Day 19: Elements I
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
We will discuss the elements of a Euclidean proposition.
In your reading, pay particular attention to the following propositions
Propositions 1-6, 11, 13, 16, 17, 22, 27, 29, 31,
41, 46, 47.
Looking ahead: Solid geometry.
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.
Proof of alternate case for a proposition.
On to Day 20.
Up to Ancient
Last modified: 28 October 2005
Comments to email@example.com