i8 73 ] STIRLING AND HEGEL 89 



general doctrine of fluxions which is the proper subject 

 of the present controversy ; and he again (iii. 356 ; 

 cf. Stirling, p. 117) talks absolute nonsense about Kepler s 

 laws. The advantage to be drawn from the study of this 

 note is a clearer grasp of that Hegelian view of the relation 

 of the continuum to the discrete, which I have already 

 signalised, and to which I need not now return. But 

 before passing on to the controversy proper, I may observe 

 that Dr. Stirling certainly does not understand Cavalleri. 

 Thus, he says that there is present in a parallelogram &quot; a 

 single regula, a single proportion, which is determinative 

 of it,&quot; and which &quot; is wholly qualitative,&quot; &quot; is the spiritual 

 soul, as it were, of the actual parallelogram.&quot; This 

 mystical conception of the regula runs through several 

 pages, and gives a fine Hegelian colour to Cavalleri s work. 

 And obviously the regula is supposed to be at bottom one 

 with the Newtonian moment, of which we have found a 

 similar account (cf. p. 126). But what is the regula? 

 Simply as its name denotes, a rule or ruler, a perfectly 

 arbitrary straight line, set down in order that other lines 

 may be drawn parallel to it. Give me a parallelogram, 

 and any line anywhere in the plane of the parallelogram 

 may be taken as the regula, the ruler by which lines 

 important for the investigation shall be drawn. The 

 regula is just as much the spiritual soul of the parallelo 

 gram as the carving-knife is the soul of a leg of mutton. 

 Dr. Stirling, then, has not understood Cavalleri, and I 

 suspect, though here I speak with diffidence, that he has 

 not understood what Hegel says of Cavalleri ; for though 

 the German philosopher is unmathematically vague in 

 what he says of regula, he does not seem to give any 

 countenance to the error of his expositor. 



Although thus, as regards Cavalleri and the mathe 

 matical side of Hegel s third note, Dr. Stirling is talking 

 quite beside the question, we are told that the gist of what 

 Hegel says in this note is pretty well &quot; the gist, at the same 

 time, of all that he has to say in the mathematical reference 



