非退化二次曲线一个定理的解析证明

On Analytic Proof of a Theorem About Nondegenerate Second-order Curve

分别在射影平面上以及在欧氏平面上利用笛卡儿直角坐标系(以圆为例)对非退化二阶曲线到自身的双射成为对合的一个充要条件定理的推论进行了解析证明。这个定理和推论将极线、巴斯加线、透视轴等相应理论联系了起来,便于将射影几何中的结论应用于解析几何和初等几何。

Analysed and proved is the corollary of the theorem of a necessary and sufficient condition for nondegererate secondorder curve biprojected by itself to involution by using rectangular (artesian coordinate system c with circle as its example) at the progective plane and euclidean plane respectively.This theorem and its corollary link with the theories of corresponding polar and pascal lines and perspective axis.The conclusion of projective geometry can be applied to analytic and elementary geometries.