DAVID CERNA-ARITHMETIC OF THE ANCIENT MEXICANS. 
21 
numbers of the latter three series are formed by adding to the word of 
the respective series the particle on or om, which now stands for plus , 
and that of each one of the first series up to 19 inclusive. For example, 
cempohuallionce 21, 20+1; cempohualliomome 22, 20+2; cempohualli- 
omei 23, 20+3; cempohuallionnahui 24, 20+4; cempohuallionmacuilli 
25, 20+5, etc. And so with the intermediate numbers of each one of 
the other two progressive series. 
The number 80 is also known by the name of xihuitl , which among its 
various significations has that of year and grass. Combining the word 
xihuitl with that of each one of the four series respectively, bringing into 
account addition and multiplication, the Nahoas arrive only as far as 80 
multiplied by 80 or 6400, contrary to the opinion of Humboldt and 
Orozco y Berra. This latter affirms that by combining the primitive 
words, ce (1), ome (2), yei (3). nahui (4), macuilli (5), mallactli (10), 
caxtolli (15), cempohualli (20), tzontli (400), and xiquipilli (8000), also, 
through multiplication and addition, any quantity imaginable can be 
formed. 
In the preparation of this imperfect article, I have carefully consulted 
the works mentioned in the appended list of bibliographical references, 
and espectally the monumental productions of my distinguished compa¬ 
triots Manuel Orozco y Berra and Alfredo Chavero. 
BIBLIOGRAPHY. 
Iytlilxochitl — Historia Chichimeca. 
Clavigero — Historia Antigua. 
Molina— Vocabulario. 
Gama— Descripcion Historica y Cronologica de las Dos Piedras. 
Brinton— The Iconographic Encyclopedia of the Arts and Sciences. 
Simeon— Archives de la Commision Scientifique du Mexique. 
Lubbock— The Origin of Civilization and the Primitive Condition of 
Man. 
Orozco y Berra— Historia Antigua y de la Conquista de Mexico. 
Chavero —Mexico a Traces de los Siglos. 
