the sun) while even numbers are designated by black knots (standing for the incomplete, as night, cold, water, earth). The left-hand tablet shown in Figure 20 represents the numbers 1–10. The right-hand tablet pictures the magic square of nine cells in which the sum of each row, column, and diagonal is 15.
70. The Chinese are known to have used three other systems of writing numbers, the Old Chinese numerals, the mercantile numerals, and what have been designated as scientific numerals. The time of the introduction of each of these systems is uncertain.
Fig. 20.—Early Chinese knots in strings, representing numerals
71. The Old Chinese numerals were written vertically, from above down. Figure 21 shows the Old Chinese numerals and mercantile numerals, also the Japanese cursive numerals.[1]
72. The Chinese scientific numerals are made up of vertical and horizontal rods according to the following plan: The numbers 1–9 are represented by the rods 𝍩, 𝍪, 𝍫, 𝍬, 𝍭, 𝍮, 𝍯, 𝍰, 𝍱; the numbers 10–90 are written thus 𝍠, 𝍡, 𝍢, 𝍣, 𝍤, 𝍥, 𝍦, 𝍧, 𝍨. According to the Chinese author Sun-Tsu, units are represented, as just shown, by vertical rods, ten’s by horizontal rods, hundred’s again by vertical rods, and so on. For example, the number 6,728 was designated by 𝍥𝍯𝍡𝍰.
73. The Japanese make use of the Old Chinese numerals, but have two series of names for the numeral symbols, one indigenous, the other derived from the Chinese language, as seen in Figure 21.
- ↑ See also Ed. Biot, Journal asiatique (December, 1839), p. 497–502; Cantor, Vorlesungen über Geschichte der Mathematik, Vol. I, p. 673; Biernatzki, Crelle’s Journal, Vol. LII (1856), p. 59–94.
