ALGEBRA : EMBRACING THE FIRST PRINCIPLES OF THE SCIENCE. BY CHARLES DAVIES, LL.D., ARITHMETIC, ELEMENTARY AUTHOR OF GEOMETRY, ELEMENTS OF SURVEYING, ELEMENTS OF DESCRIPTIVE AND ANALYTICAL GEOMETRY, ELE- AND A TREATISE ON SHADES, SHADOWS, AND PERSPECTIVE. NEW YORK: A. S. BARNES & BURR, 51 & 53 JOHN STREET. BOLD BY BOOKSELLERS, GENERALLY, THROUGHOUT THE UNITED STATES, Davies' Course of Mathematics. MATHEMATICAL WORKS, IN A SERIES OF THREE FARTS: ARITHMETICAL, ACADEMICAL, AND COLLEGIATE. BY CHARLES DAVIES, LL.D. DAVIES' LOGIC AND UTILITY OF MATHEMATICS. l'his series, combining all that is most valtable in the various methods of Eurepean instruction, improved and matured by the suggestions of more than thirty years' experience, now forms the only complete consecutive course of Mathematics. Its methods, harmonizing as the works of one mind, carry the student onward by the same analogies and the same laws of associatior, and are calculated to impart a comprehensive knowledge of the science, combining clearness in the several branches, and unity and proportion in the whole; being the system so iong in use at West Point, through which so many men, eminent for their scientific attainments, have passed, and having been adopted, as Text Books, by most of the colleges in the United States. I. THE ARITHMETICAL COURSE FOR SCHOOLS 1. PRIMARY ARITHMETIC AND TABLE-BOOK. 2. INTELLECTUAL ARITHMETIC. 3. SCHOOL ARITHMETIC. (Key separate.) 4. GRAMMAR OF ARITHMETIC. II. THE ACADEMIC COURSE. 1. THE UNIVERSITY ARITHMETIC. (Key separate.) III. THE COLLEGIATE COURSE. 1. DAVIES' BOURDON'S ALGEBRA. 2. DAVIES' LEGENDRE'S GEOMETRY AND TRIGONOMETRY. 3. DAVIES' ANALYTICAL GEOMETRY. 4. DAVIES' DESCRIPTIVE GEOMETRY. 5. DAVIES' SHADES, SHADOWS, AND PERSPECTIVE. 6. DAVIES' DIFFERENTIAL AND INTEGRAL CALCULUS. Entered according to the Act of Congress, in the year one thousand eight hundred and fifty-two, 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 AND CO STEREOTYTHRA. EDUC. PSYCH. GIFT LIBRARY 24153 D3 Educ. Svch. Library PREFACEЕ. ALTHOUGH Algebra naturally follows Arithmetic in a course of scientific studies, yet the change from the methods of reasoning on numbers to a system of reasoning entirely conducted by letters and signs, is rather abrupt and not unfrequently discourages the pupil. In this work, it has been the intention, to form a connecting link between Arithmetic and Algebra, to unite and blend, as far as possible, the reasoning on numbers with the more abstruse methods of analysis. The Algebra of M. Bourdon has been closely followed. Indeed, it has been a part of the plan, to furnish an introduction to that admirable treatise, which is justly considered, both in Europe and this country, as the best work on the subject of which it treats, that has yet appeared. The work of Bourdon, however, even in its abridged form, is too voluminous for schools, and the reasoning is too elaborate and metaphysical for beginners. It has been thought that a work which should so far modify the system of M. Bourdon as to bring it within the scope of our common schools, by giving to it a more practical and tangible form, could not fail to be useful. Such is the object of the ELEMENTARY ALGEBRA. |