of any Functions of Multinomials. 
3 5 
so was not necessary ; but it appeared advisable to make a 
distinction between the taking the fluxion with respect to c, 
i ii 
and the same operation witn respect to c, c, & c. which enter 
into the coefficients in a manner different from the first. 
The uniformity of the procedure is such, that, when we 
have arrived at the rules for one simple multinomial, a person 
of any skill in this kind of inquiry might easily divine those 
for the more difficult cases. But the most important circum- 
stance is the perfection given to inverse derivation , and the 
facility with which we may, by that means, find any large 
number of terms in the expansion of the higher kinds of mul- 
tinomials, as has been shewn in article 18 and 19. 
The last advantage I shall notice is, that the same rules of 
derivation serve equally for the expansion of a function of one 
or of a thousand multinomials : whereas, from M. Arbogast's 
methods, it would not, I imagine, be very easy to give a rule 
in words for the expansion of a function of five or six. 
( - 
cients in an unusual manner, as [ - — - 
\ e% - 6 
