ARITHMETICAL INSTRUMENTS. 



OF all those branches of human knowledge which are compre- 

 hended under the name of Science, Arithmetic is that which has 

 the most abstract character, and which, at the same time, is of the 

 most universal application in the study of natural phenomena. 

 The art of counting, or of numeration, is one of the earliest, if 

 not the earliest product of nascent civilisation ; and, in the case 

 of the savage races of mankind, the greater or less progress which 

 has been made towards the acquisition of this art affords no unfair 

 measure of the degree of culture and of intellectual development 

 which has been attained. It is said that there are races whose 

 scale of numeration is limited to two or three ; others can go to 

 five, or ten, or twenty. And we may be sure that no tribe of men, 

 untaught by a superior race, ever acquired the art of counting by 

 hundreds or thousands, without possessing a high average of mental 

 capacity, and without sharing in the privilege, accorded only to 

 certain nations, of occasionally producing men of inventive genius, 

 and real leaders of thought. 



The more favoured branches of the Semitic and Aryan families 

 the Jews, the Egyptians, the Greeks, the Sanskrit-speaking 

 nations of India must have reached this comparatively speaking- 

 advanced standard of culture at a very remote period. But it is 

 remarkable that the real extent of the domain of arithmetic a 

 domain in a certain sense coequal with that of exact science was 

 not perceived till a much later epoch. 



The Greek philosophers, at least as early as the time of Aristotle, 



