16 
TRANSACTIONS OF THE TEXAS ACADEMY OF SCIENCE. 
along side or near the others. Sometimes the term chico means half, as in 
the words cliicocua, chicocahua, cliicocuatic, etc. The particle a, among 
its various significations, has that of like; so that chico-a means half 
of the hands, or like one-half of the hands. Therefore, chico-a-ce, 
chicu-ome ( chicome ), chicu-ei, and chicu-nahui, being the first four numer¬ 
als added to the word chocua , signify respectively, the half of two hands, 
or, one hand plus one, one hand plus two, one hand plus three , and one 
hand plus four, that is, 6, 7, 8, and 9. 
The number 10 is expressed by the term matlactli , from maitl and 
tlactle, meaning the body of man from the waist upwards, or the superior 
extremities of man. Maculli is, then, a closed hand; matlactli, two closed 
hands. The next four numbers are formed by adding to the word ma¬ 
tlactli the four fundamental digital expressions linked by the syllable on 
or om in the sense of more, thus: matlactli-on-ce, two hands plus one, 11; 
matlactli-om-ome, two hands plus two, 12; matlactli-om-ei , two hands plus 
three, 13; and matlactli-on-nahui, two hands plus four, 14. 
The word caxtolli or caxtulli is used to express the number 15. The 
numbers 16, 17, 18, and 19 are formed in a similar manner to the ones 
just described, that is, by uniting to the word caxtolli the four fund¬ 
amental digital numerals by means of the ligature on or om, thus: cax- 
tolli-on-ce, 15+1, 16; caxtolli-om-ome, 15+2, 17; caxtolli-om-ei, 15+3, 
18; and caxtolli-on-nahui, 15+4, 19. But Orozco y Berra gives no ex¬ 
planation as to the meaning of the word caxtolli, simply stating that it 
stands for 15. 
For the number 20 the word cempohualli is employed. It is composed 
of cem, one, and pohuailli, a count, that is, it means the putting together 
of twenty individual units. A further analysis of the term would seem to 
give cem, one; poa, to count, and pilli or lli, the appendices, the whole 
term, cem-poa-tli or cempohualli, then, meaning a count of the appendages. 
Therefore, says Orozco y Berra, the number 20 is the number par excel¬ 
lence of the Nahoas; it is the I, the individual, composed of four parts, 
that is, two hands and two feet, each one of these parts having five ap¬ 
pendices, or 5 multiplied by four. 
More recent investigations, however, do not seem to support the con¬ 
clusions arrived at by Gama and Orozco y Berra. For, if we examine 
carefully the true origin of the words used, that is, their etymology, or 
again, take into consideration the logical reason, so to speak, of their 
application, it becomes evident that such conclusions are not entirely 
correct. 
The studies of Ramirez, and especially those of Chavero, furnish prob¬ 
ably the only correct interpretation of the phonetic system of arithmetic 
used by the Nahoas; a system which, when considered otherwise than 
phonetically, differed materially from that of the Hindoos. For exam- 
