ROBINSON'S MATHEMATICAL SERIES. NEW UNIVERSITY ALGEBRA: THEORETICAL AND PRACTICAL TREATISE, CONTAINING MANY NEW AND ORIGINAL METHODS AND APPLICATIONS. FOR COLLEGES AND HIGH SCHOOLS. BY HORATIO N. ROBINSON, LL. D., LATE PROFESSOR OF MATHEMATICS IN THE UNITED STATES NAVY, AND AUTHOR OF A NEW YORK: IVISON, PHINNEY & CO., 48 AND 50 WALKER ST. ROBINSON'S SERIES OF MATHEMATICS, The most COMPLETE, most PRACTICAL, and most SCIENTIFIC SERIES of MATHEMATICAL TEXT BOOKS ever issued in this country. IN TWENTY-TWO VOLUMES.) ....... 1. Robinson's Progressive Table-Book, 2. Robinson's Progressive Primary Arithmetic, 3. Robinson's Progressive Intellectual Arithmetic,. 4. Robinson's Rudiments of Written Arithmetic, 5. Robinson's Progressive Practical Arithmetic, 6. Robinson's Key to Practical Arithmetic,......... 7. Robinson's Progressive Higher Arithmetic,. 8. Robinson's Key to Higher Arithmetic, 9. Robinson's New Elementary Algebra,... 10. Robinson's Key to Elementary Algebra, 11. Robinson's University Algebra, ...... 12. Robinson's Key to University Algebra,. 13. Robinson's New University Algebra, ........ 14. Robinson's Key to New University Algebra,.. 15. Robinson's New Geometry and Trigonometry, 16. Robinson's Surveying and Navigation,. 17. Robinson's Analytical Geometry and Conic Sections,...... 18. Robinson's Diff. and Integ. Calculus, (in preparation).. 19. Kobinson's Elementary Astronomy, 20. Robinson's University Astronomy, 21. Robinson's Mathematical Operations, 19, Robinson's Key to Geometry and Trigonometry, Conic Sections and Analytical Geometry, Entered, according to Act of Congress, in the year 1862, by in the Clerk's Office of the District Court of the United States for the Northern District of New York. TRUAIR, SMITH & MILES, STEREOTYPERS, SYRACUSE, N. Y. ARVARD LIBRARY 46400 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 elaborated, 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 |