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4 A HISTORY OF MATHEMATICS
South America." ^ This system was used also by many of the
North Siberian and African tribes. Traces of it are found in
the languages of peoples who now use the decimal scale; for
example, in Homeric Greek. The Roman notation reveals
traces of it; viz., I, II, ••• V, VI, ••• X, XI, ••• XV, etc.
It is curious that the quinary should so frequently merge
into the vigesimal scale; that savages should have passed from
the number of fingers on one hand as an upper unit or a stopping-place,
to the total number of fingers and toes as an upper
unit or resting-point. The vigesimal system is less common
than the quinary, but, like it, is never found entirely pure. In
this the first four units are 20, 400, 8000, 160,000, and special
words for these numbers are actually found among the Mayas
of Yucatan. The transition from quinary to vigesimal is
shown in the Aztec system, which may be rej)resented thus,
1, 2, 3, 4, 6, 6 -I- 1, ••• 10, 10 -f-1, - 10 -I- 0, 10 -I- .5 -f 1, ••• 20,
20-1-1, ••• 20-1-10, 20 + 10 4-1, ••• 40, etc.'' Special words
occur here for the numbers 1, 2, 3, 4, 5, 10, 20, 40, etc. The
vigesimal system flourished in America, but was rare in the
Old World. Celtic remnants of one occur in the French words
quatre-vingts (4 x 20 or 80), si-v-vingts (6 X 20 or 120), quinzevingts
(15 x 20 or 300). Note also the English word score in
such expressions as three-score years and ten.
Of the three systems based on human anatomy, the decimal
system is the most prevalent, so prevalent, in fact, that according
to ancient traditioii it was used by all the races of the
world. It is only -within the last few centuries that the other
1 Conant, op. cit., p. 592. For further infonnation see also Port,
Die quindre und vigesimale Zdhlmethode bci t'olkcni aUer Welttheile,
Halle, 1847 ; Pott, Die Sprachverschiedenheit in Eiiropa an den Zahlwortern
nachgeioiesen, soioie die qxiiniire und vigesimale Zdhlmethodet
Halle, 1868.
2 Tylob, op. at., Vol. I., p. 202.