Educ T 128.55.753 HARVARD COLLEGE LIBRARY GIFT OF GEORGE ARTNUR PLIMPTON Entered according to Act of Congress, in the year 1845, by In the Clerk's Office of the District Court of the District of Massachusetts. STEREOTYPED AT THE S3 PREFACE. THE great difficulty, in the study of Algebra, is to attain a clear comprehension of the earliest steps. The first principles should, therefore, be communicated to the learner gradually, and in the most simple and intelligible manner. Experience proves that these principles are most successfully taught by means of easy problems. But even when this mode is pursued, a majority of pupils find trouble in expressing algebraically the conditions of the problems. The author has, therefore, placed at the commencement of his work a series of introductory exercises, designed to familiarize the learner with representing quantities and performing the simplest algebraic processes, also to prepare him for putting problems into equations. These introductory exercises, which were written about three years since, were shown to several excellent teachers, and received their approbation. They were subsequently used in two of the Boston schools, and with such success, that the author was solicited by a number of gentlemen, who were acquainted with his "Elements of Algebra," and who knew his plan in the present work, to prepare a treatise for common schools. An attempt has been made to render the science as easily attainable as possible, without prejudice to the main result; not to save the learner the trouble of thinking and reasoning, but to teach him to think and reason; not merely to supply a series of simple exercises, but to insure a good knowledge of the subject. To what extent the writer has attained his object, is left to intelligent instructors, schoolcommittees, and others, to determine. Teachers and pupils will observe that, to represent multiplication, the full point is generally used in this work rather than the sign X. But to distinguish the sign of multiplication from the period used as a decimal point, the latter is elevated by inverting the type, while the former is larger, and placed down even with the lower extremities of the figures or letters, between which it stands. THOMAS SHERWIN CONTENTS. 1. Equations having unknown terms only in the first member, and entirely known terms in the second,..23 |