We argue that Archimedes proved that the ratio of the circumference of a circle to its diameter is a constant independent of the circle and that the circumference constant equals the area constant. He stated neither result explicitly (in surviving material), but both are implied by his work. His proof required the addition of two axioms beyond those in Euclid's Elements.

Richeson, David. Circular Reasoning: Who First Proved That C Divided by d Is a Constant? The College Mathematics Journal 46, no. 3 (2015): 162-171. https://www.tandfonline.com/doi/abs/10.4169/college.math.j.46.3.162

For more information on the published version, visit Taylor and Francis's Website. Circular Reasoning: Who First Proved That C Divided by d Is a Constant? has also been published as:Richeson, David. Circular Reasoning: Who First Proved That C Divided by d Is a Constant? In The Best Writing on Mathematics 2016, edited by Mircea Pitici, 224-237. Princeton, NJ: Princeton University Press, 2017.For more information on the published version, visit Princeton University Press's Website.

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