The Nine Chapters on Mathematical Procedures is the most important classic of mathematics in China. More than a decade ago, historians of mathematics paid attention to its social background but could not obtain very significant conclusions because of lacking believable materials with definite dates. The documents on bamboo strips unearthed from ancient tombs since the middle of 1970’s provide us an opportunity to investigate this subject by convincing arguments. This paper will focus on social background of the problems related to foodstuffs in the Nine Chapters.

These problems share the same ratios given in the list titled “rule for exchanges of foodstuffs and treated foodstuffs” at the beginning of the Chapter 2. The paper paid much attention to the relation between mathematics and law of Early China. It compares them with the Shu (Mathematics) on the bamboo strips of Qin Dynasty preserved in Yuelu Academy of Hu’nan University, the Suanshushu (book of mathematics), as well as the documents of laws on the bamboo strips of Qin and Western Han Dynasties, especially those unearthed from Shuihudi and Zhangjiashan, and finds that most ratios are the same in different documents. The author concludes that the ratios are based on the regulations of the government departments of Qin State or Qin Dynasty, and the problems were formed to meet the need of strict administration of the government and thus they primarily originated from the Qin State during Pre-Qin Period. In the meantime, a few differences among different sources show that these problems were slightly changed in the process when the Nine Chapters was transmitted and reedited during Qin and Han Dynasties.