342 Mr. BaspaGcE on the Influence of Signs 
and since p of the quantities a, b, c, d, n are even and q are odd, 
this last expression is equal to 
(p—q) u—v x {the coefficient of the third term of («—1) (x +1)"} 
= (A ec UR Tere 
= (p—q)u-»} Sem gc ae Ta 
2 n—9 ae 
= (p-q)u-P Phd Fd 4 
— (p _ q) Uu-— iene v. 
If the order in which the events happened, or what corresponds to 
it, if the quantities a, 6, c,...r had been given, the process we have 
gone through could not have been completed, for the perception 
of the nature of the quantity, which in the sum of all the profits 
multiplies v, depends entirely on preserving those quantities distinct 
and unconnected with each other; a relation quite impossible, 
had each been an individual number. 
The remarkable influence of signs in the successful termination 
of this process of reasoning, claims our particular attention: 
abstract number, from its very nature, admits of amalgamation 
when subjected to the various operations expressed by algebraic 
signs: hence all trace of the mode in which it originally entered 
is completely lost ; or if this inconvenience be studiously avoided, 
by merely indicating instead of executing the arithmetical 
operations, still the individual nature of the several numbers 
presents so many points to which the attention is attracted, 
that it would be almost impossible, even for the most attentive 
observer, to seize that general view in which they all agree. 
This influence’ is still more remarkable in investigations, where 
characteristics of operation occur, and when letters are used 
to the exclusion of number, the relations are not merely more 
apparent, but the results, although attamed with difficulty, are 
more worthy of confidence: the reason of which, is to be found 
