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AND ITS APPLICATIONS ;

DESIGNED AS A

TEXT BOOK FOR COMMON SCHOOLS,

HIGH SCHOOLS, AND ACADEMIES.

BY

DANA P. COLBURN,

PRINCIPAL OF THE RHODE ISLAND STATE NORMAL SCHOOL,

PROVIDENCE.

PHILADELPHIA:

H. COWPERT I WAIT & CO.

Eduati T18.55"
Eduet 115.56.298

1872, Nov. 29

Gift of
Hilliam C. Macore,
of Bangos, W.
(H.U. 1874.)

Eutered, according to Act of Congress, in the Year 1855, by

DANA P. COLBURN,

In 11. Clerk's Office of the District Court of the District of Rhode Islana

PRINTED BY SMITH & PETERS,
Franklin Buildings, Sixth Street, below Arch,

Pbilulel; hia

PRE FACE.

The principles involved in Arithmetic are few, the methods of applying them many. To be a perfect master of the subject, a person must possess,

1. A knowledge of the nature and use of numbers, with the methods of representing and expressing them.

2. A knowledge of the nature and use of the various numerical operations, with the methods of indicating and of performing them.

3. Such mental training and cultivation of the reasoning powers as shall enable him to understand the conditions of any given problem, and to determine from them what operations are necessary to its solution.

The first of these includes every thing belonging to Notation and Numeration.

The second includes the operations of Addition, Subtraction, Multiplication, and Division; to which some would add, as a separate operation, the Comparison of Numbers, as in Fractions and Ratio.

The third requires a power of grasping the various conditions of a problem, of tracing their relations to each other, and of finding from them what operations must be performed, and what new relations determined, to obtain the result required. They are, however, mutually dependent, so that no person

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