336 Mr. BappaGce on the Influence of Signs 
numerical value, the result must be independent of it, and is 
consequently true for all possible values. It may perhaps be 
contended that by the assumption of « for the number to be 
found, it was meant to represent number in the abstract, and 
that such was also the meaning of a and b; but there exists 
this difference, that it is not in our power to alter the value of 
x, but we may give to those of a and 4 any numerical magnitude 
we may please*. 
The utility of the unknown quantities in Algebra, arises from 
their capability of being operated on without reference to the 
determined values for which they are placed, the advantage of 
employing letters for the known quantities, consists in their 
similarity to general terms in language, and the consequent ex- 
tension of the reasoning from an individual case to a numerous 
species. The light in which this question has been regarded, is 
purely arithmetical, it may however be placed in another point of 
view, in which without any change in the quantities concerned, it is 
still more general in its nature; instead of restrictmg the equation 
v—bxr=-a 
to number, it may be considered as indicating that x is composed 
of a and b in such a manner, that when its value is substituted 
in that equation, all the terms shall mutually destroy each other. 
This signification, it is true, is not contained in the original 
question, but arises from the equation into which it is translated : 
the language of signs is far more general that that of arithinetic, 
a circumstance which is not perhaps sufficiently attended to in 
the application of it to questions of pure number. In one re- 
spect this generality is not so unexpected, for if a number is 
required satisfying a certain condition, and if it should happen 
ct ees b 
* There is in truth one restriction, namely, that a must always be less than rg but 
this will be removed when the question is viewed in an algebraical light, and does not in 
the least affect the argument. 
