A 2 3 Mr, HELL I NS*S Method of finding the 
The fame value of x may be found from either of the two 
general quadratic equations given in corollary i. From the 
firft of them we get one value of * = — j . y\ nc ] f rom 
59 
the other, one value = ~ , which is alfo = i. 
59 1 
E X A M P L E HI. 
Given the equation .v 4 — L ,v + 4 o, in which two values 
2 16 
of x are equal to each other, to find them. 
By corollary a. we have * = 1 *= JL = I . Bv corol. 2 
T H E O R E M m. 
If the furfolid equation x‘ - px‘ + qx l - rx' + j# - * * o to / w „ 
equal to each other, and you make A = ISlzM? jj = 
4 PP — 1 ’ 4PP — lOq* 
s 
Q- 
H = 
A-pp— ioq 9 
F+ C 
A-.l> 
D = 
5 B - 3? 
E = 
1 = 
5A + 4/)’ 
^ ^ k = 
5£±2r 
5A + 4/)’ 
C 
a~g’ 
B - E 
5 A + 4/> 1 - A-D > 
then fall one of the equal 
values of x be = — • 
The inveftigation of this theorem being altogether fimilar to 
that oi the lafl, it is unneceflary to give it here. 
The difference of equations being taken as in the inveftiga- 
rion of theorem II. it will appear, that one of the equal roots 
-may alfo be had horn any one of the following live equations, of 
which fometiines one, Sometimes another, will be the moft 
eligible. 
/ 
r 
1 . 
