Lecture 12 We started discussing Book I of Euclid's Elements. Our goal is to arrive to the proof of Pythagoras' Theorem (Proposition I.47). We started reading all 23 Definitions, 5 Postulates and 5 Common Notions which form the preamble of Book I. In particular we commented on: Definition 1 (point), Definition 2 (line), Definition 4 (straight line) Definition 10 (right angle) Definition 15 (circle) Definition 23 (parallel straight line) Postulate 5 (parallel postulate) Common Notion 4 (principle of superposition) In addition we went over the proofs of the following Propositions: Proposition 1 Proposition 2 Click on the above links to go directly to the proofs and commentaries of the results.