PREFACE. FEW works on Intellectual Arithmetic have received more unqualified approbation, and a more extensive patronage, than this, which, for several years, was published under the title-Ray's Arithmetic, Part Second. The numerous editions demanded have again rendered necessary a renewal of the plates; this has afforded an opportunity for remodeling the work. Many important improvements have been introduced, with a design to impart completeness, and give a concise and progressive course of arithmetical analysis. The volume in its present form, embraces: 1st. Exercises on the primary principles, and their applications; together with models of analysis in the shape of solutions. 2d. A progressive and comprehensive presentation of Fractions, intended to render the subject intelligible and attractive. 3d. General Reviews, designed to test the pupil's knowledge of principles, preparatory to the applications of mental analysis which follow. 4th. Reduction and Percentage, with the application of the latter to Profit and Loss, Commission, Insurance, Interest, and Discount. The value of Intellectual Arithmetic is so highly appreciated, that little need be said in its commendation; when properly taught, it is one of the most useful and interesting studies in which pupils can engage. By its study, the pupil is taught to reason, to analyze, to think for himself; while it imparts confidence in his reasoning powers, and strengthens the mental faculties. CINCINNATI, May, 1877. (3) TO TEACHERS. THE solution of an example in Mental Arithmetic is herein regarded as a direct and natural response to the requirements of the problem; it aims to be a plain and simple statement of the successive steps leading to the final result or answer. The data afforded by the example are repeated in the solution no further than is necessary for its clear statement. Every different class of examples is furnished with a solution; in a few instances, more than one solution is given, the succeeding solutions offering a briefer method. No solution is repeated; and, when a solution, in whole or in part, occurs in a subsequent solution as a portion of the argument, its result is given as briefly as possible. Of course, there is nothing to prevent the teacher from elaborating any solution, or any portion of it, to the fullest extent he sees fit; and it may often be desirable so to do. Furthermore, those who wish can, with facility, apply the "Four Step Method" for the three step, of which each solution will furnish a clear state ment. It is obvious, that in a text-book the publishers should not occupy space with any thing more than the essentials of a solution. |