THE MACMILLAN COMPANY ATLANTA • SAN FRANCISCO MACMILLAN & CO., LIMITED MELBOURNE THE MACMILLAN CO. OF CANADA, LTD. TORONTO BEING THE FIRST THIRTY-EIGHT CHAPTERS OF HALL AND KNIGHT'S ALGEBRA FOR COLLEGES AND SCHOOLS BY H. S. HALL, M.A., AND S. R. KNIGHT, B.A REVISED AND ENLARGED FOR THE USE OF AMERICAN SCHOOLS BY F. L. SEVENOAK, A.M. STEVENS INSTITUTE OF TECHNOLOGY New York LONDON: MACMILLAN & CO., LTD. All rights reserved First edition, 1895. Second edition, revised and enlarged, 1896. Norwood Press Norwood, Mass., U.S.A. PREFACE. WITHIN a comparatively short time, the algebra requirement for admission to many of our Colleges and Schools of Science has been much increased in both thoroughness of preparation and amount of subject-matter. This increase has made necessary the rearrangement and extension of elementary algebra, and it is for this reason that the present revision of Hall and Knight's Elementary Algebra has been undertaken. The marked success of the work, and the hearty endorsement by many of our ablest educators of the treatment of the subject as therein presented, warrant the belief that the present edition, with its additional subject-matter, will be found a desirable arrangement and satisfactory treatment of every part of the subject required for admission to most of our American Colleges. Many changes in the original chapters have been made, among which we would call attention to the following: A proof, by mathematical induction, of the binomial theorem for positive integral index has been added to Chapter XXXVII.; a method of finding a factor that will rationalize any binomial surd follows the treatment of binomial quadratic surds ; Chapter xlii. has been re-written in part, and appears as a chapter on equations in quadratic form ; and the chapter on logarithms has been enlarged by the addition of a four-place table of logarithms with explanation of its use. 1 PREFACE TO SECOND EDITION. The printing of the present edition from entirely new plates has enabled us to correct a few typographical errors found in the first edition, and give, at the suggestion of friends, a somewhat fuller explanation of the more difficult parts of the subject. We hope that the addition of an explanation of the method of multiplication by detached coefficients to Chapter iv.; the method of division by detached coefficients to Chapter v.; the factor theorem to the chapter on factoring; a method for finding the nth root of any multinomial to Chapter xxi. ; and of several sets of Miscellaneous Examples, will render the book still more acceptable to those whose commendation of the former edition has given us much pleasure. Those desiring a somewhat longer course will find in the Hall and Knight Algebra for Colleges and Schools a thorough treatment of all portions of the subject usually taught in the regular course of our American Colleges and Schools of Technology. |