Source edition
Archimedes. Archimède, Volume 1. Mugler, Charles, editor. Paris: Les Belles Lettres, 1970.
Source data
Open Greek and Latin · CC BY-SA 4.0
Cloned and adapted by Humanitext, with ongoing edits.
Summary
This work, written by the ancient Greek mathematician Archimedes, presents rigorous mathematical proofs concerning the area and circumference of a circle. Consisting of three propositions, the treatise uses geometric methods to clarify the fundamental properties of a circle. In the first proposition, Archimedes proves that the area of any circle is equal to a right-angled triangle in which the height is equal to the radius and the base is equal to the circumference. The second proposition shows the approximate ratio of the area of a circle to that of its circumscribed square. In the final section, by using circumscribed and inscribed regular polygons of up to 96 sides, he systematically calculates the upper and lower bounds of the ratio of the circumference to the diameter. Ultimately, the work concludes by establishing that this ratio lies between 3 10/71 and 3 1/7.