PROGRESSIVE ARITHMETIC THIRD BOOK BY WILLIAM J. MILNE, PH.D., LL.D. LATE PRESIDENT OF NEW YORK STATE COLLEGE FOR TEACHERS ALBANY, N. Y. AMERICAN BOOK COMPANY NEW YORK CINCINNATI CHICAGO PREFACE THIS book, which is intended for use in the highest grades in our grammar schools, has been constructed upon a broader and more comprehensive plan than the preceding books in the series. The desirability of gathering together in a somewhat complete whole the knowledge that students have previously acquired, and of including the essentials of arithmetic in a single volume, has led to the adoption of the purely topical method of presentation. Great care has been expended on the method of presenting the various principles and on the solutions, with the aim of making them in the highest degree clear, concise, accurate, and practical. By treating together in some instances subjects which though logically related are usually separated, it has been possible to simplify considerably the methods of solution generally employed. Analysis of problems has received adequate attention, and algebraic methods of solution have been introduced for the purpose of simplifying the processes in certain classes of problems. The problems have been framed with the greatest care. They are not numerical puzzles, nor are they based on unreal conditions. They have been made both rational and practical, and they relate to a wide range of subjects drawn from modern life and industries. The information they embody has been gathered from reliable sources. The prime object of the book, however, is not to convey information on extraneous topics, but to teach the processes of arithmetic in the best way possible. WILLIAM J. MILNE. |