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These pages serve two purposes. First, they are notes to accompany the talk"Hyperbolic and projective geometry in constraint programming for CAD" byWalter Whiteley at the "Janos Bolyai Conference on Hyperbolic Geometry", 8--12July 2002, in Budapest, Hungary. Second, they sketch results that will beincluded in a forthcoming paper that will present the equivalence of thefirst-order rigidity theories of bar-and-joint frameworks in variousgeometries, including Euclidean, hyperbolic and spherical geometry. The bulk ofthe theory is outlined here, with remarks and comments alluding to otherresults that will make the final version of the paper.

Some notes on the equivalence of first-order rigidity in various geometries