Listed buildings in Lancaster, Lancashire century. The town stands at the lowest crossing of the River Lune, and received its first borough charter in 1193. In addition to being a market town, it became the judicial centre of the county of Lancashire, the castle being converted to serve this purpose in the 18th century. Also in the 18th century, in order to trade with the Americas, St George's Quay, with its warehouses and houses, was developed. Towards the end of that century the Lancaster Canal was built, linking the town with Preston. And in the 19th century railways came to the town, including what is
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