BY WILLIAM J. MILNE, PH.D., LL.D. PRESIDENT OF NEW YORK STATE NORMAL COLLEGE NEW YORK: CINCINNATI .:. CHICAGO COPYRIGHT, 1911, BY WILLIAM J. MILNE. ENTERED AT STATIONERS' HALL, LONDON. FIRST YEAR ALGEBRA E. P. I 629260 C PREFACE THIS book has been written to meet the growing demand for a High School Algebra that contains only the first year's work. While the order of topics resembles in general that found in the author's other algebras, yet a number of changes have been made, for the purpose of simplifying the work and deferring difficulties until the pupil is able to cope with them. One of the hardest ideas for the young student to grasp is that of negative numbers; and the common practice of presenting them at the very beginning of the book results not only in the bewilderment but also in the discouragement of the student. In this book, therefore, the pupil is first taught the symbols and the fundamental operations as applied to positive numbers, and not until he has become thoroughly familiar with these is he introduced to negative numbers. He can thus concentrate his entire attention on the one new idea, and it becomes a pleasure to him to extend his knowledge by applying the principles he has already learned to the new concept. Again, the troublesome operation of removing and inserting signs of aggregation is deferred until the pupil's gain in power of manipulating algebraic numbers renders the work comparatively easy. On the other hand, in order to arouse from the first the interest of the pupil, simple problems to be solved both arithmetically and algebraically, as well as easy solutions of simultaneous equations and of quadratic equations by factoring, are presented very early in the course, while the more difficult phases of these subjects are discussed later. Throughout the work, indeed, the greatest emphasis is placed on equations and problems, which furnish the most apt illustrations of the practical uses of algebra. |