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 which the arc "AEB" lies. Consequently, the smaller circle has half the area of the larger circle, and therefore the quarter circle AFBOA is equal in area to the semicircle AEBDA. Subtracting the crescent-shaped area AFBDA from the quarter circle gives triangle ABO and subtracting the same crescent from the semicircle gives the lune. Since the triangle and lune are both formed by subtracting equal areas from equal area, they are themselves equal in area. Using a similar proof to the one above, Alhazen showed that two lunes, formed on the two sides of a right triangle, whose outer boundaries