从《墨子》看先秦时期的几何知识

Geometrical Knowledge of Pre-Qin Period:A View Based on the Study of Mo Zi

利用《墨子》考察先秦的几何学知识不仅对研究中国早期数学史而且对了解中国思想和文化初成期的面貌有着重要的意义。文章首先分析了《墨子》中有关文献所蕴涵的几何学观念和知识,指出它们的范围、性质和特点以及在墨家整个知识系统中的位置。然后利用这些结果和有关名家的文献及上古时代的数学文献等相参照,分析当时存在的几何学知识及其基本性质和特征,并说明当时发展出相互关联的两类几何知识——注重实际应用的算法式几何知识和注重概念及其关系的理论性几何知识。后一类知识为认识古人如何从经验知识发展出抽象化、理论化的几何学提供了样本。先秦数学的多元化,与当时社会的激烈变革、思想解放、百家争鸣的大环境密切相关,是先秦学术和思想繁荣的重要组成部分。

The investigation on the geometrical knowledge of Pre-Qin China by making use of Mo Zi is significant not only for the study on the history of mathematics in early China but also for the understanding of the early stage of the forming of Chinese thought and culture. This paper analyzes the geometrical notions and knowledge in the relevant documents of Mo Zi, points out their range, nature and characteristics, and position in the system of Mohist knowledge. By comparing the results with relevant documents especially of the School of Logicians and ancient mathematics, the paper analyzes the geometrical knowledge of Pre-Qin China and its nature and characteristics, and shows that Chinese developed two interactive categories of geometrical knowledge ： the geometrical algorithms focusing on practical problems, and the theoretical knowledge of geometry focusing on the concepts and their relations. The latter category provides a sample for us to study how ancient people developed abstract and theoretical geometry from empirical knowledge. The diversification of Pre-Qin mathematics, which is closely related to the Pre-Qin background of social revolution, ideology emancipation, contention of various schools of thought, is an important component part of the prosperity of Pre-Qin learning and thoughts.