jg^ Dr. Waking on the Method \ See. 
5. Let a quantity P be a function of x 9 or the fluent of 3 
function of x x x, and the value X of it when x ^za be known, 
and the value of it when x = a-\-b be required. Find a feries 
of which the firft term is X, and which proceeds according to 
the dimenfions of b t if b be a very fmall quantity, and in 
general at leaft fo fmall that the feries from x = a to x-ay-b 
neither becomes infinite or o. 
In the fame manner, if an algebraical or fluxional equation 
or equations, expreffing the relations between x,y, z 9 v 9 &c. 
be given, find the correfpondent values of y, z 7 v, &c. to x = a> 
which let be Y, Z, V, &c.; then find feriefes for jy, %, v, &c. 
of which the firft terms let be Y, Z, V, &c. refpe&ively, and 
which proceed according to the dimenfions of b 9 but fubjedl to 
the fame conditions as in the preceding cafe. 
From fluxional equations may be deduced feries which exprefs 
the value of y , &c. in terms of x, and always diverge, or 
always converge, whatever may be its value, as appears from 
the Meditationes. 
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