从欧几里得《几何原本》谈公理化思想

On Axiomatization Thought from The Elements of Euclid

欧几里得是古希腊最负盛名的数学家.《几何原本》是欧几里得集古希腊人的几何成就与个人创造于一体的不朽之作.欧几里得采用公理化思想,即把几何直觉与逻辑推理相结合的论证方法,创造性地建立起了欧几里得几何学,被认为是古典公理化思想的成功典范.二千多年来,《几何原本》是传播几何、数学的经典著作.介绍欧几里得公理化体系的形成过程和《几何原本》的五个公理、五个公设,对比我国初等数学的公理化体系,阐述欧几里得的公理化体系对我们的影响和贡献.

Euclid was the most famous mathematician in ancient Greek,and The Elements of Euclid was an immortal piece of work integrating ancient Greek’s geometry achievements and Euclid’s own creation. Euclid crertively built Euclid Geometry,which was regarded as a classical axiomatization Thought’s successful model,known as a method which combines geometry intuition with logical reasoning. The Elements of Euclid,the classical piece of work,has been diffusing geometry and mathematics since 2000 years ago. This paper refers to the formation process of Euclid’s axiomatization system and 5 axioms,5 postulates in The Elements of Euclid,contrasting elementary mathematics’ s axiomatization thought system in China,and also explaining the influence and contribution of Euclid’s axiomatization system.