Entered according to Act of Congress, in the year 1870, by In the Clerk's Office of the District Court of the United States for the Entered according to Act of Congress, in the year 1873, by In the Office of the Librarian of Congress, at Washington, D. C. COPYRIGHT, 1876, BY WILSON, HINKLE & Co. WHITE'S INT. AR., OLD. E-P 91 PREFACE. IT is claimed for this treatise that it possesses three very important characteristics, to wit: 1. It is specially adapted to the grade of pupils for which it is designed. It presents only those operations and principles which can be mastered by intermediate classes, and each subject is treated as thoroughly as the advancement of such pupils will permit. It is also believed that the subjects are introduced in the best possible order. There are reasons in favor of placing United States Money before Fractions, but stronger reasons favor the arrangement in this work. 2. It combines mental and written arithmetic in a practical and philosophical manner. This is done by making every mental exercise preparatory to a written one; and thus these two classes of exercises, which have been so unnaturally divorced, are united as the essential complements of each other. This union is natural and complete; and, as a consequence, the several subjects are treated in much less space than is possible when mental and written exercises are presented in separate books. 3. It faithfully embodies the Inductive Method. Instead of attempting to deduce a principle or rule from a single example, as is usually done, each process is developed inductively, and the successive steps are thoroughly mastered and clearly stated by the pupil before he is confronted with the author's rule. This method not only places "processes before rules," but it teaches "rules through processes," thus observing two important inductive maxims. (iii) |