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The trigonometric table and its construction principles were introduced to China as part of calendar reform, spear-headed by Xu Guangqi (1562-1633) in the late 1620s to early 1630s. Chinese scholars attempted and succeeded in uncovering how the construction principles were established in the seventeenth century and then in the eighteenth century expanded to include more algorithms to compute the values of trigonometric lines. Successful as they were in discoursing the construction principles, most Chinese scholars did not actually construct trigonometric tables anew. In the early nineteenth century, a revolutionary approach was developed, which resembles computing a finite sum of power series to trigonometric functions of an arbitrary arc less than a one-half circle. Though hailed by many modern historians as Chinese achievements in developing 'infinite series' of trigonometric functions, this approach was viewed by the actors at the time as a quick means to construct trigonometric tables. Interestingly, even with these 'quick' methods, no trigonometric table was constructed. Besides the fact that constructing a trigonometric table afresh is a time-consuming business, the classification of the trigonometric table and their construction principles into different genres of knowledge by scholars offers an additional explanation of drastically uneven treatment of trigonometric tables and their construction principles. [ABSTRACT FROM AUTHOR]

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 筭數書, 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. [ABSTRACT FROM AUTHOR]