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Studies in the History of Natural Sciences  2020, Vol. 39 Issue (4): 395-424    DOI:
ARTICLES     
New Research on the Junshu,a Branch of Mathematics in the Early Period of Ancient China
ZOU Dahai
Institute for the History of Natural Sciences, CAS, Beijing 100190, China
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Abstract  Junshu(均输, lit. equality-based transport) was an important branch of mathematics in ancient China, and is specifically discussed in Chapter 6 of the Chinese mathematical classic, Nine Chapters on Mathematical Procedures. There are many outstanding issues still to be discussed and problems in existing studies on the origins of junshu in mathematics and its relationship with the economic policies of junshu. This article uses the increasingly abundant excavated documents and extant received works to conduct a more systematic and in-depth study on the development of the junshu in mathematics in the early period of ancient China. The article provides a new generalization of the characteristics of the junshu chapter of the Nine Chapters on Mathematical Procedures, and points out that the term “junshu” has a much broader meaning than “fair burden,” that the composition of the chapter exhibits a high degree of consistency, and that the inclusion of the mathematical problems is deliberately done by the editors and not a random arrangement. The article proves that both types of junshu in mathematics and economics have their origins in the pre-Qin period and the Qin dynasty. Though the 5 junshu problems in the extant versions of the Nine Chapters on Mathematical Procedures and 1 junshu problem in the Suanshu(算术, Mathematical Procedures) on the Western Han dynasty bamboo slips unearthed from Shuihudi were finalized in the Western Han dynasty, they should have their prototypes in the pre-Qin period and Qin dynasty. Evidence from the Shu(On Numbers) of the Qin bamboo slips preserved at the Yuelu Academy (岳麓书院) and the Suanshu shu(算数书, Book on Numbers and Computation) of the early Han bamboo slips unearthed from Zhangjiashan (张家山) indicate that some of problems 5-28 of the chapter are likely to have existed during the period from the Warring States to the early Western Han Dynasty, so there is no necessity for them having had to have been inserted in the chapter until the middle of the first century BC by Geng Shouchang.

Key words： junshu (均输equality-based transport)      Nine Chapters on Mathematical Procedures      excavated laws of the Qin and Han Dynasties      Yantie lun(盐铁论 Discourses on Salt and Iron)      Shu(数 On Numbers) on the Qin bamboo slips of the Yuelu Academy(岳麓书院)      Suanshu shu(算数书 Book on Numbers and Computation) on the Han bamboo slips excavated at Zhangjiashan (张家山)      Suanshu(算术 Mathematical Procedures) on the Han bamboo slips excavated at Shuihudi.     
Received: 02 August 2020      Published: 17 June 2021
ZTFLH:  N092  
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ZOU Dahai
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ZOU Dahai. New Research on the Junshu,a Branch of Mathematics in the Early Period of Ancient China. Studies in the History of Natural Sciences, 2020, 39(4): 395-424.

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http://www.shns.ac.cn/     OR     http://www.shns.ac.cn/Y2020/V39/I4/395

1 钱宝琮. 汉均输法考[J]. 文理, 1933,(4): 45～46.
2 宋杰. 《九章算术》与汉代社会经济[M]. 北京: 首都师范大学出版社, 1994. 184～185.
3 胡平生. 阜阳双古堆数术书简论[C]//出土文献研究. 第4辑. 北京: 中华书局, 1998. 12～30.
4 杜石然. 张家山汉简《算数书》初探[J]. 自然科学史研究, 1988, 7(3): 201～204.
5 郭书春. 古代世界数学泰斗刘徽[M]. 济南: 山东科学技术出版社, 1992. 87～90, 100～101, 303.
6 郭书春. 关于《九章算术》的编纂[C]// 陈美东,林文照,周嘉华.中国科学技术史国际学术讨论会论文集.北京:中国科学技术出版社,1992.52～56.
7 郭书春. 张苍与《九章算术》[C]//科史薪传——庆祝杜石然先生从事科学史研究40周年学术论文集. 沈阳: 辽宁教育出版社, 1997. 112～121.
8 李迪. 中国数学通史 上古到五代卷[M]. 南京: 江苏教育出版社, 1997. 96.
9 邹大海. 中国数学的兴起与先秦数学[M]. 石家庄: 河北科学技术出版社, 2001. 146～152, 451.
10 邹大海. 出土《算数书》初探[J]. 自然科学史研究, 2001, 20(3): 193～205.
11 邹大海. 睡虎地秦简与先秦数学[J]. 考古, 2005,(6): 57～65.
12 邹大海. 从出土竹简看中国早期委输算题及其社会背景[J]. 湖南大学学报(社会科学版), 2010, 24(4): 5～10.
13 钱宝琮. 中国数学史[M]. 北京: 科学出版社, 1982. 32, 34.
14 李俨. 中国数学大纲(修订本)[M]. 上册. 北京: 科学出版社, 1958. 27.
15 陈直. 九章算术著作的年代[J]. 西北大学学报(自然科学版), 1957,(1): 95～97.
16 司马迁. 史记[M]. 第4册. 北京: 中华书局, 1982. 1441.
17 班固. 汉书[M]. 第3册. 北京: 中华书局, 1964. 731.
18 邹大海. 秦汉量制与《九章算术》成书年代新探——基于文物考古材料的研究[J]. 自然科学史研究, 2017, 36(3): 293～315.
19 李迪. 江陵张家山西汉墓墓主是谁？[C]//数学史研究文集. 第4辑. 呼和浩特: 内蒙古大学出版社, 台北: 九章出版社, 1993. 5～9.
20 陈耀钧, 阎频. 江陵张家山汉墓的年代及相关问题[J]. 考古, 1985,(12): 1124～1129.
21 李俨. 中国古代数学史料[M]. 第2版. 上海: 上海科学技术出版社, 1963. 104.
22 李继闵. 东方数学典籍《九章算术》及其刘徽注研究[M]. 西安: 陕西人民教育出版社, 1990. 167.
23 李继闵. 九章算术校正[M]. 西安: 陕西科学技术出版社, 1993. 365, 367～368.
24 刘钝. 大哉言数[M]. 沈阳: 辽宁教育出版社, 1996. 165, 167.
25 郭书春. 九章筭术新校[M]. 合肥: 中国科学技术大学出版社, 2014. 217～218.
26 邹大海. 从出土简牍文献看中国早期的正负数概念[J]. 考古学报, 2010,(4): 481～504.
27 王孝通. 缉古算经[M]. 郭书春, 校点//算经十书. 台北: 九章出版社, 2001. 417.
28 王利器. 盐铁论校注(定本)[M]. 北京: 中华书局, 1992. 1～5.
29 国语[M]. 上海师范大学古籍研究所, 校点. 上海: 上海古籍出版社, 1990. 218.
30 张家山二四七号汉墓竹简整理小组. 张家山汉墓竹简[二四七号墓](释文修订本)[M]. 北京: 文物出版社, 2006. 64.
31 李冠廷, 游逸飞. 张家山汉简《二年律令·均输律》译注[J]. 史原(复刊), 2011,(2): 239～256.
32 李步嘉. 越绝书校释[M]. 武汉: 武汉大学出版社, 1992. 35.
33 陈松长. 岳麓书院藏秦简(肆)[M]. 上海: 上海辞书出版社, 2015. 42.
34 徐连达. 中国官制大辞典[M]. 上海: 上海大学出版社, 2010. 102, 452, 442.
35 孙楷. 秦会要[M]. 杨善群, 校补. 上海: 上海古籍出版社, 2004. 247～248, 252～257.
36 邹大海. 从出土文献看上古医事制度与正负数概念[J]. 中国历史文物, 2010,(5): 69～76.
37 陈松长. 岳麓书院藏秦简中的徭律例说[C]//中国文化遗产研究院. 出土文献研究. 第11辑. 北京: 中西书局, 2012. 162～166.
38 辛德勇. 北京大学藏秦水陆里程简册的性质和拟名问题[C]//简帛. 第8辑. 上海: 上海古籍出版社, 2013. 17～27.
39 萧灿. 岳麓书院藏秦简《数》研究[M]. 北京: 中国社会科学出版社, 2015. 95.
40 邹大海. 从《算数书》与《九章算术》的关系看算法式数学文献在上古时代的流传[J]. 赣南师范学院学报, 2004,(6): 6～10.
41 邹大海. 简牍文献与中国数学史[M]//中国科学技术通史 I 源远流长. 上海: 上海交通大学出版社, 2015. 191～230.
42 Chemla K, Zou D. Parts in Chinese Mathematical Texts. Interpreting the Chapter Form of The Nine Mathematical Procedures[M]//Florence Bretelle-Establet, Stéphane Schmitt Eds, Pieces and Parts in Scientific Texts. Cham: Springer International Publishing AG, part of Springer Nature, 2018. 91～133.
43 邹大海.从岳麓书院藏秦简《数》看上古时代盈不足问题的发展[J].内蒙古师范大学学报(自然科学汉文版),2019,48(6):504～515.
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