Geometric Identities, Invariant Theory, and a Theorem of Bricard Original Research Article

We prove an identity in the double algebra of a Peano space, using techniques first developed by Doubilet, Rota, and Stein, which yields a class of geometric identities in n-dimensional projective space. Special cases of this identity include a theorem of Bricard in the projective plane and one of Fontené in projective three space.