CHAPTER XII 



MERITS AND DEFECTS OF THE EIGHTEENTH- 

 CENTURY BRITISH FLUXIONAL CONCEPTIONS 



Merits 

 234. There are, perhaps, no intuitional concep- 

 tions available in the study of the calculus which 

 are clearer and sharper than motion and velocity. 

 There is, therefore, a certain advantage in approach- 

 ing the first study of the difìferential calculus or of 

 fluxions by the consideration of motion and velocity. 

 Even in modem teaching of the elements to 

 beginners, we cannot afìford to ignore this advantage 

 offered by the eighteenth-century British mode of 

 treating the calculus. 



A second point of merit lies in the abandonment 

 of the use of infinitely little quantities. Not ali 

 English authors of the eighteenth century broke 

 away from infinitesimals, but those who did vvere 

 among the leaders : Robins, Maclaurin, Simpson, 

 Vince, and a few others. The existence of infini- 

 tesimals (defined as infinitely small constants) was 

 looked upon by philosophers and by many mathe- 

 maticians as doubtful. Their subjective existence 

 was hardly more probable than their objective exist- 

 ence. These mystic creations occupied a hypo- 



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