History of geometry
Classic geometry was focused in compass and straightedge constructions. Geometry was revolutionized by Euclid, who introduced mathematical rigor and the axiomatic method still in use today. His book, "The Elements" is widely considered the most influential textbook of all time, and was known to all educated people in the West until the middle of the 20th century.
History of algebra
Euclid is regarded as the "father of geometry". His "Elements" is the most successful textbook in the history of mathematics. Although he is one of the most famous mathematicians in history there are no new discoveries attributed to him, rather he is remembered for his great explanatory skills. The "Elements" is not, as is sometimes thought, a collection of all Greek mathematical knowledge to its date, rather, it is an elementary introduction to it.