American Tutor's Assistant REVISED; OR, A COMPENDIOUS SYSTEM OF PRACTICAL ARITHMETIC; CONTAINING THE SEVERAL RULES OF THAT USEFUL SCIENCE, CONCISELY DEFINED, METHODICALLY ARRANGED, AND FULLY EXEMPLIFIED.; THE WHOLE PARTICULARLY ADAPTED TO THE EASY AND REGULAR INSTRUCTION OF YOUTH IN OUR AMERICAN SCHOOLS. Originally compiled by sundry Teachers in and near Phila- United States. TO WHICH IS ADDED, A COURSE OF Book-KEEPING by Single Entry, PHILADELPHIA, Be it Remembered, That on the Twenty-seventh Seal. day of May, in the Thirty-third Year of the Independence of the United States of America, A. D. 1809, Joseph CRUKSHANK, of the said District, bath deposited in this Office the Title of a Book, Che Right whereof he claims as Proprietor, in the words following, to wit: 6 THE American Tutor's Assistant revised; or a compen. dious System of Practical Arithmetic ; containing the several rules of that useful Science, concisely defined, methodically arranged, and fuily exemplified. The whole particularly adapted to the easy and regular instruction of Youth in our Americau Schools. Originally compiled by sundry teachers in and near Philadelphia ; now revised, and an additional number of Examplss gifen in Money of the United States. To which is added, a Course of Book-keeping by Single Entry.” 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." And also to the Act, entitled "An Act supplementary to an Act, 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 Time therein mentioned,” and extending the Benefits thereof to the Arts of designing, engraving, and etching historical and other Prints." D. CALDWELL, Clerk of the District of Pennsylvania. Lately published and for sale by Joseph Crukshank, price 75 cents. A Key to the American Tutor's Assistant, revised; in which all the sums necessary for a learner are wrought at large. Travietas PREFACE. THE former impressions of The American Tutor's Assistant having been well received by the public, the Proprietor has been induced to revise it, and has now made some amendments and additions, which he presumes will render it more acceptable to teach ers. To avoid increasing the size and price of the book, some parts have been omitted, to make room for inatter considered of more essential use. To this edition is added, a course of Book-keeping, according to the method of Single Entry, with a description of the books, and directions for using them. Much attention has been given to the revision and correction of the work, and the errors which had escaped notice in the former are corrected in this edition. Recl. o-5 NUMERATION, Page i F.llowship, 106 109 117 13 Subtraction of Decimals, 135 14 Multiplication of Decimals. 135 Addition of Dollars and Cents, 15 Division of Decimals, Subtraction of Dolars & Cents, 16 Reduction of Decimals Multiplication of Dolls. & Cts. 17 Single Rule of Three in Deci. 142 Division of Dollars & Cents, 18 Double Rule of Three in De. 144 Compound Multiplication, 38. The Square Root, 58 Arithmetical Progression, 153 Double Rule of Three, -67 Simple Interest by Decimals, 158 Lusurance, Commission, &c. 9o Permutation & Conibination 168 ICI Subtraction of Duodecimals, 169 . Explanation of Characters. + into, with, or multiplied by; as 6 X 2 =12 by (i. e. divided by) as, 6-2=3; or, 2)6(3 ::: : proportionalty; as 2:4 :: 6:12 Fourth Root ; as, ✓ 64=2, &c. Vinculum ; denoting the several quantities, 2 A RITHMETIC is the art of computing by numbers. Is has five principal rules for its operations, viz. ni meration, addition, subtraction, multiplication, and division. NUMERATION. “UMERATION teaches to express numbers by figures, set down or nam amed, and consists of two parts, viz. First, the right placing of them. Second, The true valuing of each figure, in its proper place; both which are exhibited in the following TABLE. Units Millions 1 One. 3 2 1 Three hundred and twenty-anas The above table is comprised in the following: |