Methodological analysis of mathematical theories . M. Academy of Sciences of the USSR, Central Council of Philosophical (Methodological Seminars) under the Presidium of the Academy of Sciences of the USSR, 1987. C. 205-213. According to the structural-nominative direction in the philosophy of science, scientific, including mathematical, theories have a complex polysystemic hierarchical structure. Therefore, important stages in the evolution of geometry as a mathematical theory are associated with changes in all its subsystems. Starting in one subsystem, the change usually causes a kind of chain reaction, leading to changes in other subsystems. It is shown that the most radical changes in geometry are associated with the modification of both model carriers from its model-representative subsystem, and with the construction of new functions and relations that form the naming relationship in these models. The emergence of Cartesian geometry is associated with