FOUNDATION OF ALGEBRA. 187 



of which (I speak from memory) D'Alembert drew those instances 

 in which he contended that the negative quantity is not always the 

 contrary of the positive quantity. Disregarding such points d'arrit, there 

 is another sort which frequently occurs (but only in exponential or 

 logarithmic curves), in which the abruptness of the termination is better 

 marked. Thus in y = (1 - x) log (1 - x), there is, in our present system, 

 an absolute cessation of the curve when x = I and y = 0. Here, when 

 the requisite extensions of the logarithmic theory are made, it will be 

 seen that there is not an absolute abrupt termination, but the commence- 

 ment of what French writers have called a branche pointilUe, a part of 

 a curve, which I do not remember to have seen mentioned in any English 

 work, except Professor Peacock's Report. 



A. DE MORGAN. 



University College, London, 

 October 16, 1839- 



a A2 



