ARITHMETIC, DESIGNED FOR ACADEMIES AND SCHOOLS, (WITH ANSWERS.) BY CHARLES DAVIES, LL.D. AUTHOR OF FIRST LESSONS IN ARITHMETIC, ELEMENTARY ALGEBRA, PERSPECTIVE, ANALYTICAL GEOMETRY, CALCULUS. PHILADELPHIA: PUBLISHED BY A. S. BARNES & CO. NEW YORK: PRATT, WOODFORD & CO. Public Schools, BALTIMORE, August, 1842 At a meeting of the Board of Commissioners of Public Schools, Baltimore, to hear the report of the Book Committee, upon Davies' Elementary Series. The following resolution was offered, and adopt od : Resolved,—That Davies' First Lessons in AnITHMETIC, Davies' ARITHMETIC, Davies' ALGEBRA, Davies' Practical GEOMETRY, and Davies' ELEMENTARY GEOMETRY, be introduced into the Public Schools of Baltimore. JAMES LUCAS, Commissioners. From the Minutes, John F. TILYARD, Clerk. CHAMBER OF THE CONTROLLERS OF Public Schools, Philadelphia, September 15, 1842. At a meeting of the Board of Controllers of the Public Schools of the First School District of Pennsylvania, held at the Controllers' Chamber, on Tuesday afternoon, September 13, 18-12, it was Resolved,That Davies' First LESSONS IN ARITHMETIC, and Davies' ARITHMETIC, be introduced into the Public Schools of the District; and also, that Davies' ALGEBRA be introduced therein; the latter under the Resolution of the 12th day of November, 1839. From the Minutes, THOMAS B. FLORENCE, Secretary. Entered according to the Act of Congress, in the year one thousand eight hundred and thirty-eight, by Charles Davies, in the Clerk's Office of the District Court of the United States, for the Southern District of New York. STEREOTYPED BY C. W. MURRAY & Co.-C. SerMAN, PRINTER. 12 qudt PREFACE. A CORRECT and accurate knowledge of Arithmetic is one of the most important elements of a liberal or practical education. The public should, therefore, receive with indulgence every attempt that may be made to improve this department of instruction. The Elementary Treatise, which is here presented, is an enlarged, and it is hoped, an improved edition of the Common School Arithmetic, published in 1833. The suggestions of several experienced teachers have been incorporated with the body of the work in its new form, and, indeed, nothing has been omitted which it was thought would give it value to those for whose use it is designed. It has been the intention to render the whole subject as plain as it is capable of being made, and at the same time, to treat it as concisely as possible. The name, Compound Numbers, which has heretofore been given to all numbers in which the kind of unit is expressed, has been changed to that of Denominate Numbers. This change has not been made with any ambitious spirit of innovation, but because it is deemed an improvement. It is not easy to form an idea of what is meant by the term, Compound Number, and especially so, when we find it applied to such numbers as 3 pounds, 3 dollars, 3 shillings, &c. Why is 3 pounds a compound number any more than 3? If it be answered that 3 pounds is composed or compounded of three single pounds, that does not remove the difficulty, for 3 is also composed of three units 1. Is it not then the better way to call the first a denominate number, and the other a simple number, as is done in § 45. Mr. Hasler. in his Arithmetic, has called this class of numbers, Des nominate Fractions. In the present edition, the questions referring to each section are ar ranged directly after the section, which generally brings the question and answer on the same page. This alteration will, no doubt, be found convenient to teachers. A Key has also been prepared, in which all the questions contained in the Arithmetic are resolved, and in such a manner, that the particular methods of solution can be fully understood. Many examples, not in the Arithmetic, have been imbodied in the Key, in order that the pupils may be exercised in questions not found in the books before them. Since the publication of the last edition, a small introductory work has been prepared, entitled, “ First Lessons in Arithmetic :" in consequence of which, the “ Mental Arithmetic” which has heretofore formed the introduction, has been omitted. Demonstrations of the rules for extracting the square and cube roots have also been added, and the Author now indulges the hope that no further changes will be found necessary. The opinion of teachers has been so unanimous in favor of numerous examples as to induce the Author to add a Supplement, embracing near six hundred practical questions. These examples are arranged under heads corresponding with the order followed in the Arithmetic. One of the advantages resulting from this arrangement is, that the pupils of a class may be kept together—the more proficient being employed on the Supplement until the whole are ready to be advanced. In deference to the opinions and wishes of many distinguished teachers, an edition of the Arithmetic has been prepared in which the answers to the questions are omitted. The edition, however, in which the answers are given to the alternate questions, is still published, and experience will show which method will best advance the interests of education, CONTENTS. FIRST FIVE RULES. Explanation of the Signs +, and , Subtraction of Simple Numbers, Multiplication of Simple Numbers, 5 |