Why and How Can a Line be Moved? - Examining Euclid's Elements

Explore the intricacies of Euclid's Elements and the historical debate surrounding the side-angle-side congruence theorem in this thought-provoking seminar. Delve into the philosophical and linguistic aspects of Proposition 4 in Book I, examining why ancient mathematicians believed straight lines could be moved and how they justified the complete overlap of coincident lines. Analyze the unique expressions and syntaxes used in this proposition, comparing them to similar arguments in Proposition 24 of Book III. Gain insights into the efforts of ancient mathematicians to develop more convincing proofs beyond simple superposition of figures. This 1-hour 25-minute talk, presented by Ken Saito, Ph.D. from Yakkaichi University, is part of the Orange County Inland Empire (OCIE) Seminar series in History and Philosophy of Mathematics hosted by Chapman University's Schmid College.