FREE BOOKS

Author's List




PREV.   NEXT  
|<   116   117   118   119   120   121   122   123   124   125   126   127   128   129   130   131   132   133   134   135   136   137   138   139   140  
141   142   143   144   >>  
x 400. 7600. caxtolli onnauhtzontli = 19 x 400. 8000. cenxiquipilli, or cexiquipilli. 160,000. cempoalxiquipilli = 20 x 8000. 3,200,000. centzonxiquipilli = 400 x 8000. 64,000,000. cempoaltzonxiquipilli = 20 x 400 x 8000. Up to 160,000 the Nahuatl system is as simple and regular in its construction as the English. But at this point it fails in the formation of a new unit, or rather in the expression of its new unit by a simple word; and in the expression of all higher numbers it is forced to resort in some measure to compound terms, just as the English might have done had it not been able to borrow from the Italian. The higher numeral terms, under such conditions, rapidly become complex and cumbersome, as the following analysis of the number 1,279,999,999 shows.[366] The analysis will be readily understood when it is remembered that _ipan_ signifies plus. _Caxtolli onnauhpoaltzonxiquipilli ipan caxtolli onnauhtzonxiquipilli ipan caxtolli onnauhpoalxiquipilli ipan caxtolli onnauhxiquipilli ipan caxtolli onnauhtzontli ipan caxtolli onnauhpoalli ipan caxtolli onnaui;_ _i.e._ 1,216,000,000 + 60,800,000 + 3,040,000 + 152,000 + 7600 + 380 + 19. To show the compounding which takes place in the higher numerals, the analysis may be made more literally, thus: + (15 + 4) x 400 x 800 + (15 + 4) x 20 x 8000 + (15 + 4) x 8000 + (15 + 4) x 400 + (15 + 4) x 20 + 15 + 4. Of course this resolution suffers from the fact that it is given in digits arranged in accordance with decimal notation, while the Nahuatl numerals express values by a base twice as great. This gives the effect of a complexity and awkwardness greater than really existed in the actual use of the scale. Except for the presence of the quinary element the number just given is really expressed with just as great simplicity as it could be in English words if our words "million" and "billion" were replaced by "thousand thousand" and "thousand thousand thousand." If Mexico had remained undisturbed by Europeans, and science and commerce had been left to their natural growth and development, uncompounded words would undoubtedly have been found for the higher units, 160,000, 3,200,000, etc., and the system thus rendered as simple as it is possible for a quinary-vigesimal system to be. Other number scales of this region are given as follows: HUASTECA.[367] 10. laluh. 20. hum-inic = 1 man. 30. hum-inic
PREV.   NEXT  
|<   116   117   118   119   120   121   122   123   124   125   126   127   128   129   130   131   132   133   134   135   136   137   138   139   140  
141   142   143   144   >>  



Top keywords:
caxtolli
 

thousand

 

higher

 
English
 
analysis
 
simple
 

number

 

system

 

quinary

 

numerals


Nahuatl
 
expression
 

onnauhtzontli

 

Except

 

presence

 

element

 

arranged

 

digits

 

expressed

 

accordance


effect
 

simplicity

 

express

 
complexity
 

values

 
existed
 
decimal
 

greater

 

awkwardness

 

notation


actual

 

vigesimal

 
rendered
 
undoubtedly
 

scales

 
region
 

HUASTECA

 

uncompounded

 

replaced

 

Mexico


billion

 

million

 
remained
 

undisturbed

 
natural
 
growth
 

development

 

Europeans

 
science
 

commerce