D ADVANCED ARITHMETIC FOR SECONDARY SCHOOLS (HIGH SCHOOLS, ACADEMIES, SEMINARIES, AND NORMAL SCHOOLS) A COMPREHENSIVE TREATISE ON THE SCIENCE OF BY JOHN H. FRENCH, LL.D. NEW YORK HARPER & BROTHERS, FRANKLIN SQUARE due T 118,89.405 Harvard University', TRANSFERRED TO KYARD COLLEGE LIBRARY Copyright, 1889, by Harper & BROTHERS. All rights reserved. PUBLISHERS' NOTE. HARPER'S ADVANCED ARITHMETIC, by John H. French, LL.D., is the last work of that distinguished mathematician and educator, having been completed by him only a few days before his death. It embodies the results of life-long study and observation made serviceable by habits of critical analysis and a rare mathematical judgment. The principles and methods which it expounds have been evolved and perfected through an experience of nearly half a century in the practical work of the school-room and the teachers' institute. It is at once scholarly and complete, embracing the whole science of Arithmetic. The order of arrangement of topics, as well as the general plan of the work, may be understood by a study of the table of contents. In view of the distinguished services which were rendered by Dr. French to the cause of education in this country, it is deemed fitting to preface this volume with the following brief sketch of his life: JOHN H. FRENCH was born in Batavia, Genesee County, New York, July 7, 1824. While he was yet a child his father died, leaving a family of four children entirely dependent upon the labor and good management of their mother. As may be inferred, his early opportunities for obtaining an education were extremely limited. Working on a farm in the summer, and attending a district school for a few months each winter, he nevertheless acquired such a fund of information that at the age of seventeen he was able to teach a successful term of school in the town of Alabama, Genesee County. His life from this time, it may be said, was spent in the school-room or in work directly connected with it. In 1845, while teaching at Seneca Castle, in Ontario County, he made his first attempt at mathematical authorship by undertaking the revision of Adams's Arithmetic, at that time the standard work on that subject. Two years afterwards he went to Keene, N. H., where he wrote, for Adams's Series of Mathematics, a Mental Arithmetic, a work on Mensuration, and one on Book-keeping. In 1849 he was elected Principal of the High School at Clyde, N. Y., a position which he held for three years, and resigned to accept the principalship of the Newtown (Conn.) Academy. Returning to his native State in 1855, he engaged in the preparation and publication of town and city maps from actual surveys, |