Did Lobachevsky have a model of his Imaginary geometry?

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Usage 1987
Downloads 1987
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Rodin, Andrei
preprint description
Lobachevsky's Imaginary geometry in its original form involved an extension of rather than a radical departure from Euclidean intuition. It wasn't anything like a formal theory in Hilbert's sense and hence didn't require anything like a model. However, rather surprisingly, Lobachevsky uses what in modern terms can be called a non-standard model of Euclidean plane, namely as a specific surface (a horisphere) in a Hyperbolic space. In this paper I critically review some popular accounts of the discovery of Non-Euclidean geometries and suggest a revision of the epistemic view on the issue dating back to Hilbert's Grundlagen.