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
Earth's circumference shadow on the ground. Using the length of the rod, and the length of the shadow, as the legs of a triangle, he calculated the angle of the sun's rays. This angle was about 7°, or 1/50th the circumference of a circle; taking the Earth as perfectly spherical, he concluded that the Earth's circumference was 50 times the known distance from Alexandra to Syene (5,000 stadia, a figure that was checked yearly), i.e. 250,000 stadia. Depending on whether he used the "Olympic stade" (176.4m) or the Italian stade (184.8m), this would imply a circumference of 44,100 km (an error of