LIMITS AND FLUXIONS 



INTRODUCTION 



I. EVERV great epoch in the progress of science is 

 preceded by a period of preparation and prevision. 

 The invention of the differential and integrai calculus 

 is said to mark a " crisis " in the history of mathe- 

 matics. The conceptions brought into action at 

 that great time had been long in preparation. The 

 fluxional idea occurs among the schoolmen — among 

 Galileo, Roberval, Napier, Barrow, and others. The 

 differences or differentials of Leibniz are found in 

 crude form among Cavalieri, Barrow, and others. 

 The undeveloped notion of limits is contained in 

 the ancient method of exhaustion ; limits are found 

 in the writings of Gregory St. Vincent and many 

 others. The history of the conceptions which led 

 up to the invention of the calculus is so extensive 

 that a good-sized volume could be written thereon. 

 We shall not yield to the temptation of lingering 

 on this pre-history at this time, but shall proceed 

 at once to the subject-matter of the present 

 monograph. 



