I read a lot of historical articles that doubt the possibility that Gauss saw in the pseudosphere the realization of hyperbolic geometry; that geodetic triangles on the pseudosphere obey the same trigonometric rules valid in hyperbolic geometry (that can be modelled by the hyperbolic plane). Even proponents of the view that Gauss was in fact at full possesion of non-euclidean geometry, like Felix Klein (see: https://projecteuclid.org/download/pdf_1/euclid.bams/1183417390), doubt whether or not Gauss saw this connection, despite that to my opinion it's one of the more obvious conclusions of hyperbolic geometry.
I suspect he did see this connection, simply because he possesed all the essential elements needed in order to make this conclusion: he proved Gauss-Bonnet theorem for geodetic triangles on any surface, from his differential geometry he developed the equations of the pseudosphere (he called it "counterpart of the sphere") - the first example of a surface with constant negative curvature, and in his 1832 letter to Janos Bolyai he provided a synthetic proof of the angular deficit theorem in the hypothetic non-euclidean geometry (hyperbolic geometry). So if he knew both the angular deficit theorem of hyperbolic geometry and the Gauss-Bonnet theorem of differential geometry, and also had in hand an example of a surface with constant negative curvature, why there is still a long way to make this cnclusion?
I ask this question simply because i want to gain additional understanding of the subject of hyperbolic geometry. It's a simple fact that people tend to believe what they want to believe, and i personally have huge admiration for Gauss (so i preffer to believe he did make this conclusion), but i still want to gain better insight into this riddle.