In 1911 W. Blaschke and J. Grnwald described the group ~ of proper motions of the euclidean plane d' in the following way: Let (P, fg)be the real three-dimensional projective space, let ~ C P be an isomorphic image of g, and let U ~ f# such that ~ tA U is the projective closure of in P. Then there is a bijection x : ~ ~ P ' := P \ U called the kinematic mapping and an injective mapping ~ × ~ ~ ...