FOR PRIMARY AND INTERMEDIATE CLASSES IN BY WILLIAM J. MILNE, PH.D., LL.D. NEW YORK .:. CINCINNATI CHICAGO MILNE'S MATHEMATICS MILNE'S ELEMENTS OF ARITHMETIC MILNE'S MENTAL ARITHMETIC MILNE'S ELEMENTS OF ALGEBRA MILNE'S GRAMMAR SCHOOL ALGEBRA MILNE'S HIGH SCHOOL ALGEBRA MILNE'S PLANE AND SOLID GEOMETRY MILNE'S PLANE GEOMETRY-SEPARATE Copyright, 1893, by AMERICAN BOOK COMPANY Elmts. Ar. E-P68 PREFACE. THIS work has been prepared to meet a demand for a book that contains, within brief compass, an elementary course in arithmetic. It is also designed to be an introduction to the more thorough and exhaustive treatment of the science which is given in the author's STANDARD ARITHMETIC. The first part of the book contains exercises arranged in such a manner that they secure an easy and natural development of the ideas of numbers, and they afford sufficient practice to fix the results in memory. Ready knowledge of results can be secured only by frequent repetition and thorough drill, and the lessons that have been prepared are believed to be admirably adapted to produce expertness in computing, without sacrificing interest in the subject through constant practice with abstract numbers. When the more systematic treatment of the science is presented, the pupil is led by natural, progressive, and logical steps to an understanding of the definitions, principles, processes, and rules, before he is required to state them; consequently, all definitions, principles, and rules are but the expressions of what he already knows. It is evident, therefore, that the plan pursued in the work will develop in the student the habit of investigating for himself any subject which may claim his attention, and this is an extremely important part of proper teaching. The number of oral examples is large enough to supply all the necessary training in "mental" arithmetic, and the frequent exercises for review will fix in the memory all the knowledge of the science that has been acquired. The treatment of the subjects has been adapted to the comprehension of young pupils, and subjects which are too difficult for them have been omitted; and yet in no instance has accuracy of statement or correctness of process been sacrificed in what has been presented. 85123 8 3 |