DAVID CERNA-ARITHMETIC OF THE ANCIENT MEXICANS. 15 
In this we may count by means of the thumb, upon the upper, middle, 
and lower row of phalanges of the other four fingers. Thus, the first 
row of phalanges would give us 1, 2, 3, and 4; the second row, 5, 6, 7, 
and 8; the third row, 9, 10, 11, and 12. The advantage of this system 
lies in the fact that easy calculations by divisions can be made, which 
give as the result a whole number, whether the division be made by 2, 3, 
or 4. That there is advantage in this, is apparent from the fact that, for 
instance, we divide the foot into 12 inches, the inch into twelve lines, 
and the line into 12 points. 
In studying the sj^stem of phonetic arithmetic employed by the ancient 
Mexicans, we first have to deal with the Nahoas, among the first, if not 
the first, of the civilized races inhabiting Anahuac of old. The Nahoas 
were a polysyllabic race, whose historical record bears the impress of its 
having had a foreign origin. Absolutely ignorant of this origin, the 
only thing we possess, so far, is a more or less accurate knowledge of 
the civilization of the Nahoas, the predecessors of the great Toltecs, from 
studies of their hieroglyphical writings. 
Orozco y Berra, who follows Gama on the subject, states that the form¬ 
ation of the numerals among the Nahoas originated in the five fingers of 
one hand. By computing, afterward, the fingers of the other hand, the 
number 10 is obtained, and counting, again, the toes of both feet, the 
number 20 is formed. 
To designate the first four numbers single words are used; thus, 1 is 
known as ce or cem; 2, as ome\ 3, as yet or ei ; and 4, as naliui. Above 
these four numerals, for each succeeding number, as far as 9 inclusive, a 
compound term is employed. Thus, 5 is called macuilli. This name, to 
follow Gama, is derived from the compound verb macueloa, the latter 
word in turn being composed of maitl , the hand, and the simple verb 
cueloa , to double or bend upon itself. Orozco y Berra, again, believes 
that the word mapilli is derived from maitl , the hand, and pilli, child or 
son; and thus it signifies, figuratively speaking, the children or the ap¬ 
pendices of the hand. Now, macuilli , formed from maitl , the hand, the 
verb cui, to take, and pilli , or simply illi, referring to the appendices or 
digits, would mean the fingers taken with the hand , or the fist. This author, 
then, entertains the idea that the first five units are counted according as 
each finger of the hand is being bent upon itself, until the fist is formed. 
He finds, also, that the words xopilli , toes of the feet, and macpalli , palm 
of the hand, have a similar origin. 
The numbers 6 to 9 inclusive, are expressed likewise by compound 
terms, thus: cliecuace , 6; chicome , 7; chicuei , 8; and chiconahui, 9. Ac¬ 
cording to Gama, chicoace or cliicuace is formed from the verb chico, which 
means by my side , and the preposition huan , meaning near another , the 
whole term c hicohuance, of which chicoace is a contraction, signifies one 
