Edue T128.96.795 Barvard College Library Dec. 20, 1010. Transferred from ducation Library. COPYRIGHT, 1894, BY MACMILLAN AND CO. Set up and electrotyped June, 1894. Reprinted September, 1894; February, August, 1895. PREFACE TO THE AMERICAN EDITION. The transition from the traditional algebra of many of our secondary schools to the reconstructed algebra of the best American colleges is more abrupt than is necessary or creditable. This lack of articulation between the work of the schools and the colleges emphasizes the need of a fuller and more thorough course in elementary algebra than is furnished by the text-books now most commonly used. It is with the hope of supplying this new demand that an American edition of Charles Smith's Elementary Algebra is published; a work whose excellencies, as represented in former editions, have been recognized by able critics on both sides of the Atlantic. In the rearrangement of the work and in its adaptation to American schools many changes have been made, too many to be noted in a short preface, and a considerable amount of new subject-matter has been introduced. The following are innovations of some importance: Chapter I., consisting of a series of introductory lessons, is wholly new, and Chapter XIII. is partly new and partly transferred from Chapter XXVIII. of the second edition. Horner's synthetic division is made prominent in the chapter on division, an early introduction to quadratic equations finds its appropriate place in the chapter on factoring, the binomial theorenu for posi tive integral exponents is demonstrated by elementary methods in the chapter on powers and roots, the chapter on surds has been enlarged by a short discussion of complex numbers, the chapter on exponentials and logarithms has been re-written, and Chapters XXVII, XXVIII, XXX, XXXI, XXXII, XXXVII, and XXXVIII are wholly new. Some new collections of examples have been introduced, and several of the older lists have been extended. As thus reconstructed, the book constitutes a rounded course in what may be called the newer elementary algebra, and includes all the subjects prescribed for admission to American Colleges and Schools of Technology. It will prove especially helpful to students preparing for such colleges as are using Mr. Smith's Treatise on Algebra for advanced work. The most important sources that have been drawn upon in the preparation of the new chapters are Professor Chrystal's Text-Book of Algebra and Mr. Smith's own larger book, the Treatise. I am indebted to my colleagues of the mathematical department of the University of California for valuable suggestions, but especially to Professor Haskell and Dr. Hengstler for contributions to subject matter and for reading many of the proof-sheets. Special thanks are due to Mr. Smith, for allowing free scope for this revision. IRVING STRINGHAM. UNIVERSITY OF CALIFORNIA, February, 1895. CONTENTS. II. The Language of Algebra. Definitions.. Positive and Negative Quantities.... Product of Multinomial Expressions... Division by Multinomial Expressions... VIII. Simultaneous Equations of the First Degree... Elimination by Addition and Subtraction.. Other Methods of Elimination... Equations with Three Unknown Quantities.. XII. Lowest Common Multiples..... XIII. Miscellaneous Theorems and Examples.. Factor Theorem. Remainder Theorem Reduction to a Common Denominator,. XV. Equations with Fractions . Relations between the Coefficients and the Roots.... 249 XVII. Equations of Higher Degree than the Second. |