The geometrical principles of perspective have been thoroughly analysed and well understood. Nevertheless by this analysis the question of the relationship between painting and geometry is usually considered to be exhausted. The aim of the paper is to push the study of the analogies between painting and geometry further, through mannerism and baroque till cubism and abstract art.
Our basic thesis is, that some paintings of the high baroque as Les Meninas of Diego Velazquez or some of the illusionistic decorations painted by Andrea Pozzo have the same pictorial form (in the sense of Wittgenstein's Tractatus) as the picture embodied in the texts on non-Euclidean geometry (Lobachevsky, Beltrami). Thus the technical innovations, which were used by Lobachevsky and Beltrami in their discovery of the non-Euclidean geometry, were more than a century earlier developed by the baroque painters.
Further the analogy between the impressionist way of creating space (in Turner, Monet, and Seurat) and the geometrical ideas of Cayley and Klein to use projective space as a basis for non- Euclidean geometry is discussed. Next the paper describes the parallel between the creation of space in the paintings of Cezanne and Picasso and the concept of space in algebraic topology.