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ARITHMETIC.

DESIGNED FOR THE USE OF ACADEMIES AND SCHOOLS.

BY CHARLES DAVIES,

AUTHOR OF ELEMENTS OF SURVEYING,
ELEMENTS OF DESCRIPTIVE GEOMETRY, SHADES SHADOWS AND
PERSPECTIVE, ANALYTICAL GEOMETRY, AND DIFFE-

RENTIAL AND INTEGRAL CALCULUS.

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Entered according to the Act of Congress, in the year one thousand eight hundred and thirty-eight, by CHARLES Davies, in the Clerk's Office of the District Court of the United States, for the Southern District of New York.

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PREFACE.

A CORRECT and accurate knowledge of Arithmetic is one of the most important elements of a liberal or practical education. The public should, therefore, receive with indulgence every attempt that may be made to improve this department of instruction.

The Elementary Treatise, which is here presented, is an enlarged, and it is hoped, an improved edition of the Common School Arithmetic, published in 1833. The suggestions of several experienced teachers have been incorporated with the body of the work in its new form, and, indeed, nothing has been omitted which it was thought would give it value to those for whose use it is designed. It has been the intention to render the whole subject as plain as it is capable of being made, and at the same time, to treat it as concisely as possible.

The reasons for most of the rules are given. It was not, however, thought best to demonstrate the rules for the extraction of roots, nor that for finding the sum of a geometrical series.

The name, Compound Numbers, which has heretofore been given to all numbers in which the kind of unit is expressed, has been changed to that of Denominate Numbers. This change has not been made with any ambitious spirit of innovation, but because it is deemed an improvement

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