A 3. ELEMENTS OF ALGEBRA: INCLUDING STURMS' THEOREM. TRANSLATED FROM THE FRENCH OF M. BOURDON. ADAPTED TO THE COURSE OF MATHEMATICAL INSTRUCTION IN THE BY CHARLES DAVIES, LL.D. AUTHOR OF ARITHMETIC, ELEMENTARY ALGEBRA, ELEMENTARY GEOMETRY, OF DIFFERENTIAL AND INTEGRAL CALCULUS, AND A TREATISE ON SHADES, SHAD- OWS, AND PERSPECTIVE. NEW YORK: PUBLISHED BY A. S. BARNES & CO. 1847. COURSE OF DAVIES' FIRST LESSONS IN ARITHMETIC-For Beginners. DAVIES' ARITHMETIC-Designed for the use of Academies and Schools. KEY TO DAVIES' ARITHMETIC. DAVIES' UNIVERSITY ARITHMETIC-Embracing the Science of Numbers and their numerous Applications. KEY TO DAVIES' UNIVERSITY ARITHMETIC. DAVIES' ELEMENTARY ALGEBRA-Being an introduction to the Science, and forming a connecting link between ARITHMETIC and ALGEBRA. KEY TO DAVIES' ELEMENTARY ALGEBRA. DAVIES' ELEMENTARY GEOMETRY.-This work embraces the elementary principles of Geometry. The reasoning is plain and concise, but at the same time strictly rigorous. DAVIES' ELEMENTS OF DRAWING AND MENSURATION — Applied to the Mechanic Arts. DAVIES' BOURDON'S ALGEBRA—Including STURM'S THEOREM-Being an abridgment of the Work of M. BOURDON, with the addition of practical examples. DAVIES' LEGENDRE'S GEOMETRY AND TRIGONOMETRY-Being an abridgment of the work of M. Legendre, with the addition of a Treatise on MENSURATION OF PLANES AND SOLIDS, and a Table of LOGARITHMS and LOGARITHMIC SINES. DAVIES' SURVEYING-With a description and plates of the THEODOLITE, COMPASS, PLANE-TABLE, and LEVEL; also, Maps of the TOPOGRAPHICAL SIGNS adopted by the Engineer Department-an explanation of the method of surveying the Public Lands, and an Elementary Treatise on NAVIGATION. DAVIES' ANALYTICAL GEOMETRY - Embracing the EQUATIONS OF THE POINT AND STRAIGHT LINE-of the CONIC SECTIONS-of the LINE AND PLANE IN SPACE; also, the discussion of the GENERAL EQUATION of the second degree, and of SURFACES of the second order. DAVIES' DESCRIPTIVE GEOMETRY-With its application to SP HERICAL PROJECTIONS. DAVIES' SHADOWS AND LINEAR PERSPECTIVE, DAVIES' DIFFERENTIAL AND INTEGRAL CALCULUS. Entered, according to Act of Congress, in the year 1844, by CHARLES DAVIES, in the Clerk's Office of the District Court of the United States, in and for the Southern District of New York. Lib. of C.S. Denison 3-23-82 PREFACE THE Treatise on Algebra, by M. Bourdon, is a work of singular excellence and merit. In France, it is one of the leading text books. Shortly after its first publication, it passed through several editions, and has formed the basis of every subsequent work on the subject of Algebra. The original work is, however, a full and complete treatise on the subject of Algebra, the later editions containing about eight hundred pages octavo. The time which is given to the study of Algebra, in this country, 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 to abandon it altogether. The following work is abridged from a translation of M. Bourdon, made by Lieut. Ross, now the distinguished professor of mathematics in Kenyon College, Ohio. The Algebra of M. Bourdon, however, has been regarded only as a standard or model. The order of arrangement, in many parts, has been changed; new rules and new methods have been introduced; and all the modifications which have been suggested by teaching and a careful comparison with other standard works, have been freely made. It would, perhaps, not be just to regard M. Bourdon as responsible for the work in its present form. It has been the intention to unite in this work, the scientific 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. CHARLES DAVIES. WEST POINT, June, 1844. |