On Qin Jiushao’s writing system

The Mathematical Book in Nine Chapters, written by Qin Jiushao in 1247, is a masterpiece that is representative of Chinese mathematics at that time. Most of the previous studies have focused on its mathematical achievements, while few works have addressed the counting diagrams that Qin used as a writing system. Based on a seventeenth-century copy of Qin’s treatise (i.e., Zhao Qimei’s 1616 handwritten copy), this paper systematically analyzes the writing system, which includes both a numeral system and a linear system. It argues that Qin provided a new representation of mathematics in addition to textual procedures, detailed solutions, and operations carried out with counting rods. Moreover, this new representation was used to connect mathematical practices within and outside the text and should be understood in its textual context. Therefore, Qin’s writing system represents an intermediate phase in the textualization and symbolization of Chinese mathematics in thirteenth-century China.