Desargues’ Theorem in Laguerre Planes

Abstract Kahn [3] showed in 1980 that the Full Bundle Theorem characterizes ovoidal Laguerre planes. The spears and cycles (circles) of a general Laguerre plane can be represented by affine planes and points, respectively, of a near-linear space. In this space the Full Bundle Theorem takes a form analogous to the Veblen–Young Axiom for projective spaces. A proof that a form of Desargues’ Theorem within this near-linear space is equivalent to the Full Bundle Theorem is provided. Thus a Laguerre plane is desarguesian, in the sense of this paper, if, and only if, it is ovoidal.