[ 2 8o ] 
in-\-nn =.in-\-nn\ 
xx in-{-nn =E 4*7//* -{- 4 xn 3 -f- xn * 
yx in\nn l — 8 yn z -f* iiyn* + 6j yn* &c. 
zx a«+»» 4 = 1 62r/2 + 4. 3 2 ,s »5 
&x zn-\-nn} = 32«« s £?r. 
And the fum of thefe is equal to the logarithm of 
the fquare of i+». 
If an equation be formed, of the coefficients of «*, 
in each of thefe expreffions of the logarithm of that 
fquare, 
Then zx = 1 + 4 X i whence *— d = x. 
And, by proceding in the fame manner with the 
coefficients of n 3 , n s , &c. and fupplying the 
places of x, y, z , &c. as they arife, by the numbers 
(fo found) we fhall have 
2>’ = — 4 + 8^5 whence -f £=y ; 
2 z = — i+ -x+ l(fc; whence — 4 ~ z '> 
2u = § — -^-j-32«; whence + j ; 
Confequently, the logarithm of 1 -\-n will be ex- 
preffed by n — d n % + 7 » 3 — 4 + f « s > fifc. as 
above after ted. 
Again, fince = i+w + «*-f « 3 +» 4 -|-« 5 , 
as appears by the following divifton : 
1 — n )i ( 1 +«+»*, &c. 
1 — n 
~n 
+ n — nn 
nn 
And, fince the excefs of that feries, above unity, 
is the feries n + »* + 7;3 + n \ &V* 
Therefore 
