A = 
U, U' 
a, a 
, P = 
B = 
U, U' 
b, b' 
, Q = 
c = 
U, U' 
c, c' 
, R = 
D = 
U, U' 
, s = 
d, d' 
NOTE ON BEZOUT’S METHOD OF ELIMINATION 
[From the Oxford, Cambridge and Dublin Messenger of Mathematics, vol. II. (1864), 
pp. 88, 89.] 
Let U, U' be any two rational and integral functions of x of the same order; 
to fix the ideas let them be the cubic functions 
U = ax? + bx 2 + cx + d, 
U' = a'x 3 + b'x? + c'x + d!. 
Write 
a, a 
U , U' 
ax + b, a'x + b' 
U , U' 
ax 2 + bx + c, a'x 2 + b'x + c 
Ü , U' 
ax 3 + bx 2 + cx + d, a'x 3 + b'x? + c'x + d' 
P=A, 
Q = Ax + B, 
B = Ax 2 + Bx + C, 
S = Ax 3 + Bx 2 + Cx + D, =0, 
then we have