Page:Indian mathematics, Kaye (1915).djvu/56

 of the distance of an island from the shore, and the solution given occurs in Āryabhata's Gaņita some two centuries later. The Wu-t'sao written before the 6th century appears to indicate some deterioration. It contains the erroneous rule for areas given by Brahmagupta and Mahāvīra. The arithmetic of Chang-Ch'iu-chien written in the 6th century contains a great deal of matter that may have been the basis of the later Indian works. Indeed the later Indian works seem to bear a much closer resemblance to Chang's arithmetic than they do to any earlier Indian work. The problem of "the hundred hens" is of considerable interest. Chang gives the following example: "A cock costs 5 pieces of money, a hen 3 pieces and 3 chickens 1 piece. If then we buy with 100 pieces 100 of them what will be their respective numbers?" No mention of this problem is made by Brahmagupta, but it occurs in Mahāvīra and Bhāskara in the following form: "Five doves are to be had for 3 drammas, "7 cranes for 5, 9 geese for 7 and 3 peacocks for 9. Bring 100 of these birds for 100 drammas for the prince's gratification." It is noteworthy that this problem was also very fully treated by Abū Kāmil (Shogâ) in the 9th century, and in Europe in the middle ages it acquired considerable celebrity. Enough has been said to show that there existed a very considerable intimacy between the mathematics of the Indians and Chinese; and assuming that the chronology is roughly correct, the distinct priority of the Chinese mathematics is established. On the other hand Brahmagupta gives more advanced developments of indeterminate equations than occurs in the Chinese works of his period, and it is not until after Bhāskara that Ch'in Chu-sheo recorded (in A.D. 1247) the celebrated t'ai-yen ch'in-yi-shu or process of indeterminate analysis, which is, however, attributed to I'-hsing nearly six centuries earlier. The Chinese had maintained intellectual intercourse with India since the