EAKLY NUMERICAL IDEAS. 197 



magnitudes most frequently observed were magnitudes of 

 extension, it follows that geometry and arithmetic had a 

 simultaneous origin. 



Not only are the first distinct ideas of number co-ordiu 

 ate with ideas of likeness and equality, but the first efforts 

 at numeration displayed the same relationship. On read 

 ing the accounts of various savage tribes, we find that the 

 method of counting by the fingers, still followed by many 

 children, is the aboriginal method. Neglecting the several 

 cases in which the ability to enumerate does not reach even 

 to the number of fingers on one hand, there are many cases 

 in which it does not extend beyond ten the limit of the 

 simple finger notation. The fact that in so many instances, 

 remote, and seemingly unrelated nations, have adopted ten 

 as their basic number ; together with the fact that in the re 

 maining instances the basic number is eitherj^e (the fingers 

 of one hand) or twenty (the fingers and toes) ; almost of 

 themselves show that the fingers were the original units of 

 numeration. The still surviving use of the word digit, as 

 the general name for a figure in arithmetic, is significant ; 

 and it is even said that our word ten (Sax. tyn ; Dutch, 

 tien ; German, zehn) means in its primitive expanded form 

 two hands. So that originally, to say there were ten things, 

 was to say there were two hands of them. 



From all which evidence it is tolerably clear that the 

 earliest mode of conveying the idea of any number of 

 things, was by holding up as many fingers as there were 

 things ; that is using a symbol which was equal, in respect 

 of multiplicity, to the group symbolized. For which infer 

 ence there is, indeed, strong confirmation in the recent 

 statement that our own soldiers are even now spontaneous 

 ly adopting this device in their dealings with the Turks. 

 And here it should be remarked that in this recombination 

 of the notion of equality with that of multiplicity, by which 

 the first steps in numeration are effected, we may see one 



