中国上古时代数学门类均输新探  

New Research on the Junshu,a Branch of Mathematicsin the Early Period of Ancient China

作　　者：邹大海[1] ZOU Dahai(Institute for the History of Natural Sciences,CAS,Beijing 100190,China)

机构地区：[1]中国科学院自然科学史研究所,北京100190

出　　处：《自然科学史研究》2020年第4期395-424,共30页Studies in The History of Natural Sciences

基　　金：中国科学院自然科学史研究所重大项目“科技知识的创造与传播”子课题“出土简牍与秦汉数学史”。

摘　　要：均输是中国古代数学的一个重要门类,数学经典《九章算术》专设第6章讨论它。前人对其渊源和它与作为经济政策的均输之关系,都多有未及或存在若干问题。文章利用更为丰富的考古文献和传世文献,对中国上古时代均输的发展进行较为系统深入的研究。文章对《九章算术》“均输”章算题的特征进行了新的概括,指出“均输”的含义比前人理解的公平负担要宽泛,“均输”章的构成具有高度的一致性,算题的列入是编者刻意为之,而非随意安排。文章证明,不论是数学上的两类均输算题还是经济上的两种均输都有先秦及秦代的渊源,现存《九章算术》“均输”章的5个均输算题和睡虎地汉简《算术》中的一个均输算题虽然都定型于西汉,但在先秦及秦代应该已有其蓝本。岳麓书院藏秦简《数》和张家山汉简《算数书》证明,“均输”章后24题中有一部分在战国到西汉初期就很可能存在,不必等到公元前1世纪由耿寿昌补入。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

关 键 词：均输 《九章算术》 秦汉法律简牍 《盐铁论》 岳麓书院藏秦 简《数》 张家山汉简《算数书》 睡虎地汉简《算术》 

分 类 号：N092[自然科学总论—科学技术哲学]