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The Antikythera mechanism is believed to be the earliest mechanical analog "computer", according to Derek J. de Solla Price. It was designed to calculate astronomical positions. It was discovered in 1901 in the Antikythera wreck off the Greek island of Antikythera, between Kythera and Crete, and has been dated to circa 100 BC. Devices of a level of complexity comparable to that of the Antikythera mechanism would not reappear until a thousand years later.

What is thought to be the first mechanical analog computer?
The Antikythera mechanism