《射影几何》中仿射性质证明错误的纠正

The correction of the proof of affine property in the textbook related to projective geometry

《射影几何》中关于仿射性质有一个重要结论"两个三角形面积之比是仿射不变量",一些教材中关于该结论的证明存在错误。本文用坐标系转换的方法,纠正了错误证明,给出了详细的证明过程,旨在教授学生正确的证明方法,引导学生采用合理的类比思维。

Errors about the proof of an important conclusion that two triangular area ratio is affine invariant exist in some textbooks of introduction to Geometry. Aimed to teach the proper method of proof and to guide to apply reasonable analogy-thinking, errors in one of these books are corrected by means of reproving the core property of the affine transformation with the method of coordinate transformation.