Source edition
Archimedes. Archimède, Volume 2. Mugler, Charles, editor. Paris: Les Belles Lettres, 1971.
Source data
Open Greek and Latin · CC BY-SA 4.0
Cloned and adapted by Humanitext, with ongoing edits.
Summary
Written as a letter addressed to King Gelo of Syracuse, this mathematical treatise proposes a unique system for representing and calculating arbitrarily large numbers, demonstrating it by estimating the number of grains of sand required to fill the universe. Archimedes begins by establishing astronomical premises, adopting the heliocentric model of Aristarchus of Samos and determining the sizes and distances of the Earth, Moon, and Sun through precise observational experiments and geometric proofs. To overcome the limitations of the traditional Greek numbering system, which only went up to a myriad of myriads, he defines a new system of counting based on periods and octads, while also introducing the law of exponents for geometric progressions. Ultimately, starting from the scale of a single poppy seed, he calculates the maximum number of sand grains that could fit into spheres of increasing size, culminating in the proof that even the vast universe of Aristarchus can be filled with a number of sand grains that easily fits within his newly established numerical system.