ELEMENTS OF ALGEBRA: ON Louis Perre Marie EMBRACING STURM'S AND HORNER'S THEOREMS, AND PRACTICAL EXAMPLES. BY CHARLES DAVIES, LL.D. AUTFIOR OF ARITHMETIC, ELEMENTARY ALGEBRA, ELEMENTARY GEOMETRY, PRACTICAL ANALYTICAL GEOMETRY, ELEMENTS OF DIFFERENTIAL ON SHADES, SHADOWS AND PER- SPECTIVE. NEW YORK: PUBLISHED BY A. S. BARNES & CO., No. 51 JOHN STREET. 1857. 1957 Auto of Rafn Broun the drept try of Sinsigheid bloss of 1843 Math 2058.57 Atatti 2008.LA VIES' UNIVERSITY Babies' Arithmetical Table-Book. numerous Applications. ing a counecting link between ARITHMETIC and ALGEBRA. MENSURATION. -This work embraces the elementary principles of Geometry and rigorous. ples of Drawing, Architecture, Mensuration, and Logarithms, with Applications to the Mechanic Arts. Bavies' Bourdon's Algebra— Including Sturm's THEOREM-Being an abridg. ment of the Work of M. BOURDON, with the addition of practical examples. Davies' Zegendre's Geometry and Trigonometry-From the works of A. M. Legendre, with the addition of a Treatise on MENSURATION OF PLANES AND Solids, and a Table of LOGARITHMS and LogARITHMIC SINES. PA-S, PLANE-TABLE, and LEVEL; also, Maps of the TOPOGRAPHICAL Signs adopted on NAVIGATION. Davies' Descriptive Genmetry— With its application to SPHERICAL PROJEC TIONS. Davies' Shades, Shadows, AND Linear Perspective. Straight Line-of the Conic Sections—of the LINE AND PLANE IN SPACE; FACES of the second order. 1521 54-135 8 나 4 ENTERED according to Act of Congress, in the year one thousand eight hundred and fifty-three by CHARLES Davies, in the Clerk's Office of the District Court of the United States for the Southern District of New York. J P. JONES & CO., STBE BOTYPERS. 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 alto gether. In the following work, the original Treatise of Bourdon has been regarded only as a mode). The order of arrangenient, 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 in the Military Academy have been freely inade, for the purpose of giving to the work a more practical character, and bringing it into closer harmony with the trains of thought and improved systems of instruction which prevail in that institution. But the work, in its present form, is greatly indebted to the labors of William G. Peck, A. M., U. S. Topographical Engineers, and Assistant Professor of Mathematics in the Military Academy. Many of the new definitions, new rules and improved methods of illustration, are his. His experience as teacher of mathematics has enabled him to bestow upon the work much valuable labor which will be found to bear the marks of profound study and the freshness of daily instruction. FISHKILL LANDING, May, 1863. } a CONTENTS. ALGEBRA – Definitions—Explanation of the Algebraic Signs.. Similar Terms Reduction of Similar Terms... Multiplication-Rule for Monomials and Signs. Signification of the Symbol ao. Remarks on the division of Polynomials. When m is entire, am_bm is divisible by a—b.... |