连续性是高等数学中极其重要的概念,为数学分析的基础。自从戴德金(Dedekind)建立了实数连续的理论以来,它在分析学中起的作用久已为大家所重视。但是这个概念对于初等几何学是不是有用处呢?从高等数学应该指导初等数学的观点来看,是不是平面几何中有一些基本问题,它的解决过程中一定要用到连续的概念呢?在这篇短文里,笔者想用两个例子说明连续概念在初等几何中的重要性。这两个问题几何学中一般称之为圆规命题,命题如下: Continuity is an extremely important concept in higher mathematics and is the basis of mathematical analysis. Since Dedekind established the theory of continuous real numbers, its role in analytics has long been valued by everyone. But is this concept useful for elementary geometry? From the viewpoint that higher mathematics should guide elementary mathematics, is there some basic problem in plane geometry, and it must use continuous concepts in its solution? In this short essay, I want to illustrate two examples of the importance of the concept of continuity in elementary geometry. In these two problem geometries, generally known as the compass proposition, the propositions are as follows: