Abstract
When reading Bolyai and Lobachevsky, one is struck by the similarities of their ways. The importance of the trigonometrical developments must be emphasised; they gave an analytical basis to the new Geometry, guaranteeing, to some extent, the consistence of the construction. This construction is not axiomatic; on the contrary, modern axiomatics came from a reflexion made necessary by the existence of the non-Euclidean Geometry.
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