A Problem From 1725

archimedes problem

Suppose that when Marcellus besieged Syracuse, Archimedes was standing at a corner of the city wall. A ditch runs parallel to the wall, separated from it by a distance a. To Archimedes’ left at distance b along the wall stands a catapult, which is distance c from a line perpendicular to the ditch. If Archimedes’ line of sight to the camp runs perpendicular to the wall and the ditch, show that he stood a distance ab/c from the camp.

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