John Playfair. Portrait of John Playfair (1748- 1819), Scottish geologist and mathematician. In 1802 Playfair published Illustrations of the Huttonian Theory of the Earth. This book explained James Hutton's uniformitarian theories of geological activity. These had been very difficult to understand as written by their author, but Playfair's book popularised the revolutionary theories. In 1795 Playfair published Elements of Geometry in which he set out an alternative form of Euclid's fifth postulate. This is now known as Playfair's Axiom and states that for any point (P) not on a line (L), there can only be one line which goes through P whilst being parallel to L.