定义　设四面体 A1A2 A3 A4的外心为 O,外接球面的半径为 R,若点 E满足OE =12 ∑4i=1OAi (* )则以点 E为球心、R2 为半径的球面 ,称为四面体A1A2 A3 A4的欧拉球面 .根据这个定义 ,我们可以推得定理　四面体 A1A2 A3 A4的欧拉球心 E与任一条棱的中点的连线 ,必垂直对棱 .(图略 ) The definition is to set the center of the tetrahedron A1A2 A3 A4 to O, and the radius of the circumscribed sphere to R. If the point E satisfies OE =12 ∑4i=1OAi (*), point E is the sphere center and R2 is the radius sphere, which is called The Euler sphere of the tetrahedron A1A2 A3 A4. According to this definition, we can deduce that the line connecting the Euler spherical center E of the theorem tetrahedron A1A2 A3 A4 with the midpoint of any of the edges must be perpendicular to the edge. (Slightly omitted)