兰伯特的几何学思想探析

On Lambert’s Geometrical Thoughts

德国数学家兰伯特在《平行线理论》中通过类比球面提出锐角假设在虚半径球面上成立,这一思想成为后来数学家建立和发展非欧几何的关键。兰伯特在对公理和定义的讨论中体现的几何哲学,使得他证明平行公设时回避了困扰前人的几何直观。他在同时期的数学工作中将圆函数和双曲函数类比,反映出其虚半径球面类比思想的来源和应用。

German mathematician Lambert proposed that the hypothesis of acute is established on the imaginary radius sphere.This idea,which plays a crucial role in the establishment and development of non-Euclidean geometry,was on the analogy of sphere.Lambert’s geometrical philosophy embodied in the discussion of axioms and definitions made him avoid the geometric intuition that plagued his predecessors when he proved the parallel postulate.His analogy thought between the circular function and the hyperbolic function in his cotemporaneous mathematics work,reflecting the origin and application of the analogy thought of the imaginary sphere.