88 LECTURES AND ESSAYS [1869- 



rule, but by continuous motion. The astronomer, for 

 example, has to deal with the eccentric angle of the 

 earth s orbit. Is it according to Nature to say that for 

 every minute of time some two seconds of arc are clapped 

 on to this angle ? Does not Nature compel him to say 

 that the sides of the angle are opening out continuously, 

 and that so the angle grows ? So blind is the critic to this 

 sense that, in quoting from my paper Newton s statements 

 on the point, he breaks his quotation in order to omit the 

 decisive sentence which I had carefully italicised. Hae 

 Geneses in renim natura locum vere habent et in motu 

 corporum quotidie cernuntur. And now, in passing from 

 this head, I will simply ask Dr. Stirling whether he believes 

 in a geometry without intuition, whether the necessity for 

 intuition may not extend to the geometry of motion as well 

 as the geometry of rest, and whether, therefore, it may not 

 be the case that in this matter the notion is inseparable 

 from the intuition ? A presumption at least that this is 

 the case flows from the fact which I now pass on to 

 establish, that Hegel s own abstract notion breaks down 

 mathematically in the completest way. This, it will be 

 remembered, is the second and last part of the work 

 before me. 



In The Secret of Hegel, only the first of Hegel s mathe 

 matical notes were reproduced. But as the philosopher 

 himself considers the real difficulty of the calculus to lie 

 in its application, my paper extended to the second note, 

 and showed that it is just in the application that Hegel s 

 notion fails. Dr. Stirling now suggests that it is best 

 to begin with the third note, which deals mainly with 

 Cavalleri s method of indivisibles. There is something to 

 be said in favour of this suggestion. Cavalleri s method, 

 in its more elementary examples, is easier than the general 

 theory of Newton, and on the whole Hegel has understood 

 the mathematical work involved pretty well. He does 

 not, however, follow with intelligence anything that is not 

 extremely elementary, and still very remote from that 



