S72 
Mr. Wood on the 
of A 2 ,, which is impossible ; consequently no alteration is, in 
this case, made in the conclusion, by the introduction of A 7 '. 
3 . When P does not vanish, then every divisor of P is a 
divisor of Ax n ~ x + Bx n ~ 2 -}- Cx n ~3 + and of A 2 (ax* 
+ bx n ~ l -f- cx 71 —' 2 -f- &c.); and therefore of ax n -{- bx n ~ 1 
+ cx n 2 -j- &c. unless A 2, = 0 , in which case the remainder, 
P, becomes a B (Bx n ~ 2 -f- &c.), every divisor of which 
is a divisor of Ba :”~ 2 -f- Cx n ~~ 3 &c. whether it be a. divisor 
of ax n -f- bx n ~ x -{- cx n ~ 2 -{- &c. or not. That is, there are two 
values of the indeterminate quantity A, which, if retained, will 
produce erroneous conclusions. 
4 . A 2 enters every term of the second remainder (Q), and 
the two values, before introduced, may therefore be again rejected. 
The coefficient of the first term of this remainder is C oc — B (3 1 
x + $ 2 — ay . A; and, by substituting for a, (3 and y, their va- 
lues, and retaining only those terms in which A is not found, 
and those in which it is only of one dimension, we have 
C« = — 6 BCA + aCB z 
— a C 2 A 
— B/3 = + 6 BCA— a CB 2 
+ a B DA 
e « — B/3 a C 2 A + a BDA 
c7=Bj§ . « = — a 2 B 2 C 2 A + a 2 B 3 DA 
. A= fl 2 B 2 C 2 A — a 2 B 3 DA ; 
therefore, those parts of C a — B 13 . a -f (2 Z — ay. A, in which A 
is of one dimension, and in which it is not found, vanish. 
In the same manner it appears, that A a enters every other 
term of the remainder Q. 
