NORMAL ELEMENTARY ALGEBRA: CONTAINING THE FIRST PRINCIPLES OF THE SCIENCE, DEVELOPED WITH CONCISENESS AND SIMPLICITY, FOR COMMON SCHOOLS, ACADEMIES, SEMINARIES AND NORMAL SCHOOL& REVISED EDITION. BY EDWARD BROOKS, A. M., PH.D., SUPERINTENDENT OF PUBLIC SCHOOLS OF PHILADELPHIA, LATE PRINCIPAL OF NOMETRY," PHILOSOPHY OF ARITHMETIC," ETC. "Mathematical studies cultivate clearness of thought, acuteness of analysis QUI NON PRO PROFIGIT-DEFICIT PHILADELPHIA: CHRISTOPHER SOWER COMPANY, 124 NORTH EIGHTEENTH STREET. Entered according to Act of Congress, in the year 1871, 59 In the Office of the Librarian of Congress, at Washington Copyright, 1888, by EDWARD BROOKS. Subtraction of Radicals................ 189 Multiplication of Radicals............ 190 Division of Radicals ..................... 192 Square Root of Numbers............... 173 | Imaginary Quantities.. PREFACE. EDUCATION aims at mental culture and practical skill; and for the attainment of both of these objects the mathematical sciences have in all · ages been highly valued. They train the mind to logical methods of thought, give vigor and intensity to its operations, and lead to the important habit of resting only in certainty of results; while as instruments of investigation they stand pre-eminent. Among the three fundamental branches of mathematics, Algebra occupies a prominent position in view of both of these objects. As a method of calculation it is the most powerful of them all, and for giving mental acuteness and the habit of analytic thought it is unequaled. With the advance of education this science is growing in popularity, and is being introduced into our best public schools, as well as academies and seminaries. Many teachers are beginning to see that a knowledge of elementary algebra is worth more than a knowledge of higher arithmetic, and are omitting the arithmetic, when necessary, for the algebra. This has increased the demand for good text-books upon the subject; and to assist in meeting this demand the present work has been prepared. Some of its general and special features will be briefly stated. GENERAL FEATURES.-This work is not a mere collection of problems and solutions, but the evolution of a carefully-matured plan, the embodi ment of an ideal formed by long and thoughtful experience in the schoolroom. Attention is called to its extent, its matter and its method. Extent. The work embraces just about as many topics as it is thought the ordinary pupil in elementary algebra should be required to study. These topics have been presented, not superficially, but with comparative thoroughness, so that the knowledge given may be of actual use in calcu lation, and afford a basis for the study of a higher work if desired. While not presenting quite as much as some teachers might prefer, the author has been careful not to make the work too elementary. Superficial scholarship is one of the growing evils of our country, and teachers and text-books are responsible for it. It should never be forgotten that it is better to know much of a few things than to know a little of many things. While endeavoring to avoid superficiality, the author has been careful to so simplify the subject as to render it suitable to those beginning the b |