关于Pappus定理和Pascal定理的透视问题

About Perspective in the Pappus Theorem and Pascal Theorem

Pappus定理和Pascal定理分别是退化和非退化二阶曲线中关于三点共线的重要定理 ,应用广泛。笔者主要介绍常见资料均未提及的关于Pascal定理中的透视问题 ,文中将在Pappus定理中的三双对应点成透视的充要条件 ,这样一个定理的基础上 ,介绍借助于由两三点形成透视的概念得出的Pascal定理的一个相应定理。

The Pappus theorem and Pascal theorem are the important theorems of three points colinearity of degenerate and non degenerate two stage curves respectively.Thye′re widely used.This article mainly introduces the perspective issue of Pascal Theorem which is not mentioned in many other materials.It also presents a relative theorem resulted from the concept of forming perspectivism by two triangles,which is on the basis of the full condition that three pairs of corresponding points form perspectioism in Pappus Theorem.It draws a full condition of the coincidence of the Pascal line and perspective axis of two perspective triangles whose vertexes are on the non degenerate two stage curves.