ΑΝ ELEMENTARY TREATISE ON ALGEBRA, THEORETICAL AND PRACTICAL; WITH ATTEMPTS TO SIMPLIFY SOME OF THE MORE DIFFICULT PARTS PARTICULARLY THE DEMONSTRATION OF THE BINOMIAL THEOREM IN ITS MOST GENERAL FORM; THE SUMMATION OF INFINITE SERIES; THE SOLUTION OF EQUATIONS OF THE HIGHER ORDER, &c. FOR THE USE OF STUDENTS. BY J. R. YOUNG, PROFESSOR OF MATHEMATICS IN THE ROYAL COLLEGE, BELFAST, And Author of "Elements of Geometry;" "Elements of Mechanics ;""Elements of Plane and Spherical A NEW AMERICAN, FROM THE LAST LONDON EDITION, PHILADELPHIA : HOGAN AND THOMPSON, No. 30, NORTH FOURTH STREET. 1839. HARVARD Buch 2058.39 UNIVERSITY LIBRARY Treadwell Fund Entered according to the Act of Congress, in the year 1838, by Carey, Lea & BLANCHARD, in the Clerk's office of the district court for the eastern district of Pennsylvania. ΤΟ OLINTHUS GREGORY, ESQ., LL.D. F.R.A.S. Corresponding Associate of the Academy of Dijon, Honorary Member of the Literary and Institution of Civil Engineers, &c. &c.; and Professor of Mathematics in the Royal Military Academy. SIR, IN permitting me to dedicate to you the following pages, you have conferred upon me an honour for which I feel truly grateful. Your profound attainments as a Mathematician and Philosopher are so universally acknowledged, and so highly appreciated, that any production, however humble, which is introduced to the world under the sanction of your good opinion, will be considered as entitled to some degree of attention. With these claims to notice, the present performance possesses advantages which I did not originally presume to anticipate, and, in laying it before you, allow me to assure you that I am, Sir, With the profoundest respect, Your most obliged and most obedient servant, THE AUTHOR. PREFACE TO THE ENGLISH EDITION. THE first edition of the present work was printed in octavo, and published at a price too high to warrant any very sanguine expectations as to the extent of its circulation. It gradually, however, found its way into the principal educational establishments of this kingdom-was adopted in the colleges of the United States*-in the African College at the Cape of Good Hope-and in New South Wales. This extensive patronage, unexpected alike by the publisher and myself, I attribute-not to any novelties contained in the book, but entirely to the efforts I made to simplify as much as possible the more difficult parts of the subject, and thus to present to the young mathematical student a clear and perspicuous view of the fundamental principles of analytical calculation. Many complaints have, however, reached me from mathematical teachers, to the effect that the practical examples were not found sufficient in number fully to illustrate the theory. My own experience has proved to me the justness of this complaint, and has, moreover, led me to detect several other blemishes in the work. In this new edition, it is hoped that these faults will be found in a great measure to have disappeared. The practical part has been considerably augmented throughout, the theory corrected and improved, and several new and interesting topics added. One subject, touched upon in the former edition, it has been thought advisable to exclude from this,―the chapter on the Theory of the Higher Equations; but the exclusion which has been thus made, as well as the additional matter which has been introduced, seemed equally necessary, to render the book better adapted to the wants of beginners, and more suitable for junior mathematical classes, in places of public education. Besides, in the progress of any science towards perfection, some departments of it are always found to receive more from the contributions of time than others; these departments gradually increase in magnitude and importance, till at length, detaching themselves from the main body, they become objects of individual importance and of distinct attention. Such has been the case with the Theory of Equations. That it is strictly a branch of pure Algebra there is no doubt; but it has exercised the talents and received the contributions of so many great men, and * An American reprint, ably edited by Mr. Ward, of Columbia College, was published, in 1832, at Philadelphia. |