Historic Investigation of Legendre’s Proof about the 5th Postulate of “Elements” for Reeducation of Mathematics Teacher

Karasawa Toshimitsu
(University of Manchester, UK)

Abstract: We investigate the history of trials in proving the fifth axiom in “Elements” in order to develop a teaching material for high school mathematics. Arguments in “Elements” themselves are very clear, but the fifth axiom is apparently too complex as compared to the other four axioms. Here, we show the first to fifth axioms.

Key words: reeducation of teacher, Legendre’s Proof, 5th Postulate elements