HORATIO N. ROBINSON, LL D LATE PROFESSOR OF MATHEMATICS IN THE UNITED STATES NAVY, AND AUTHOR OF A NEW YORK: IVISON, PHINNEY, BLAKEMAN & CO., CHICAGO: S. C. GRIGGS & CO. mis P. m LIBRARY Vegg ROBINSON'S gg Series of Mathematics, The most COMPLETE, most PRACTICAL, and most SCIENTIFIC SERIES of MATHEMATICAL TEXT-BOOKS ever issued in this country. Robinson's Progressive Primary Arithmetic, - Robinson's Progressive Higher Arithmetic, Lobinson's Arithmetical Examples, Robinson's New Elementary Algebra, Robinson's Key to Elementary Algebra, Robinson's University Algebra, Robinson's Key to University Algebra, Robinson's New University Algebra, Robinson's Key to New University Algebra, Robinson's New Geometry and Trigonometry, Robinson's Surveying and Navigation, Robinson's Analyt. Geometry and Conic Sections, Robinson's Differen. and Int. Calculus, KIDDLE'S NEW ELEMENTARY ASTRONOMY, Robinson's University Astronomy, Robinson's Mathematical Operations, Robinson's Key to Geometry and Trigonometry, Conic Sections and Analytical Geometry, Entered, according to Act of Congress, in the year 1862, by DANIEL W. FISH, A. M., in the Clerk's Office of the District Court of the United States for the Northern District of New York. PREFACE. In the preparation of the New University Algebra, care has been taken to preserve every feature of the original work, on which rested, in any degree, its claims to superiority. The aim has been to make that which was good, decidedly better. Hence the changes that have been made, consist, for the most part, in more apt arrangement, in large additions of original matter, and in presenting the whole in more attractive form. The treatise, as now submitted to the public, is, indeed, far more complete than the former, not only in the range of topics, but also in general discussions and practical applications. In many parts the methods of investigation are essentially different,-the object being, in some instances, to secure simplicity in logical arrangement, and in others, to establish principles and rules by more general and rigorous demonstrations. The articles on Inequalities, Differential Method of Series, and Interpolation, which, in the old treatise, appear as an appendix, have been elabo rated, and made to take their appropriate place in the body of the work. The section on Radical Quantities is quite full, embracing the more important properties of Imaginary Quantities and Quadratic Surds, besides a complete logical development of the Theory of Exponents. As, in the author's New Elementary Algebra, the Binomial Theorem has been fully investigated with reference to integral exponents, it has been deemed unnecessary to repeat here the particular demonstration. Accordingly, the whole subject is deferred till the section on Series is reached, where a general demonstration of this theorem is given in a concise way, and a full variety of applications added. The whole subject, as presented in this connection, with the accompanying illustrations, can not fail to interest the lovers of Algebra. The General Theory of Equations is treated in two sections, the one embracing the general properties of equations, and the other the solution of numerical equations of all degrees. The whole subject is here presented, however, in a condensed form, the student being conducted, in a manner direct as possible, from the theoretical to the practical. The section on the Properties of Equations, it is proper to say, owes its improved character to the able hand of Prof. I. F. QUINBY, of the University of Rochester, whose services in perfecting other books of this Series deserves especial mention. The effort which has been made in this treatise, to combine the best practical with the highest theoretical character, is specially commended to the notice of the true educator. Great care has been taken everywhere to set forth in distinct form the principles of the science, their exact logical relations being noted by proper references; while due prominence has been given to those numerous precepts and expedients which are so necessary to the constitution of an expert Algebraist. The design throughout has been, not to conceal, but fully to reveal the difficulties of the science, and to encourage the learner, not to avoid, but to grapple with, and overcome them; since, to the student of Mathematics, labor rightly directed, is discipline,—and discipline, after all, is the true end of education. It is but just to state, that J. C. PORTER, A. M., has had the constant care and supervision of the present work, having also rendered important assistance in the preparation of some other works of the Scries,—a fact which, considering his long and distinguished success as a teacher of Mathematics, and his acknowledged ability as a mathematical scholar, ought to afford a sufficient guarantee for the utmost accuracy and classroom fitness on every page. Thus distinguished for fullness of matter; for scientific arrangement; for ample discussion and rigid demonstration; for clear statement and close definition; for rules brief and of easy application; for examples numerous, apt and strictly practical; for the nicest adaptation to the purposes of teaching; for the finest mechanical execution; for whatever, in short, care, skill, science and taste can accomplish;-the New University Algebra is submitted to the pul·lic. July, 1862. |