In mathematics, the fundamental theorem of projective geometry states that if Pⁿ is a projective space and F and F′ are frames of Pⁿ, then there exists a unique projective transformation sending F to F′.

In case n = 1 this comes down to saying that given two ordered triples of distinct points, there is a projective transformation of the projective line taking the first triple to the second. This is a basic result on Möbius transformations, saying that the group they form is "triply" transitive.