1873] HEGEL AND THE CALCULUS 19 



resolved to turn to Nature herself, and inquire how 

 quantity is really generated in the objective universe. 

 &quot; Lineae,&quot; he writes, &quot; describuntur ac describendo 

 generantur non per appositiones partium sed per motum 

 continuum punctorum ; superficies per motum linearum ; 

 solida per motum superficierum ; anguli per rotationem 

 laterum ; tempora per fluxum continuum et sic in caeteris. 

 Hae Geneses in rerum natura locum vere nabent et in motu 

 corporum quotidie cernuntur.&quot; (Introd. ad Quad. Curv.} 



In a word, Newton s fundamental position is, that the 

 arithmetical conception of quantity is not that with 

 which Nature herself presents us, and is not, therefore, 

 universally applicable. On the other hand, every quantity 

 that has objective reality [i.e. is an object of real intuition] 

 is generated by continuous motion, with definite (constant 

 or variable) velocity within definite limits of time. The 

 metaphysical nature of time and motion Newton has 

 nothing to do with. It is enough for him that mathe 

 matical time, conceived as an independent variable 

 flowing uniformly, is clearly the true time made known 

 to us in nature (Principia ; Schol. to the Defs.), and that 

 the existence of a definite velocity at each point of a 

 motion is in like manner an undoubted physical fact. 



By means of these profound yet simple considerations, 

 Newton is at once able to revolutionise the whole theory 

 of quantity, and to substitute for the relation of unit and 

 sum that of velocity and quantity generated, or, in 

 Newton s own language, of fluxion and fluent. It must 

 be remembered that we have said nothing of space, so 

 that fluent is not limited to extensive quantity, while 

 velocity, or as we should rather say rate, has a corre 

 spondingly wide application. Thus, any fluxion may 

 itself be treated as a fluent quantity, and its fluxion 

 sought, the only independent variable being time, which 

 is thus a fluent which has no variable fluxion. 



This conception of time, as the one absolute and 

 independent variable, is undoubtedly one of the most 



