用射影几何方法探讨Desargues逆命题

On the converse proposition of Desargues with projective geometry

藉助射影几何的理论通过将直线投影到无穷远,由两相交直线投影成二平行直线及任意四边形投影成平行四边形的引入,首先给出了Desargues逆命题在平面域内的证明,然后用射影几何方法构造了一个辅助三点形,最终导致了该逆命题在空间域内的证明.

At first,with the theory of projective geometry,by means of projecting straight line onto infinite distance and introducing the projection of two intersecting lines onto two parallel lines as well as arbitrary quadrangle onto parallelogram,the converse proposition of Desargues within the plane area is proved.Then an auxiliary threepoint shape is made up by using the method of projective geometry.Finally the result of testifying the converse proposition of Desargues within the space is obtained.