The philosophical context of creating analytic geometry

The article discusses the history of the formation of analytical geometry. This area of geometry is one of the stages of the transition from Euclidean geometry to non-Euclidean. The main methodological principles of this theory are: Leibniz continuity principle and Bohr complementarity principle. Analytical geometry is not absorbed by non-Euclidean geometry, but continues to evolve and is one of the foundations of modern mathematics.