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. DISTRICT OF PENNSYLVANIA, TO WIT: Be it Remembered, That on the Twenty-seventh day of May, in the Thirty-third Year of the In- A. D. 1809, JOSEPH CRUXSHANK, of the said 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 American Schools. Originally compiled by sundry teachers in and near Philadelphia ; now revised, and an additional number of Examples gigen 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 vised; in which all the sums necessary for a learner are wrought at large. Trawer's PREFACE. THE former impressions of The Americàn 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 matter 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 bcoks, 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 144 TUMERATION, Page 1 F.-llowship, 106 13 Subtraction of Decimals, 135 14 Multiplication of Decimals. Addition of Dollars and Cents, 15 Division of Decimals, 136 Subtraction of Dollars & Cents, 16 Reduction of Decimals 138 Multiplication of Dolls. & Cts. 17 Single Rule of Three in Deci. 142 Division of Dollars & Cents, 18 Double Rule of Three in De. Compound Subtraction, 30 Evolution, Compound Multiplication, 38 The Square Root, 58 Arithmetical Progression, 153 Inverse Proportion, 136 Double Rule of Three, -67 Simple Interest by Decimals, 158 Simple Interest, 84 Double Position, Lusurance, Commission, &c. 90 Permatation & Combination, 99 Addition of Duodecimals, 169 ICI Subtraction of Duodecimals, Explanation of Characers. + into, with, or multiplied by ; as 6x2 =12 by (i. e. divided by) as, 6+2=3 ; or, 2)6(3 ::: : proportionalty; as 2 : 4 :: 6:12 a Vinculum ; denoting the several quantities, ༢༠༤ 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 named, 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. Millions 1 | One. 3 2 1 Three hundred and twenty-ana4 3 2 1 4 Thousand 321 5 4 3 2 1 56 Thousand 321 6 5 4 3 2 1 654 Thousand 321 7 6 5 4 3 2 1 7 Million 654 Thousand 321 8 7 6 5 4 3 2 1 87 Million 654 Thousand 321 9 8 7 6 5 4 3 2 1987 Million 654 Thousand 391 The above table is comprised in the following :-- |