Page:A History Of Mathematical Notations Vol I (1928).djvu/63

Rh local value, are of interest as exhibiting not only quinary, decimal, and vigesimal systems, but also ternary, quaternary, and octonary systems.

68. The Maya of Central America. and Southern Mexico developed hieroglyphic writing, as found on inscriptions and codices, dating apparently from about the beginning of the Christian Era. which discloses the use of a remarkable number system and chronology.‘2 The number system discloses the application of the principle of local value, and the use of a symbol for zero centuries before the Hindus began to use their symbol for zero. The Maya system was vigesimal, except in one step. That is, 20 units (kins, or “days”) make 1 unit of the next higher order (uz'nals, or 20 days), 18 uinals make 1 unit of the third order (tun, or 360 days), 20 tuns make 1 unit of the fourth order (Kalun, or 7,200 days), 20 Kaluns make 1 unit of the fifth order (cycle, or 144,000 days), and finally 20 cycles make 1 great cycle of 2,880,000 days. In the Maya codices we find symbols for 1719, expressed by bars and dots. Each bar stands for 5 units, each dot for 1 unit. For instance,



The zero is represented by a symbol that looks roughly like a halfelosed eye. In writing 20 the principle of local value enters. It is expressed by a dot placed over the symbol for zero The numbers are written vertically, the lowest order being assigned the lowest position (see Fig. 19). The largest number found in the codices is 12,489,781.

69. According to tradition, the oldest Chinese representation of number was by the aid of knots in strings, such as are found later among the early inhabitants of Peru. There are extant two Chinese tabletsa exhibiting knots representing numbers, odd numbers being designated by white knots (standing for the complete, as day, warmth,

1 W. C. Eells, “Numberagystems of North Mathematical Alonlhly, Vol. XX (1913), p. 26 malice (311 series, 1913), Vol. XIII, p. 218A22.

2 Our information is drawn from S. G. Morley, An Inlruduclion lo the Study of (he Maya [Iiernglyphs (Washington, 1915).

3 Paul l’erny, Grammairc de la langue chinaise male 2! écrile (Paris, 1876)I Vol. II, p. 5—7; Cantor, VarlL-sungen filler Geschiclile der AIulhcnlulik, Vol. 1 (3d ed), p. 674.