几何中有所谓欧拉定理:三角形的垂心、重心、外心共线,并且重心把连结垂心和外心的线段分成2:1.本文给出欧拉定理的一种推广.定理1 设 D、E、F 分别是△ABC 的三边 BC、CA、AB 的中点,G 是重心,P 是平面上任一点,过 D、E、F 分别作 AP、BP、CP 的平行线,那么:(1)三条平行线交于一点 P′;(2)P′、G、P 三点共线;(3)P′G=(1/2)PG. There is the so-called Euler’s theorem in geometry: the triangle’s vertical center of gravity, center of gravity, and outer core collinearity, and the center of gravity divides the line segment linking the vertical center and the outer heart into 2:1. This paper gives a generalization of Euler’s theorem. Theorem 1 Let D, E and F are the mid points of three sides BC, CA, and AB of △ABC, G is the center of gravity, P is any point on the plane, and D, E, and F are the parallel lines of AP, BP, and CP, respectively. Then: (1 ) Three parallel lines intersect at one point P’; (2) P’, G, P three points collinear; (3) P’G = (1/2) PG.