What can I, a novice programmer, learn by reading Euclid's Elements?

I am currently at one of the few colleges in America that still has a class that teaches with Euclid's Elements, a 2000+ year old book of mathematics composed entirely of proofs. (Don't ask how I got here) We've nearly finished the book, and while it's definitely been a very interesting class on math, the most interesting I've taken so far, I can't help but feel there's an important connection here I'm missing. The proofs in this book occasionally remind me of code. I guess they are code, in a sense.

I think there's something I can learn from this about programming, and proof writing as it relates to programming, but I'm having trouble articulating it.

I'm sorry if I'm being unclear. I'd also like this to be a discussion thread on Euclid, if my main topic does not attract enough interest