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tion on the part of the teacher. No book can present a subject 80 fully as to make it clear to every mind; and it should be the constant endeavor of the teacher to ascertain just what part the pupil fails to understand, and aid him by suggestion, rather than by exhaustive explanation.

The late action of Congress, authorizing the use of the Metrical System of Weights and Measures in this country, has rendered it necessary to introduce into American school-books an explanation of this subject. Based on the decimal system, its treatment properly follows decimal fractions.

The chapter on the Metrical System has been compiled chiefly from late French works, and has been critically revised by H. A. Newton, Professor of Mathematics in Yale College. We take great pleasure in acknowledging our obligations to Prof. Newton, whose unwearied exertions in favor of the adoption of the Metrio System in this country, entitles him to the cordial thanks of all friends of educational progress.

CINCINNATI, Oct. 1866.

RA Y'S

RUDIMENTS OF ARITHMETIC.

DEFINITIONS. 1. Arithmetic is the science of numbers and the art of computing by them.

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

3. A Unit is a single thing; as, one book, one slate, one desk.

4. The Fundamental Rules of Arithmetic are Notation and Numeration, Addition, Subtraction, Multiplication, and Division.

NOTATION AND NUMERATION 5. Notation is the art of expressing numbers by letters or figures.

6. Numeration is the art of reading numbers.

7. Two methods of Notation are in common uso, the man and Arabic.

8. In the Roman method, letters are used; in the Arabic, figures.

ROMAN NOTATION. 9. In the Roman method of Notation, numbers are expressed by letters.

The following are used : I, V, X, L, C, D, and M.

I denotes one; V, five; X, ten; L, fifty; C, ono hundred; D, five hundred; and M, one thousand.

Repeating a letter repeats its value; thus, II de. notes two; XXX, thirty; CCCC, four hundred.

If a letter is placed before one of greater value, the less is taken from the greater; but if placed after, its value is added to the greater; thus, IV denotes four, while VI denotes six.

TABLE OF ROMAN NOTATION.

Imm

I
II
III.
IV
V
VI
IX
X
XI
XIV
XV
XVI
XVIII
XIX
XX

One.
Two.
Three.
Four.
Five.
Six.
Nine.
Ten.
Eleven.
Fourteen.
Fifteen.
Sixteen.
Eighteen.
Nineteen.
Twenty,

XXI Twenty-one.
XXX

Thirty
XL Forty.
L

Fifty.
LX

Sixty
XO Ninety.
C

One hundred.
СССС Four hundred.
D

Five hundred. DC Six hundred. DCC Seven hundred DCCC

Eight hundred DCCCC Nine hundred.

One thousand. MM. Two thousand.

M

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Read the following numbers: , 1. XXXVII.

7. DCCCXI. 2. XLIX.

8. MDLXXIV. 3. XCVIII.

9. MDCCXXII. 4. CXVI.

10. MDCCXLIV 5. CCXIX.

11. MDCCLXXVI. 6. DCXXIV.

12. MDCCCLXVII.

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