GRAMMAR SCHOOL ARITHMETIC. BY G. A. WENTWORTH, A.M., PROFESSOR OF MATHEMATICS IN PHILLIPS EXETER ACADEMY. -oooo BOSTON: 1886. Entered, according to Act of Congress, in the year 1835, by :..GEORGE A. WENTWORTH, in the Office of the Librarian of Congress, at Washington. J. S. CUSHING & Co., PRINTERS, BOSTON. PREFACE. THIS Arithmetic is designed to give pupils of the grammar-school age an intelligent knowledge of the subject and a moderate power of independent thought. Whether Arithmetic is studied for mental discipline or for practical mastery over the every-day problems of common life, mechanical processes and routine methods are of no value. Pupils can be trained to logical habits of mind and stimulated to a high degree of intellectual energy by solving problems adapted to their capacities. They become practical arithmeticians, not by learning special business forms, but by founding their knowledge on reasoning which they fully comprehend, and by being so thoroughly exercised in logical analysis that they are independent of arbitrary rules. The book contains a great number of well-graded and progressive problems, made up for youths from ten to fourteen years of age. Definitions and explanations are made as brief and simple as possible. It is not intended that definitions shall be committed to memory, but that they shall be simply discussed by teacher and pupils. Every teacher, of course, will be at liberty to give better definitions, and to make a better presentation of methods, than those given in the book. In short, the chief object in view will be gained if pupils are trained to solve the problems by neat and intelligent methods, and are kept free from set rules and formulas. A great many number-problems are given in the first pages of the book, so that the necessary facility and accuracy in computing under the four fundamental rules may be acquired ; as want of accuracy and rapidity in mere calculations distracts the attention which should be given to the investigation and correct statement of clothed exercises. The pupil should be required to do only so many of these number-problems as are found to be necessary to give him facility and accuracy in the four fundamental operations. The chapter on the Metric System is put near the end of the book because many grammar-school pupils have no time for it, while those who have time can as well learn the system at this stage of their progress as earlier. The chapter on Mensuration is suited to the ability of beginners. The intention is not to give a system of Geometry, but to render familiar the notions of geometry that are indispensable for practical purposes. The whole subject has been illustrated and enforced by many practical examples. The chapter on Miscellaneous Problems and Examination Papers is intended as a review of the subject-matter of Arithmetic and as a test of the learner's knowledge. The author is under obligations to many teachers who have given valuable suggestions and assistance in the preparation of this work. G. A. WENTWORTH. PHILLIPS EXETER ACADEMY, Sept., 1885. |