Projective harmonic conjugate

（重定向自Harmonic division）

D is the harmonic conjugate of C w.r.t. A and B.A, D, B, C form a harmonic range.KLMN is a complete quadrangle generating it.

Midpoint and infinity are harmonic conjugates.

In projective geometry, the harmonic conjugate point of an ordered triple of points on the real projective line is defined by the following construction:

The point D does not depend on what point L is taken initially, nor upon what line through C is used to find M and N. This fact follows from Desargues theorem; it can also be defined in terms of the cross-ratio as (A, B; C, D) = −1.

单词	Harmonic division
释义	Harmonic division 英语百科 Projective harmonic conjugate （重定向自Harmonic division） In projective geometry, the harmonic conjugate point of an ordered triple of points on the real projective line is defined by the following construction: The point D does not depend on what point L is taken initially, nor upon what line through C is used to find M and N. This fact follows from Desargues theorem; it can also be defined in terms of the cross-ratio as (A, B; C, D) = −1.
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