EMBRACING A COMPLETE COURSE FOR SCHOOLS AND ACADEMIES 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 Educ T 119, 20.568 HARVARD Copyright, 1892, 1895, and 1911, by Copyright, 1920, by ROCHESTER TRUST AND SAFE DEPOSIT COMPANY, Stand. Ar. E-P 176 PREFACE. In the preparation of this work the author has aimed to secure two results; namely, skill in numerical computations, and a proper understanding of the reasons for the steps in the explanation of processes and the solution of problems. Skill in computing may be acquired without any intelligent apprehension of arithmetical science, and a profound insight into the truths and principles of arithmetic may be attained without much facility in using numbers. Very many people will prefer to have the student trained to be rapid and accurate in computations, and they will esteem a rapid accountant more competent in mathematics than the learned astronomers of our time; while others will prefer that training which cultivates the reasoning powers, even at the expense of practical expertness in the use of numbers. The author has endeavored to secure both these ends by embodying in the book a large number of examples upon which the pupil may be trained to accuracy and rapidity, while at the same time he has not failed to incorporate in it a large number of problems that are designed to train the analytical powers and to develop the reasoning faculties. In practical business life, the processes learned in schools are often of very little value, because they are not the natural processes of the business man. Students who learn to work examples in a mechanical way find themselves unable to solve with certainty very simple problems, after they have left school a few weeks, because they have been taught a school method rather than a natural method. The author has, therefore, adopted business methods of computation wherever they could be wisely substituted for |