Excerpt from An Arithmetic for Colleges and Schools My experience has taught me that it is between the ages of twelve and fifteen according to the degree of precocity ma the study of reasoned arithmetic should begin. Before that period, a child can only master the four plain rules, which he ought to learn as soon as practicable; they being for him then a mere mechanical process. But it is only by long habit that he can perform with readiness these four fundamental operations 3 and there fore he should begin early. But, beyond this training of the numerical faculties of the mind, I would not torment a child with the abstruseness of arithmetic before the above-named period. In the following pages, I have endeavored to avoid both the obscurity and confusion of purely practical arithmetics, which furnish no thread to guide the y'outhful mind in the per plexing labyrinth in which he is frequently lost, and Degreesthe other exti'eme of abstruseness, which some theoretical treatises a're' obnoxious to. My object has been to secure the knowledge of this science in a short, and, above all, in a permanent' way, and to make the transition from it to algebra simple and natural. While I have endeavored to facilitate the pro gress of the student, I have not forgotten to make the work C convenient for the teacher, who will find in it numerous3 carefully graduated examples. In these examples, I have given the answers only when no part of the Operation is supplied by them. Answers, in that case, are a great assistance to the teacher, while they merely warn the pupil of his mistake, without doing away the necessity of his going through the details of the exercises. The work is divided into Lessons, some of which may be' omitted with beginners; while others may be only rapidly reviewed with more advanced pupils, the work being in tended for both classes of students. This treatise will consist of two arts The first, containing only the elementary principles and fundamental rules of arithmetic. The second, their combinations and applications to ques tions of practical'fitility, and particularly the mahner of re ducing these to numerical statements. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.