从《算数书》与《九章算术》的关系看算法式数学文献在上古时代的流传

The Spread of Literatures on Algorithmic-pattern Mathematics in Early Ancient China:A Research Based on the Investigation of the Relation between the Suanshu Shu and the Nine Chapters on Mathematical Procedures

证明出土《算数书》不是中国最早的数学著作,它与今传汉代编定的《九章算术》之间没有直接的影响关系。《九章》的先秦祖本或其衍生本是《算数书》各部分作者学习的对象.上古算法式数学文献分为经典和非经典两个系统,经典文献的流传可以简单表示为西周初年"九数"———调整和发展中的"九数"———调整和发展中的《九章算术》祖本———《九章算术》,它代表着当时算法式数学的发展水平和基本框架;非经典文献包括各种受经典文献直接或间接影响的数学著作,它又可大致分为专业型和应用型两类.两个系统的文献互相影响,而以前者影响后者居多.后者对前者的影响中,又以专业型文献的影响力为大.

.The paper demonstrates: The unearthed Suanshu Shu is not the earliest book of mathematics in China, and has no direct mutual influence with the Nine Chapters on Mathematical Procedures. The forerunners of Nine Chapters in the Pre-Qin Period or its variations were learned by the writers of different parts of the Suanshu Shu. The early ancient Chinese literatures of the algorithmic-pattern Mathematics can be classified into two groups: the classics and the non-classics. The spread of the former can be simply expressed as.'Jiu Shu' (nine branches of mathematics) of the early days of Western Zhou Dynasty—the developing'Jiu Shu'—the developing forerunners of the Nine Chapters—Nine Chapters, which mark the levels and fundamental framework of mathematics of their times. The non-classics were written under the direct or indirect influence of the classics, and can be approximately classified into two patterns: the professional and the practical. The two groups interacted each other, but the classics' impact on the non-classics is more than the non-classics' impact on the classics. Of the non-classics' impacts on the classics, the impact of the professional literatures is more than that of the practical.