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.
Neusis construction
T. L. Heath, the historian of mathematics, has suggested that the Greek mathematician Oenopides (ca. 440 BC) was the first to put compass-and-straightedge constructions above "neuseis". The principle to avoid "neuseis" whenever possible may have been spread by Hippocrates of Chios (ca. 430 BC), who originated from the same island as Oenopides, and who was—as far as we know—the first to write a systematically ordered geometry textbook. One hundred years after him Euclid too shunned "neuseis" in his very influential textbook, "The Elements".