become very marked. Fortunately, just about this time, the Emperor Tenchi (Tenji) began his short but noteworthy reign (668-671).[1] While yet crown princes this liberal-minded man invented a water clock, and divided the day into a hundred hours, and upon ascending the throne he showed his further interest by founding a school to which two doctors of arithmetic and twenty students of the subject were appointed. An observatory was also established, and from this time mathematics had recognized standing in Japan.
Fig. 1. Shōtoku Taishi, with a soroban. From a bronze statuette.
The official records show that a university system was established by the Emperor Monbu in 701, and the mathematical studies were recognized and were regulated in the higher institutions of learning. Nine Chinese works were specified, as follows:—(1) Chou-pei (Suan-ching), (2) Sun-tsu (Suan-ching), (3) Liu-chang, (4) San-k’ai Chung-ch’a, (5) Wu-t’sao (Suan-shu), (6) Hai-tao (Suan-shu), (7) Chiu-szu, (8) Chiu-chang, (9) Chui-shu.[2] Of these works, apparently the most famous of their time, the third, fourth, and seventh are lost. The others are probably known, and although they are not of native Japanese production they so greatly influenced the mathematics of Japan as to deserve some description at this time. We shall therefore consider them in the order above given.
1. Chuo-pei Suan-ching. This is one of the oldest of the Chinese works on mathematics, and is commonly known in
