Given two intersecting lines and
forming an angle with vertex at and a point inside the angle , the Philo line (or Philon line) is the shortest line segment touching both lines and passing through . The line is named for Philo of Byzantium who considered the
line while attempting to duplicate the cube. The line can be constructed by finding
such that (Wells 1991).

The distances along the angle edges and
and the lengths along the Philo line and
can be computed by solving the simultaneous equations