HOW DO EXCAVATED MANUSCRIPTS AND TRANSMITTED CANONS AND COMMENTARIES SHED LIGHT ON EACH OTHER? AN OUTLOOK FROM MATHEMATICS

Abstract Before the mathematical manuscript titled Writings on Mathematical Procedures (Suanshu shu 筭數書) was found at Zhangjiashan, historians of mathematics could trace mathematics in early imperial China only on the basis of the received canonical literature, notably The Nine Chapters on Mathematical Procedures (Jiuzhang suanshu 九章算術). After the Zhangjiashan and other mathematical manuscripts were found, they were mainly compared with The Nine Chapters, in the belief that these were all early imperial mathematical works and therefore adequate objects of comparison. As such, The Nine Chapters was transmitted with layers of commentaries and subcommentaries. This article argues that Writings on Mathematical Procedures presents important parallels with the commentarial literature on The Nine Chapters. This sheds light on how such exegeses were composed. The article further demonstrates that examination of these commentaries and subcommentaries allows us to perceive parallels between Writings on Mathematical Procedures and The Nine Chapters that to date have not been considered.