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 any of our Colleges or Schools of Technology. 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 xxxix.; 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. Chapters XXI., XXV., XXX., XXXIII., XXXVIII., XLII., XLIII., XLIV., XLV., XLVI., XLVII., XLIX., and L. treat of portions of the subject that have not appeared in former editions. A chapter on General Theory of Equations is not usually found in an Elementary Algebra, but properly finds here a place in accordance with the purpose of the present revision; and its introduction makes the work available for use in college classes. Carefully selected exercises are given with each chapter, and at the end of the work a large miscellaneous collection will be found. The Higher Algebra of Messrs. Hall and Knight has been drawn upon, and the works of Todhunter, Chrystal, and De Morgan consulted in preparing the new chapters. I gratefully acknowledge my indebtedness to Prof. J. Burkitt Webb of the Stevens Institute of Technology both for contributions of subject-matter, and valuable suggestions as to methods of treatment. My thanks are also due to Prof. W. H. Bristol, of the same institution, for suggestions as to the arrangement of the chapter on General Theory of Equations. FRANK L. SEVENOAK. JUNE, 1895. CONTENTS II. Negative Quantities. Addition of Like Terms III. Simple Brackets. Addition Multiplication of Compound Expressions Division of Compound Expressions VII. Removal and Insertions of Brackets X. Problems Leading to Simple Equations Sum or Difference of Two Cubes XVI. Complex Fractions. Mixed Expressions . . XIX. Simultaneous Equations of the First Degree 135 Elimination by Addition or Subtraction . Equations Involving Three Unknown Quantities 140 Literal Simultaneous Equations . XXI. Indeterminate and Impossible Problems. Nega- 000 Square Root of Compound Expression Cube Root of Compound Expression. Square and Cube Roots of Numbers XXVII. Equations in Quadratic Form XXVIII. Simultaneous Quadratic Equations Homogeneous Equations of the Same Degree . 202 XXX. Indeterminate Equations of the First Degree 213 Rationalizing Denominator 234 |