Solve these three problems, within the constraints of Greek construction rules: use only an unmarked straightedge and a compass (preferably collapsible)...no measurement markings permitted on the straightedge.
Problem 1: Given an arbitrary angle, construct an angle one third as large.
Problem 2: Construct a square equal in area to the area of any given circle.
Problem 3: Given a cube, construct a cube that has twice the volume.
Source: Greece, circa 300 B.C.