几何命题的衍变推广

TRANSFORMATIONAL EXTENSION OF GEOMETRICAL PROBLEMS

欧氏几何是仿射几何的子几何,但就内容而言,欧氏几何远比仿射几何丰富,在本文中,将欧氏几何中与圆有关的七个命题,利用仿射变换将圆映射为常态二次曲线,从而衍变推广为仿射几何的命题,以丰富仿射几何的内容。

Euclidean geometry is a subgeometry of affie geometry. But if we use an affine transformation on a circle, we can obtain a conic to make aff'me geometry more abundant. Seven examples are given here.