menelaus定理与ceva定理的综合推广.doc

Menelaus定理与Ceva定理的综合推广

摘要：主要利用定比分点坐标的一个结论，将梅涅劳斯定理和塞瓦定理条件中的三角形拓广为空间闭折线、二次曲面，得到一些比式乘积为1的结论，还将条件中的直线拓宽为二次曲线、二次曲面，三角形拓广为空间闭折线,也得出类似的结论。在仿射平面内，引入无穷远元素，利用单比，分别将两个定理的几种形式统一起来，在射影平面内，利用交比推广了这两个定理，得到了在射影几何中的证明共点线或共线点的有力工具。
关键词：Menelaus定理；Ceva定理；二次曲线；二次曲面；定比分点；闭折线；

Menelaus theorem and Ceva theorem integrated promotion

Abstract : The main point of using the coordinates of the match to a conclusion, will Menelaus theorem and Ceva's Theorem for the triangular space for Extension of closing dogleg, the second surface, - some more than a product of the conclusions, but also the conditions for the linear quadratic curve widening, the second surface, Extension of the triangular space closing dogleg, and came to similar conclusions. Affine plane, the introduction of infinite elements, single-use ratio, respectively, the two theorems of several forms of unification, in the projective plane, the cross-promotion than the two theorems been in projective geometry of the total proven point line or total points are powerful tools.
Keywords : Menelaus theorem ;Ceva theorem; Quadratic curve; Conicoid; Set match point; Closing dogleg.