PRACTICAL ARITHMETIC.

DEFINITIONS.

1. Quantity is any thing that can be increased, diminished, or measured.

2. Mathematics is, the science of quantity.

3. A Unit is one, or a single thing.

4. A Number is a unit, or a collection of units.

5. An Integer is a whole number.

6. The Unit of a Number is one of the same kind or

name as the number.

Thus, the unit of 23 is 1; of 23 dollars,

1 dollar; of 23 feet, 1 foot.

7. Like Numbers have the same kind of unit. Thus, 74, 16, and 250; 7 dollars and 62 dollars; 19 pounds, 320 pounds, and 86 pounds; 4 feet 6 inches, and 17 feet 9 inches.

8. An Abstract Number is a number used without reference to any particular thing or quantity. Thus, 17; 365; 8540. 9. A Concrete Number is a number used with reference to some particular thing or quantity. Thus, 17 dollars; 365 days; 8540 men.

NOTES. 1. The unit of an abstract number is 1, and is called Unity. 2. Concrete numbers are, by some, called Denominate Numbers Denomination means the name of the unit of a concrete number.

10. Arithmetic is the Science of numbers, and the Art of computation.

11. A Sign is a character indicating an operation to be performed.

12. A Rule is a prescribed method of performing an op

eration.

Define quantity. Mathematics. A unit. A number. An integer. The unit of a number. Like numbers. An abstract number. A concrete number. The unit of an abstract number. Denominate numbers. Arithmetic. A sign, or symbol. A rule.

NOTATION AND NUMERATION.

13. Notation is a method of writing or expressing numbers by characters; and,

14. Numeration is a method of reading numbers expressed by characters.

15. Two systems of notation are in general use - the Roman and the Arabic.

NOTE. The Roman Notation is supposed to have been first used by the Romans; hence its name. The Arabic Notation was introduced into Europe by the Arabs, by whom it was supposed to have been invented. But investigations have shown that it was adopted by them about 600 years ago, and that it has been in use among the Hindoos more than 2000 years. From this latter fact it is sometimes called the Indian Notation.

THE ROMAN NOTATION

16. Employs seven capital letters to express numbers, thus:

17. The Roman notation is founded upon five principles,

as follows:

1st. Repeating a letter repeats its value. sents two, XX twenty, CCC three hundred.

Thus, II repre

2d. If a letter of any value be placed after one of greater value, its value is to be united to that of the greater. Thus, XI represents eleven, LX sixty, DC six hundred.

3d. If a letter of any value be placed before one of greater value, its value is to be taken from that of the greater. Thus, IX represents nine, XL forty, CD four hundred.

Define notation. Numeration. What systems of notation are now in general use? From what are their names derived? What are used to express numbers in the Roman notation? What is the value of each? What is the first principle of combination? Second? Third?

4th. If a letter of any value be placed between two letters, each of greater value, its value is to be taken from the united value of the other two. Thus, XIV represents fourteen, XXIX twenty-nine, XCIV ninety-four.

5th. A bar or dash placed over a letter increases its value one thousand fold. Thus, V signifies five, and V five thousand; L fifty, and L fifty thousand.

NOTE. The system of Roman netation is not well adapted to the purposes of numerical calculation; it is principally confined to the numbering of chapters and sections of books, public documents, &c.

Express the following numbers by letters:

1. Eleven.

2. Fifteen.

Ans. XI.

Ans.

Fourth Fifth? Repeat the table. What is the value of LVII? CLXXIII?. XCVIII? CDXXXII?

XCIX?

DCXIX?

VMDCCXLIX? MDXXVCDLXXXIX ? To what uses is the

Roman notation now principally confined?