28o LIMITS AND FLUXIONS 



analysis, that, apparently, certain British writers 

 held the view that fluxions were a branch of geo- 

 metry. In the preface to the GentlemarCs Diary of 

 London, the new editor, Mr Wildbore, said at the 

 commencement of his editorship in 1781, *'the 

 doctrine of fluxions depends on principles purely 

 geometrical, as is very satisfactorily demonstrated 

 by that incomparable geometer, the late Dr Robert 

 Simson of Glasgow in his Opera posthuma. " 



In the second place, as pointed out by Landen 

 and Woodhouse, there was an unnaturalness in 

 founding the calculus upon the notions of motion 

 and velocity. In a real way, these notions seem 

 to apply only to a limited field in the applications of 

 the calculus, namely, to dynamics. In other fields, 

 motion and velocity are wholly foreign concepts 

 which, if applicable at ali, are so only in a figurative 

 sense. 



238. Newtonian writers lay great stress upon 

 such conceptions as a line generated by the motion 

 of a point, a surface generated by the motion of a 

 line, and a solid generated by the motion of a 

 surface. We have already referred to the pedago- 

 gica! advantages of this view, in teaching beginners. 

 But as a final logicai foundation this view is inade- 

 quate. Not ali continuous curves can be conceived 

 as traceable by the motion of a point. An example 

 frequently quoted, in discussions of this sort, is 

 the curve 



y — for ;r = o, y = x sin for x =^ 0. 



