22 LECTURES AND ESSAYS [1869- 



delineations,&quot; assigning to the &quot; definitions and proposi 

 tions so presented a real sense per se,&quot; in which sense they 

 were &quot; applied in proof of the main positions concerned.&quot; 

 If there is any meaning at all in these statements, which 

 are the gist of a somewhat lengthy discussion (Werke, iii. 

 324 ; Stirling, ii. 375), that meaning must be that Newton 

 and others first differentiated a function, then sought a 

 geometrical construction to suit, and finally invented a 

 physical proposition to correspond. Purely analytical 

 considerations without any physical basis were held, 

 Hegel thinks, to furnish in this way physical laws. In 

 support of this view, Hegel triumphantly refers to &quot; the 

 Newtonian proof of his fundamental proposition in the 

 theory of gravitation compared with Schubert s A stronomy, 

 where it is admitted that ... in the point, which is the 

 nerve of the proof, the truth is not as Newton assumes 

 it &quot; [!] And so upheld by the dictum of this forgotten 

 astronomer, Hegel goes on to inveigh against the mere 

 jugglery by which Newton, already knowing Kepler s 

 results, avails himself of the &quot; mist of the infinitely little &quot; 

 to bring out apparent mathematical proofs of these 

 results. One does not know whether the singular perver 

 sity of this accusation against Newton s moral character, 

 or the incredible ignorance of the argument by which it is 

 supported, is most to be wondered at ; for, not only do 

 the reasonings of the Principia rest throughout on the 

 experimental laws of motion on which Newton s first 

 proposition is expressly based, but the proof itself depends 

 not on the interpretation of an analytical process, but on 

 the essentially physical or, more definitely, kinematical 

 considerations above developed. Nay, so little is it the 

 case that the &quot; mist of the infinitely little &quot; is needed to 

 give a show of plausibility to Newton s process, that the 

 whole gist of the proof lies in the one conception of quantity 

 generated at a definite though variable rate, and that 

 thus, without any change in the spirit of the proof, by 

 simply introducing explicitly a theorem about moments 



