[ 335 ] 



flow uniformly. Then by Taylor's theorem whilftjv changes its value 



R P T~) 



from a to^, x will from A become AH A 4. , &c. 



I I. 2 I. 2. 3 



For more readily ufing the preceding problems, it will ge- 

 nerally be of ufe to clear the given equations from fradions, 

 furds, &c. and fometimes alfo to take the 2d, &c. fluxions generally, 

 in order to have a more convenient equation, from which the par- 

 ticular fluxions of the higher orders are to be deduced. The parti- 

 cular fluxions of the different orders are to be taken per Jaltu7n by • 

 the preceding problems, fubflituting at the fame time whenever con- 

 venient the values of x, ^, x, &c. previoufly found. 



The utility and pradice of- this method will befl appear by 

 examples.. 



Example I. From the cubic equation x'' ■\- q x ■\- r = 0, to 

 deduce the values of :v in a feries afcending by the powers of r, 



Solution. Let the fuccefUve fluxions of this equation be 



• X ' X 



taken by Cor. Prob. i, making a = x, b = — , c = — &c. and 

 ^ " ' 1.2 i.g.3 



r conftant. 



<l 



