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