Скачать или смотреть Fourth harmonic point on a range

The green point forms - together with the three given points (that should have been tagged with colours for better identification) - two harmonic point pairs that have cross ratio -1. Such pairs are always separating each other.

Pairwise separation is a projective property since it remains invariant under any projective transformation. This is in contrast to "between-ness" (of a point relative to two other points) which is not (in general) invariant under a projective transformation.

For more information, videos and interactive material, see my blog pages on
• Projective geometry: https://tinyurl.com/ya65amsq
• Projective metrics: https://tinyurl.com/ybdy957z
• The Euclidean degeneration: https://tinyurl.com/ybs2lyr6