THE YOUTH'S ASSISTANT IN THEORETIC AND PRACTICAL ARITHMETIC. DESIGNED FOR THE USE OF SCHOOLS IN THE UNITED STATES, BY ZADOCK THOMPSON, A. M. IMPROVED EDITION. Joodstock, Ut. PRINTED BY DAVID WATSON, DISTRICT OF VERMONT, ss. E IT REMEMBERED, that on the third day L. S. dependence of the United Sta:es of America, ZaDOCK THOMPSON, of the said District, bath depos. ited in this office the title of a book, the right whereof he claims as Author, in the words fol. ing, 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 Verinont. 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. 344 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, coubined, form, it is believed, as complete a system of intellectual and writ. ten arithmetic as can be found elsewhere within the same limits, or can be purchased for the same expense. The first part is n holly devoted to intellectual arithmetie on the exo cellent plaii ot Culburn, and to such tables, definitions and other mate ters, as may be profitably learned by cbildren 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 explarations and di. rections for using this part, will be found in the preliminary observations, and interspersed with the subsequent articles. The second part devoted to written arithmetic on the inductive plan of Lacroix Here the principles are first developed by the ana. lysis of familiar esamples, and the method of applying these priciples to the solution of questions is then expressed in general terms, denominated the Rule, which is still furtber illustrated by a great va. riety 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 mitled-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 subtractiou 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 divtsion are arranged in the same way, and only one general rule for each is given, which was thought betier than to perplex the pupil with a moltiplicity 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 tbe solution of questions clearly shown ; and also the wethod 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 |