Colin Maclarty


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.