192 
Mr . maseres’s Method of 
l+x 
in 
multiplied into the fame power of the fraction 
order to accelerate their convergency, and then inquiring 
what .would be the co-efficients of the terms of fuch a 
feries, if fuch a feries is poffible, and what would be the 
ligns to be prefixed to them, or in what manner they 
would be connecSted with the firft term, whether by ad- 
dition or fubtracfion. In order to this inquiry, I denoted 
the unknown co-efficients of the affumed feries by the 
capital letters p, q_, r, s, t, v, &c. and wrote down the 
terms of it near each other, without prefixing to hem 
either of the figns 
and - 
>ut 
each other only by a comma; fo 
equation, from which I derivt-f 
above-mentioned, was as follows •. 
aratedi them from 
it the fundamental 
e differential feries 
b x + c x x-dx^+e. x 1 
-fx i +gx ( ‘—hx n ‘ + See. is = f, 
QJ 
T X 
a r x\ 
3 ^ 
I -h^V I+£ 
v A 3 
&:c. By neceffary deductions from this equation 
it appeared that p would be equal to a\ and that all 
the following terms, of the affumed feries, to wit, 
OX RAA sa 3 TA 4 V * 5 _ _ , _ , _ . 
— =rT> Sec. muff be fubtracted 
I+Ai I+U I+d I+A’I 
from the firft term p, or a; and that would be equal to 
b-C) or d 1 ; and r =b-c-[c^d, or b-zc+d, or d 11 ; and 
2C+d~ [c— 2 d+e : or b- %c+ £d~ey or D 111 ; and 
