445 
148] MEMOIR ON THE RESULTANT OF A SYSTEM OF TWO EQUATIONS. 
where it is to be observed that the figures in the squares of the third column are 
obtained from those in the corresponding squares of the first and second columns by 
the ordinary rule for the multiplication of determinants,—taking care to multiply the 
dexter lines (i. e. lines in the direction \) of the first square by the sinister lines 
(i.e. lines in the direction/) of the second square in order to obtain the sinister lines 
of the third square. Thus, for instance, the figures in the square 
are obtained as follows, viz. the first sinister line (+3, — 1) by 
(-1, + 1) (— 2, +1)= 2 + 1 = + 3, 
(-1, + 1)(+1, 0) = — l+0 = — 1, 
and the second sinister line (— 1, 0) by 
(0, — 1) (— 2, +1) = 0-1= — 1, 
(0, -1)(+1, 0) = 0 + 0= 0. 
I have calculated the determinants required for the calculation, bjr the preceding 
process, of the Resultant of two quartic equations, and have indeed used them for 
the verification of the expression as found by the method of symmetric functions; as 
the determinants in question are useful for other purposes, I think the values are 
worth preserving. 
and 
Table of the Determinants of the Matrices, 
( a, 
b, 
C, 
d, 
e ) 
a, b, 
C, 
d, 
e 
a, b, c, 
d, 
e 
a, b, c, d, 
e, 
( P> 
q> 
r, 
s, 
* ) 
p> q> 
r, 
s, 
t 
p, q, r, 
s, 
t 
P, q, r, s, 
t