Page:A history of Japanese mathematics (IA historyofjapanes00smitiala).pdf/32

20 of rods, ch’eou. The earliest definite information that we have of the use of these rods is the Han Shu (Records of the Han Dynasty), which was written by Pan Ku of the Later Han period, in the year 80 of our era. According to him the ancient arithmeticians used comparatively long rods, and the commentary of Sou Lin on the Han history tells us that two hundred seventy-one of these formed a set. Furthermore, in the Che-chouo (Narrative of the Century), written by Lieou Yi-k’ing in the fifth century, it appears that ivory rods were used. We also find that the ancient ideograph for swan (reckoning) is, a form that is manifestly derived from the rods, and that is evidently the source of the present Chinese ideograph. Mei Wen-ting says that it is impossible to give the origin of these rods, but he believes that the ancient classic, the Yih-king, gives evidence, in its mystic trigrams, of their very early use. As to the size of the rods in ancient times we are not informed, none being now extant, but an early work on cooking, the Chong-k’ouei-lou, speaks of cutting pieces of meat 3 inches long, like a calculating rod, from which we get some idea of their length.

As to the early Chinese method of representing numbers, we have a description by Ts’ai Ch’en, surnamed, Kieou-fong (1167—1230), a philosopher of the Song dynasty. In his Hong-fan (Book of Annals) he gives the numerals as follows: