试论刘徽的数学理论体系

On Liu Hui's System of Mathematical Theory

魏景元四年(263年)刘徽注《九章算术》,它与《九章算书》成书一样,是中国数学史上划时代的大事。从《九章算术》到刘徽注,标志着中国古代数学理论体系的形成。为了说明这个问题,首先要回顾一下《九章算术》的风格和特点。《九章算术》分方田、粟米、衰分、少广、商功、均输、盈不足、方程和勾股九部分,包括近百年基本公式和解法,其中有许多世界意义的成就,全国概括了东汉初年以前中国数学的主要内容和成就,基本上奠定了中国古代数学的框架。

Liu Hui's Notes (263) on Jiu Zhang Suan Shu is an epoch-making event in China's mathematical history.While the aforeementioned work decided the framwork,form and characteristics of the ancient Chinese mathematics,the Notes constitutes a great enrichment and generalization of the work.The generalization is scattered throughout the Notes which.if taken as a whole,manifests some sorts of systematical and logical coherence existng in Liu Hui's mathematical theory.Besides,his logic is based on deductive logic.However,this does not necessarly mean that Liu Hui formulated a deductive system or axiomatical system.Further study is needed on the difference between his method and Euclidean system in terms of superiority or inferiority.