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 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