problem in question. The mere thought of real as variable 

 facilitates and even demands the recognition of the succes 

 sive moments of the logical determination of real. For real 

 referred to variable is individual because it is in itself a 

 single real variable ; general because it comprehends under 

 itself every other real variable ; universal because it either 

 is in itself or comprehends under itself every real variable. 

 The imagined vanishing of all moments of the logical deter 

 mination of real leads to the invention or discovery of the 

 logical determination of imaginary 



imaginary &amp;lt; 



Since there are no real differential elements in the logical 

 determination of imaginary, it is impossible to enumerate 

 more than one imaginary variable, namely which is 



therefore the only as well as any imaginary variable. 



USE 



Because the present problem is the highest or most gen 

 eral of all possible general problems, the presented resolution 

 demonstrates the universality of every single analytical 

 principle that can be abstracted from it, for instance, the 

 principle that there exists a differential coefficient for a 

 given function. 



Because all that can ever be known is unknown function, 

 the presented and explained development of function into 

 the sequence and x, and of x into the series individ 



ual general universal, proves the universal validity of Kant s 

 theory that knowledge begins in intuition and advances 

 in concept and ends in idea, by making function by degrees 

 completely known according to that theory. 



Because the problem which I have elsewhere reduced to 

 the analytical expression Science { function } Analysis re 

 quires first of all to be completely determined by means of 

 the thorough development of function in that place, this 

 thorough development of function in the abstract is propae 

 deutic to the consideration of that analytical expression. 



GEORGE ASHTON BLACK 

 New York, 621 W. 113th Street 



Published July, 1906 



