De oorsprong van het tientallig positiestelsel

Abstract

SUMMARY On the origin of the positional numeral system with base 10. — There are well-founded reasons not to accept without any restriction the general opinion that the decimal positional numeral system should have come into existence in India. In this contribution some arguments are advanced in favour of the view, first expressed by Wang Ling [13], later by Needham [9], that the origin of the positional number system is Chinese. As early as the 14th century before Christ a written number system was known in China, in which in principle only nine symbols were used. Zero as a dot did not appear in China until the first half of the 8th century A. D. The origin of it is probably Indian. It is definitely established that zero was only invented after the positional principle had come into being. The positional numeral system in India is of more recent date. It is generally assumed that it appeared in India ca. 500 A. D. Convincing arguments that tell in favour of the Chinese origin of the positional system arc found by comparing the old Chinese works about mathematics with Indian ones. Even Kaye [5] and Needham [9] already pointed to the Chinese influence on Hindu mathematics. The Hindus seem to have consulted almost all available mathematical works that were published 600 A. D. Even the mistakes out of a not so important work as the Wu-t’sao Suan-ching were exactly copied by Brahmagupta and Mahavira. The Chinese influence is clearly proved by comparing the example of a multiplication, given in the Sun-Tzu Suan-ching (4th century) with the Indian example of the Kapatha-Sandhi method. Both methods seem to be identical, the Indian example using the same numbers as the Chinese one. That clearly shows that the Hindus owe their arithmetic methods to the Chinese, also that they are very unlikely to have discovered the positional principle independent of the Chinese.