Vlll PREFACE. 



The Third Tract was believed to be required for elucidating 

 D'Alembert's extension of the Integral Calculus, there being 

 no distinct account anywhere of the history of that important 

 step, nor indeed any very clear statement of its nature and 

 limits. 



The Eleventh and Twelfth Tracts may possibly prove use- 

 ful to students of the Principia ; at all events, they give the 

 analytical treatment of the fundamental truths in the system 

 andled by Newton synthetically and with extreme concise- 

 ness, and therefore elliptically. 



The Fourth Tract, on the Greek Geometry, it is hoped may 

 have a tendency to encourage the study of the Ancient Analysis 

 in conjunction with the modern, from which it is too often 

 severed. The authority of M. Chasles is referred to in 

 Note II. to this Tract, in favour of close attention to the 

 Ancient Analysis. That he is far from undervaluing the 

 modem is manifest ; indeed, his work on the Higher Geometry 

 sufficiently proves this ; and he occupies the chair of Pro- 

 fessor of that science, the first appointed since its establishment 

 an inestimable benefit bestowed upon mathematical science 

 by the government of France. Let us hope that this our 

 University will receive the same benefit from the government 

 of our own country ; a hope which may appear well grounded 

 when we recollect that of its three most important members, 

 one has been representative of Cambridge and pupil of 



