296 THIRD REPORT — 1833. 



out in a very clear and striking form; and, like all otlier 

 woi'ks of this author, it is written in a manner well calculated 

 to fix strongly the attention of the student, and to make him 

 reflect attentively upon the particular processes which are fol- 

 lowed, and upon the reasons which lead to their adoption. 



The circumstances attending the publication and reception of 

 this work in the University of Cambridge were sufficiently re- 

 markable. It was opposed and stigmatized by many of the older 

 members, as tending to produce a dangerous innovation in the 

 existing course of academical studies, and to subvert the pre- 

 valent taste for the geometrical form of conducting investiga- 

 tions and of exhibiting results which had been adopted hy 

 Newton in the greatest of his works, and which it became us, 

 therefore, from a regard to the national honour and our own, 

 to maintain unaltered. It was contended, also, that the primary 

 object of academical education, namely, the severe cultivation 

 and discipline of the mind, was more effectually attained by 

 geometrical than by analytical studies, in which the objects of 

 our reasoning are less definite and tangible, and where the 

 processes of demonstration are much less logical and complete. 

 The opposition, however, to this change, though urged with 

 considerable violence, experienced the ordinary fate of attempts 

 made to resist the inevitable progress of knowledge and the 

 increased wants and improving spirit of the age. In the course 

 of a few years the work in question was universally adopted. 

 The antiquated fluxional notation which interfered so greatly 

 with the familiar study of the works of Euler, Lagrange, La- 

 place, and the other great records of analytical and philoso- 

 phical knowledge, was abandoned * ; the works of the best 

 mathematical writers on the continent of Europe were rapidly 

 introduced into the course of the studies of the University ; and 

 the secure foundations were laid of a system of mathematical 

 and philosophical education at once severe and comprehensive, 

 which is now producing, and is likely to continue to produce, 

 the most important effects upon the scientific character of the 

 nation. 



Theory of Equations. 1 . Composition of Equations. — The 

 first and one of the most difficult propositions which presents 

 itself in the theory of equations is to prove " that all equations 

 under a rational form, and arranged according to the method 



* The continental notation of the differential calculus was first publicly 

 introduced into the Senate House examinations in 1817- Though the change 

 ■was strongly deprecated at the time, it was very speedily adopted, and in 

 less than two years from that time the fluxional notation had altogether dis- 

 appeared. 



