过四点的二次曲线系调和分割x和f(x)

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mathworld.wolfram.com/Isoconjugation.html
maths.gla.ac.uk/wws/cabripages/triangle/ninep … nt/isoconjugates.htm
bernard-gibert.fr/gloss/isoconjugation.html
maths.gla.ac.uk/wws/cabripages/triangle/ninepoint/nkharmonic.htm
$L_1$是过△ABC的内心$I$,旁心$I_1,I_2,I_3$的二次曲线，P,Q是一对等角共轭点，证明：P关于$L_1$的极线过Q.

易知不包括边的等角共轭变换$f$是对合，所以过$f$的不动点$I,I_1,I_2,I_3$的二次曲线调和分割x和f(x)