ELEMENTS OF ALGEBRA: ON THE BASIS OF M. BOURDON: EMBRACING STURM'S AND HORNER'S THEOREMS, CALMORNIA PRACTICAL EXAMPLES. BY CHARLES DAVIES, LL.D. AUTHOR OF ARITHMETIC, ELEMENTARY ALGEBRA, ELEMENTARY GEOMETRY, PRACTIC ANALYTICAL GEOMETRY, ELEMENTS OF DIFFERENTIAL AND INTEGRAL CALCULUS, AND A TREATISE ON SHADES, SHADOWS AND PER- SPECTIVE. NEW YORK: A. S. BARNES & BURR, 51 & 53 JOHN STREET SOLD BY BOOKSELLERS, GENERALLY, THROUGHOUT THE UNITED STATES. 1860. Dept. Course of Mathematics. Davies' Primary Arithmetic AND Table-Book-Designed for Beginners; containing the elementary tables of Addition, Subtraction, Multiplication, Division, and Denominate Numbers; with a large number of easy and practical questions, both mental and written. Babies' First Lessons in Arithmetic-Combining the Oral Method with the Method of Teaching the Combinations of Figures by Sight. Babies' Entellectual Arithmetic-An Analysis of the Science of Numbers, with especial reference to Mental Training and Development. Davies' New School Arithmetic-Analytical and Practical. Key to Davies' New School Arithmetic. Davies' Grammar of Arithmetic-An Analysis of the Language of Numbers and the Science of Figures. Babies' New University Arithmetic--Embracing the Science of Numbers, and their Applications according to the most Improved Methods of Analysis and Cancellation. Key to Babies' New University Arithmetic. : Davies' Elementary Algebra-Embracing the First Principles of the Science. Key to Davies' Elementary. Algebra.. Babies' Elementach · Gedmstry· AND: Trigonometry-With Applications in Mensuration. Davies' Practical Mathematics--With Drawing and Mensuration applied to the Mechanic Arts. Davies' University Algebra-Embracing a Logical Development of the Science, with graded examples. Davies' Bourdon's Algebra-Including Sturm's and Horner's Theorems, and practical examples. Davies' Legendre's Geometry and Trigonometry-Revised and adapted to the course of Mathematical Instruction in the United States. Davies' Elements of Surveying AND Navigation-Containing descriptions of the Instruments and necessary Tables. Davies' Analytical Geometry-Embracing the Equations of the Point, the Straight Line, the Conic Sections, and Surfaces of the first and second order. Babies' Differential AND Entegral Calculus. Davies' Descriptive Geometry-With its application to Spherical Trigonometry, Spherical Projections, and Warped Surfaces. Babies' Shades, Shadows, and Perspective. Davies' Logic and Utility of Mathematics-With the best methods of Instruction Explained and Illustrated. Davies' and Peck's Mathematical Dictionary and Cyclopedia of Mathematical Science-Comprising Definitions of all the terms employed n Mathematics-an Analysis of each Branch, and of the whole, as forming a single Science. ENTERED according to Act of Congress, in the year one thousand eight hundred and fiftythree, by CHARLES DAVIES, in the Clerk's Office or the District Court of the United States for the Southern District of New York. WILLIAM DENYSE, STEREOTYPER AND ELECTROTYPER, 183 William Street, New York. 1 PREFACE THE Treatise on Algebra, by M. Bourdon, is a work of singular excellence and merit. In France, it has long been one of the standard 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, both in Europe and in this country. 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 essentially, or to abandon it altogether. In the following work, the original Treatise of Bourdon has been regarded only as a model. The order of arrangement, in many parts, has been changed; new rules and new methods have been introduced: the modifications indicated by its use, for twenty years, as a text book M254902 |