INTERMEDIATE ARITHMETIC ON THE INDUCTIVE METHOD, WITH PARALLEL MENTAL BY J. W. NICHOLSON, A. M. Professor of Mathematics in the Louisiana State University and Agricultural NEW ORLEANS PRACTICAL EDUCATIONAL SERIES. Chambers' Twenty Lessons in Book-keeping. Hansell's Penmanship. Nicholson's Primary Arithmetic. Nicholson's Intermediate Arithmetic. Nicholson's Complete Arithmetic. Entered according to Act of Congress in the year 1885, by F. F. HANSELL & BRO., In the office of the Librarian of Congress, Washington, D. C. PREFACE. 4102 THE chief difference between a good and an inferior Arithmetic is not so much a question of matter and rules, as it is of method in the presentation and development of principles. In the former, few mathematicians would be bold enough to lay claim to originality; but in the latter every one will, perhaps, admit there is room for improvement. In the preparation of this three-book series, consisting of a Primary, an Intermediate, and a Complete Arithmetic, the author has been influenced by the following considerations: 1o. Arithmetic treats of the whole and its parts. These are the magnitudes or objects about which Analysis and Synthesis are conversant, and on the consideration of which depends the solution of every problem. Hence, the early introduction of these terms, and frequent reference to them in the deduction of succeeding principles, are of the greatest importance. 2o. By Induction a pupil is led by easy steps, by familiar illustrations and commonplace parallelisms, into a clear apprehension of principles and definitions. Hence, each subject should be introduced with inductive exercises. 3o. Pupils advance intelligently in any new subject just in proportion as they perceive in it a continuation of the principles with which they are familiar. Hence, whatever of sameness and of difference there is in the old and the new should be made as conspicuous as possible. 4°. Mental and written work are equally important, and should be mutually supplemental. A problem intended for written work should, in general, be preceded by a parallel question designed for mental, and also as an inductive exercise. 5°. The representing of objects by the first letters of their names, as, a for apple, and b for boy or box, is not only a matter of convenience, but serves to lead pupils into the habit of generalization. M306092 |