MATHEMATICS IN CHINA AND JAPAN. 19/ 



and the calendrical reform in the Kwansei Era (1789-1801) ^^ were 

 powerful factors in introducing European mathematics into Japan. 

 Takahashi Yoshitoki ^^M0# (l'^64-1804) studied the astronomical work 

 of La Lande and composed volumes of reviews about it, in which he 

 recorded something of the formulae of integration, which he compared 

 with the results of the Japanese method of limits and thus acknowledged 

 ilie correctness of the method. It appears therefore that he had understood 

 tlie Occidental mathematics in this work by dint of his previous 

 knowledge of Japanese mathematics. If he had been an expert in 

 mathematics besides being an astronomer, or had he been in intimate 

 relationship with specialists in mathematics, he might well have 

 considerably influenced the Japanese mathematicians of his day in favor 

 of the study of the European science. But such was not the case. 

 The custom of schools based on the principle of inherited traditions 

 seems to have shut the doors of tlie studies of Japanese matheuiaticians 

 to new knowledge from without. 



Some of the writings of Japanese mathematicians contain passages 

 in which it is maintained that China and the West are superior in 

 astronomy and calendrical subjects, but that in the field of mathematics, 

 Japan surpasses China and the West. Such was certainly the general 

 opinion among the mathematicians of the day. Although the astronouier 

 Takahashi had justly acknowledged the true value of European 

 mathematics, there were none among the matliematicians who shared 

 his view. It happened in considerably later years that Uchida Gokan 

 |^B351il called his school by the European name ''Mathematica" and 

 that Yanagi Narayoshi :|^P;j^'|;^ studied the differential and integral 

 calculus of the West. Uchida knew a little Dutch, but his linguistic 

 knowledge was very limited. It is very remarkable that there was not 

 a single person well versed in Dutch oi- other European languages 

 among the old Japanese matheujaticians even in the latest years of the 

 Wo.san, whereas the astronomers contemporary with them were most 

 of them learned in European languages and European science. The 

 mathematicians of those days would have had little to learn, if they 

 had read European works on arithmetic or algebra ; as to advanced 

 works, they could not have understood anything and (^o these must 

 have been left untouched. tSuch circumstances made it very hard for 

 the European science to exercise a })0werful influence o\'er Japanese 

 mathematics. It follows therefore that the Wasan or old Japanese 

 mathematics was left, on the whole, to pursue its own course until 



