A NEW INTRODUCTION TO THE SCIENCE OF ALGEBRA; DESIGNED FOR STUDENTS IN COLLEGES, AND THE HIGHER SCHOOLS AND ACADEMIES. By SILAS TOTTEN, M. A. PROFESSOR OF MATH. AND NAT. PHIL., WASHINGTON COLLEGE. HARTFORD: ASYLUM STREET. Entered according to Act of Congress, in the year 1836, hy F. J. HUNTINGTON, in the Clerk's Office of the district Court of Connecticut. Arner, Univ 1-13-39 376866 PREFACE. . While engaged as a teacher of elementary mathematics, the author has often felt the want of a Treatise on Algebra, which might serve as an introduction to the higher, and more difficult parts of that science; a treatise which, commencing with the first principles of Arithmetic, might conduct the learner by gradual and easy steps, from the expression of quantity by numbers, to the investigation of the relations of quantity, by algebraic symbols. In most of our public schools, the pupil commences the study of Algebra, with a very imperfect knowledge of arithmetic. He has been taught arithmetic, it is true, but mercantile arithmetic only. He has been taught to perform operations upon numbers, by rules, the principles of which, he is rarely required to investigate, and which, for the most part, the books that are put into his hands, do not even profess to demonstrate. He thus begins the study of algebra, unacquainted with the first principles of mathematical science, and finds himself perplexed at the same time with a kind of reasoning, to which he is wholly unaccustomed, and new symbols for the expression of quantity, the nature and use of which, he finds it difficult to comprehend. With these difficulties to encounter, it is |