The word gnomon goes back farther than Aristotle and Euclid.  Even though the boy connects it  with geometry, Joyce also uses the older meaning of the word.  For millennia before Aristotle, the gnomon was the style of the sundial.  Here's a more modern picture of a gnomon that you might find amusing:

It's not the rod Neil Armstrong is holding, but the one in the ground that is the gnomon..  "Gnomon" was a common term in the Apollo flights.

	Originally, the gnomon was the stylus of a sundial together with its shadow.  This forms the "L" shape that Euclid and Aristotle describe. I understand the reference, but I don't understand the point.