186 YoSHIO MlKAMl 



scholars appeared, the learning of mathematics became more popular 

 than before, and rapid progress was made. The custom of secrecy was 

 still, however, a lamentable barrier to progress. The consequence was 

 that there were no Japanese mathematicians of those times who had 

 done creditable work in their younger days. 



The teaching of mathematics was not systematic. Almost nothing 

 efiBcient was done in the way of teaching, for the pupils were only given 

 problems, which they were left to solve themselves. When they succeeded 

 in solving them, they were given further problems ; but if they did not 

 succeed, they were left to the study of the same problems, thus making 

 their progress very tedious. But in this way, selections were naturally 

 effected, and talented persons only were left to continue in their studies, 

 a fact which certainly did much to foster creative work. 



10. The sangi ^if., or ''calculating sticks," formed the abacus 

 commonly used in Japan, having been brought from China in old times. 

 They were still in use when Japanese mathematics was rising in the 17th 

 century, and were aiding in the develo],»ment of Japanese algebra, which 

 was based on the tengenjutsu 5^7C^15; ^^' ^^^ Chinese abacus algebra of 

 the single element. It was through the Suan-hsueh-CJi'i-meng '^^^^ 

 of 1299 that early Japanese mathematicians studied this sort of Chinese 

 algebra. Jn China, the same abacus algebra had long been forgotten 

 and its meaning was only restored b}^ a comparison with the chieh-ken- 

 fang \^^'^'J], or "root borrowing process," literally, which meant the 

 algebra that had been newly brought from Euiope. 



The Japanese, on the contrary, succeeded in understanding how to 

 proceed in the matter, without borrowing any external aid from European 

 knowledge, although the subject was presented in the Chinese book in a 

 hardly intelligible manner. They soon succeeded also in establishing a 

 written system of algebra, which was a direct extension of the Chinese 

 science. The endan-jutsu I^^Htj and the tenzan-jutsit ifiJtlftf both deal 

 with this system ; they are usually ascribed to Seki. The Japanese 

 system of algebra being carried out in writing, it might be doubted 

 not without reason whether it had not been influenced by European 

 algebra, a doubt that might well be strengthend by the knowledge of 

 the existence of intercourse between the Japanese and the Dutch, though 

 under very limited conditions, contemporaneously with Seki's work. 

 There was also a Jax)anese who had learned mathematics at Leyden, 

 and another who had learned medicaie in Namban '^^, possibly a 

 European colony in the south of Asia, and bad returned to Japan. But 



