A PRACTICAL TREATISE ON ALGEBRA, DESIGNED FOR THE USE OF STUDENTS IN HIGH SCHOOLS AND ACADEMIES. BY BENJAMIN GREENLEAF, A. M. AUTHOR OF THE "NATIONAL ARITHMETIC," ETC. BOSTON: PUBLISHED BY ROBERT S. DAVIS & CO. NEW YORK: PRATT, WOODFORD, & Co., AND CADY AND BURGESS. And sold by the trade generally. EducT 128.52. 420 204 1882, Nov. 27, Gift of W. Tinghast, Entered according to Act of Congress, in the year 1852, by BENJAMIN GREENLEAF, In the Clerk's Office of the District Court of the District of Massachusetts. GREENLEAF'S SERIES OF MATHEMATICS. 1. MENTAL ARITHMETIC, upon the Inductive Plan; designed for Primary and Intermediate Schools. Revised and enlarged edition, 144 pp. 2. INTRODUCTION TO THE NATIONAL ARITHMETIC; OR, COMMON SCHOOL ARITHMETIC. Improved stereotype edition. 324 pp. 3. THE NATIONAL ARITHMETIC, for advanced scholars in Common Schools and Academies. Improved stereotype edition. 360 pp. COMPLETE KEYS TO THE INTRODUCTION, AND NATIONAL ARITHMETIC, containing Solutions and Explanations, for Teachers only. 4. PRACTICAL ALGEBRA, for Academies and High Schools, and for advanced Students in Common Schools. KEY TO THE PRACTICAL ALGEBRA, containing the Answers, and full Solutions and Explanations, for Teachers only. BOSTON: THURSTON, TORRY, AND EMERSON, PREFACE. THE following Treatise is designed to present a system of theoretical and practical Algebra. It is intended to be both elementary and comprehensive, and adapted to the wants of beginners, as well as those who are advanced in the study. In the course of his labors the author has consulted the most approved European treatises on the subject, and availed himself of whatever he thought might add to the interest and usefulness of his work. It has been the aim of the author throughout his investigations, to give to it a practical character, that those who study it may know how to apply their knowledge to useful purposes. It will be seen, that a place is given in this volume to the subject of Proportion, which was deemed desirable on account of those, who may study Algebra before they enter upon Geometry. The demonstrations connected with the several Roots, will greatly aid those who wish for a complete and thorough knowledge of Evolution in Arithmetic. A large number of Examples have been placed under each Rule; and the pupil, who will carefully and intelligently perform them, will gain a more thorough knowledge of the principles of the science, than he could do by any other means. Long experience in teaching has-convinced the author, that in both Arithmetic and Algebra, it is highly important for the learner to apply his knowledge to practice; and, to this end, he should solve a variety of problems, and some of them difficult; in this way, and in no other, as the author conceives, can one become a thorough and accomplished mathematician. The subject of minus and plus on page 29, and also the completing the square in Affected Equations, page 166, the author has illustrated by diagrams. This method he has seen in no other work. |