TITLE: Models of hyperbolic geometry
QUESTION [5 upvotes]: Wikipedia states the following:

[The Poincaré half-plane model of hyperbolic geometry] is named after Henri Poincaré, but originated with Eugenio Beltrami, who used it, along with the Klein model and the Poincaré disk model (due to Riemann)

But it doesn't give any sources. I would like to know about the real history of the models of hyperbolic geometry, i.e. Beltrami-Klein, Poincaré disk model, Poincaré half-plane model. When and by whom where they discovered?

REPLY [2 votes]: Actually, one of the very few formulas in Riemann's Habilitation provides a metric $\sqrt{\sum dx^2}/(1+\alpha/4\sum x^2)$ which, for various values of $\alpha$, gives hyperbolic, spherical, and Euclidean metric.