If this cross-ratio equals −1 the four tangents are said to be four harmonic tangents.
If we take the points in a different order, the value of the cross-ratio will change.
The cross-ratio of any four points in one equals that of the corresponding points in the other.
It is convenient to let the point at infinity occupy the last place in the symbolic expression for the cross-ratio.
Before we draw conclusions from this result, we must investigate the meaning of a cross-ratio somewhat more fully.
