PREFACE. 



I HAVE endeavoured in the present work to exhibit a 

 comprehensive view of the Differential Calculus on the 

 method of Limits. In the more elementary portions I have 

 entered into considerable detail in the explanations with the 

 hope that a reader who is without the assistance of a tutor 

 may be enabled to acquire a competent acquaintance with' 

 the subject. To the different Chapters will be found ap- 

 pended Examples sufficiently numerous to render another 

 book unnecessary. These examples have been selected 

 almost exclusively from the College and University Ex- 

 amination Papers ; the greater part of them will be found 

 to present no very serious difficulty to the student, although 

 a few may require peculiar analytical skill. 



I have frequently given more than one investigation of 

 a theorem, because I believe that the student derives ad- 

 vantage from viewing the same proposition under different 

 aspects, and that, in order to succeed in the examinations 

 which he may have to undergo, he should be prepared for 

 a considerable variety in the order of arranging the several 

 branches of the subject, and for a corresponding variety in 

 the mode of demonstration. 



In the composition of the first edition of this work, while 



