MJ THE MA TICS IN CHINA AND JAP A A ]%] 



that the Japanese scieace was foimdecl on the Chinese system. Never- 

 theless Japanese mathematics was by no means entirely defective in 

 geometry. Geometry in its Greek sense, of course, did not develop in 

 Japan. Japan, where the science of logic was little studied, was not 

 a favourable soil for the fostering of a rigorous kind of mathematics 

 and consequently the science of geometry as a logical system of 

 deductions never developed. But at the same time, it is true that Jai)an 

 gave birth to a peculiar sort of geometry indigenous to the land. 



Though Japanese mathematicians were accustomed to seek algebraical 

 means for their solution of geometrical problems, yet they could not 

 accomplish their purpose without n^aking certain geometrical conside- 

 rations. Some preliminary knowledge of a geometrical nature thus 

 being indispensable, even in early times such treatises were composed 

 as Hoshino's Kohkjen-slw ^Sf^sl^^^iil? (1672), Seki's Kendai ^^ 

 and the like. Yamada [IjHjES (1659) and Isomura H#^^, (1660) 

 proved the relation of the volume of a triangular pyramid. The proof 

 of the sides-relation of a right triangle was given in a variety of ways. 

 Thus, there gTadually accumulated a group of what might be called 

 geometrical theorems, or geometrical relations more properly, among 

 which were certainly a number of beautiful ones. 



During the early years of Jaimnese mathematics, problems were 

 often proposed which could be solved only by resorting to very complicated 

 equations of high degrees, such complication being regarded as elegant. 

 But by and by arose claims for simplicity, which caused the atmosphere 

 of the mathematical circle to undergo a complete change. Seki was one of 

 the first mathematicians to lay claim to this merit, and the subsequent 

 efforts of Kurushima, Ajima and others were instrumental in simplifying 

 the nature of the geometrical problems attempted and of their solutions. 

 Now those problems only were highly prized, which could be solved 

 without using complicated equations. Afterwards appeared a variety 

 of problems, whose solutions corresponded to beautiful geometrical 

 theorems. It was then that there were made a number of collections of 

 formulae. 



The yodai ^^ and yajntsu ^^1^ were favourite subjects of 

 Japanese mathematicians. These Avere names given to the problems 

 and methods relating to figures inscribed one within another. Those 

 geometrical problems which were studied in Japan always concerned 

 figures in contact, both inscribed and circumscribed. Figures whose 

 parts wei-e separated were hardly ever considered. 



