i8 73 ] HEGEL AND THE CALCULUS 17 



&quot; Coin a formal lie on t 

 To make the knight o ercome the giant.&quot; 



We must begin, then, by examining the principles on 

 which Newton based his doctrine of Fluxions. In doing 

 this, it is not necessary to inquire how far Newton s own 

 views varied during his life. Hegel knows Newton s 

 method from the Principia only, and a quotation from the 

 second Lemma of the Second Book (Werke, iii. 305) shows 

 that it was the current text of the Principia (that of the 

 second edition) which he had before him. In fact, Hegel s 

 acquaintance with Newton s writings was clearly of the 

 most superficial character, embracing apparently little 

 if anything beyond the section on Prime and Ultimate 

 Ratios, and the Lemma just referred to. These facts 

 make all merely bibliographical inquiries superfluous in 

 dealing with Hegel s objections. I may refer, however, 

 to a paper by Professor de Morgan, in the Philosophical 

 Magazine for 1852, on the &quot; Early History of Infinitesimals 

 in England,&quot; in which it is shown &quot; that Newton never 

 varied in his meaning of ^ &quot; ; or, in other words, that 

 Newton &quot;held to the conception of the velocity or fluxion,&quot; 

 although he at first &quot; used the infinitely small increment &quot; 

 (only of the first order, however), &quot; as a means of deter 

 mining it.&quot; What follows will, I hope, serve to show that 

 these facts imply that Newton had all along a firm grasp 

 of the principle of his method, and that his frequent 

 employment of abbreviated practical processes was really 

 based on a consciousness of the strength of his method, 

 according to the general principle of mathematicians, 

 who never hesitate to apply the boldest symbolical 

 methods in detail, when they feel confident of the starting- 

 point in the use of these symbols. This, in fact, is a point 

 that metaphysicians have never properly attended to. 

 One is disposed to cap Dr. Stirling s wish that some great 

 analyst would study Hegel, by expressing a hope that 

 some metaphysician of real ability may pay sufficient 

 attention to what are technically called the &quot; Symbolical 



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