He also constructively proved the infinitude of primes.
This man names a type of ordered field in which all non-negative elements are squares. The fact that the integers form a type of domain named for this man is used to prove Bezout's Lemma, which is related to this man's algorithm for finding(*) greatest common divisors. Playfair's axiom may replace this mathematician's Parallel Postulate, which is accepted in his namesake type of geometry. He also constructively proved the infinitude of primes. For 10 points, name this ancient Greek mathematician who wrote The Elements, the father of geometry.
This man names a type of ordered field in which all non-negative elements are squares.
{Euclid} of Alexandria