PREFACE The design of this Treatise is to explain all that is commonly included in a First Part of Algebra. In the arrangement of the Chapters I have followed the advice of experienced Teachers. I have carefully abstained from making extracts from books in common use. The only work to which I am indebted for any material assistance is the Algebra of the late Dean Peacock, which I took as the model for the commencement of my Treatise. The Examples, progressive and easy, have been selected from University and College Examination Papers and from old English, French and German works. Much care has been taken to secure accuracy in the Answers, but in a collection of more than 2300 Examples it is to be feared that some errors have yet to be detected. I shall be grateful for having my attention called to them. I am preparing a book of Miscellaneous Exercises adapted to this work and arranged in a progressive order so as to supply constant practice for the student. In conclusion, I have to express my thanks for the encouragement and advice received by me from many correspondents. J. HAMBLIN SMITH. CAMBRIDGE, 1870. CONTENTS CHAPTER I. ON THE RESOLUTION OF EXPRESSIONS INTO FACTORS . PROBLEMS LEADING TO SIMPLE EQUATIONS . ON THE METHOD OF FINDING THE HIGHEST COMMON FACTOR ON ADDITION AND SUBTRACTION OF FRACTIONS PROBLEMS IN FRACTIONAL EQUATIONS SIMULTANEOUS EQUATIONS OF THE FIRST DEGREE ON SIMULTANEOUS EQUATIONS INVOLVING QUADRATICS . 186 ON PROBLEMS RESULTING IN QUADRATIC EQUATIONS CHAPTER XXVI. CHAPTER XXVII. CHAPTER XXX. CHAPTER XXXI. CHAPTER XXXIII. CHAPTER XXXIV. CHAPTER XXXV. THE BINOMIAL THEOREM. POSITIVE ÎNTEGRAL INDEX 296 THE BINOMIAL THEOREM. FRACTIONAL AND NEGATIVE INDICES 307 CHAPTER XXXVIII. . . . |