A COMMON SCHOOL ARITHMETIC BY BOTHWELL GRAHAM, PROFESSOR OF MATHEMATICS, STATE NORMAL SCHOOL, ATHENS, Ga. BOSTON, U.S. A. AND LONDON. 1895. PREFACE. ARITHMETIC is probably one of the most poorly taught of the common school branches. The texts in common use are chiefly at fault. They burden the learner with so great a number of minor details and useless applications as to render it impossible for him to unify the lesser truths about the greater. Thus the pupil fails not only of a competent practical knowledge of the subject, but also of the highest discipline which is the outcome of mastery alone. The method, therefore, adopted in this treatise is the Intensive. Clearness, however, has in no case been sacrificed to conciseness; but, on the contrary, it is believed that the treatment in general, and the demonstrations in particular, will be found to be not simply brief but at the same time pointed and luminous. The Vertebral Principle of the book is Ratio. This, the Newtonian conception of number, not only imparts a new dignity and importance to Proportion as making it sustain the same relation to Arithmetic that the Equation does to Algebra, but also integrates the several membral divisions of Arithmetic into the strictest unity. The book will therefore be found to be easy of thorough mastery the first desideratum in a text. iii |