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REVISED AND ADAPTED TO THE COURSES OF MATHEMATICAL INSTRUCTION

IN THE UNITED STATES;

BY CHARLES DAVIES,

PROFESSOR OF MATHEMATICS IN THE MILITARY ACADEMY

AND
AUTHOR OF THE COMMON SCHOOL ARITHMETIC, ELEMENTS OF
DESCRIPTIVE GEOMETRY, SURVEYING, AND A TREATISE

ON SHADOWS AND PERSPECTIVE.

NEW YORK :

PUBLISHED BY WILEY & LONG,

No. 161 Broadway.

STEREOTYPED BY A. CHANDLER.

HARVARD
UNIVERSITY
LIBRARY

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

PREFACE.

The Treatise on ilgebra, by Bourdon, is a work of sin. gular excellence and merit. In France, it is one of the · leading text books, and shortly after its publication, had

passed through several editions. It has been translated, in part, by Professor De Morgan, of the London University, and it is now used in the University of Cambridge.

A translation was made by Lt. Ross, and published in 1831, since which time it has been adopted as a text book in the Military Academy, the University of the City of NewYork, Union College, Princeton College, Geneva College, and in Kenyon College, in Ohio.

The original work is a full and complete treatise on the subject of Algebra, and contains six hundred and seventy pages octavo. The time which is given to the study of Algebra, even in those seminaries where the course of mathematics is the fullest, is too short to accomplish so voluminous a work, and hence it has been found necessary either to modify it, or abandon it altogether.

The work which is here presented to the public, is an abridgment of Bourdon; with such modifications, as experience in teaching it, and a very careful comparison with other standard works, have suggested.

It has been the intention to unite in this work, the scien. tific discussions of the French, with the practical methods of the English school; that theory and practice, science and art, may mutually aid and illustrate each other.

MILITARY ACADEMY, March, 1835.

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