Colin Maclarty

Affiliation: 

Case Western Reserve University, Cleveland

The rise of Euclidean axiomatics

We apply ideas from Ian Mueller and David Fowler to the rise of Euclidean axiomatics. Hippocrates of Chios invokes a curvilinear case of the Pythagorean theorem about 200 years before Euclid. A Euclid-style treatment of this case would require extending proofs in Euclid's Books I, VI, and XII. The evidence suggests Hippocrates used an argument in a few lines, while Euclid I.47 takes scores of pages just for the familiar case of squares on a right triangle.