 It is, of course, true, that no amount of consistent deductions in the new geometry rules out the possibility that a contradiction does exist, but the intriguing relationship of the new geometry to spherical geometry, and the existence of trigonometric formulae for triangles strongly suggested that the new geometry was at least consistent. Those who did accept it, and they were very few before the 1860s, nonetheless may well have welcomed a better account than the one Bolyai and Lobachevskii provided. Even so, many geometers were to find the formulae convincing ‘proofs’ of the validity of the new geometry even after the reformulations of Riemann and Beltrami (for example, Enriques in his major essay (1907) on the principles of geometry).