For line segments, distance from a point to one end divided by distance from the point to other end {harmonic section} {harmonic ratio} equals negative of distance from one point {ideal point, line} on line-segment extension to one end divided by distance from ideal point to other end: PE1 / PE2 = - IE1 / IE2. For all other line-segment points, ratios {anharmonic ratio} are not harmonic. Point position determines ideal-point position {harmonic conjugate, endpoint}. If ideal point is at infinity, line-segment point is at midpoint. Projections keep harmonic ratio and relative positions the same.
Mathematical Sciences>Geometry>Kinds>Projective Geometry
3-Geometry-Kinds-Projective Geometry
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Date Modified: 2022.0224