P. HISTORY OF ' AATHEMATICAL - School of Mathematics

OLD NUMERAL SYMBOLS 41
"Bourkel refers to medicine cords with olivella shells attached
among the Tonto and Chiricahua Apache of Arizona and the Zufii.
This may be a related form.
"I think that there can be no question the instances of the second
type are historically related. Whether the Yakima and Nicola Valley
usage is connected with these is not established."
AZTECS
66. "For figures, one of the numerical signs was the dot (.), which
marked the units, and which was repeated either up to 20 or up to the
figure 10, represented by a lozenge. The number 20 was represented
by a flag, which, repeated five times, gave the number 100, which was
FIG. 18.-Aztec numerals
marked by drawing quarter of the barbs of a feather. Half the barbs
was equivalent to 200, three-fourths to 300, the entire feather to 400.
Four hundred multiplied by the figure 20 gave 8,000, which had a
purse for its symb01."~ The symbols were as shown in the first line of
Figure 18.
The symbols for 20, 400, and 8,000 disclose the number 20 as the
base of Aztec numeration; in the juxtaposition of symbols the additive
principle is employed. This is seen in the second line3 of Figure 18,
which represents
67. The number systems of the Indian tribes of North America,
while disclosing no use of a symbol for zero nor of the principle of
Op. cit., p. 550 ff.
Lucien Biart, The Aztecs (trans. J. L. Garner; Chicago, 1905), p. 319.
a Consult A. F. Pott, Die quiniire und vigesimde Zahlmethode bei V6lh
aUer
WeUtheiZe (Halle, 1847).