184 YoSHIO MlKAMl 



ascribed, liovvever, to lack of geniiia, but mainly to the attitude of attack 

 of the Chinese scholars. To this matter we shall return later, but now 

 hastily pass it over in order to consider Japanese mathematics, for the 

 limited space does not allow us to enter here in further detail into the 

 progress of luathematics in modern China. 



Part II. Japan. 



8. In the oklest times of which there is a record, Japan had no 

 kind of mathematics worthy of the name. But the roots of the Jai3anese 

 numerals : hi {I), Im ('2), mi (3), yo (4), tm{tu){5), mu (6), ya (8), to (10), 

 are noteworthy in being so formed that a change in the vowel, the 

 consonant remaiuing the same, denotes a double, characteristic not known 

 to occur in any language of neighbouring or distant tribes. The word 

 itsidsu, that represents 5, consists of the prefix i and suffix tsu attached 

 to the root Uu, which is the middle syllable. In Japanese classical 

 works frequent mention is made of great numbers like Yaoyorozu /\/^^, 

 or ''Eight hundred m.yriads," literally, and the like, the enumeration 

 recurring in myriads. This was, however, a usage certainly learned from 

 China. iSome documents of the 8th century give such actual examples 

 of counting as 12 sen 5 hyahu or ''12 thousand and 5 hundred," 

 recurring in thousands instead of in myriads. The Japanese knew of 

 mathematics only after the introduction of the Chinese science. 



The capitals of the Emperor at Nara and Heian (tlie present Kyoto) 

 were built according to the scheme of the Chinese capital Chang-an ^^, 

 but they differed notably from the latter in the method of naming or 

 numbering the streets, in that the idea of coordinates was employed, 

 which was altogether foreign to the Chinese. 



The mamoko-date f^^i; vvas a kind of game resembling the 

 European Josephus' problem and not found in China. It was in use in 

 Japan after the 11th century, being recorded in a number of old documents. 

 It was destined to attract much attention when the Japanese science of 

 mathematics arose in subsequent years. It will be worth remembering 

 that such a game prevailed in an age when nothing was done in the 

 domain of mathematics. 



9. In Japan for a very long period after the introduction of the 

 Chinese science of mathematics, nothing worthy of mention was accom- 

 plished, except those casual occurrences referred to above. But imder 

 the Tokugawa b^hogunate, there came a change. At that time, appeared 



