NOTION AND DEFINITION OF NUMBER. 



numerals among the most various races. In the Indo-Germanic 

 tongues the numeral words from ten to ninety-nine are formed by 

 composition from smaller numeral words. Two methods remain 

 for continuing the formation of the numerals : either to take a new 

 root as our basis of composition (hundred) or to go on counting 

 from ninety-nine, saying tenty, eleventy, etc. If we were logically 

 to follow out this second method we should get tenty-ty for a thou- 

 sand, tenty-ty-ty for ten thousand, etc. But in the utterance of such 

 words, the syllable ty would be so frequently repeated that the same 

 inconvenience would be produced as above in our individual num- 

 ber-pictures. For this reason the genius which controls the for- 

 mation of speech took the first course. 



But this course is only logically carried out in the old Indian 

 numeral words. In Sanskrit we not only have for ten, hundred, 

 and thousand a new root, but new bases of composition also exist 

 for ten thousand, one hundred thousand, ten millions, etc., which 

 are in no wise related with the words for smaller numbers. Such 

 roots exist among the Hindus for all numerals up to the number ex- 

 pressed by a one and fifty-four appended naughts. In no other lan- 

 guage do we find this principle carried so far. In most languages the 

 numeral words for the numbers consisting of a one with four and 

 five appended naughts are compounded, and in further formations 

 use is made of the words million, billion, trillion, etc., which really 

 exhibit only one root, before which numeral words of the Latin 

 tongue are placed. 



Besides numeral word-systems based on the number fen, only lo- 

 gical systems are found based on the number five and on the number 

 twenty. Systems of numeral words which have the basis five occur 

 in equatorial Africa. (See the language-tables of Stanley's books 

 on Africa.) The Aztecs and Mayas of ancient Mexico had the base 

 twenty. In Europe it was mainly the Celts who reckoned with 

 twenty as base. The French language still shows some few traces 

 of the Celtic vicenary system, as in its word for eighty, quatrc-vin^t. 

 The choice of five and of twenty as bases is explained simply enough 

 by the fact that each hand has five fingers, and that hands and feet 

 together have twenty fingers and toes. 



