Day 19: Elements I

Summary

Book I of the Elements.
Building from the definitions, common notions, postulates we covered last class, Book I of the Elements contains 48 Propositions on plane geometry.
Propositions 1-26 mostly concern triangles, but also include some propositions to do with angles made by lines and intersecting lines.
Propositions 27-32 cover the theory of parallels and include the proof that the sum of the angles of a triangle equals two right angles
Propositions 33-48 concern the existence of parallelograms, results on equivalent figures including triangles and squares, and ends with the Pythagorean theorem.
We will discuss the elements of a Euclidean proposition.

In your reading, pay particular attention to the following propositions in Book I:
Propositions 1-6, 11, 13, 16, 17, 22, 27, 29, 31, 35, 41, 46, 47.

Euclid, Elements I.  Heath's version is on reserve, or you may look at David Joyce's Elements on the web.
J. Fauvel and J.Gray, The History of Mathematics, Chapter 3.
V.J. Katz, A History of Mathematics, Section 2.4.

Homework

Proof of alternate case for a proposition.
On to Day 20.

Up to Ancient and Classical Mathematics