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# Title: Leibniz-Handschriften zur Mathematik LH 35, 4, 3
# Folio 10r, page id 00068000:0019
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068000&page=19
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s
ML L =
fgg
2M = f99 + fht
Oc
N+ M = bCC
M = L = fhh
2L = fgg- fhA
N(-M = b dd
V = fgh
A = bcd
nAN (V= (nH Pet Mn +ZnA LHH L n
,ob VV = MM = LL
ob AN = NN - MM
sit M = A + V A f fiet M = (AL tVIFNE + 2AV = 2NN = 2VY =(NAAVV)
sit V = Ea H et fiet N 4 2X e - 2 = 2E H = 0. Et A = HC, 1 - 28,i, 2, s - C
Seu f= 28 - 1, FF, 2, (C- 1)
2
V- e
a
= f +g fg9 + f hh
CL = fgg- fhh
=bcd fit b = 2C- 1. I
agh
2N = bcc + bdd
2, C- 1, cd
2M = bcc - bdd fit fgg + fhh = bcc D bdd
et pro f et b substitutis duobuqvaloribus sit eid + =
seu
et
Ogua sih
dum
Rg
=
infit 20. = (C+ ) r(F 1) = Ld, +)
a n
a g
20-1 
c
20-2 0 ln 20-2 C
20 -1 cc-dd. - - ((2 - 1) = (C t.d)1
2C22 Cd
 fint (c+d) Y = gc +V
e
2-2 = cd; cad
(Cc - dd)r = cd + C - d sit d= 4(c- d)
d= C9:, et 9
C+d= c +C (C +9c; Y = 9c + 1, 9+ 1
Haec aequatio ib solvenia superest
ed his missis videamus autres Aequationes Wre = MM+ LL
VV
aY
re-1 d
Wr= mn- LL
Z MM = L.L Ad = NN - MM, n M = A A + VV solvere
dficent per suries series dyadicas. Quommus 
et ssumimus _ L = 10 + uY + 12 yy + etc. posito y signisieare 2
de  10, 1, 12, etc esse 0 vel 1. similiter sit M = 20 +217+ryy
s
 N = 30 + 31 ) +B2yy + etc quia autem et  = 40+4050 + 51y+ 5rqu
L
et M = 60 +61y +62yy + et. et V = 70+71y17 2yy+ etc
dratur Ve A per aeq. 1. et V per aeq. 2, et A per aeq3
ingendo, quid fiat si finiamus, et pro fin progressionem quaerendo efficiendu
videndo
Si cautem semper ut numeri sint positivi
 isile erit condere generalem
F iCanonem pro differentia quadralor quadrulo aequanda, vel quod ide
summa quadralar quadrato aequanda sit quia NN = NN. MM, ponere
possumus aN + e L egq N - M = fhR 2N = fgg+ fhh 2M = fgg = fhh
Ergo pro serie us solum assumere duo quadrota. sit N = (9 M= fR. fiet R.g = 9 +hh
R = 99-kh si N, M, X priminter ge
ent f=1
ex AC
+-
a2
11
1
1a
e
2