Page:Popular Science Monthly Volume 80.djvu/602

598 wrote in Ujjain in the seventh century, was indebted for at least one of his problems to the great Chinese classic, the Chiu-chang Suan-shu.

Of the scholars whose contributions to mathematics were noteworthy, it will suffice to mention only a few, although it should be stated that these are the greatest of their respective periods so far as we now know.

No one knows how far back the Chow-pi goes. It purports to be a dialogue between Chow Kung and Kao (or Shang Kao) and to have been written c. 1100 B.C. Wylie translates part of it, and shows that it contains a reference to the Pythagorean proposition and to a primitive trigonometry. It has long been known that the discovery of Pythagoras was the proof and not merely the fact, for the latter is mentioned in Egyptian writings before his time, and in Hindu works that probably antedated him, so that it is not surprising to find it in China.

Chang T'sang, who died in 153 restored the Chiu-chang Suanshu, or Arithmetical Rules in Nine Sections, for the antiquity of which, in its original form, great claims are made.

From the standpoint of mathematics the most interesting features of this work are the use of negative numbers, the trigonometry of the right triangle, and the fang-ch'êng process. The last named constituted one of the nine sections and concerned the solution of simultaneous linear equations. This would hardly be worth mentioning except for three reasons: (1) We have nothing of this kind in the algebra of Europe as early as this; (2) from this method of the Chinese came, by direct descent, the early Japanese method that led by obvious steps to the invention of determinants by Seki before the idea occurred to Leibnitz; (3) the method for the extraction of roots led Ch'in Chiu-shao, in 1247, to anticipate Horner's method, as will presently be shown.

Sun-tsǔ, whose date is unknown, but who probably lived in the third century of the Christian era, wrote a work on arithmetic in which he set forth the process known as t'ai-yen ch'iu-yi-shu, a form of indeterminate analysis that was afterwards employed with much success. It