## 초록

Chinese mathematical writings Zhangjiashan Hanjian<Suan shu shu> is a part of Dynasty Han(漢) books which were excavated in Zhangjiashan of Jiangling(江陵) County, Hubei(湖北) Province in 1983 and consists of 69 arithmetical questions written on 190 bamboo strips. This writings has very similar pattern like Nine Chapters on Mathematical procedures(九章算術; Jiuzhangsuanshu) and consists of subject, question, answer and general rule for its solution starting with terminology ‘術’(technique). Furthermore, some questions of the text are the same as Nine Chapters on Mathematical procedures and some are quite similar or identical. Although Suan shu shu is considered as original text for Nine Chapters on Mathematical procedures, it would be necessary to study more carefully through analysis of content. It is not so easy to find out what position Suan shu shu has in history of ancient chinese mathematics. Suan shu shu may not be systematically classified and unified literary work because of the followings; some inconsistencies in the arithmetic expression that exist among questions of Suan shu shu, two people named Yang(楊) and Wang(王) who are assumed as instructors appeared in the text, and many questions having identical name. From this point of view, this article is focused on the compilation and formation process of Suan shu shu by analyzing content and classifying the questions systematically. Unlike the western algebra generally uses mathematical symbolic code or sign, chinese algebra couldn’t had developed because of the limitation of vertical writing on bamboo slips. Under this circumstances, the fraction have two ways of expression as (1)N分m or (2)N分之m. The difference between the expression (1) and (2) is whether the character ‘之’(zhi) exits or not, and mostly the expression (1)is used. The diversity of Suan shu shu is highlighted from the fact that main expression of fraction is (2)N分之m in Nine Chapters on Mathematical procedures. In case of division, seven kinds of different expressions are found from omission of a divisor and a dividend to 實如法而一(count 1 for each time the dividend accommodates the divisor) which has the fixed form of a divisor and a dividend. Although these expressions might coexist in certain point of time, generally it infers the formation chronicle of questions in Suan shu shu. There also appears ‘楊’(Yang), ‘王’(Wang), ‘楊已讎’(Checked by Yang), ‘王楊讎’(Checked by Wang) in text regardless of the arithmetical questions. This implies that the arithmetical questions were instructed by certain experts family named ‘Yang’ or ‘Wang’. It is so interesting that the expression of fraction is classified according to instructors such as N分之m by Yang and N分m by Wang. They are instructors having the different ways of expression and terminologies of mathematics. Considering this point, Suan shu shu is apparently the text which is recorded from arithmetical questions of these two lines. Meanwhile, there are overlaps in the subject such the same names as 羽矢(Feathering arrows) and 粟求米(Seeking hulled from unhulled grain), and the similar name like 女織(The women weaving) and 婦織(Women weaving)in Suan shu shu. It would be unsuitable that some questions in Suan shu shu have the identical names with the different content. Therefore, it can be inferred that the text is the combined work of many kinds of categories. This would be resulted from the unclassified subjects in the process of editing questions made by different study groups. In conclusion, Suan shu shu would rather not be a simply mathematical text for teaching arithmetic theories, but be an accumulating work referred and recorded from many kinds of arithmetic texts which was written by experiences of the actual life for several years or even centuries. The diversity of category in Suan shu shu would be a meaningful example which shows a mark of tradition in pre-unified Dynasty while most of the field was setting up standard after establishing Qin(秦) and Han Dynasty.

## 키워드

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Zhang jia shan han jian, Suan shu shu, Jiu zhang suan shu, Wang and Yang, Divisor and dividend, Ancient mathematics, Feathering arrows