equidistant vs midpoint

equidistant

adj
  • Occupying a position midway between two ends or sides. 

  • Describing a map projection that preserves scale. No map can show scale correctly throughout the entire map but some can show true scale between one or two points and every point or along every meridian and these are referred to as equidistant. 

  • Occupying a position that is an equal distance between several points. Note that in a one-dimensional space this position can be identified with two points, in a two-dimensional space with three points (not on the same straight line), and in a three-dimensional space with four points (not in the same plane). 

midpoint

noun
  • A point equidistant between two extremes. 

  • A point which divides a line segment into two lines of equal length. 

How often have the words equidistant and midpoint occurred in a corpus of books? (source: Google Ngram Viewer )