For the record, plane geometry wasn't solved by Euclid's "Elements"; the conjecture about the 5th postulate remained open for a substantial amount of time, and

For the record, plane geometry wasn't solved by Euclid's "Elements"; the conjecture about the 5th postulate remained open for a substantial amount of time, and other axioms were introduced when it was pointed out that Euclid's work relied on numerous implied axioms.