Dependencies are identified in two recently proposed first-order axiom systems for plane hyperbolic geometry. Since the dependencies do not specifically concern hyperbolic geometry, our results yield ...

SINCE the time when Riemann and Helmholtz began their investigations on the axioms of geometry so much has been written on this subject in learned papers and in a more or less popular form that it.

Euclidean geometry, as presented by Euclid, consists of straightedge-and-compass constructions and rigorous reasoning about the results of those constructions. We show that Euclidean geometry can be ...

MR. ROBT. B. HAYWARD has written to me that some of the statements in my article, “The Axioms of Geometry,” in NATURE, March 13 (p. 453), are too sweeping, and that in particular Euclid I. 16 does not ...