was a late product, papyrus being unknown in Greece for example before the seventh century B. C., parchment being an invention of the fifth[1] century B. C., paper being a relatively late product,[2] and metal and stone being the common media for the transmission of written knowledge in the earlier centuries in China. On account of the crude numeral systems of the ancients and the scarcity of convenient writing material, there were invented in very early times various forms of the abacus, and this instrumental arithmetic did not give way to the graphical in western Europe until well into the Renaissance period.[3] In eastern Europe it never has been replaced, for the tschotii is used everywhere in Russia today, and when one passes over into Persia the same type of abacus[4] is common in all the bazaars. In China the swan-pan is universally used for purposes of computation, and in Japan the soroban is as strongly entrenched as it was before the invasion of western ideas.
The Japanese soroban is a comparatively recent invention, having been derived from the Chinese swan-pan (Fig. 10), which is also relatively modern. The earlier means employed in China are known to us chiefly through the masterly work of Mei Wen-ting (1633-1721)[5] entitled Kou-swan-k’i-k’ao.[6] Mei Wen-ting was one of the greatest Chinese mathematicians, the author of upwards of eighty works or memoirs, and one of the leading writers on the history of mathematics among his people. He tells us that the early instrument of calculation was a set
- ↑ Pliny says of the second century B. C.
- ↑ It seems to have been brought into Europe by the Moors in the twelfth century.
- ↑ See Smith, D. E., Rara Arithmetica, Boston 1909, index under Counters.
- ↑ Known in Armenia as the choreb, in Turkey as the coulba.
- ↑ Surnamed Ting-kieou and Wou-ngan. He lived in the brilliant reign of Kang-hi, who had been educated partly under the influence of Jesuit missionaries.
- ↑ Researches on ancient calculating instruments. See Vissière, loc. cit., p. 7, from whom I have freely quoted; Wylie, A., Notes on Chinese Literature, p. 91.
