PRACTICAL TREATISE ON ALGEBRA, DESIGNED FOR THE USE OF STUDENTS IN HIGH SCHOOLS AND ACADEMIES. BY BENJAMIN GREENLEAF, A.M., Thirty-Fifth Emproved Stereotype Edition. BOSTON: PUBLISHED BY ROBERT S. DAVIS & CO. NEW YORK: D. APPLETON & CO., AND MASON BROTHERS. 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. Entered according to Act of Congress, in the year 1853, by In the Clerk's Office of the District Court of the District of Massachusetts. GREENLEAF'S SERIES OF MATHEMATICS. 1. PRIMARY ARITHMETIC; OR, MENTAL ARITHMETIC, upon the Inductive Plan; designed for Primary Schools. Improved electrotype edition. 72 pp. 2. INTELLECTUAL ARITHMETIC; OR, HIGHER MENTAL ARITHMETIC, upon the Inductive Plan; designed for Common Schools and Academies. Improved edition. 3. COMMON SCHOOL ARITHMETIC; OR, INTRODUCTION TO THE NATIONAL ARITHMETIC. Improved stereotype edition. 324 pp. 4. HIGHER ARITHMETIC; OR, THE NATIONAL ARITHMETIC, being a complete course of Higher Arithmetic, for advanced scholars in Common Schools and Acade mies. New electrotype edition, with additions and improvements. 444 pp. 5. PRACTICAL TREATISE ON ALGEBRA, for Academies and High Schools, and for advanced Students in Common Schools. Improved stereotype edition. 360 pp. 6. ELEMENTS OF GEOMETRY, for Academies and High Schools, and for Advanced Students in Common Schools. Electrotype edition. 320 pp. Just published. COMPLETE KEYS TO THE INTRODUCTION, AND NATIONAL ARITHMETIC, AND THE PRACTICAL TREATISE ON ALGEBRA, containing Solutions and Explanations, for Teachers only. In 3 volumes. Two editions of the NATIONAL ARITHMETIC, and also of the COMMON SCHOOL ARITHMETIC, one containing the ANSWERS to the examples, and the other without them, are published. Teachers are requested to state in their orders which edition they prefer. Stereotyped by HOBART & ROBBINS, New England Type and Stereotype Foundery, HARVARD 1047*122 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. The demonstrations connected with the several Roots, will greatly aid those who wish for a complete and thorough knowledge of Evolution in Arithmetic. The method of solving Cubic Equations by completing the square, the author believes, will be very useful. This method will not apply to all problems; but, wherever it will apply, it not only very much abridges the labor, but the result is perfect accuracy, which is not always the fact by the common method of approximation. The Table of Logarithms at the end of the work, will be often found convenient and useful. The examples, of which a large number have been placed under each Rule, are intended to be neither too numerous nor too difficult; and all who may use the work, either by themselves or in connection with a class, are advised to solve all the problems, in the order in which they are given. No labor on the part of the pupil will be productive of more intellectual and practical benefit. The answers to several questions have been designedly omitted, that the pupil may try his skill as upon an original problem. |