i8 73 ] STIRLING AND HEGEL 91 



criticism of Newton, that Hegel finds invincible logical 

 obstacles to all attempts to give a mathematical proof of 

 the relation of fluxion to fluent. The fluxion, he says, is 

 simply one term of a mathematical expansion the term, 

 namely, in which a certain qualitative meaning lies. It 

 is vain to attempt to isolate this term from the other terms 

 of the series by regarding the latter as relatively insignific 

 ant in quantity ; you should simply define such a term of 

 the expansion as the fluxion, and then show, in concrete 

 problems of geometry, that this term has a geometric (and 

 so qualitative) meaning. Any other way of dealing with 

 the matter, and therefore all ways previous to Lagrange, 

 involve certain inadmissible logical assumptions, and so 

 give but a simulation of proof, where there is really only 

 the observation of the fact, that the calculus, regarded as a 

 rule of art, gives (methodically and more easily) results 

 which the ancient geometry had proved synthetically. 

 These strictures are developed in a passage translated by 

 Dr. Stirling (p. 134, sq.) with special reference to Barrow, 

 but it is certain that Hegel regarded them as not wholly 

 inapplicable to Newton. It is really incredible that Dr. 

 Stirling should not see that the whole state of the case as 

 here set down is quite changed, when we find that 

 Newton, contrary to Hegel s belief, had actually succeeded 

 in proving the deduction of the fluxion without any 

 objectionable use of the infinitely small. For in this case 

 the supposed &quot; simulation &quot; had disappeared from the 

 calculus long before Lagrange was born, and there is no 

 particle of ground for bestowing on the French analyst the 

 credit of &quot; striking into the scientific path proper.&quot; 

 Therefore I have said, and now repeat, that Hegel stumbled 

 on Lagrange s method in the dark, through sheer ignorance 

 of what Newton had already achieved. 



But, again, Hegel pursues Lagrange s method in dark 

 ness, or rather, proposing to pursue it, diverges from it into 

 absurdity. What the mathematician and the meta 

 physician have in common is to make the formation of the 



