Philon's Line
Philon of
Byzantium , sometimes called Philo, was a lessor
known scientist/mathematician living around 280 BC. One of his projects
in geomery was the ancient problem of making a cube with twice the volume
of a given cube. In trying to solve the problem, he encountered and
solved the following problem:
Given an angle BAC and a point X, interior
to the angle, find the shortest line segment through X reaching from ray
AC to ray AB. (see figure)
Philon's
discovery was that the shortest segment occurred when the distance from
the point X to one ray was equal to the distance from the other ray to
the foot (G in the figure) of the perpendicular to the segment from
A .
Philon's only surviving work is
his treatise on mechanics. It appears that he travelled throughout
the Eastern Mediterranean studying the construction of catapults.
He may have been a militrary advisor of some sort. He is mentioned
in the writings of Heron of Alexandria. You can find more about his
life at the St
Andrews University web site.