ALGEBRA.
CHAPTER I.
Definitions. Substitutions.
1. Algebra treats of quantities as in Arithmetic, but with greater generality; for while the quantities used in arithmetical processes are denoted by figures, which have a single definite value, algebraic quantities are denoted by symbols, which may have any value we choose to assign to them.
The symbols of quantity employed are usually the letters of our own alphabet; and, though there is no restriction as to the numerical values a symbol may represent, it is understood that in the same piece of work it keeps the same value throughout. Thus, when we say "let a equal 1," we do not mean that a must have the value 1 always, but only in the particular example we are considering. Moreover, we may operate with symbols without assigning to them any particular numerical value; indeed it is with such operations that Algebra is chiefly concerned.
We begin with the definitions of Algebra, premising that the symbols , , , , , will have the same meanings as in Arithmetic. Also, for the present, it will be assumed that all the algebraic symbols employed represent integral numbers.
2. An algebraic expression is a collection of symbols; it may consist of one or more terms, which are the parts sepa-
