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Arenarius, or sand reckoner), a small treatise, addressed to Gelo, the eldest son of Hiero, expounding, as applied to reckoning the number of grains of sand that could be contained in a sphere of the size of our "universe," a system of naming large numbers according to "orders" and "periods" which would enable any number to be expressed up to that which we should write with I followed by 80,000 ciphers!

Of lost works by Archimedes we can identify the following: (I) investigations on polyhedra mentioned by Pappus; (2) Archai, Principles, a book addressed to Zeuxippus and dealing with the naming of numbers on the system explained in the Sand Reckoner; (3) Peri zygon, On balances or levers; (4) Kentrobarika, On centres of gravity; (5) Katoptrika, an optical work from which Theon of Alexandria quotes a remark about refraction; (6) Ephodion, a Method, mentioned by Suidas; (7) Peri sphairopeoia, On Sphere-making, in which Archimedes explained the construction of the sphere which he made to imitate the motions of the sun, the moon and the five planets in the heavens.

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