Euclid's Partition Problem is the problem of constructing one-nth of a given segment using only a compass and straightedge. There are many well-known constructions that solve this problem, including the standard construction involving parallel lines. This new construction uses Ceva's Theorem and is simpler than many of the other constructions. Furthermore, it easily generalizes to construct m-nths of any given segment using only compass and straightedge.
"Euclid's Partition Problem and Ceva's Theorem,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 8:
1, Article 5.
Available at: https://scholar.rose-hulman.edu/rhumj/vol8/iss1/5