Preliminaries for the teaching of non-Euclidean geometries

According to contemporary principles of methodology, there are good reasons for teaching the three geometries – namely Euclidean, spherical and hyperbolic – in parallel, despite the belief of some teachers that it makes little sense in contemporary conditions. I have been looking for historical data that prove that this parallelism is natural, and precedents can be found not only in ancient Greek history, but also in the Hungarian history of science.