A Study on the Mathematical Treatise: The Third Manuscript on Qin Bamboo Slips Preserved at Peking University

The recently published Qin bamboo manuscripts preserved at Peking University include three previously unknown mathematical works, one of which is the Mathematical Treatise: The Third Manuscript (Suanshu bingzhong 算书丙种), a work of moderate length that needs to be studied systematically. This paper provides a comprehensive analysis of the work, focusing on its structure, compilation features, types of knowledge and mathematical methods, as well as its related context. It points out that this manuscript is a copy rather than an original draft. The work is characterized by an algorithm-centric approach. The compiler had more consideration about the system of the book, but not thoughtful enough. Furthermore, this manuscript provides new evidence for Liu Hui's account that the Nine Chapters on Mathematical Procedures (Jiuzhang suanshu 九章算术) has its pre-Qin ancestors, and offers sources and justifications for understanding the types of mathematical knowledge beyond the scope of the Nine Chapters, thereby enriching our understanding of early Chinese mathematics and the society and economy of that time.