son Gelon. It appears from a passage of Diodorus that he spent a considerable time at Alexandria, where it may be inferred that he studied with the successors of Euclid. It may have been at Alexandria that he made the acquaintance of Conon of Samos (for whom he had the highest regard both as a mathematician and as a personal friend) and of Eratosthenes. To the former he was in the habit of communicating his discoveries before their publication, and it is to the latter that the famous Cattle-problem purports to have been sent. Another friend, to whom he dedicated several of his works, was Dositheus of Pelusium, a pupil of Conon, presumably at Alexandria though at a date subsequent to Archimedes' sojourn there.
After his return to Syracuse he lived a life entirely devoted to mathematical research. Incidentally he made himself famous by a variety of ingenious mechanical inventions. These things were however merely the "diversions of geometry at play[1]," and he attached no importance to them. In the words of Plutarch, "he possessed so high a spirit, so profound a soul, and such treasures of scientific knowledge that, though these inventions had obtained for him the renown of more than human sagacity, he yet would not deign to leave behind him any written work on such subjects, but, regarding as ignoble and sordid the business of mechanics and every sort of art which is directed to use and profit, he placed his whole ambition in those speculations in whose beauty and subtlety there is no admixture of the common needs of life[2]." In fact he wrote only one such mechanical book, On Sphere-making to which allusion will be made later.
Some of his mechanical inventions were used with great effect against the Romans during the siege of Syracuse. Thus he contrived
