NEW PRACTICAL ARITHMETIC; IN WHICH THE SCIENCE AND ITS APPLICATIONS ARE SIMPLIFIED BY INDUCTION AND ANALYSIS. PREPARED TO ACCOMPANY THE MATHEMATICAL SERIES OF BENJAMIN GREENLEAF, A. M. 66 BY THE EDITOR OF NEW ELEMENTARY ALGEBRA," BOSTON: PUBLISHED BY ROBERT S. DAVIS & CO. NEW YORK: BAKER, PRATT, & CO., 142 & 144 GRAND STREET. PHILADELPHIA: J. A. BANCROFT & COMPANY. ST. LOUIS: GRAY, BAKER, & COMPANY. CHICAGO: JANSEN, MCCLURG, & CO. 1875. EducT 118.75.444 MISS ELLEN L. WENTWORTH SEP 13 1941 GREENLEAF'S NEW COMPREHENSIVE SERIES. An ENTIRELY NEW MATHEMATICAL COURSE, Analytical ana KEYS to NEW PRACTICAL ARITHMETIC, ALGEBRAS, GE- Entered, according to Act of Congress, in the year 1866, and again in the year 1867, by in the Clerk's Office of the District Court of Massachusetts Entered, according to Act of Congress, in the year 1873, by in the Office of the Librarian of Congress, at Washington. RIVERSIDE, CAMBRIDGE: ELECTROTYPED AND PRINTED BY H. O. HOUGHTON AND COMPANY. INTRODUCTION. CULTURE is progressive in its nature. Higher, still higher, is the true educational spirit. Advance in methods of instruction makes new, improved text-books a necessity; and, to subserve wants apparently not heretofore fully provided for, this work has been carefully prepared. Without being in any respect redundant, it is intended to be complete in details and comprehensive in scope; Combining with processes the most scientific the greatest simplicity; Developing principles by inductive methods, deducing rules from rational solutions, and encouraging self-reliance and originality by numerous exercises in analysis; Making written arithmetic in all its steps intellectual; and Keeping prominently in view the practical uses of numbers, by various applications of a business character. While it avoids obsolete or useless material, it properly treats new topics requiring attention, such as the Metric System of Weights and Measures, Annual Interest, Internal Revenue, etc.; and Enforces thorough educational results, by orderly arrangement of subjects, and by systematic review questions and exercises. (III) The prominence given in this book to the enunciation of Principles, will, it is believed, commend itself to the enlightened educator, since, without a knowledge of these principles, the art of using numbers becomes mere mechanical ciphering. Multiplication and Division of Decimal Fractions have been much simplified by assimilating their processes to those of like cases in Common Fractions, and by making the corresponding rules substantially the same. By treating of Fractions before Compound Denominate Numbers, the Reduction of the latter is made more thorough, and a number of special rules is avoided. Many rules of limited application are also dispensed with, by analyzing single examples, of some anomalous kind, as a guide to the solution of all others of its class. The examples have been selected with special reference to their adaptation to the present wants of active life. Encouraged by the marked appreciation of this book, shown by its extensive introduction into the best schools, and by its constantly increasing sales, great care is taken to keep it up with the times, in all respects. The present edition includes a description of the latest United States Securities, and recognizes the changes made by the Laws of 1873, in relation to coinage and the par of exchange between Great Britain and the United States. There have been appended so as not to disturb classification, in the use of the book, useful methods of contracting computations; rules and applications of a technical nature of great value to farmers, mechanics, and other manual laborers; also, Test Examples for the convenience of teachers; the whole enriching the work, and rendering it very practical and complete. KINGSTON, MASS., June, 1873. |