# Projective Geometry

## Cross Ratio

Projections do not keep distances constant, nor do they enlarge or shrink them in an obvious way. In Figure 2, for instance, D'C' is a little smaller than CD, but A'B' is much larger than AB. There is, however, a rather obscure constancy about a projection's effect on **distance**. It is known as the "cross ratio." If A, B, C, and D are points in order on a line and if they are projected through a point P into points A', B', C', and D' on another line, then the two expressions and are equal.

Cross rations play an important part in many of projective geometry's theorems.

J. Paul Moulton

## Additional topics

Science EncyclopediaScience & Philosophy: *Positive Number* to *Propaganda - World War Ii*Projective Geometry - Desargues' Theorem, Coordinate Projective Geometry, Cross Ratio