VIII. Mathematics in China and Japan. 



By 



YosTiio MiKAMi. 



Part I. China. 



1. The liistoiy of mathematics in China may he conveniently 

 divided into five periods. The first period is that of ancient times, 

 from which no antlientic mathenjatical treatises have been handed 

 down and of which little is known concerning the achievements made 

 in the field of njathematics. The second period comprises some ten 

 or more centnries heginning abont the Christian era, dnring which the 

 oldest treatises now existent, which are ten in number, were coujposed 

 or used- The third is a brief period covering the age of the ascendency 

 of the Mongol invaders, when the study of the older mathematics was 

 pursued and brought into a prominence never known before ; it was 

 followed by an age of mathematical decline. The fourtli period follows, 

 beginning with the end of the 16th century, during which European 

 niissionaries introduced the European sciences of astronomy and mathe- 

 matics into China. During this period, the older mode of mathematics 

 was also studied side by side with the newly brought methods. The 

 fifth and last is our own age ; and nowadays the Chinese are chiefly 

 studying the systems of mathematics now prevalent in the Western 

 World. 



2. The study of the older mathematics down to the Han ^ 

 Dynasty (B. C. 206-24 A. D.) is very obscure, because there are now 

 no matliematical books dating from such remote ages. "Rut the art of 

 calendar-making had reached a high development in antiquity, although 

 it is still a moot question whether it was original with the Chinese 

 as maintained by Prof. S. Shinjo or of Greek origin as Prof. T. lijima 

 believes. In either case, however, the Chinese made astronomical 

 observations and calculations from at least the third or fourth centuries 

 before Christ. To answer the astronomical demands of the time, there 

 must have lieen a certain amount of mathematical knowledge. Some 



