Page:A history of Japanese mathematics (IA historyofjapanes00smitiala).pdf/23

Rh Liu Hui who wrote a treatise entitled Chung-ch’a, but this seems to be No. 4 in the list.

4. San-k’ai Chung-ch’a. This is also unknown, but is perhaps Liu Hui's Chung-ch’a-keal-tsih-wang-chi-shuh (The whole system of measuring by the observation of several beacons), published in 263. The author also wrote a commentary on the Chiu-chang (No. 8 in this list). It relates to the mensuration of heights and distances, and gives only the rules without any explanation. About 1250 Yang Hway published a work entitled Siang-kiai-Kew-chang-Swan-fa (Explanation of the arithmetic of the Nine Sections), but this is too late for our purposes. He also wrote a work with a similar title Siang-kiai-Feh-yung-Swan-fa (Explanation of arithmetic for daily use).

5. Wu-t’sao Suan-shu. The author and the date of this work are both unknown, but it seems to have been written in the 2d or 3d century. It is one of the standard treatises on arithmetic to the Chinese.

6. Hai-tao Suan-shu. This was a republication of No. 4, and appeared about the time of the Japanese decree of 701. The name signifies “The Island Arithmetical Classic”, and seems to come from the first problem, which relates to the measuring of an island from a distant point.

7. Chiu-szu. This work, which was probably a commentary on the Suan-shu (Swan-king) of No. 8, is lost.

8. Chiu-chang. Chiu-chang Swan-shu means “Arithmetical Rules in Nine Sections”. It is the greatest arithmetical classic of China, and tradition assigns to it remote antiquity. It is related in the ancient Tung-kien-kang-muh (General History of China) that the Emperor Hwang-ti, who lived in 2637 B. C.,