THE YOUTH'S ASSISTANT IN THEORETIC AND PRACTICAL ARITHMETIC; DESIGNED FOR THE USE OF SCHOOLS IN THE UNITED STATES. BY ZADOCK THOMPSON, A. M., FOURTH EDITION. BURLINGTON, VT.: CHAUNCEY GOODRICH. 1832. DISTRICT OF VERMONT, SS. 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 daposited in this office, the title of a book, the right whereof he claims as Author, in the words following, 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 proprietors 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. The following explanations and table not being contained in the Written Arithmetic, are inserted here for the convenience of those who have not studied the Mental Arithmetic. EQUALITY is expressed by two horizontal marks; thus 100 cts.= 1 dollar, signifies that 100 cents are equal to one dollar. +ADDITION is denoted by a cross, formed by one horizontal and one perpendicular line, placed between the numbers; as 4+5=9, signifying that 4 added to 5 equals 9. XMULTIPLICATION is denoted by a cross, formed by two oblique lines placed between the numbers; as 5x3=15, signifying that 5 multiplied by 3, or 3 times 5 are equal to 15. -SUBTRACTION is denoted by one horizontal mark, placed between the numbers; as 7—4—3, signifying that 4 taken from 7 leave 3. )(,or & DIVISION is denoted three different ways; 1st. by the reversed parenthesis; 2dly. by a horizontal line placed between the numbers with a dot on each side of it; and 3dly. by writing the number to be divided over the other in the form of a fraction; thus 2)6(3, and 6÷2-=3 and 2=3, all signify the same thing, namely that if 6 be divided by 2 the quotient is 3. MULTIPLICATION AND DIVISION TABLE. 1 2 3 4 5 6 7 8 9 10 11 12 9|18|27|36|45|54|63|72| 81] 90| 99|108: 10|20|30|40|50|60|70|80| 90|100|110|120: 11|22|33|44|55|66|77|88| 99|110|121|132; 12|24|36|48|60|72|84|96|108|120|132|144 NARVARD COLLEGE LIBRARY ADVERTISEMENT. WHEN the improved edition of this work was published, in 1828, it was intended that the Written Arithmetic, which forms the second and third part should always be accompanied by the Mental Arithmetic embraced in the first part. Since that time it has, however, been thought best to transpose such tables from the Mental to the Written Arithmetic, as to render the latter complete without the former, in order to lessen the expense of the book to those who do not wish to study mental arithmetic, or who have studied some other treatise; and, thus prepared, it is now presented 'to the public. No alteration has been made from the last edition in the arrangement of the rules, and the whole of the second part is presented, as before, on the inductive plan of Lacroix. 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, forming a Rule, which is still further illustrated by a great variety of practical questions. The analysis is printed in small type, occupies but little space, and may be omittedby those who wish to use rules without understunding them. Addition and Multiplication, both involving the same principles, are presented in connexion, and also 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 have 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, be 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 columns 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 deeimally, 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. The written arithmetic of fractions being, to young pupils, somewhat difficult to be understood, is deferred till they are made familiar with the most important arithmetical operations performed with whole numbers and decimals. The nature of roots and powers has been more fully explained in the present edition, and several new di. agrams introduced for their elucidation. Throughout the second |