On the First Printed Edition of Mathematical Book in Nine Chapters (1842)

Mathematical Book in Nine Chapters (Shushu Jiuzhang, hereafter Mathematical Book), completed by Qin Jiushao (1208–1268) in 1247, was one of the representative mathematical works in thirteenth-century China. Previous scholarly studies heavily rely on the first printed edition of Mathematical Book (Yijiatang edition) that was published in Yijiatang Collectanea in 1842. However, our recent research shows that a seventeenth century manuscript of Mathematical Book (Zhao Qimei’s manuscript, 1616) contains very important pieces of information on the use of counting rods, which were not reproduced in the first printed edition. This chapter aims to revisit the formation of the 1842 edition, and evaluate its influence on the subsequent historiography of mathematics. Firstly, we introduce the textual history of Mathematical Book before 1800, the scholarly background in the Qian-Jia Period (1736–1820), and Yu Songnian’s and Song Jingchang’s contributions to the Yijiatang Collectanea and the first printed edition. Secondly, we analyze the writing system and three representations of the Chinese Remainder Theorem in the 1616 manuscript, highlighting the difference between the 1616 manuscript and the 1842 printed edition: the key type of representation using lines and diagrams for the operational procedures of counting rods was lost in the printed edition. Finally, the reception of Mathematical Book in the nineteenth century is discussed. We show the influence of the printed edition, we also point out that, in this context, scholars were specifically interested in interpreting ancient mathematics using modern mathematics. In conclusion, we argue that the first printed edition of Mathematical Book exerted a strong influence in shaping the image of the book in the historiography.