儒学经典中的数学知识初探——以贾公彦对《周礼·考工记》“■氏为量”的注疏为例

Preliminary Research on Mathematical Knowledge in the Confucian Classics: The Case of Jia Gongyan's Commentary on the Rites of Zhou

通过分析唐代学者贾公彦对《周礼·考工记》"■氏为量"的注疏,揭示出其数学知识与以《九章筭术》为代表的传统数学不尽相同。其不同之处体现在贾氏算法的结构、对数和图形的认识、推理的方式以及对于算筹的运用等方面。由于这些特色在贾氏其他注疏以及初唐诸儒编订的《五经正义》中亦有体现,说明其具有一般性。此外,与贾公彦一同注释儒学经典的王真儒,稍后也与李淳风等一同注释了十部算经,这一事实揭示了儒学与数学关系的复杂性。对于儒学经典中的数学知识,有必要进一步深入系统研究。

By analysing an excerpt from Jia Gongyan＇s commentary on the Rites of Zhou, this paper uncovers mathematical knowledge different to that previously known from Chinese mathematical sources, for example the Nine Chapters on Mathematical Procedures. The differences cover several as- pects： the structure of procedures, cognition of numbers and figures, modes of reasoning, and the use of counting rods. On the other hand, similar mathematical knowledge to that of Jia Gongyan exists in other Confucian canons. Moreover, a scholar, Wang Zhenru, commented on Confucian canons with Jia Gongyan, and later commented on mathematical books with Li Chunfeng. This paper empha- sizes the necessity for further study of the mathematical knowledge in Confucian canons, and the relationship between Confucianism and mathematics.