Basic Mathematics

Author(s): L C Jain
Publisher: Rajasthan Prakrit Bharti Sansthan Jaipur

Page 31

Analogy with Sumerian or ancient Egyptian is therefore not valid; Hebrew doubtfully competes."36
Strong reasons have been given that influence of Mesopotamian culture was only very limited in China. Apart from a few traditional cycles, there is little sign of sexagesimal arithmetic, and no special symbol for the fraction 4. This fraction was considered very important in Mesopotamia.
A numerical notation of only nine figures combined with placevalue components have been found in China as early as -14th century. In the primitive form, the zero, the black space on the counting board appears in -4th century.
The extraction of square and cube roots was in a developed stage in-1st century. Rule of three is found in Han Chiu Chang, earlier than any Indian Sanskrit text. Negative numbers appear in -1st century, the Pythagorean theorem in + 3rd century commentary of Chou Pei, geometrical survey material in + 3rd century commentary of Liu Hui. The fundamental identity of algebraic and geometrical relations was appreciated by Chinese throughout the previous millennium. Indeterminate analysis was taken up in +4th century in Sun Tzu.
It is quite strange to see that Euclid's geometry reaches China by + 1275, so also trigonometric methods seem to have been in use in + 1270.
Thus Mikami opines that the greatest deficiency in old Chinese mathematical thought was the absence of the idea of rigorous proof. He correlates this with the failure of formal logic to develop in China. Chinese mathematicians never spontaneously invented any symbolic way of writing formulae. Land mensuration, survey, granary dimensions, making of dykes and canals, taxation, rate of exchange, alongwith calendrical calculations were considered important. There was practically nothing of mathematics “for the sake of mathematics"37.
(d) Greece :
From -600, Greece is world famous for its unparalleled progress in geometry and conics since -650. Thales and Pythagoras based mathematics on logic and illustrated the natural events through arithmetic. Yet the
36. Cf. ibid. p. xlii (author's note). 37. Cf. ibid., pp. 151–153.
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