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This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Excerpt from An Algebraic Arithmetic: An Exposition of the Theory, and Practice of Advanced Arithmetic The introduction of elementary algebra into the schools is of more doubtful value for two principal reasons. The conceptions of geometry can be represented by fig ures and objects, and are therefore readily grasped by the child, but those of algebra can be so represented only to a very limited degree; and, for the most part, are abstractions the nature of which the child comprehends with difficulty. Moreover, the time that can be allotted to the subject in the grammar school is barely sufficient to carry the pupil over the essentially uninteresting details of algebraic manipulation that necessarily precede any but the Simplest applications of the science. But while the wisdom of introducing elementary algebra into the schools may, for these and minor reasons, be seriously questioned, the experience of several years as a teacher has led the author to the conclusion that the application of certain algebraic conceptions to arithmetic would contribute largely toward the rational presentation of the subject, thus increasing its disciplinary value, and at the same time preparing the way for a natural transi tion to the algebra of the high school. These conceptions are the use of letters as the general representatives of (positive) numbers and of the equation to express their relations. 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.

This is a reproduction of a book published before 1923. This book may have occasional imperfections such as missing or blurred pages, poor pictures, errant marks, etc. that were either part of the original artifact, or were introduced by the scanning process. We believe this work is culturally important, and despite the imperfections, have elected to bring it back into print as part of our continuing commitment to the preservation of printed works worldwide. We appreciate your understanding of the imperfections in the preservation process, and hope you enjoy this valuable book.

Excerpt from An Algebraic Arithmetic: An Exposition of the Theory, and Practice of Advanced Arithmetic This arithmetic is not offered to the public as a refinement or super-refinement of the methods of existing textbooks on the subject. It is a new departure. For a number of years arithmetics have been undergoing a progressive change. Voluminous works, in which the isolated treatment of related topics and the multiplicity of detail relating to business arithmetic completely obscured the unity of the science, have by degrees given place to more compendious works. The change has, however, been little more than a process of successive elimination. To the former plethora has succeeded an ever-increasing leanness, until at last the skeleton of the subject stands revealed indeed, for it alone remains. The arithmetic of to-day is merely a compilation of examples, classified and miscellaneous, with illustrative solutions accompanied by brief explanatory notes and a few definitions. The task of infusing a living, rational principle into these dry bones is left entirely to the teacher. A second change in the mathematics of the grammar school, contemporaneous with that above mentioned, has been the introduction of elementary geometry and, more recently, of elementary algebra. 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.

This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work was reproduced from the original artifact, and remains as true to the original work as possible. Therefore, you will see the original copyright references, library stamps (as most of these works have been housed in our most important libraries around the world), and other notations in the work. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work.As a reproduction of a historical artifact, this work may contain missing or blurred pages, poor pictures, errant marks, etc. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.