Twentieth-century developments in logic and mathematics have led many people to view Euclid's proofs as inherently informal, especially due to the use of diagrams in proofs. In "Euclid and His Twentieth-Century Rivals," Nathaniel Miller discusses the history of diagrams in Euclidean Geometry, develops a formal system for working with them, and concludes that they can indeed be used rigorously. Miller also introduces a diagrammatic computer proof system, based on this formal system. This volume will be of interest to mathematicians, computer scientists, and anyone interested in the use of diagrams in geometry.