## 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.

Looking ahead: Solid geometry.

### Reading

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

Last modified: 28 October 2005

Duncan J.
Melville

Comments to dmelville@stlawu.edu