中古算书中的田地面积算法与土地制度——以《五曹算经》"田曹"卷为中心的考察

关注了前人少有深入探究的一些中古实用算书的特点和相关社会制度背景.通过对有关社会经济史料和算书中的田地面积算题进行纵向和横向的比较与细密的分析,指出<五曹算经>中"田曹"的面积计算法具有求多而不求精的特点,与北朝田制特别是均田制下出现频繁测量、分划田地的急切需要有着密切的关系,<敦煌算书>、<夏侯阳算经>等书中田地面积计算法的特点,不仅与均田制的盛衰,而且与整个社会的文化和数学的发展有关,其中后者还带有编者讲求学理和精简的意图.社会因素不仅可以影响到数学讨论的对象,还可以影响到数学知识的本身.

Methods of Area Calculation in the Mathematical Books and the Land System of Mid-Ancient China

By comparing the problems concerning area calculation among several mathematics book with each other and analyzing the land policies in the Mid-Ancient Period, this article points out that the Wucao Suanjing seeks extensiveness more than accuracy in the methods of area calculation , and this characteristic is closely related to the Equal Field System (Juntian System), which made the fields to be frequently measured and frequently divided into smaller ones as well. These methods became more exact and classified in such subsequent mathematical books as Dunhuang Suanjing and Xiahou Yang Suanjing. When the latter book was compiled, the Equal Field System had declined. The article indicates that social elements can influence not only the objects dealt with mathematics, but also influence the expression of the mathematical texts.