90 A New Method of Resolving certain Equations: 
From this we have the 
Rote. 
o find a, when i Hed gde Sh Mii dcietidinh 
c) “Pind z, in the Ree es coe 
12abc+ 2a? d+-2c? =0. 
(D) Find «,in the quadratic, a A 
OE fk 
+c “45 
{t may be seen that this ole might also be applied 
to equations of the third degree ; for every such equation 
may by simple multi pResGaelaiy any quantity, (x+-w) be 
raised to one of the fourth degree, containing a variable in 
its co-efficients. In the cubic (C,) if we destroy se- 
cond term by substitution, the remainuin cones nt in the 
rent dqunton ie s (4ac — 36? —d) ; and, as (2) enters but 
once into each of the quantities denoted by a, 4, ¢, d, itis 
evident that the co-efficient named, can never rise 
an to the second degree. It may, then, be supposed to 
vanieli and the given equation is reduced to a cubic of the 
form, 2'°-+-c’=0. 
Neither of these solutions presents any advantages in 
practice. Whatever value they possess, must be ascribed 
to the fact that they are apparently new in their form, and 
in the mode of investigation. 
1822. 
New- Haven, 
