Squaring the circle the circular arc b around O with radius , it results S'. Bisect the line segment in D and draw the semicircle b over D. Draw a straight line from O through C up to the semicircle b, it cuts b in E. The line segment is the mean proportional between and , also called geometric mean. Extend the line segment beyond O and transfer twice more, it results F and A, and thus the length of the line segment with the above described approximation value of formula_3, the half circumference of the circle. Bisect the line segment in G
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