conjugate points | harmonic segment

Given collinear points W, X, Y, and Z, Y and Z are harmonic conjugates with respect to W and X if ( left bracketing bar W Y right bracketing bar )/( left bracketing bar Y X right bracketing bar ) = ( left bracketing bar W Z right bracketing bar )/( left bracketing bar X Z right bracketing bar ). W and X are also harmonic conjugates with respect to Y and Z. The distances between such points are said to be in a harmonic range, and the line segment depicted above is called a harmonic segment. In other words, harmonic points divide a line segment internally and externally in the same ratio.

harmonic range | inversion pole | polar