COLLEGE, NEW BRUNSWICK, N. J., MEMBER OF THE AMERICAN ACADEMY OF ARTS AND SCIENCES. NEW YORK: PRATT, OAKLEY & CO., No. 21 MURRAY STREET. 1859. Math 2058, 59 1856 HARVARD COLLEGE ENTERED, ACCORDING TO ACT OF CONGRESS, IN THE YEAR 1859, BY PRATT, OAKLEY & CO., IN THE CLERK'S OFFICE OF THE DISTRICT COURT OF THE UNITED STATES FOR WILLIAM DENYSE, STEREOTYPER AND ELECTROTyper, 183 William-st., N. Y. 1=40 PREFACE. My principal object in the preparation of this work has been to give the results of certain speculations which have occupied my attention, and which seem to constitute very important additions to the science of Algebra. Thus, at page 439, etc., the roots of an equation are developed into a series, and thence it is shown that an equation of the nth degree must have n roots. At pages 457, etc., and 464, etc., the solutions of Binomial Equations and the Irreducible case of Cubic Equations are completed by pure Algebra. And at page 512, etc., a new and general method is given for the development of the roots of equations, which seems to be much more simple than any heretofore proposed. I have endeavored to give a full view of the present state of the Science, and to adapt my work to the wants of teachers and pupils, not only in our Colleges and Academies, but in schools of a primary character. Great pains have been taken to present the principles and processes of the Science in so clear a manner that the student may readily understand them, and be fully satisfied as to their correctness. Should it be thought that too great labor has been bestowed on certain parts of the work, my apology is, my anxiety to satisfy in the fullest manner the supposed wants of the student with reference to the parts thus treated. With these prefatory remarks, I commend my work to teachers and others, hoping that it may be satisfactory, and that it may contribute to the advancement of sound Science. THE AUTHOR. CONTENTS. Expression of Quantities by Arbitrary Characters Signs of Equality, Addition, and Subtraction Positive and Negative Quantities-Signs of Multiplication and Division. Algebraic Quantity-Monomial-Binomial-Polynomial. PAGE |