A HIGHER ARITHMETIC. BY G. P. QUACKENBOS, LL. D., AUTHOR OF "A PRACTICAL ARITHMETIC; METIC; 66 AN ELEMENTARY ARITHMETIC;" A PRIMARY ARTH SONS IN COMPOSITION; ADVANCED COURSE OF COMPOSITION AND RHETORIC; "A NATURAL PHILOSOPHY;" "ILLUSTRATED SCHOOL HISTORY OF THE UNITED STATES;" ETC. UPON THE BASIS OF THE WORKS OF GEO. R. PERKINS, LL. D. NEW YORK: CINCINNATI: CHICAGO FROM THE PRESS OF D. APPLETON & COMPANY. 428130 [PUBLISHERS' NOTICE.] APPLETONS' MATHEMATICAL SERIES. By G. P. QUACKENBOS, LL.D. A Primary Arithmetic. Beautifully illustrated; carries the beginner through the first four Rules and the simple Tables, combining mental exercises with examples for the slate. 16mo. 108 pages. An Elementary Arithmetic. Reviews the subjects of the Primary in a style adapted to somewhat maturer minds. Also embraces Fractions, Federal Money, Reduction, and the Compound Rules. 12mo. 144 pages. A Practical Arithmetic. Prepared with direct reference to the wants of Common Schools, giving special prominence to the branches of Mercantile Arithmetic. 12mo. 336 pages. Key to Practical Arithmetic. 12mo. 72 pages. A Higher Arithmetic. A comprehensive text-book on the science of Arithmetic and its practical applications; specially designed as an aid in preparing for the counting-house. 12mo. 420 pages. Key to Higher Arithmetic. 12mo. 96 pages. A Mental Arithmetic Designed to impart readiness in mental calculations, and extending them to the various operations needed in business life. Introduces short methods, and new and beautiful processes. 16mo. 168 pages. Entered, according to Act of Congress, in the year 1874, by In the Office of the Librarian of Congress, at Washington. PREFACE. THIS work, which completes our Arithmetical Series, is designed for the use of high-schools, academies, business colleges, advanced classes in private and grammar schools, and all who desire a thorough preparation for the duties of the countinghouse, and have had such previous training as will enable them to enter on a higher course intelligently and profitably. It is complete in itself, furnishing, in addition to a comprehensive course in all the higher topics, a brief summary also of the elementary parts of the subject. When it was remembered how easy it is to forget notation and numeration while laboring in partial payments, cube root, etc., it was deemed unsafe to leave out any link in the chain. Yet, in treating the elementary topics referred to, the fact that they had already been studied was distinctly kept in view: they are discussed in a manner adapted to maturer minds; more has been left for the student himself to develop; additional matter, of interest and importance, has been introduced; and subjects have been presented in new connections and different combinations. Classes may, therefore, be placed at the very commencement of this book, with no risk of losing time by a useless re-traversing of ground too familiar to be again gone over with profit. Merchants often complain that young men who have had the best school advantages, on entering stores, are quite ignorant of business processes, and unable to make a prompt and efficient use of their arithmetical knowledge in off-hand calculations even of the simplest character. One great aim in preparing the present work has been to remove all ground for this complaint, by treating the various branches of commercial arithmetic with special |