FIRST LESSONS IN ALGEBRA, IN WHICH THE ELEMENTS OF THE SCIENCE ARE FAMILIARLY EXPLAINED. BY SAMUEL ALSOP, AUTHOR OF "TREATISE ON ALGEBRA." NEW EDITION. PHILADELPHIA: E. C. & J. BIDDLE, No. 8 MINOR STREET, (Between Market and Chestnut, and Fifth and Sixth Sts.) V HARVARD COLLEGE LIBRANT Tules College Entered, according to Act of Congress, in the year 1853, by in the Clerk's Office of the District Court of the Eastern District of Pennsylvania. OFFICE OF THE CONTROLLERS OF PUBLIC SCHOOLS, Philadelphia, May 14th, 1851. Ar a meeting of the Controllers of Public Schools, First District of Pennsylvania, held at the Controllers' Chamber, on Tuesday, May 13th, 1851, the following Resolution was adopted: Resolved, That "Alsop's First Lessons in Algebra" be introduced as a class-book into the Grammar Schools of this District. (Signed) ROBERT J. HEMPHILL, PREFACE. In the following elementary treatise on Algebra, the author has endeavored to present the subject in a manner so simple that a child of ordinary intellectual power, who has acquired a knowledge of Arithmetic, can fully comprehend it. He has sought to explain, concisely but clearly, every principle presented, so as to enable such a pupil to surmount every difficulty as it occurs; but his aim has not been to make a treatise on Arithmetic, in disguise, nor to remove every difficulty from the path of the student, leaving nothing to exercise and strengthen his mental powers. By thus confining himself within the real bounds of the science, and avoiding long dissertations on unimportant subjects, and tedious explanations which a teacher could give much better orally, in a few words, to the very small number of pupils for whom they may be thought necessary, the author has been enabled to comprise within a small compass a larger amount of real algebraic matter than will be found in many treatises of much larger dimensions. A very large number of examples, illustrative of the principles elucidated, are given. These have been, so far as practicable, made progressive in their character, so that the mind of the pupil shall be gradually led from those which are simple to others presenting greater difficulties, and designed to test the advancement he has made; none, however, being introduced which are deemed inconsistent with the elementary character of this work. The Binomial Theorem, it will be observed, is introduced early in the work. The manner of illustrating it is, in some respects, novel; and, it is believed, presents the reasons for the rules in a plain and compre 3 |