In its preparation no labor has been spared to adapt it to the end for which it is designed. It has been submitted to many practical teachers, and thus embodies valuable suggestions from many sources. Especial credit is due MR. J. P. PAYSON, Master of the Williams School, Chelsea, Mass., and it makes its way to the public through the hands of PROF. JAMES H. EATON, Ph. D., son of the author of Eaton's Series of Arithmetics. It is hoped that it will prove worthy to stand beside the former works of the same wellknown author.

Boston, Sept. 30, 1867.

ELEMENTS OF ARITHMETIC.

ARTICLE 1. A UNIT is one, that is, any single thing; as, a horse, a day, an apple, an inch.

2. A NUMBER is a unit or a collection of units; as, one, two, six, three men, ten pints.

ARITHMETIC is the science of numbers, and the art of reckoning or computation.

3.

4. There are six and only six different operations in Arithmetic, namely, Notation, Numeration, Addition, Sub, traction, Multiplication, and Division.

NOTATION AND NUMERATION.

5. NOTATION is the art of writing or expressing numbers and their relations to each other by means of figures and signs. 6. NUMERATION is the art of reading numbers which have been written or expressed by figures.

7.

There are two methods of notation in common usc, namely, the Arabic and the Roman.

8. The ARABIC NOTATION employs ten figures to express numbers, namely:

0, 1, 2, 3, 4, 5, 6, 7, 8,

Naught, One, Two, Three, Four, Five, Six,

9.

Seven, Eight,

Nine.

What is

3.

What are

QUESTIONS. 1. What is a Unit? 2. What is a Number? Arithmetic? 4. How many operations are there in Arithmetic? they called? 5. What is Notation? 6. Numeration? 7. How many methods of Notation in common use? What are they? 8. How many and what figures in the Arabic Notation?

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9. The first Arabic figure, 0, is called a cipher, naught, or sero, and when used without any other figure it stands for nothing; thus, O apples means no apples.

Each of the other nine figures stands for or signifies the same as the word written under it, and to distinguish them from 0, they are called significant figures.

10. To express numbers greater than nine, these figures. are repeated and combined in various ways. Ten is expressed by writing the figure 1 at the left of the cipher; thus, 10. In like manner twenty, thirty, forty, etc., are expressed by placing 2, 3, 4, etc., at the left of 0; thus,

20, 30, 40, 50, 60, 70, 80, 90. Twenty, Thirty, Forty, Fifty, Sixty, Seventy, Eighty, Ninety. 11. The numbers from 10 to 20 are expressed by placing the figure 1 at the left of each significant figure; thus,

11, Eleven,

12, 13, 11, 15, 16, 17, etc. Twelve, Thirteen, Fourteen, Fifteen, Sixteen, Seventeen, etc. In a similar manner all the numbers, up to one hundred, be written; thus,

may

12. One hundred is expressed by placing the figure 1 at the left of two ciphers; thus, 100. In like manner two hundred, three hundred, etc., are written; thus,

9. Names of the first figure, 0? Its value? What are the other figures called? Why? 10. How are numbers greater than 9 expressed? Illustrate. 11. Numbers from 10 to 20, how expressed? Other numbers to 100? 12. One hundred, two hundred, etc., how expressed?