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20
III. The Development of the Soroban.

of rods, ch’eou.[1] 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,[2] and the commentary of Sou Lin on the Han history tells us that two hundred seventy-one of these formed a set.[3] 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 祘, 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.[4] 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:

I II III IIII IIIII I II III IIII ... I II ... II IIIII IIII I ... I IIII ... IIII IIII
1 2 3 4 5 6 7 8 9 12 25 46 69 99
  1. ↑ There is not space in this work to enter into a discussion of the possible earlier use of knotted cords, a primitive system in many parts of the world. Lao-tze “the old philosopher”, refers to them in his Tao-teh-king, a famous classic of the sixth century B. C., saying: “Let the people return to knotted cords (chieng-shing) and use them.” See the English edition by Dr. P. Carus. Chicago, 1898, pp. 137, 272, 323.
  2. ↑ The text say 6 units (inches) but we do not know the length of the unit (inch) of that period.
  3. ↑ The old word means, possibly, a handful.
  4. ↑ The date of the Yih-king or Book of Changes in uncertain. It is often spoken of as Antiquissimus Sinarum liber, as in an edition by Julius Mohl, Stuttgart, 1834—9, 2 vols. It is ascribed to Fuh-hi (B. C. 3322) the fabled founder of the nation. There is an extensive literature upon this subject.
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