PREFACE. THIS work is called a COMPLETE ARITHMETIC, because it embraces all the subjects which properly belong to a school arithmetic, and because it treats these subjects both analytically and inductively. It is designed to be a complete text-book for pupils who have mastered the elements of numbers. The work is characterized by the same features as the lower books of the series, It combines final and Written Aithnetic in a practical and philosophical manner. This is done by making the mental exercises preparatory to the written and thus these two classes of exercises, which have been so long and so unnaturally divorced, are united as the essential complements of each other. It faithfidly embodies the inductive method of feading. The written methods are preceded by the analysis of mental problems, and both the written methods and the principles which they involve, are derived inductively from the analytic processes. The successive steps of each process are mastered by the pupil through the solution of problems, and he is required to deduce and state the rules before he is confronted with the authors generalization. All definitions which are deducible from the processes, and, with few exceptions, all principles ancl rules, are placed after the problems-a feature peculiar to this Series. It is specially adapted, both in matter and method, to the grade of pupils for which it is clesigned. The greater portion of the work is devoted to a progressive and thorough treatment of subjects not embraced in the lower books-an arrangement which spemzets....