Menelaus定理與Ceva定理的綜合推廣

摘要：主要利用定比分點(diǎn)坐標(biāo)的一個(gè)結(jié)論，將梅涅勞斯定理和塞瓦定理?xiàng)l件中的三角形拓廣為空間閉折線、二次曲面，得到一些比式乘積為1的結(jié)論，還將條件中的直線拓寬為二次曲線、二次曲面，三角形拓廣為空間閉折線,也得出類似的結(jié)論。在仿射平面內(nèi)，引入無窮遠(yuǎn)元素，利用單比，分別將兩個(gè)定理的幾種形式統(tǒng)一起來，在射影平面內(nèi)，利用交比推廣了這兩個(gè)定理，得到了在射影幾何中的證明共點(diǎn)線或共線點(diǎn)的有力工具。
關(guān)鍵詞：Menelaus定理；Ceva定理；二次曲線；二次曲面；定比分點(diǎn)；閉折線；

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.