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[ 21 ] 
another, becomes very troublefome and laborious ; 
and, what is worfe, the Law of continuation, where- 
by a part of the labour might be avoided, is exceed- 
ingly hard, if not impoflibe, this way to be difcovered. 
In the following paper fomething is attempted to- 
wards obviating the laid inconveniencies ; but whe- 
ther the fuccefs has been anfwerable, I fhall not take 
upon me to determine. 
Problem I. 
To find a feries exhibiting the value of i + - J 
n 
xi+ - x i + -| x i + ^ &c. in Ample terms 5 x 
being indeterminate, and <7, b> c , m, n, />, &c. 
any given numbers, whole or broken, pofltive or 
negative. 
m 
n 
Put il — l J r -J , W—l + || 5 y = i+ x - 
1 X? J 
I + d &C . 
Alfo let A —u wy z, &c. (== the quantity pro- 
pofed) . 
Then, in fluxions, A — itwyz, &c. +uwyz, 
&c. -j- nw yz, &c -}- u wy z, &c, &c. Which 
equation, divided by the preceding one, gives 
— = - 4-. - + — h - & c * 
A » wy'z 
But, 
