THE YOUTH'S ASSISTANT IN THEORETIC AND PRACTICAL ARITHMETIC. DESIGNED FOR THE USE OF SCHOOLS IN THE UNITED STATES, BY ZADOCK THOMPSON, A. M. AUTHOR OF THE GAZETTEER OF THE STATE OF VERMONT. IMPROVED EDITION. Woodstock, Vt. PRINTED BY DAVID WATSON. DISTRICT OF VERMONT, ss. 茶業 L. S. B E IT REMEMBERED, that on the third day of October, in the fifty-third year of the Independence of the United States of America, ZADOCK THOMPSON, of the said District, hath depos ****ited in this office, the title of a book, the right whereof he claims as Author, in the words foling, to wit: "Thompson's New Arithmetic. The Youth's Assistant in Theoretic and Practical Arithmetic. Designed for the use of Schools in the United States. By Zadock Thompson, A M. Author of the Gazetteer of the State of Vermont. Improved Edition." In conformity to the act of the Congress of the United States, entitled "an act for the encouragement of learning, by securing the copies of maps, charts and books to the authors and propriotors of such copies, during the times therein mentioned." JESSE GOVE, Clerk of the District of Vermont. A true copy of record, examined and sealed by me. J. GOVE, Clerk. Tutthe 6-18-21 34424 PREFACE. Although the present edition of the Youth's Assistant retains the original title, it will be found to differ very considerably from the original work. It is divided into three distinct parts which, combined, form, it is believed, as complete a system of intellectual and written arithmetic as can be found elsewhere within the same limits, or can be purchased for the same expense. The first part is wholly devoted to intellectual arithmetic on the excellent plan of Colburn, and to such tables, definitions and other matters, as may be profitably learned by children at an early age. This part is designed to be done up separately for children and in connexion with the other parts for older scholars. The explanations and directions for using this part, will be found in the preliminary observations, and interspersed with the subsequent articles. The second part is devoted to written arithmetic on the inductive plan of Lacroix. Here the principles are first developed by the analysis of familiar examples, and the method of applying these principles to the solution of questions is then expressed in general terms, denominated the Rule, which is still further illustrated by a great variety of practical questions. The rules and questions for practice are much like those in the former edition, while the analysis is printed in small type, occupies but little space and may be omitted-by such as wish to be taught dogmatically and make use of rules which they do not understand. As the principles of multiplication are the same as those of addition, we have presented those rules in connexion and the same remark will apply to subtraction and division. A knowledge of decimals being necessary to a good understanding of our Federal currency and this knowledge being easily acquired by such as bave learned the notation of whole numbers, decimals and Federal money are introduced immediately after the first section on simple numbers. By acquainting the pupil thus early with decimals, he will be likely to understand them better and to avail himself of the facilities they afford in the solution of questions and the transaction of business. Reduction ascending and descending are arranged in parallel colums and the answers to the questions of one column are found in the corresponding questions of the other. Compound multiplication and division are arranged in the same way, and only one general rule for each is given, which was thought better than to perplex the pupil with a multiplicity of cases. Interest and other calculations by the hundred are all treated decimally, that method being most simple and conformable to the notation of our currency. The nature and principles of proportion are fully developed and the method of applying them to the solution of questions clearly shown; and also the method of solving the same questions by analysis. The written arithmetic of fractions being, to young pupils, somewhat difficult to be understood, is defered till they are made familiar |