MATHEMATICS IN CHINA AND JAPAN. 195 



Chinese works, Lut they were soon able to establish their own new 

 science and to surpass their Chinese predecessors in the details of their 

 studies. The subjects mentioned above were all unlvno\vn in China. 

 Japanese mathematics may be truly said to be modelled on the Chinese 

 science ; it proceeded, however, into regions previously unexplored. 



Japanese and Chinese mathematicians of modern times have 

 sometimes considered similar problems and used similar methods, 

 a circumstance obviously due to the fact that both were following the 

 older Chinese science along parallel lines. But in most of these cases, 

 the Japanese were ahead of the Chinese. Moreover, the former generally 

 obtaind superior results, sometinjes problems being attempted that were 

 altogether unknown in China. The foundation of algebra in the written 

 style, the organization of a peculiar sort of geometry, and studies in 

 the theory of numbers, in the polygonal theory, and so on, were themes 

 in the study of which the Japanese only, and not the Chinese, were 

 able to arrive at brilliant results. In the measurement of the circle, 

 the studies of equations, method of differences, summation of progressions, 

 etc., the Japanese were superior to the Chinese. There is almost 

 nothing, however, to record of contrary cases. 



The sorohan ^^ was brought from China to Japan. The oldest 

 examples in existence are one in Ise Province belonging to the Bun-an 

 Era (1444 49) ;^^ and one that was used by Mayeda Toshi-iye ^g 

 ^Ij^ and handed down to his family, Marquis Mayeda. The Japanese at 

 tirst used instruments imported from China or those made after the 

 Chinese fashion. But there soon arose Japanese styled instruments, in 

 which the balls were made sharply edged, whereas the Chinese abacus was 

 provided with somewhat rounded balls. In China there is no evidence 

 that the development of mathematics was influenced by the sorohan. 

 It was otherwise in Japan. As the sorohan was simpler to manipulate 

 than the calculating sticks, Japanese mathematicians were in general 

 desirous of making as much use of the former as the case would permit. 

 But higher equations could be solved only by means of the sticks, and 

 not by the sorohan. Consequently mathematicians hoped to devise 

 a method by which calculations of all sorts could be carried out by 

 means of the sorohan. The establishment of infinite expansions and 

 successive approximations resulted. There appears no trace, on the 

 contrary, in Chinese mathematics contemporary or otherwise, of the 

 sorohan's having had so important an influence. 



]9. After the end of the 16th century, Chinese mathematics 



