Edue T 118 48 815 ii HARVARD COLLEGE LIBRARY GIFT OF THE GRADUATE SCHOOL OF EDUCATION 2 1929. The following explanations and table, not being contained in the Written Arithmetic, are inserted here for the convenience of those who have not studied 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 number; as 4+5 9, signifying that 4 added to 5 equals 9. XMultiplcation is denoted by a cross, formed by two oblique lines placed between the numbers: as 5×3-15, 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; 2ndly, 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 3, all signify the same thing, namely, that if 6 be divided by 2 the quotient is 3, MULTIPLICATION AND DIVISION TABLE. 1 45 6 7 8 9 10 11 12 2 4 6 8 10 12 14 16 18 20 22 24 4 8 12 16 20 241 28 32 36 40 441 48j Entered according to Act of Congress, in the year one thousand sight hundred and twenty eight, by ZADOCK THOMPSON, in the Clerk's Office of the District of Vermont. WHEN the improved edition of this work was published, in 1828, it was intended that the Written Arithmetic which forms the sec. ond and third parts 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 coinplete 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 devolved 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 omitted by those who wish to use rules without understanding 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, 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 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 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. The written arithmetic of fractions being, to young pupils, somewhat difficult to be understood, is deferred till they are made familliar with the most important arithmetical operation perform. ed with whole numbers and decimals. The nature of roots and powers has been more fully explained in the present edition, and several new diagrams introduced for their elucidation. Through. out the second part, it has been our main object to familiarize the pupil with the fundamental principles of the science, believing that when these are well understood, he will find no difficulty n applying them to the particular cases which may occur. |