内接于二阶曲线的完全六点形对边点共线的充要条件

The Sufficient and Essential Condition of Collinearity of Diagonal Points of a Complete Six-Point Shape Inscribed in the Curve of Second Order

在Pascal定理中,若二阶曲线退化为两条直线时,Pascal定理就变为Pappus定理.同样地,若定理“对于任意一个内接于非退化二阶曲线的完全六点形,它的6对对边的交点共线的充要条件是3对对顶点的连线共点”中的二阶曲线也退化为两条直线时,此定理就变为另一定理——“Pappus线过两底交点的充要条件是两点列对应点的连线共点”.

Pascal theorem turns into Pappus theorem when the curve of second order is degenerated into two straight lines.Similarly,in the theorem of 'for any complete six-point shape inscribed in the curve of second order,the intersection points of its six pairs of opposite sides become collinear if and only if the connecting lines of the three pairs of opposite vertexes are concurrent',if the curve of second order is degenerated into two straight lines,then this theorem turns into another theorem-'the Pappus line passes through the intersection point of two bottom sides if and only if the connecting lines of the corresponding points of two tiers are concurrent.'