I.

Introduction.

The principal definitions are put at the beginning of the book for convenient reference. They are not to be committed to memory. It is a good plan to have definitions and explanations read aloud in the class, and to encourage pupils to make comments upon them, and ask questions about them.

1. Algebra.

Algebra, like Arithmetic, treats of numbers.

2. Units.

In counting separate objects or in measuring magnitudes, the standards by which we count or measure are called units.

Thus, in counting the boys in a school, the unit is a boy; in selling eggs by the dozen, the unit is a dozen eggs; in selling bricks by the thousand, the unit is a thousand bricks; in measuring short distances, the unit is an inch, a foot, or a yard; in measuring long distances, the unit is a rod or a mile.

3. Numbers.

Repetitions of the unit are expressed by numbers.

4. Quantities.

A number of specified units of any kind is called a quantity; as, $4$ pounds, $5$ oranges.

5. Number-Symbols in Arithmetic.

Arithmetic employs the arbitrary symbols, $1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9$, $0$, called figures, to represent numbers.

6. Number-Symbols in Algebra.

Algebra employs the letters of the alphabet in addition to the figures of Arithmetic to represent numbers. Letters are used as general symbols of numbers to which any particular values may be assigned.