Area of a circle of Cnidus in the fifth century B.C. had found that the area of a disk is proportional to its radius squared. Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius in his book "Measurement of a Circle". The circumference is 2"r", and the area of a triangle is half the base times the height, yielding the area "r" for the disk. Prior to Archimedes, Hippocrates of Chios was the first
Circle line (London Underground) the southern portion of the line. Due to conflict between the two companies it was not until October 1884 that the inner circle was completed. The line was electrified in 1905, and in 1933 the companies were amalgamated into the London Passenger Transport Board. In 1949 the Circle line appeared as a separate line for the first time on the Tube map. In 2009 the closed loop around the centre of London on the north side of the River Thames was broken at Edgware Road and extended west to become a spiral to Hammersmith. The signalling system is being upgraded