MATHEMATICS LV C 11 IN A AND JAPAN. 183 



Of these four elements, one represents the unknown and the other three 

 are taken as parameters. Four of such equations serve for tlie elimination 

 of the three parameters. The abacus algebra of the four elements was 

 the highest development of the Chinese in the fiekl of algebra. We 

 know nothing of any kind of abacus algebra that was developed outside 

 of China except in the countries to which the Chinese science was 

 brought. 



7. For nearly three centuries after this period, the study of 

 mathematics reiuained in an unfavourable state. At the close of the 16th 

 century, there was an inclination toward progress, when the European 

 sciences of astronomy and mathematics were brought to China by 

 Christian, missionaries. Shortly after, trigonometry was introduced in 

 connection with calendrical matters. Still later, the logarithmic tables 

 were brought. The Frenchman Pierre Jartoux at the beginning of the 

 18th century taught three formulae of trigonometric functions expressed 

 in infinite series. 



Thus the Chinese science would have been Europeanised altogether, 

 had not a reactionary tendency, characteristic of the Chinese, arisen. 

 Mathematical treatises of old times were searched for and were studied 

 diligently side by side with the newly brought European mathematics. 

 The works of Mei Wen-ting |^^|ffJ (1633-1721) well represent this 

 tendency. But the introduction of Western works was soon interrupted, 

 until in the middle of the 19th century Alexander Wylie began for a 

 second time the work of translation by rendering into Chinese Loomis' 

 work on analytic geometry and calculus. Several other translations were 

 subsequently made by a few foreign scholars. The Chinese mathematicians 

 were content with these translated works, and none are known to have 

 studied the European or American works themselves. But in the 20th 

 century, those among the Chinese who went al)road in quest of matheiua- 

 tical knowledge were not a few. Foieign mathematicians also came to 

 China to teach mathematics in Chinese schools and colleges. Japanese 

 works based on recent Western, science were read abundantly in China. All 

 these factors are now working together to make Western niatlieuiatics 

 popular in China of our t)wn day. But it lies beyond our immediate 

 'purpose to discuss the present state of ujathematics in China. 



During the three centuries after the end of the 16th century, there 

 appeared a good many matliematicians and also many writings on this 

 subject. Some of them are not without luerit, but oidy a few are in 

 the class of wt»rks of discovery or originality. This fact must not be 



