The earliest extant mathematical books from China contain a lot of problems and data about grains. They also betray a close relationship with imperial bureaucracy in this respect. Indeed, these texts quote administrative regulations about grains. For instance, the Book on mathematical procedures cae center dot ae >, found in a tomb sealed ca. 186 BCE, has a section in common with the "regulations on granaries" from the Qin statutes in eighteen domains, known thanks to slips excavated at Shuihudi. Mathematical writings also deal with official vessels used to measure grains. They cast light on statements from, and practices evidenced by, official histories and administrative documents. This article addresses the following issues. Which information about the concrete management of grains can we derive from mathematical writings in relation to administrative documents? Which data can we find in these writings about continuities and changes in the management of grains in the time span between the Qin and Han dynasties? In particular, how can we account for the fact that in a later mathematical text, namely, The Nine Chapters, probably completed in the first century CE, there was a change in the form in which the data about grain equivalences were given, by comparison with the "regulations on granaries"? Finally, what do our conclusions imply with respect to the nature of the earliest extant mathematical writings. In this article, we gather the various types of statement that mathematical writings contain about grains and offer several elements of interpretation for the "regulations on granaries" and the related text in The Nine Chapters. From this perspective, we offer several hypotheses about the management of grain in the Qin and Han dynasties.
展开▼
机译：中国现存的最早的数学书籍包含许多关于谷物的问题和数据。在这方面，他们还背叛了与帝国官僚机构的密切关系。实际上，这些文本引用了有关谷物的行政法规。例如，《数学程序手册》中的“ cae center dot ae>”（约中点ae>）出现在一个密封的坟墓中。公元前186年，在十八个领域中与秦法规中的“粮仓规定”有一个共同的部分，这要归功于在水户slip发掘出的泥石。数学著作还涉及用于测量谷物的官方船只。他们对官方历史和行政文件中的陈述和实践作了说明。本文解决以下问题。我们可以从有关行政文件的数学著作中获得哪些有关谷物具体管理的信息？我们可以在这些著作中找到哪些数据说明秦汉时期之间谷物管理的连续性和变化？尤其是，我们如何解释一个事实，即在后来的数学教科书《九章》中，大概在公元一世纪完成了该书，通过比较，给出了谷物当量数据的形式发生了变化。与“粮仓规定”有关？最后，关于现存最早的数学著作的性质，我们的结论意味着什么。在本文中，我们收集了数学著作所包含的关于谷物的各种类型的陈述，并为“粮仓规定”和“第九章”中的相关文本提供了几种解释要素。从这个角度出发，我们提供了关于秦汉时期谷物管理的几种假设。
展开▼
