Area of a circle Measurement of a Circle" (c. 260 BCE), compare the area enclosed by a circle to a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius. If the area of the circle is not equal to that of the triangle, then it must be either greater or less. We eliminate each of these by contradiction, leaving equality as the only possibility. We use regular polygons in the same way. Suppose that the area "C" enclosed by the circle is greater than the area "T" = ⁄"cr" of the triangle. Let "E" denote
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