刘徽的无限思想及其解释

LIU HUI'S IDEAS OF INFINITY AND THEIR EXPLANATIONS

该文包括两方面的内容。一是从无限分割过程、不可分量可积性、有限过程等几个方面重新考察了刘徽的无限思想，力图澄清此课题的研究中存在的若干误解。二是从中国古代数学传统，刘徽的思想渊源特别是他受墨家、道家和玄学思想的影响等方面，对刘徽利用无限思想处理问题的方式进行解释。

This paper discusses Liu Hut's ideas of infinity in the light of the infinite process,the integrability of indivisibles,and the finite process,and tries to correct some misunderstandings in the study of Liu Hut'S ideas of infinity.Analysing the influences of the tradition of ancient Chinese mathematics, and of ancient Chinese philosophy,especially those of the Mohist School,the Theory of Tao and Wang Bi'S philosophy on Liu Hui,the author explains the heuristics with which Liu Hut employed his ideas of infinity to solve differentkinds of problems.