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Trinity College Dublin


ET7246 - Geometry and Trigonometry
Dr. David R. Wilkins
Axiom Systems for Synthetic Geometry

Hilbert's Axioms

Eliakim Hastings Moore, “One the Projective Axioms of Geometry”, Transactions of the American Mathematical Society, Vol. 3, No. 1 (1902), pp. 142–158 (on JSTOR)

Birkhoff's Axioms

George D. Birkhoff, “A Set of Postulates for Plane Geometry, Based on Scale and Protractor”, Annals of Mathematics, Vol. 33, No. 2 (1932), pp. 329–345 (on JSTOR)

Tarski's Axioms

Alfred Tarski and Steven Givant, “Tarski's System of Geometry”, The Bulletin of Symbolic Logic, Vol 5. No. 2 (1999), pp. 175–214 (on JSTOR)


Marvin Jay Greenberg, “Old and New Results in the Foundations of Elementary Plane Euclidean and Non-Euclidean Geometries”, The American Mathematical Monthly, Vol 117, No. 3 (2010), pp. 198–219 (on JSTOR)

Dr. David R. Wilkins, School of Mathematics, Trinity College Dublin.