In the problems given for solution it has been the aim of the author to use the language of trade, when no error is conveyed thereby, thus accustoming the student to the forms of expression needed in after life; and in general the author has striven after clearness of statement rather than technical accuracy of expression.

It would be pedantry to specify the departments in which excellence or originality may be found, but it is hoped that a careful examination will exhibit the logical sequence of the steps in all the processes, the perspicuity and accuracy of the analyses, and the brevity and correctness of the definitions, principles, and rules.

The author takes pleasure in acknowledging his indebtedness to Prof. J. B. DE MOTTE, of Indiana Asbury University, and to several other teachers of ability and experience, for timely and valuable suggestions.

Trusting that the book will, in some measure, supply the popular demand for a brief and comprehensive treatise upon Arithmetic, the author presents his work to the public.

W. J. M.

STATE NORMAL SCHOOL,

GENESEO, N. Y., September, 1877.

RITHMETIC

Article 1. A Unit is a single thing.

2. A Number is a unit or collection of units.

3. In counting a large number of objects it is natural to group them.

Thus, coins are put in piles and the piles counted, envelopes in packages and the packages counted, etc. These piles and packages may themselves be piled and put in larger packages, and the process continued indefinitely.

4. To express numbers so that all may understand what is meant by the characters which represent them, the system of grouping by tens has been adopted. There are, therefore, single things, or units; groups of ten units, or tens; groups containing ten tens, or hundreds, etc.

5. The method of grouping by tens is called the Decimal System.

Decimal is derived from the Latin word decem, which means ten.

Numbers may be expressed by words or other characters, viz: figures and letters.

6. Notation is the method of expressing numbers by figures and letters.

The Arabic Notation is the method of expressing numbers by means of figures. Its name is derived from the Arabs, by whom it was introduced into Europe. The Roman Notation is the method of expressing numbers by means of letters. It is so called because it was used by the ancient Romans.

7. Numeration is the method of reading numbers expressed by figures or letters.

ARABIC SYSTEM.

8. In this system ten figures are employed to express numbers, viz:

Figures. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
Names. Naught, One, Two, Three, Four, Five, Six, Seven, Eight, Nine.
Each of these, except naught, is called a significant figure.
Naught is also called zero and cipher.

9. By combining these figures according to certain principles, we can express any number.

10. PRINCIPLE. When figures are written side by side, the one at the right expresses units, the next tens, and the next hundreds.

EXERCISES.

11. 1. In 79, what does the 7 express? What does the 9 express? Read the number, beginning at the left.

2. In 58, what does the 5 express? What does the 8 express? Read the number, beginning at the left.

3. In 740, what does the 7 express? What does the 4 express? What does the 0 express? Read the number.

4. Begin at the left and read 76, 176, 106, 360, 203.