Dr. waring on the General Refolution , & fc. 87 
refolution of an equation of n dimeniions, of which 
the n roots are given, and alfo deduces innumerable e- 
quations of n dimeniions, which contain n - 1. indepen- 
dent coefficients. From whence it feems probable, that 
this new method of mine may contain the rn oft general 
refolution of algebraical equations that ever has, or, 
perhaps, ever will be invented. 
The general refolution is x-a\Zp + b\^'p z + c\/p^ + 
dj'p \ . ..+r\ // p”~ 3 +s-yp ii ~ , +t\/p x ~' + p if the equation 
be X n -kX n ~ l + BA 1 " -1 - ex " -3 + DA * -4 - &c. =0. 
I fhall add the refolution of fome particular equa- 
tions from this method, and then fubjoin the equation 
to which x — as/p + b\/p z -rclp'p 1 + &c. is the general re- 
folution. 
1. Let the refolution be x~a J/p + b-yp 2 , and the cor- 
refpondent equation free from radicals will be found 
x l -$ abpx-alp-bf 1 — o. Let x^-vx - qj=o be a cubic 
equation whofe refolution is required, which fuppofe the 
fame as the equation found above, and confequently their 
correfpondent terms equal, i. e. p = 3 abp and op= a l p + 
bf\ whence p = i, which value being fubftituted for 
?a 2 
bV' 
In 
p in the fecond equation, there refults o_= — + 
this equation for a or b may be affumed unity, or any 
other 
