DANA P. COLBURN,

FRINCIPAL OF THE RHODE ISLAND STATE NORMAL SCHOOL, BRISTOL, 2 1
AUTHOR OF "ARITHMETIC AND ITS APPLICATIONS," ETC.

PHILADELPHIA:

COWPERTHWAIT & CO.

1869.

Entered, according to the Act of Congress, in the year 1858, by
DANA F. COLBURN,

in the Clerk's Office of the District Court of the United States for the District of

Rhode Island.

PREFACE.

THE title of this work indicates its character. It has been prepared for a text-book in Common Schools, and is designed to be a thoroughly practical treatise. It contains an exposition of the leading principles of Arithmetic, and illustrates their most important practical applications.

Its lessons are arranged in what seems to the author a natural and logical order; and their mutual dependencies and connections are, as far as possible, indicated. Its exercises and problems are numerous and varied, requiring, it is believed, such practice as will secure skill in performing numerical operations, and readiness in applying them.

The author has endeavored to illustrate clearly or demonstrate rigidly the truth of every principle and process; to make every definition and every statement clear and accurate; to avoid arbitrary rules and processes; and, in short, to prepare a work which shall be adapted to the wants and circumstances of pupils in Common Schools, and which shall at the same time tend to elevate the standard of elementary mathematical instruction.

(iii)

Some subjects usually treated in School Arithmetics are omitted in this, and others of great practical importance are made very full and complete. Among the former are "Single and Double Position," "Circulating Decimals," "General Average," "Tonnage of Vessels," and "Permutations and Combinations"-subjects which are usually learned arbitrarily, if at all, and which, to the great mass of pupils, will never be of the slightest practical value. Among the latter are "Numeration," and the "Ground Rules," "Accounts," "Fractions," "Interest," and Problems pertaining to business life. The articles on "Bills," "Accounts," "Promissory Notes," "Orders," "Drafts," etc. will be found specially valuable.

The author claims for this, as for the other books of his series, that whatever be its merits or defects, it is the result of much careful thought and study, of considerable experience as a teacher, and of an honest effort to arrange such a course of lessons as shall tend to develop the youthful mind, and form correct habits of study.