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
Measurement of a Circle two legs being "c" and "r". This proposition is proved by the method of exhaustion. Proposition two states: The area of a circle is to the square on its diameter as 11 to 14. This proposition could not have been placed by Archimedes, for it relies on the outcome of the third proposition. Proposition three states: The ratio of the circumference of any circle to its diameter is greater than formula_1 but less than formula_2. This approximates what we now call the mathematical constant π. He found these bounds on the value of π by inscribing and circumscribing a circle