DAVID CERNA-ARITHMETIC OF THE ANCIENT MEXICANS. 
17 
pie, among the Hindoos, it will be remembered, 10 is the principal num¬ 
ber, the basis. Their perfect series was from 1 to 10. This 10 was again 
considered as the first term for later progressive series, and constantly 
used as the multiplier. Among the Nahoas the essential numbers were 
four and five, this leading to the perfect series from 1 to 20. The 20 
was the result of 5 multiplied by 4, and for later progressive series the 
20 was employed as the common multiplier; but in the development of 
their progressive series the last term was only 80, or 20 multiplied by 4. 
Again, unlike the symbolic numbers of the eastern nation, which were 
the 3, 5, 7, 9, and 10, the symbolic numbers of the Nahoas were the 2, 
4, 9, 13, and 20, all these being formed on a combination of the 1 and 
the 4. Thus: 1 —(— 1 = 2. The two was represented by Ometecuhtli , the 
chief god, the word meaning two gods, or two in the same person, this 
being the basis of their dualistic religion. The same number 2 was rep¬ 
resented by the Omeyocan , the highest of the heavens, where Ometecuhtli 
was placed. Omeyocan means similarly two places, or two places in one. 
The number 4 stands for the four suns, the four seasons, the four initial 
signs of the days. The 1+4, or 5, signifies the five suns of the Mexica, 
a later tribe, the five days of the tianquiztli , the period of five centuries. 
The 1+4+4, or 9, means the nine months of the half year, a whole year 
being composed of eighteen months. The 1+4+4+4, or 13, has refer¬ 
ence to the number of years of each one of the four tlapilli in which the 
century of 52 years was divided. Finally, 1+4, or 5, multiplied by 4 
produces 20, this latter number representing the 20 days of each month, 
or the perfect series of 1 to 20 inclusive. 
As has been observed, only the first four numbers are spoken of as, or 
expressed by, simple words, that is, ce or cem 1, ome 2, yei or ei 3, and 
nahui 4. The first fifth, or 5. is called macuilli , and the four numbers 
succeeding it take in the first four initial digits; that is ,chicuace, 6; chic- 
one, 7; chicuei , 8; and chiconahui, 9. The second fifth, or 10, has also 
a distinct appellation, that of matlactli , and each one of the succeeding 
numbers up to 14 inclusive, is composed of the word matlactli , incorpor¬ 
ating with it, respectively, the same four initial numbers and the particle 
on or om, that is, matlactli-on-ce, 11; matlactli-om-ome, 12; matlactli-om-ei, 
13; and matlactli-on-nahui, 14. For the third fifth, or 15, there is like¬ 
wise a separate name, that of caxtolli, which serves as a basis for the next 
four numbers up to 19 inclusive, each one of these, again, being com¬ 
posed of the term caxtolli, the particle on or om, and the first four initial 
numbers, respectively, as follows: caxtolli-on-ce, 16; caxtolli-on-ome, 17; 
caxtolli-om-ei, 18; and caxlolli-on-nahui, 19. Finally, the fourth fifth, 
or 20, has once more its own name, that of cempohualli. 
It becomes evident, therefore, that the Nahoas intended always to 
make a marked distinction of the first four initial numerals, to differen- 
