268 
Mr. Wilson’s Essay on the 
i. e. to their lowest rational dimension, with unity always for 
the coefficient of the highest power of the unknown quantity ; 
in which state, every simple equation is already resolved. The 
resolution of all other degrees, is the finding the simple equations 
of which they are compounded : but, to do this in a general man- 
ner, it is evident we must seek, instead of the particular equa- 
tions themselves directly, a general expression representing them 
all ; which general expression is called the formula of resolution, 
such as, the common quadratic resolution, or that given for 
cubics by Cardan's Rule. 
6. These formulas, properly speaking, are rather the rever- 
sion of an equation, than the resolution of it: for, although the 
unknown quantity be evolved or reduced to a simple dimension, 
the known parts are necessarily involved or affected with a surd 
at least as high as the dimension of the equation, in order to 
exhibit the proper number of correspondent values belonging 
to the unknown quantity in an equation of that degree. Thus, 
the equation (x 1 — px q = o) and its common resolution 
are both the same quadratic ; only, under 
the first form, the unknown quantity, being of the dimension 
of the second degree, has two values ; whereas, in the second 
form, it has only one, and the double value is transferred, by the 
quadratic surd, to the known parts on the opposite side of the 
equation. Thus also, the equation (a: 3 — qx -f- r = o) and the 
Cardan ic formula belonging to it 
are, in the same manner, the same 
cubic merely reverted. But, as equations are usually denomi- 
nated from the dimension of the unknown quantity, these reso- 
