Furthermore the great astronomer and engineer of the Mongol dynasty, Kouo-Sheou-kin (1281), in his Sheou-she Li, a treatise on the calendar, gives the number 198617 in the following form, which may be compared with the Japanese sangi of which we shall presently speak: I IIII I̱̱̱ I I II. This plan is much older than the thirteenth century, however, for in the Sun-tsu Suan-ching mentioned in Chapter II, written by Sun-tsu about the third century, it is stated that the units should be vertical, the tens horizontal, the hundreds vertical, the thousands horizontal, and so on, and that for 6 one should not use six rods, because a single rod suffices for 5. These rules are repeated, almost verbatim, in the Hia-heou Yang Suan-ching, one of the Chinese mathematical classics, probably of the sixth century. The rods are therefore very old, and they were the common means of representing members in China, as we shall see was also the case in Japan, until a relatively late period.
As to the methods of operating with the rods, Yang Houei, in his Siu-kou-Ch’ai-ki-Swan-fa of 1275 or 1276, gives the following example in multiplication:
| ═ | IIII | I̱̱ | = | multiplier | = | 247 | |||
| I̱̱ | III | I̱ | = | multiplicand | = | 736 | |||
| I | I̱̱̱ | I | I̱̱ | IIII | ═ | = | product | = | 181 792 |
From China the calculating rods passed to Korea where the natives use them even to this day. These sticks are commonly made of bamboo, split into square prisms, and numbering about 150 in a set. They are kept in a bamboo case, although some are made of bone and are kept in a cloth bag as shown in the illustration, (Fig. 4.). The Korean represents his numbers from left to right, laying the rods as follows:
| I | II | III | IIII | X | XI | XII | XIII | XIIII | — | T[1] |
| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
- ↑ We are indebted to an educated Korean, Mr. C. Cho, of the Methodist Publishing House in Tokio, for this information. On the mathematics of Korea in general, see Lowell, P., The Land of the Morning Calm. Boston 1886, p. 250. One of the leading classics of the country is the Song yang hoei soan fa, or Song tang houi san pep (Treatise on Arithmetic by Yang Hoei of the Song Dynasty), written in 1275 byYang Hoei, whose literary name was Khien Koang; see M. Courant, Bibliographie Coréenne. Paris 1896, vol. III, p. 1.
