Abstract: Euclid is most famous for his work in Geometry, but he also worked on several Algebra proofs. What are studied as algebra proofs today, were written by Euclid to look like geometry proofs because, at the time, Algebra was not studied the way that it is today. In our talk, we will discuss a brief history of Euclid and then look at some of his most famous work. We will be comparing how Euclid's Lemma and Euclid's Algorithm were written in their original language, with the modern proofs that are taught in Abstract Algebra courses today.