## Day 21: Elements VII-IX

### Summary

The number theory in Books VII-IX. Between them, they have
102 propositions, prefaced by 22 definitions in Book VII. The
material in these books is probably older than that in Books V and VI
and some results that were proved there for magnitudes are proved in
these books for numbers.

Pay particular attention to the Definitions in Book VII, as well
as Propositions 2, 16 and 19; Book VIII, Propositions 8 and 23, and
Book
IX, Propositions 20, 35 and 36.

### Reading

Euclid, *Elements* VII-IX. Heath's version is
on reserve, or you may look at David Joyce's Elements
on the web.

### Homework

Euclidean Number Theory handout.

On to Day 22.

Up to Ancient
and Classical Mathematics

Last modified: 4 November 2005

Duncan J. Melville

Comments to dmelville@stlawu.edu