AN ELEMENTARY ARITHMETIC BY D. B. HAGAR, PRINCIPAL OF STATE NORMAL SCHOOL, SALEM, MASS. PHILADELPHIA: COWPERTHWAIT & COMPANY. MARYARD COLLEGE LIBRARY FROM THE GIFT OF CHARLES HERBERT THURBER HAGAR'S MATHEMATICAL SERIES. 1. PRIMARY LESSONS IN NUMBERS. II. ELEMENTARY ARITHMETIC. III. COMMON SCHOOL ARITHMETIC. IV. ELEMENTARY ALGEBRA. (IN PREPARATION.) To be followed by other Books of a Complete Series. Entered, according to Act of Congress, in the year 1871, by WESTCOTT & THOMSON, Stereotypers and Electrotypers, Philada. SHERMAN & Co., Printers, Philada. INTRODUCTION. THE purpose of this manual is to facilitate the advance of young learners in the science of numbers by gradual steps. The lessons are intended to secure that normal development and discipline of the reasoning powers, and those correct habits of investigation, which alone form a sure foundation for progress in any branch of knowledge. The principles and rules have been carefully established by induction. The plan has been to make the reasons for each process entirely clear, and to enable the learner to state them in concise language. Mental and written exercises admitting substantially of the same solution have been combined, so as to render unnecessary the use of a separate mental arithmetic, and otherwise to abridge advantageously the ordinary course of arithmetical study. Pictorial illustrations, from original designs, have been freely introduced, with the view of making some parts of the subjects treated more easily understood, through the medium of the eye. It is hoped that this work, which is complete in itself, may satisfactorily meet the wants of intermediate classes in graded schools; and also may prove useful in many district schools, in which the attendance is too limited to warrant the use of a more extended treatise. |