River Lune to the Irish Sea at Glasson Dock. In 1847 the Commissioners built a pair of lighthouses near Cockersand Abbey to help guide ships into the port. The lower lighthouse, known as the Plover Scar Lighthouse, (sometimes called Abbey lighthouse) still stands on Plover Scar, and it remains operational. The old high light, a square wooden tower, was demolished in 1954; but the former keepers' cottage, built alongside the high light, can still be seen. Lancaster (and hence also Lancashire) is named after the Lune. The name of the ancient hundred of Lonsdale is also derived from the river. The river
Lune of Hippocrates circle. He proved that the lune bounded by the arcs labeled "E" and "F" in the figure has the same area as triangle "ABO". This afforded some hope of solving the circle-squaring problem, since the lune is bounded only by arcs of circles. Heath concludes that, in proving his result, Hippocrates was also the first to prove that the area of a circle is proportional to the square of its diameter. Hippocrates' book on geometry in which this result appears, "Elements", has been lost, but may have formed the model for Euclid's "Elements". Hippocrates' proof was preserved through the "History