50 
Mr. Knight on the Expansion 
reigns throughout, in this manner of treating the subject; 
and the regularity with which we proceed from the easy to 
the more complex cases. By means of this analogy also, the 
reader may without difficulty keep all the rules in his me- 
mory. 
2. I shall begin with the expansion of any junction of a simple 
multinomial . 
First method '* If f (c + z) represent any function of c -]- z, 
and the fluxions be taken, separately, with respect to c and z, 
the fluxional coefficient is the same in both cases : or 
mised, let 
/ n m 
f (c-\-cx c x* -f- c x 3 + ) = B-j- B x + B at 2 -f- Bx 3 -f* 
12. 3 
4 - Br 4-, &c (l) ; 
n 
iii 
let B, B, B, &c. represent the fluxional coefficients of B, B, B, 
i z i x 
See. with respect to c, and we shall have 
= B-|-B^4“Bx 2 -|-Ba: 3 -{- + Rr"4“. 
I 2. 3 n 
i a hi ••ft 
If we multiply this by cx~{~2cxx-l~sc x z x n c 
x n ~ l x 4- and take the fluent, we shall get, by what was just 
/ II HI 
now shewn, another expansion of f (c c x c x* c x z 
f (c -{- C X + c . 
* See La Criox, ‘ Traite element, de Calc. Different p. 25, note; where a simi- 
lar proceeding is used for binomial functions. 
