X
M- H = 5
aEt F C = m + Y = n + n m = n m + n
M = A = Y + n = s L n. Ergo  = A + Y, ut constat, ne
itaque ex datis tribus differentiis non possunt haberi termini. Quia revera
data sunt fantum duo, cum ex duabus differentis detur tertia
+ m N l+n =M men = L
= N - m = M = n fit m = N - M + n = L - n . Ergo n = L + M - N, 12
Ergo ex datis tribus summis d dantu res numeri. Itaque si tres
summae sunt quadrati s _ seu pro L, M, N, scubabum LL, MM, NN, fiet
2C = MM + NN - LL 2m = LL + NN -MM 2n = LL +MM = N V
sint jam et disferentiae quadrati l - m = VV
Ln = nM m - n = AA
Erit  et + N_ a 2l = _a VV + NN 2m = LL + M
finc
MM - (a iu
LL - X X
=te + M M + L L
VV = MM = LL
etiam
= + (M + MM
= -H + MM + NN
= NN- VV
= = AM+ LL+ NN
Hin 2LL = YV L MM- MM = A A = 4 Y
NN
MM = NN = LL
 Hinc M(M = XA + VV
Ex summis El = MM + NN = LL 2m = LL + NN - MM
AX = NN - MM
2n = LLTMM - XN
ex differentiis, non possunt invoniri l et n absolute sed supposito m, Erg
+VV
n = na AI
fint 2l =  2NV +L +) XN ( 2MM
2= Mm NNL LL
G = m = X fint 2n = (3LL +(D N N (=  MM, = 2X X
b= 
1) MM ( XN
Ergo ex duplici valore a fit 2VV + 3LL + NN = 3MM
ipsius 21,
Et duplii valore ipsius 2n fit
2AN F3MM = LL + 3NN
Eu YV = MM _ = LL
a = MN (FNN. - LL = 2VV + LL(+ NN) - MM Zo
2n = (LL  MM - XN = (L D + NN - MM = 2 dc
unde quia rr+M = pn. sequitur NN - LL = M
NN MM
Tantum ergo pus
est solvi has bina, aequationes tras vr = MM - LL, XA = XN - Mm
et tandem
14+ a= N NtrV = e
n=