NEW ELEMENTARY ALGEBRA. EMBRACING THE FIRST PRINCIPLES OF THE SCIENCE. BY CHARLES DAVIES, LL.D., PROFESSOR OF HIGHER MATHEMATICS, COLUMBIA COLLEGE A. S. BARNES & COMPANY, THE WEST POINT COURSE, And Only Thorough and Complete Mathematical Series. IN THREE PARTS. I. COMMON SCHOOL COURSE. Davies' Primary Arithmetic.-The fundamental principles displayed in Object Lessons. Davies' Intellectual Arithmetic.-Referring all operations to the unit 1 as the only tangible basis for logical development. Davies' Elements of Written Arithmetic.-A practical introduction to the whole subject. Theory subordinated to Practice. Davies' Practical Arithmetic.*-The most successful combination of Theory and Practice, clear, exact, brief, and comprehensive. II. ACADEMIC COURSE. Davies' University Arithmetic.*-Treating the subject exhaustively as a science, in a logical series of connected propositions. Davies' Elementary Algebra.*-A connecting link, conducting the pupil easily from arithmetical processes to abstract analysis. Davies' University Algebra.*-For institutions desiring a more complete but not the fullest course in pure Algebra. Davies' Practical Mathematics.-The science practically applied to the useful arts, as Drawing, Architecture, Surveying, Mechanics, etc. Davies' Elementary Geometry.-The important principles in simple form, but with all the exactness of vigorous reasoning. Davies' Elements of Surveying.-Re-written in 1870. The simplest and most practical presentation for youths of 12 to 16. III. COLLEGIATE COURSE. Davies' Bourdon's Algebra.*-Embracing Sturm's Theorem, and a most exhaustive and scholarly course. Davies' University Algebra.*-A shorter course than Bourdon, for Institu tions have less time to give the subject. Davies' Legendre's Geometry-Acknowledged the only satisfactory treatise of its grade. 300,000 copies have been sold. Davies' Analytical Geometry and Calculus.-The shorter treatises, combined in one volume, are more available for American courses of study. Davies' Analytical Geometry. The original compendiums, for those deDavies' Diff. & Int. Calculus. siring to give full time to each branch. Davies' Descriptive Geometry. With application to Spherical Trigonometry, Spherical Projections, and Warped Surfaces. Davies' Shades, Shadows, and Perspective.-A succinct exposition of the mathematical principles involved. Davies' Science of Mathematics.-For teachers, embracing I. GRAMMAR OF ARITHMETIC, II. OUTLINES OF MATHEMATICS, III. LOGIC AND UTILITY OF MATHEMATICS, Keys may be obtained from the Publishers by Teachers only. Entered, according to Act of Congress, in the year 1859, by CHARLES DAVIES, In the Clerk's Office of the District Court of the United States for the Southern District of New York. N. E. A. PREFACE. ALGEBRA naturally follows Arithmetic in a course of scien tific studies. The language of figures, and the elementary combinations of numbers, are acquired at an early age. When the pupil passes to a new system, conducted by letters and signs, the change seems abrupt; and he often experiences much difficulty before perceiving that Algebra is but Arithmetic written in a different language. It is the design of this work to supply a connecting link between Arithmetic and Algebra; to indicate the unity of the methods, and to conduct the pupil from the arithmetical processes to the more abstract methods of analysis, by easy and simple gradations. The work is also introductory to the University Algebra, and to the Algebra of M. Bourdon, which is justly considered, both in this country and in Europe, as the best text-book on the subject, which has yet appeared. In the Introduction, or Mental Exercises, the language of figures and letters are both employed. Each Lesson is 30 arranged as to introduce a single principle, not known |