Abstract

The Erlanger Program of F. Klein ensures a ground for the ὲ́κθεσις procedure, which has not been much studied in the recent debates about geometrical analysis, but refers to a more general problem: the identity of a sign within a sign system, and the attempts of reduction of the mentioned system by another one. The exampIe considered is the reduction of the conics to characteristic rectangles realized by Apollonius. Starting from Klein and Apollonius, as weIl as from cartesian geometry, the figures are considered as geometric signs, and the proposed analysis of sign identity are conceived as models to follow in the analysis of identity of mathematical signs in general.